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Journal articles on the topic 'Nonparametrica'

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Published: 9 March 2023
Last updated: 10 March 2023

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1

Firpha, Rosse Millania Pichago, and Anneke Iswani Achmad. "Regresi Nonparametrik Spline Truncated untuk Pemodelan Persentase Penduduk Miskin di Jawa Barat Pada Tahun 2021." Bandung Conference Series: Statistics 2, no. 2 (2022): 454–58. http://dx.doi.org/10.29313/bcss.v2i2.4720.

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Abstract. Nonparametric regression is a statistical method used to model the relationship between response variables and predictor variables whose pattern shape is unknown. In nonparametric regression there are several approaches, one of which is the spline. Spline nonparametric regression, if there is one predictor variable then the regression is called univariable spline nonparametric regression. Conversely, if there is one response variable with more than one predictor variable then the regression is called a multivariable spline nonparametric regression. In nonparametric regression there is a truncated spline model. The truncated spline function is a polynomial function that is dismembered at a knot point. A knot point is a joint fusion point where the function is truncated, or a point that describes a change in data behavior at a certain sub-sub-interval. Therefore, truncated spline models have an excellent ability to handle data whose behavior is arbitrary at certain sub-sub intervals. This study will use truncated spline nonparametric regression to model the number of poor people in West Java in 2021. The data used is secondary data sourced from the publication of the Indonesian Central Statistics Agency (BPS).
 Abstrak. Regresi nonparametrik adalah suatu metode statistika yang digunakan untuk memodelkan hubungan antara variabel respon dengan variabel prediktor yang tidak diketahui bentuk polanya. Dalam regresi nonparametrik terdapat beberapa pendekatan salah satunya spline. Regresi nonparametrik spline, jika terdapat satu variabel prediktor maka regresi tersebut dinamakan regresi nonparametrik spline univariabel. Sebaliknya, apabila terdapat satu variabel respon dengan lebih dari satu variabel prediktor maka regresi tersebut disebut regresi nonparametrik spline multivariable. Dalam regresi nonparametrik terdapat model Spline Truncated. Fungsi Spline Truncated merupakan fungsi polinomial yang terpotong-potong pada suatu titik knot. Titik knot merupakan titik perpaduan bersama dimana fungsi tersebut terpotong, atau titik yang menggambarkan terjadinya perubahan perilaku data pada sub-sub interval tertentu. Oleh karena itu, model Spline Truncated memiliki kemampuan yang sangat baik untuk menangani data yang perilakunya berubah-ubah pada sub-sub interval tertentu. Pada penelitian ini akan menggunakan regresi nonparametrik Spline Truncated untuk mememodelkan jumlah penduduk miskin di Jawa Barat pada tahun 2021. Data yang digunakan adalah data sekunder yang bersumber dari publikasi Badan Pusat Statistika (BPS) Indonesia.
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2

Hallam, Arne. "A Brief Overview of Nonparametric Methods in Economics." Northeastern Journal of Agricultural and Resource Economics 21, no. 2 (1992): 98–112. http://dx.doi.org/10.1017/s0899367x00002610.

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The concept of nonparametric analysis, estimation, and inference has a long and storied existence in the annals of economic measurement. At least four rather distinct types of analysis are lumped under the broad heading of nonparametrics. The oldest, and perhaps most common, is that associated with distribution-free methods and order statistics. Similar in spirit, but different in emphasis, is nonparametric density estimation, such as the currently popular kernel estimator for regression. Semi-parametric or semi-nonparametric estimation combines parametric analysis of portions of the problem with nonparametric specification for the remainder, such as the specification of a specific functional form for a regression function with a nonparametric representation of the error distribution. The final type of nonparametrics is that associated with data envelopment analysis and revealed preference, although the use of the term nonparametrics for this research is perhaps a misnomer. This paper will briefly review each of the four types of analysis, leaning heavily on other published work for more detailed exposition. The paper will then discuss in more detail the application of the revealed-preference approach to four specific economic problems: efficiency, the structure of technology or preferences, technical or taste change, and risky choice. The paper is not complete, exhaustive, or detailed. The primary purpose is to expose the reader to a variety of techniques and provide ample reference to the relevant literature.
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Dani, Andrea Tri Rian, and Narita Yuri Adrianingsih. "Pemodelan Regresi Nonparametrik dengan Estimator Spline Truncated vs Deret Fourier." Jambura Journal of Mathematics 1, no. 1 (2021): 26–36. http://dx.doi.org/10.34312/jjom.v1i1.7713.

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ABSTRAKPendekatan regresi nonparametrik digunakan apabila hubungan antara variabel prediktor dan variabel respon tidak diketahui polanya. Spline truncated dan deret Fourier merupakan estimator dalam pendekatan nonparametrik yang terkenal, karena memiliki fleksibilitas yang tinggi dan mampu menyesuaikan terhadap sifat lokal data secara efektif. Penelitian ini bertujuan untuk mendapatkan estimator model regresi nonparametrik terbaik menggunakan spline truncated dan deret Fourier. Metode estimasi kurva regresi nonparametrik dilakukan dengan menyelesaikan optimasi Ordinary Least Squares (OLS). Kriteria kebaikan model menggunakan GCV, R2 dan MSE. Pemodelan regresi nonparametrik diterapkan pada data Case Fatality Rate (CFR) akibat Demam Berdarah Dengue (DBD) di Indonesia. Berdasarkan hasil analisis, hasil estimasi dari pemodelan regresi nonparametrik menunjukkan bahwa estimator spline truncated memberikan performa yang lebih baik dibandingkan estimator deret Fourier. Hal ini ditunjukkan dengan nilai R2 dari estimator spline truncated yaitu sebesar 91,80% dan MSE sebesar 0,04, sedangkan dengan estimator deret Fourier diperoleh nilai R2 sebesar 65,44% dan MSE sebesar 0,19.ABSTRACTThe nonparametric regression approach is used when the relationship between the predictor variable and the response variable is unknown. Spline truncated and Fourier series are well-known estimators in the nonparametric approach because they have high flexibility and are able to adjust to the local properties of the data effectively. This study aims to obtain the best nonparametric regression model estimator using the truncated spline and the Fourier series. The nonparametric regression curve estimation method is done by completing the Ordinary Least Squares (OLS) optimization. The criteria for the goodness of the model use GCV, R2, and MSE. Nonparametric regression modeling is applied to Case Fatality Rate (CFR) modeling due to Dengue Hemorrhagic Fever (DBD) in Indonesia. Based on the analysis, the estimation results from the nonparametric regression modeling show that the truncated spline estimator provides better performance than the Fourier series estimator. This is shown by the R2 value of the truncated spline estimator which is 91.80% and the MSE is 0.04, while the Fourier series estimator obtained an R2 value of 65.44% and MSE of 0.19.
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Dani, Andrea Tri Rian, and Narita Yuri Adrianingsih. "Pemodelan Regresi Nonparametrik dengan Estimator Spline Truncated vs Deret Fourier." Jambura Journal of Mathematics 3, no. 1 (2021): 26–36. http://dx.doi.org/10.34312/jjom.v3i1.7713.

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ABSTRAKPendekatan regresi nonparametrik digunakan apabila hubungan antara variabel prediktor dan variabel respon tidak diketahui polanya. Spline truncated dan deret Fourier merupakan estimator dalam pendekatan nonparametrik yang terkenal, karena memiliki fleksibilitas yang tinggi dan mampu menyesuaikan terhadap sifat lokal data secara efektif. Penelitian ini bertujuan untuk mendapatkan estimator model regresi nonparametrik terbaik menggunakan spline truncated dan deret Fourier. Metode estimasi kurva regresi nonparametrik dilakukan dengan menyelesaikan optimasi Ordinary Least Squares (OLS). Kriteria kebaikan model menggunakan GCV, R2 dan MSE. Pemodelan regresi nonparametrik diterapkan pada data Case Fatality Rate (CFR) akibat Demam Berdarah Dengue (DBD) di Indonesia. Berdasarkan hasil analisis, hasil estimasi dari pemodelan regresi nonparametrik menunjukkan bahwa estimator spline truncated memberikan performa yang lebih baik dibandingkan estimator deret Fourier. Hal ini ditunjukkan dengan nilai R2 dari estimator spline truncated yaitu sebesar 91,80% dan MSE sebesar 0,04, sedangkan dengan estimator deret Fourier diperoleh nilai R2 sebesar 65,44% dan MSE sebesar 0,19.ABSTRACTThe nonparametric regression approach is used when the relationship between the predictor variable and the response variable is unknown. Spline truncated and Fourier series are well-known estimators in the nonparametric approach because they have high flexibility and are able to adjust to the local properties of the data effectively. This study aims to obtain the best nonparametric regression model estimator using the truncated spline and the Fourier series. The nonparametric regression curve estimation method is done by completing the Ordinary Least Squares (OLS) optimization. The criteria for the goodness of the model use GCV, R2, and MSE. Nonparametric regression modeling is applied to Case Fatality Rate (CFR) modeling due to Dengue Hemorrhagic Fever (DBD) in Indonesia. Based on the analysis, the estimation results from the nonparametric regression modeling show that the truncated spline estimator provides better performance than the Fourier series estimator. This is shown by the R2 value of the truncated spline estimator which is 91.80% and the MSE is 0.04, while the Fourier series estimator obtained an R2 value of 65.44% and MSE of 0.19.
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Lestari, Budi. "Estimasi Fungsi Regresi Dalam Model Regresi Nonparametrik Birespon Menggunakan Estimator Smoothing Spline dan Estimator Kernel." Jurnal Matematika Statistika dan Komputasi 15, no. 2 (2018): 20. http://dx.doi.org/10.20956/jmsk.v15i2.5710.

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Abstract Regression model of bi-respond nonparametric is a regression model which is illustrating of the connection pattern between respond variable and one or more predictor variables, where between first respond and second respond have correlation each other. In this paper, we discuss the estimating functions of regression in regression model of bi-respond nonparametric by using different two estimation techniques, namely, smoothing spline and kernel. This study showed that for using smoothing spline and kernel, the estimator function of regression which has been obtained in observation is a regression linier. In addition, both estimators that are obtained from those two techniques are systematically only different on smoothing matrices. Keywords: kernel estimator, smoothing spline estimator, regression function, bi-respond nonparametric regression model. AbstrakModel regresi nonparametrik birespon adalah suatu model regresi yang menggambarkan pola hubungan antara dua variabel respon dan satu atau beberapa variabel prediktor dimana antara respon pertama dan respon kedua berkorelasi. Dalam makalah ini dibahas estimasi fungsi regresi dalam model regresi nonparametrik birespon menggunakan dua teknik estimasi yang berbeda, yaitu smoothing spline dan kernel. Hasil studi ini menunjukkan bahwa, baik menggunakan smoothing spline maupun menggunakan kernel, estimator fungsi regresi yang didapatkan merupakan fungsi linier dalam observasi. Selain itu, kedua estimator fungsi regresi yang didapatkan dari kedua teknik estimasi tersebut secara matematis hanya dibedakan oleh matriks penghalusnya.Kata Kunci : Estimator Kernel, Estimator Smoothing Spline, Fungsi Regresi, Model Regresi Nonparametrik Birespon.
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Safni Chusnaifah Junianingsih. "Regresi Nonparametrik Kernel dalam Pemodelan Jumlah Kelahiran Bayi di Jawa Barat Tahun 2017." Bandung Conference Series: Statistics 1, no. 1 (2021): 30–37. http://dx.doi.org/10.29313/bcss.v1i1.39.

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Abstract. Regression analysis is one of the analytical tools used to determine the effect of multiple predictor variables (X) on response variables (Y). The approach in regression analysis is divided into two, parametric approaches and nonparametric approaches. On nonparametric regression analysis, the shape of the regression curve is unknown, the data arega expected to look for its own estimation form so that it has high flexibility. Estimation of regression functions is performed with the Nadaraya Watson kernel estimator using Gaussian kernel functions. In this method requires bandwidth (h) or finer parameters as a balance controller between the smoothness of the function and the suitability of the function of the data. Optimum bandwidth (h) is obtained by minimizing the Generalized Cross Validation (GCV) value. Based on the analysis, obtained in a simple linear regression model obtained a Mean Square Error (MSE) value of 552976772 and a Standard Error (SE) of 24437,98. While in the kernel nonparametric regression model, the optimum bandwidth (h) is 0,50, Mean Square Error (MSE) is 96832714, and the Standard Error (SE) value is 10226,4. So it can be concluded that the kernel nonparametric regression model is better than a simple linear regression model.
 Abstrak. Analisis regresi merupakan salah satu alat analisis yang digunakan untuk mengetahui pengaruh dari beberapa variabel prediktor (X) terhadap variabel respon (Y). Pendekatan dalam analisis regresi dibagi menjadi dua, yaitu pendekatan parametrik dan pendekatan nonparametrik. Pada analisis regresi nonparametrik bentuk kurva regresi tidak diketahui, data diharapkan mencari sendiri bentuk estimasinya sehingga memiliki fleksibilitas yang tinggi. Estimasi fungsi regresi dilakukan dengan estimator kernel Nadaraya Watson menggunakan fungsi kernel Gaussian. Metode ini membutuhkan bandwidth (h) atau parameter penghalus sebagai pengontrol keseimbangan antara kemulusan fungsi dan kesesuaian fungsi terhadap data. Bandwidth (h) optimum diperoleh dengan meminimumkan nilai Generalized Cross Validation (GCV). Berdasarkan analisis diperoleh pada model regresi linear sederhana diperoleh nilai Mean Square Error (MSE) sebesar 552976772 dan niai Standard Error (SE) sebesar 24437,98. Sedangkan pada model regresi nonparametrik kernel diperoleh bandwidth (h) optimum sebesar 0,50, Mean Square Error (MSE) sebesar 96832714, dan nilai Standard Error (SE) sebesar 10226,4. Sehingga dapat disimpulkan bahwa model regresi nonparametrik kernel lebih baik daripada model regresi linear sederhana.
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Dani, Andrea Tri Rian, Narita Yuri Adrianingsih, Alifta Ainurrochmah, and Riry Sriningsih. "Flexibility of Nonparametric Regression Spline Truncated on Data without a Specific Pattern." Jurnal Litbang Edusaintech 2, no. 1 (2021): 37–43. http://dx.doi.org/10.51402/jle.v2i1.30.

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Bentuk pola hubungan antara variabel prediktor dan variabel respon ada yang diketahui, namun pada nyatanya ada pula yang tidak diketahui. Apabila bentuk pola hubungan antara variabel respon dan variabel prediktor tidak diketahui, pendekatan regresi nonparametrik merupakan pendekatan yang paling sesuai. Pendekatan regresi nonparametrik tidak tergantung pada asumsi bentuk kurva regresi tertentu, sehingga akan memberikan fleksibilitas yang tinggi. Salah satu estimator regresi nonparametrik yang terkenal adalah spline truncated. Spline truncated merupakan potongan-potongan polinomial yang memiliki sifat tersegmen dan kontinu. Pada penelitian ini, akan disimulasikan pola hubungan antara kedua variabel yaitu respon dan prediktor yang tidak memiliki pola tertentu, yang kemudian didekati dengan dua pendekatan regresi, yaitu parametrik dan nonparametrik. Berdasarkan ukuran kebaikan estimasi kurva regresi menggunakan koefisien determinasi diperoleh hasil bahwa pendekatan regresi nonparametrik lebih baik daripada pendekatan regresi parametrik. Hal ini dikarenakan pendekatan regresi nonparametric memiliki fleksibilitas yang tinggi sehingga mampu menyesuaikan sendiri bentuk estimasi kurva regresi.
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Sanusi, Wahidah, Rahmat Syam, and Rabiatul Adawiyah. "Model Regresi Nonparametrik dengan Pendekatan Spline (Studi Kasus: Berat Badan Lahir Rendah di Rumah Sakit Ibu dan Anak Siti Fatimah Makassar)." Journal of Mathematics, Computations, and Statistics 2, no. 1 (2020): 70. http://dx.doi.org/10.35580/jmathcos.v2i1.12460.

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Pendekatan nonparametrik merupakan suatu pendekatan yang digunakan apabila bentuk hubungan antara variabel respon dan variabel prediktornya tidak diketahui atau tidak adanya informasi mengenai bentuk fungsi regresinya. Spline merupakan suatu teknik yang dilakukan untuk mengestimasi parameter dalam regresi nonparametrik. Penelitian ini bertujuan untuk mengetahui model hubungan antara berat badan lahir rendah dan faktor-faktor yang mempengaruhi berdasarkan model spline. Faktor-faktor tersebut adalah usia ibu, usia kehamilan, dan jarak kehamilan. Data tersebut diperoleh dari rumah sakit ibu dan anak siti Fatimah Makassar tahun 2017. Dimana untuk mendapatkan model spline terbaik langkah awal yang dilakukan adalah menentukan knot dengan nilai Generalized Cross Validation (GCV) yang minimum. Berdasarkan penelitian yang telah dilakukan, dua variabel dinyatakan berpengaruh terhadap berat badan lahir rendah yaitu usia ibu, dan usia kehamilan. Model regresi nonparametrik dengan pendekatan Spline yang terbentuk memiliki koefisien determinasi sebesar 78,19%, serta nilai GCV dengan tiga titik knot yaitu 0.0117.Kata kunci: Regresi Nonparametrik, Spline, Berat Badan Lahir Rendah, Generalized Cross Validation The non-parametric approach is an approach that is used if the form of the relationship between the response variable and the predictor variable is unknown or the absence of information about the shapes of regression functions. The Spline is a technique performed to estimate the parameters in the nonparametric regression. This study aims to determine the model of the relationship between low birth weight and the factors that affect the based on the spline model. Such factors are maternal age, gestational age, and pregnancy distance. The Data is obtained from the mother and child hospital siti Fatimah Makassar 2017. Where to get a spline model best the initial step is to determine the knots with the value of the Generalized Cross Validation (GCV) which is a minimum. Based on the research that has been done, the two variables stated effect against low birth weight, namely age of mother, and gestational age. Nonparametric regression Model with the approach of the Spline that is formed has a coefficient of determination of 78.19 to%, as well as the value of the GCV with a three-point knot that is 0.0117.Keyword : Nonparametric Regression, Spline, Low Birth Weight, Generalized Cross Validation
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Ilmi, Hillidatul, Sifriyani, and Surya Prangga. "Geographically Weighted Spline Nonparametric Regression dengan Fungsi Pembobot Bisquare dan Gaussian Pada Tingkat Pengangguran Terbuka Di Pulau Kalimantan." J Statistika 14, no. 2 (2022): 84–92. http://dx.doi.org/10.36456/jstat.vol14.no2.a4470.

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Geographically weighted spline nonparametric regression merupakan pengembangan regresi nonparametrik untuk data spasial dengan estimator parameter bersifat lokal setiap lokasi pengamatan yang diaplikasikan pada kasus tingkat pengangguran terbuka. Tingkat pengangguran terbuka menjadi alat ukur kualitas kesejahteraan di suatu wilayah yang mengindikasikan besarnya persentase penduduk usia kerja yang aktif secara ekonomi. Tujuan penelitian ini yaitu untuk mengidentifikasi faktor-faktor yang mempengaruhi tingkat pengangguran terbuka 56 Kabupaten/Kota di Kalimantan. Metode yang digunakan adalah geographically weighted spline nonparametric regression dengan pembobot fungsi kernel eksponensial. Model terbaik geographically weighted spline nonparametric regression dengan pembobot fungsi kernel eksponensial pada orde 1 titik knot 1 dengan nilai R-Square sebesar 86,410 persen, nilai AIC sebesar 12,152, nilai RMSE sebesar 0,584 serta nilai CV terkecil adalah fungsi kernel bisquare sebesar 77,175. Adapun faktor-faktor yang berpengaruh signifikan terhadap tingkat pengangguran terbuka yaitu tingkat partisipan angkatan kerja, jumlah penduduk, indeks pembangunan manusia, harapan lama sekolah dan upah minimum.
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Rahayu, Nisrina Fajriati, and Lisnur Wachidah. "Regresi Nonparametrik Spline untuk Memodelkan Faktor-faktor yang Memengaruhi Indeks Pembangunan Gender (IPG) di Jawa Barat Tahun 2020." Bandung Conference Series: Statistics 2, no. 2 (2022): 273–81. http://dx.doi.org/10.29313/bcss.v2i2.4037.

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Abstract. Regression analysis is a statistical method used to determine the pattern of the relationship between the independent variable and the dependent variable. There are three kinds of regression analysis, namely parametric regression analysis, semiparametric regression analysis and nonparametric regression analysis. Parametric regression analysis can be used when the assumptions are met but not all data can meet the parametric assumptions, an alternative to parametric regression is nonparametric regression because its use does not require strict assumptions. Spline nonparametric regression is a method used to get the estimated regression curve through the estimation of the data pattern according to the movement. The selection of the best model for Spline regression is seen from the Generalized Cross Validiation (GCV) value using the minimum knot point. In this study, the dependent variable used is the Gender Development Index (GDI) in West Java Province in 2020 which consists of 18 districts and 9 cities with the independent variables consisting of the average length of schooling for women, the expected length of schooling for women, the open unemployment rate for women, female labor force participation rate, women with health complaints and sex ratio. The results of the analysis obtained that the best nonparametric Spline regression model was using the order of one and three knot points with the minimum GCV value of 0.2471, and the coefficient of determination was 99.98%. The six independent variables used have a significant influence on GPA in West Java in 2020.
 Abstrak. Analisis regresi adalah metode statistika yang digunakan untuk menentukan pola hubungan antara variabel bebas dengan variabel terikat. Terdapat tiga macam analisis regresi, yaitu analisis regresi parametrik, analisis regresi semiparametrik dan analisis regesi nonparametrik. Analisis regresi parametrik dapat digunakan ketika asumsi terpenuhi akan tetapi tidak semua data dapat memenuhi asumsi parametrik, alternatif dari regresi parametrik adalah regresi nonparametrik karena penggunaanya tidak memerlukan asumsi yang ketat. Regresi nonparametrik Spline merupakan metode yang digunakan untuk mendapatkan dugaan kurva regresi melalui pendekatan estimasi pola data sesuai pergerakannya. Pemilihan model terbaik pada regesi Spline dilihat dari nilai Generalized Cross Validiation (GCV) dengan menggunakan titik knot yang paling minimum. Pada penelitian ini variabel terikat yang digunakan adalah Indeks Pembangunan Gender (IPG) di Provinsi Jawa Barat Tahun 2020 yang terdiri dari 18 kabupaten dan 9 kota dengan variabel bebas yang terdiri dari rata-rata lama sekolah perempuan, harapan lama sekolah perempuan, tingkat pengangguran terbuka perempuan, tingkat partisipasi angkatan kerja perempuan, perempuan yang memiliki keluhan kesehatan dan rasio jenis kelamin. Hasil dari analisis diperoleh model regresi nonparametrik Spline yang terbaik adalah dengan menggunakan orde satu dan tiga titik knot dengan nilai GCV yang paling minimum 0,2471, serta didapatkan nilai koefisien determinasi sebesar 99,98%. Dengan ke enam variabel bebas yang digunakan memiliki pengaruh yang signifikan terhadap IPG di Jawa Barat tahun 2020.
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FITRIANI, ANNA, I. GUSTI AYU MADE SRINADI, and MADE SUSILAWATI. "ESTIMASI MODEL REGRESI SEMIPARAMETRIK MENGGUNAKAN ESTIMATOR KERNEL UNIFORM (Studi Kasus: Pasien DBD di RS Puri Raharja)." E-Jurnal Matematika 4, no. 4 (2015): 176. http://dx.doi.org/10.24843/mtk.2015.v04.i04.p108.

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Semiparametric regression model estimation is an estimation that combines both parametric and nonparametric regression model. In semiparametric regression, some of the variables are parametrics and the others are nonparametrics. Semiparametric regression is used when relationship pattern between independent and depentdent variables is half known and half unknown. Regression curve smoothing technique in nonparametric components in this study was using uniform kernel function. The optimal semiparametric regression curve estimation was obtained by optimal bandwidth. By choosing optimal bandwidth, we would obtain a smooth regression curve estimation in respect to data pattern. In choosing optimal bandwidth, we use minimum GCV as a criteria.The purpose of this study was to estimate the semiparametric regression function of dengue fever case using uniform kernel estimator. There were 6 independent variables namely age (in years) body temperature (in Celcius), heartbeat (in times/minutes) hematocryte ratio (in percent), amount of trombocyte (× 103/ul) and fever duration ( in days). Age, body temperature, heartbeat, amount of trombosyte and fever duration are parametric components and hematocryte ration is a nonparametric component. The optimal bandwidth (h) which was obtained with minimum GCVwas 0,005. The value of MSE which was obtained by using multiple linear regression analysis was 0,031 and by using semiparametric regression was 0,00437119.
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Linton, Oliver B., and Yang Yan. "Semi- and Nonparametric ARCH Processes." Journal of Probability and Statistics 2011 (2011): 1–17. http://dx.doi.org/10.1155/2011/906212.

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ARCH/GARCH modelling has been successfully applied in empirical finance for many years. This paper surveys the semiparametric and nonparametric methods in univariate and multivariate ARCH/GARCH models. First, we introduce some specific semiparametric models and investigate the semiparametric and nonparametrics estimation techniques applied to: the error density, the functional form of the volatility function, the relationship between mean and variance, long memory processes, locally stationary processes, continuous time processes and multivariate models. The second part of the paper is about the general properties of such processes, including stationary conditions, ergodic conditions and mixing conditions. The last part is on the estimation methods in ARCH/GARCH processes.
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Muliere, Pietro, and Marco Scarsini. "Change-point problems: A Bayesian nonparametric approach." Applications of Mathematics 30, no. 6 (1985): 397–402. http://dx.doi.org/10.21136/am.1985.104169.

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Al Azies, Harun, and Dea Trishnanti. "Pemodelan Pengaruh Imunisasi DPT Terhadap Angka Kematian Bayi di Jawa Timur Tahun 2016 Menggunakan Pendekatan Regresi Nonparametrik Spline." J Statistika: Jurnal Ilmiah Teori dan Aplikasi Statistika 12, no. 1 (2019): 26–31. http://dx.doi.org/10.36456/jstat.vol12.no1.a1995.

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East Java is one of the provinces with a high IMR level. Based on the District / City report in East Java, in 2006 it was 0.035 live births and became 0.0032 live births in 2008. Identification of factors that influence both indicators correctly can be done by modeling, namely by nonparametric regression analysis. The nonparametric regression approach used is Spline, with its strengths the model tends to look for estimates wherever the data moves. This is because there is a knot point which is a joint fusion point which indicates a change in data behavior patterns. Based on the results of analysis and discussion using Spline analysis, it is known that the factors that influence the incidence of IMR in East Java are toddlers receiving type 3 DPT immunization. The best Spline nonparametric regression model is a linear Spline model with three point knots. The GCV value produced was 51.34. Factors of children under five obtained immunizations affecting infant mortality rates in districts / cities in East Java in 2016. This research still uses linear spline regression program with a combination of one, two, and three knots with R square of 65.92%. The need to develop programs into quadratic and cubic orders using a combination of knots.
 Jawa Timur merupakan salah satu provinsi dengan tingkat AKB yang tinggi. Berdasarkan laporan Kabupaten/Kota di Jawa Timur, pada tahun 2006 sebesar 0,035 kelahiran hidup dan menjadi 0,0032 kelahiran hidup pada tahun 2008. Jika suatu daerah dengan AKB yang tinggi, maka terdapat kemungkinan bahwa daerah sekitarnya akan memiliki beban AKB yang sama pula. Identifikasi faktor-faktor yang mempengaruhi kedua indikator secara tepat dapat dilakukan dengan pemodelan, yaitu dengan analisis regresi nonparametrik. Pendekatan regresi nonparametric yang digunakan adalah Spline, dengan kelebihannya model cenderung mencari estimasinya kemanapun data tersebut bergerak. Hal ini dikarenakan terdapat titik knot yang merupakan titik perpaduan bersama yang menunjukkan terjadinya perubahan pola perilaku data. Berdasarkan hasil analisis dan pembahasan dengan menggunakan analisis Spline diketahui bahwa faktor yang berpengaruh terhadap kejadian AKB di Jawa Timur adalah balita memperoleh imunisasi DPT tipe 3. Model regresi nonparametrik Spline terbaik adalah model Spline linear dengan tiga titik knot. Nilai GCV yang dihasilkan adalah 51,34. Faktor balita memperoleh imunisasi mempengaruhi angka kematian bayi di kabupaten/kota di Jawa Timur pada tahun 2016. Penelitian ini masih menggunakan program regresi spline linier dengan kombinasi satu, dua, dan tiga knot dengan R square sebesar 65,92%. Perlu adanya pengembangan program menjadi orde kuadratik dan kubik dengan menggunakan kombinasi knot.
 
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Side, Syafruddin, Wahidah Sanusi, and Mustati'atul Waidah Maksum. "Model Regresi Semiparametrik Spline untuk D ata Longitudinal pada Kasus Demam Berdarah Dengue di Kota Makassar." Journal of Mathematics Computations and Statistics 3, no. 1 (2021): 20. http://dx.doi.org/10.35580/jmathcos.v3i1.19181.

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Abstrak. Regresi semiparametrik merupakan model regresi yang memuat komponen parametrik dan komponen nonparametrik dalam suatu model. Pada penelitian ini digunakan model regresi semiparametrik spline untuk data longitudinal dengan studi kasus penderita Demam Berdarah Dengue (DBD) di Rumah Sakit Universitas Hasanuddin Makassar periode bulan Januari sampai bulan Maret 2018. Estimasi model regresi terbaik didapat dari pemilihan titik knot optimal dengan melihat nilai Generalized Cross Validation (GCV) dan Mean Square Error (MSE) yang minimum. Komponen parametrik pada penelitian ini adalah hemoglobin (g/dL) dan umur (tahun), suhu tubuh ( ), trombosit ( ) sebagai komponen nonparametrik dengan nilai GCV minimum sebesar 221,67745153 dicapai pada titik knot yaitu 14,552; 14,987; dan 15,096; nilai MSE sebesar 199,1032; dan nilai koefisien determinasi sebesar 75,3% yang diperoleh dari model regresi semiparametrik spline linear dengan tiga titik knot..Kata Kunci: regresi semiparametrik, spline, knot, Generalized Cross Validation, Demam Berdarah Dengue.Abstract. Semiparametric regression is a regression model that includes parametric and nonparametric components in it. The regression model in this research is spline semiparametric regression with case studies of patients with Dengue Hemorrahagic Fever (DHF) at University of Hasanuddin Makassar Hospital during the period of January to March 2018. The best regression model estimation is obtained from the selection of optimal knot which has minimum Generalized Cross Validation (GCV) and Mean Square Error (MSE). Parametric component in this research is hemoglobin (g/dL) and age (years), body temperature (
 
 ), platelets (
 
 ) as a nonparametric components. The minimum value of GCV is 221,67745153 achieved at the point 14,552; 14,987; and 15,096 knot; MSE value of 199,1032; and the value of coefficient determination is 75,3% obtained from semiparametric regression model linear spline with third point of knots.Keywords: semiparametric regression, spline, knot, Generalized Cross Validation, Dengue Hemorrahagic Fever.
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Islamiyati, Anna, Anisa Anisa, Raupong Raupong, et al. "Estimasi Model Regresi Spline Kubik Tersegmen dengan Metode Penalized Least Square." Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam 10, no. 2 (2022): 139–48. http://dx.doi.org/10.24256/jpmipa.v10i2.3197.

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Abstract:Nonparametric regression is used for data whose data pattern is non-parametric. One of the estimators that can be developed is a segmented cubic spline which is able to show several segmentation changes in the data. This article examines the estimation of segmented cubic spline nonparametric regression models using the Penalized Least Square estimation criteria. The method involves knot points and smoothing parameters simultaneously. In addition, the model is used to analyze data on BPJS claims based on patient age. The results show that the optimal model is at two-knot points, namely 26 and 52 with a smoothing parameter of 0.89. There are three segmentation changes from the cubic data, which consist of young people up to 26 years old, 26-52 years old, and 52 years and over. Abstrak:Regresi nonparametrik digunakan untuk data yang pola datanya bentuk non parametrik. Salah satu estimator yang dapat dikembangkan adalah spline kubik tersegmen yang mampu menunjukkan beberapa segmentasi perubahan pada data. Artikel ini mengkaji estimasi model regresi nonparametrik spline kubik tersegmen melalui kriteria estimasi menggunakan Penalized Least Square. Metode tersebut melibatkan titik knot dan parameter penghalus secara bersamaan. Selain itu, model digunakan untuk menganalisis data klaim BPJS berdasarkan usia pasien. Hasil menunjukkan bahwa model optimal pada dua titik knot yaitu 26 dan 52 dengan parameter penghalus sebesar 0,89. Terdapat tiga segmentasi perubahan data secara kubik, yaitu usia muda hingga 26 tahun, usia 26-52 tahun, dan usia 52 tahun ke atas.
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Lin Jiarui, 林嘉睿, 孙佳蕾 Sun Jialei, 张饶 Zhang Rao, 郑书彦 Zheng Shuyan та 邾继贵 Zhu Jigui. "大尺度线结构激光面的非参数模型标定方法". Acta Optica Sinica 41, № 16 (2021): 1612001. http://dx.doi.org/10.3788/aos202141.1612001.

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Vincent, Odhiambo, Hellen Waititu, and Nyakundi Omwando Cornelious. "Nonparametric Estimation of Error Variance under Simple Random Sampling without Replacement." International Journal of Mathematics And Computer Research 10, no. 10 (2022): 2925–33. http://dx.doi.org/10.47191/ijmcr/v10i10.02.

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This study adopts a nonparametric approach in the estimation of a finite population error variance in the setting where the variance is a constant (homoscedastic) using a model-based technique under simple random sampling without replacement (SRSWOR). A mean square analysis of the estimator has been conducted, including the asymptotic behaviour of the estimator and the results show that the asymptotic distribution in a homoscedastic setting is asymptotically unbiased and consistent. The performance of the developed estimator is compared to that of other existing estimators using real data. R statistical software was utilized to analyze data and numerical results presented graphically for selected models.
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Cooper, Joseph C. "Nonparametric and Semi‐Nonparametric Recreational Demand Analysis." American Journal of Agricultural Economics 82, no. 2 (2000): 451–62. http://dx.doi.org/10.1111/0002-9092.00038.

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Theofani, Eukaristianica, and Ike Herdiana. "Meningkatkan resiliensi penyintas pelesual melalui terapi pemaafan." Jurnal Ilmiah Psikologi Terapan 8, no. 1 (2020): 1. http://dx.doi.org/10.22219/jipt.v8i1.9865.

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Abstrak. Kehamilan yang tidak diinginkan akibat pelecehan seksual terasa sangat berat bagi wanita sehingga dibutuhkan kemampuan untuk bangkit dari keterpurukan yang disebut resiliensi. Individu yang resilien mampu menghadapi hal yang menekan dalam hidupnya dan berusaha untuk mengatasi tekanan melalui strategi koping, salah satunya dengan melakukan pemaafan. Terapi pemaafan adalah salah satu bentuk intervensi yang dapat meningkatkan resiliensi. Tujuan penelitian ini adalah untuk mengetahui peningkatan resiliensi pada wanita penyintas pelecehan seksual melalui terapi pemaafan. Penelitian ini menggunakan metode eksperimen semu dengan desain reversal A-B. Subjek penelitian adalah 3 orang wanita penyintas pelecehan seksual yang mengalami kehamilan yang tidak diinginkan dengan tingkat resiliensi rendah atau sedang berdasarkan kategorisasi skala CYRM-28. Data dianalisis dengan analisis visual dan analisis nonparametrik Wilcoxon. Hasil analisis visual menunjukkan peningkatan resiliensi, sedangkan hasil analisis nonparametrik menunjukkan perbedaan resiliensi yang tidak signifikan (0,109 > 0,05) antara sebelum dan setelah intervensi diberikan. Meskipun demikian, pengukuran effect size menunjukkan bahwa terapi pemaafan berpengaruh besar (0,926 > 0,8) untuk meningkatkan resiliensi wanita penyintas pelecehan seksual yang mengalami kehamilan yang tidak diinginkan.Kata kunci: kehamilan tidak diinginkan, pelecehan seksual, resiliensi, terapi pemaafanAbstract. An unwanted pregnancy due to sexual abuse feels so heavy for a woman so that it needs the ability to rise from adversity called resilience. Resilient individuals are able to deal with pressures in their lives and try to deal with stress through coping strategies, which is to forgive. Forgiveness therapy is a form of intervention that can increase resilience. The purpose of this study was to determine the increase in resilience in women survivors of sexual abuse who experienced an unwanted pregnancy through forgiveness therapy. This research uses quasi-experimental method with A-B reversal design. Subjects were 3 survivors of sexual abuse who experienced an unwanted pregnancy with low or moderate resilience based on the CYRM-28 scale categorization. Data were analyzed by Wilcoxon visual analysis and nonparametric analysis. The results of visual analysis showed an increase in resilience, while the results of the nonparametric analysis showed a non-significant difference in resilience (0.109> 0.05) between before and after the intervention was given. Even so, measurement of effect size shows that forgiveness therapy has a big effect (0.926> 0.8) to increase the resilience of survivors of sexual abuse who experienced an unwanted pregnancy.Keywords: unwanted pregnancy, sexual abuse, resilience, forgiveness therapy
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Epifani, Ilenia. "Bayesian Nonparametrics." Journal of the American Statistical Association 99, no. 467 (2004): 898–99. http://dx.doi.org/10.1198/jasa.2004.s346.

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Shang, Han Lin. "Bayesian Nonparametrics." Journal of Applied Statistics 38, no. 12 (2011): 2990. http://dx.doi.org/10.1080/02664763.2011.559374.

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Kuželka, K., and R. Marušák. "Use of nonparametric regression methods for developing a local stem form model." Journal of Forest Science 60, No. 11 (2014): 464–71. http://dx.doi.org/10.17221/56/2014-jfs.

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A local mean stem curve of spruce was represented using regression splines. Abilities of smoothing spline and P-spline to model the mean stem curve were evaluated using data of 85 carefully measured stems of Norway spruce. For both techniques the optimal amount of smoothing was investigated in dependence on the number of training stems using a cross-validation method. Representatives of main groups of parametric models – single models, segmented models and models with variable coefficient – were compared with spline models using five statistic criteria. Both regression splines performed comparably or better as all representatives of parametric models independently of the numbers of stems used as training data.  
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Blanco-Oliver, A., A. Irimia-Dieguez, M. D. Oliver-Alfonso, and M. J. Vázquez-Cueto. "Hybrid model using logit and nonparametric methods for predicting micro-entity failure." Investment Management and Financial Innovations 13, no. 3 (2016): 35–46. http://dx.doi.org/10.21511/imfi.13(3).2016.03.

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Following the calls from literature on bankruptcy, a parsimonious hybrid bankruptcy model is developed in this paper by combining parametric and non-parametric approaches.To this end, the variables with the highest predictive power to detect bankruptcy are selected using logistic regression (LR). Subsequently, alternative non-parametric methods (Multilayer Perceptron, Rough Set, and Classification-Regression Trees) are applied, in turn, to firms classified as either “bankrupt” or “not bankrupt”. Our findings show that hybrid models, particularly those combining LR and Multilayer Perceptron, offer better accuracy performance and interpretability and converge faster than each method implemented in isolation. Moreover, the authors demonstrate that the introduction of non-financial and macroeconomic variables complement financial ratios for bankruptcy prediction
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Belcher, John. "Nonparametric methods." Nurse Researcher 9, no. 1 (2001): 17–25. http://dx.doi.org/10.7748/nr2001.10.9.1.17.c6172.

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Krzywinski, Martin, and Naomi Altman. "Nonparametric tests." Nature Methods 11, no. 5 (2014): 467–68. http://dx.doi.org/10.1038/nmeth.2937.

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Racine, Jeffrey S. "Nonparametric Econometrics." Journal of the American Statistical Association 96, no. 453 (2001): 339–55. http://dx.doi.org/10.1198/jasa.2001.s374.

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Ueda, Naonori. "Nonparametric Bayes." Journal of The Institute of Image Information and Television Engineers 70, no. 5 (2016): 478–80. http://dx.doi.org/10.3169/itej.70.478.

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Brown, George W., and Gregory F. Hayden. "Nonparametric Methods." Clinical Pediatrics 24, no. 9 (1985): 490–98. http://dx.doi.org/10.1177/000992288502400905.

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Dias, Ronaldo. "Nonparametric econometrics." Brazilian Review of Econometrics 22, no. 1 (2002): 127. http://dx.doi.org/10.12660/bre.v22n12002.2747.

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Linton, O. B. "Nonparametric econometrics." Journal of Statistical Planning and Inference 92, no. 1-2 (2001): 299–300. http://dx.doi.org/10.1016/s0378-3758(00)00070-7.

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Lehmkuhl, L. Don. "Nonparametric Statistics." JPO Journal of Prosthetics and Orthotics 8, no. 3 (1996): 24A. http://dx.doi.org/10.1097/00008526-199607000-00008.

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Pettitt, A. N., P. R. Krishnaiah, and P. K. Sen. "Nonparametric Methods." Journal of the Royal Statistical Society. Series A (General) 150, no. 2 (1987): 172. http://dx.doi.org/10.2307/2981642.

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Ozertem, Umut, and Deniz Erdogmus. "Nonparametric Snakes." IEEE Transactions on Image Processing 16, no. 9 (2007): 2361–68. http://dx.doi.org/10.1109/tip.2007.902335.

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Praagman, J. "Nonparametric methods." European Journal of Operational Research 28, no. 2 (1987): 238–39. http://dx.doi.org/10.1016/0377-2217(87)90234-7.

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Chou, Chien-fu, and Gabriel Talmain. "Nonparametric search." Journal of Economic Dynamics and Control 17, no. 5-6 (1993): 771–84. http://dx.doi.org/10.1016/0165-1889(93)90014-j.

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Pandis, Nikolaos. "Nonparametric methods." American Journal of Orthodontics and Dentofacial Orthopedics 148, no. 4 (2015): 695. http://dx.doi.org/10.1016/j.ajodo.2015.07.014.

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38

Grama, Ion G., and Michael H. Neumann. "Asymptotic equivalence of nonparametric autoregression and nonparametric regression." Annals of Statistics 34, no. 4 (2006): 1701–32. http://dx.doi.org/10.1214/009053606000000560.

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39

Ali Fadhil Abduljabbar and Afrah Mohammed Kadhim. "Comparison the Robust Estimators Nonparametric of Nonparametric Regressions." Tikrit Journal of Pure Science 28, no. 1 (2023): 96–100. http://dx.doi.org/10.25130/tjps.v28i1.1271.

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In order to get rid of or reduce the abnormal values ​​of some phenomena that may be the reason for not obtaining the desired results. This makes us to get conclusions far from reality for the phenomenon we are studying. That the traditional nonparametric estimators are very sensitive to anomalous values, which prompted us to use the fortified estimators because they are not much affected by the anomalous values, as well as the nonparametric regression because it does not depend on the previous determinants or assumptions, but it depends directly and fundamentally on the data.
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Trifonov, J., and B. Potanin. "Semi-Nonparametric Generalized Autoregressive Conditional Heteroscedasticity Model with Application to Bitcoin Volatility Estimation." Higher School of Economics Economic Journal 26, no. 4 (2022): 623–46. http://dx.doi.org/10.17323/1813-8691-2022-26-4-623-646.

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Corain, Livio, and Luigi Salmaso. "Multivariate And Multistrata Nonparametric Tests: The NonParametric Combination Method." Journal of Modern Applied Statistical Methods 3, no. 2 (2004): 443–61. http://dx.doi.org/10.22237/jmasm/1099268160.

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42

Coolen, Frank P. A., and Sulafah Bin Himd. "Nonparametric Predictive Inference for Reproducibility of Basic Nonparametric Tests." Journal of Statistical Theory and Practice 8, no. 4 (2014): 591–618. http://dx.doi.org/10.1080/15598608.2013.819792.

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43

Blanciforti, Laura A. "Consumer Demand Analysis According to GARP: Discussion." Northeastern Journal of Agricultural and Resource Economics 21, no. 2 (1992): 140–41. http://dx.doi.org/10.1017/s0899367x00002658.

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This paper explores the issue of the power of nonparametric tests to check for the consistency of data with utility maximization. Alston and Chalfant provide an excellent review of nonparametric approaches to consumer-demand analysis. They test for consistency, separability, and power. The authors address two important questions: First, how does one define power for nonparametric situations, and is that definition comparable to the parametric situation? Second, can the power of nonparametric tests be improved? The authors measure the statistical power of nonparametric methods using a parametric test, though they do not address whether it is legitimate to use parametric tests on nonparametric methods.
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Royeen, C. B., and W. L. Seaver. "Promise in Nonparametrics." American Journal of Occupational Therapy 40, no. 3 (1986): 191–93. http://dx.doi.org/10.5014/ajot.40.3.191.

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Hall, P. "Biometrika Centenary: Nonparametrics." Biometrika 88, no. 1 (2001): 143–65. http://dx.doi.org/10.1093/biomet/88.1.143.

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46

Sriliana, Idhia, Dian Agustina, and Etis Sunandi. "Pemetaan Kemiskinan di Kabupaten Mukomuko Menggunakan Small Area Estimation Dengan Pendekatan Regresi Penalized Spline." Jurnal Matematika Integratif 12, no. 2 (2017): 125. http://dx.doi.org/10.24198/jmi.v12.n2.11929.125-133.

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Penelitian ini bertujuan untuk melakukan pemetaan kemiskinan di Kabupaten Mukomuko ProvinsiBengkulu. Metode yang digunakan dalam penelitian ini adalah Small Area Estimation (SAE) denganpendekatan regresi Penalized Spline (P-Spline). Pendugaan parametr model dasar SAE umumnyamembangun suatu model linier campuran yang mengasumsikan bahwa variabel respon dan variabelprediktor mempunyai hubungan linear. Ketika asumsi tersebut tidak terpenuhi, maka dilakukanpendekatan nonparametrik sebagai alternatif pilihan. Salah satunya adalah pendekatan nonparametrikP-Spline. Pada penelitian ini, dilakukan pendugaan parameter model menggunakan P-Spline sehinggadiperoleh suatu persamaan regresi efek campuran sebagai model SAE. Selanjutnya model tersebutdigunakan untuk menduga tingkat kemiskinan pada area yang tersampling., sehingga diperoleh pendugatingkat kemiskinan pada level desa di Kabupaten Mukomuko yang disajikan dalam bentuk petakemiskinan. Hasil penelitian menunjukkan pendugaan menggunakan model SAE dengan P-Splinememiliki trend (kecenderungan) yang sama dengan penduga langsung. Kecamatan yang memiliki tingkatkemiskinan tinggi menyebar di bagian Timur Laut dan Tenggara dari Kabupaten Mukomuko, yaituKecamatan Selagan Raya, Teramang Jaya, Pondok Suguh, dan Air Rami masing-masing memiliki rata-rata kemiskinan yang tinggi. Sedangkan kecamatan dengan tingkat kemiskinan rendah adalahKecamatan Lubuk Pinang.
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Sriliana, Idhia, Dian Agustina, and Etis Sunandi. "Pemetaan Kemiskinan di Kabupaten Mukomuko Menggunakan Small Area Estimation Dengan Pendekatan Regresi Penalized Spline." Jurnal Matematika Integratif 12, no. 2 (2017): 59. http://dx.doi.org/10.24198/jmi.v12.n2.11929.59-67.

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Penelitian ini bertujuan untuk melakukan pemetaan kemiskinan di Kabupaten Mukomuko ProvinsiBengkulu. Metode yang digunakan dalam penelitian ini adalah Small Area Estimation (SAE) denganpendekatan regresi Penalized Spline (P-Spline). Pendugaan parametr model dasar SAE umumnyamembangun suatu model linier campuran yang mengasumsikan bahwa variabel respon dan variabelprediktor mempunyai hubungan linear. Ketika asumsi tersebut tidak terpenuhi, maka dilakukanpendekatan nonparametrik sebagai alternatif pilihan. Salah satunya adalah pendekatan nonparametrikP-Spline. Pada penelitian ini, dilakukan pendugaan parameter model menggunakan P-Spline sehinggadiperoleh suatu persamaan regresi efek campuran sebagai model SAE. Selanjutnya model tersebutdigunakan untuk menduga tingkat kemiskinan pada area yang tersampling., sehingga diperoleh pendugatingkat kemiskinan pada level desa di Kabupaten Mukomuko yang disajikan dalam bentuk petakemiskinan. Hasil penelitian menunjukkan pendugaan menggunakan model SAE dengan P-Splinememiliki trend (kecenderungan) yang sama dengan penduga langsung. Kecamatan yang memiliki tingkatkemiskinan tinggi menyebar di bagian Timur Laut dan Tenggara dari Kabupaten Mukomuko, yaituKecamatan Selagan Raya, Teramang Jaya, Pondok Suguh, dan Air Rami masing-masing memiliki rata-rata kemiskinan yang tinggi. Sedangkan kecamatan dengan tingkat kemiskinan rendah adalahKecamatan Lubuk Pinang.
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48

Sriliana, Idhia, Dian Agustina, and Etis Sunandi. "Pemetaan Kemiskinan di Kabupaten Mukomuko Menggunakan Small Area Estimation Dengan Pendekatan Regresi Penalized Spline." Jurnal Matematika Integratif 12, no. 2 (2017): 125. http://dx.doi.org/10.24198/jmi.v12i2.11929.

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Penelitian ini bertujuan untuk melakukan pemetaan kemiskinan di Kabupaten Mukomuko ProvinsiBengkulu. Metode yang digunakan dalam penelitian ini adalah Small Area Estimation (SAE) denganpendekatan regresi Penalized Spline (P-Spline). Pendugaan parametr model dasar SAE umumnyamembangun suatu model linier campuran yang mengasumsikan bahwa variabel respon dan variabelprediktor mempunyai hubungan linear. Ketika asumsi tersebut tidak terpenuhi, maka dilakukanpendekatan nonparametrik sebagai alternatif pilihan. Salah satunya adalah pendekatan nonparametrikP-Spline. Pada penelitian ini, dilakukan pendugaan parameter model menggunakan P-Spline sehinggadiperoleh suatu persamaan regresi efek campuran sebagai model SAE. Selanjutnya model tersebutdigunakan untuk menduga tingkat kemiskinan pada area yang tersampling., sehingga diperoleh pendugatingkat kemiskinan pada level desa di Kabupaten Mukomuko yang disajikan dalam bentuk petakemiskinan. Hasil penelitian menunjukkan pendugaan menggunakan model SAE dengan P-Splinememiliki trend (kecenderungan) yang sama dengan penduga langsung. Kecamatan yang memiliki tingkatkemiskinan tinggi menyebar di bagian Timur Laut dan Tenggara dari Kabupaten Mukomuko, yaituKecamatan Selagan Raya, Teramang Jaya, Pondok Suguh, dan Air Rami masing-masing memiliki rata-rata kemiskinan yang tinggi. Sedangkan kecamatan dengan tingkat kemiskinan rendah adalahKecamatan Lubuk Pinang.
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Adamowski, Kaz, and W. Feluch. "Application of nonparametric regression to groundwater level prediction." Canadian Journal of Civil Engineering 18, no. 4 (1991): 600–606. http://dx.doi.org/10.1139/l91-073.

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A new nonparametric regression model is proposed to investigate the relationship between groundwater level fluctuations and streamflow time series observations. The developed nonparametric model does not force the relationship between variables into a rigidly defined class (i.e., linear regression) and is capable of inferring complicated relationships. The results from the analysis indicate that the nonparametric method gives more accurate prediction results than those obtained from parametric regression. A split-sample experiment shows that nonparametric regression gives accurate prediction (extrapolation) results at the validation stage. Key words: nonparametric regression, cross-validation method, groundwater level, streamflow.
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50

Gringras, D., M. Alvo, and K. Adamowski. "Regional Flood Relationships by Nonparametric Regression." Hydrology Research 26, no. 2 (1995): 73–90. http://dx.doi.org/10.2166/nh.1995.0005.

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Abstract:
Since some theoretical assumptions needed in linear regression are not always fulfilled in practical applications, nonparametric regression was investigated as an alternative method in regional flood relationship development. Simulation studies were developed to compare the bias, the variance and the root-mean-square-errors of nonparametric and parametric regressions. It was concluded that when an appropriate parametric model can be determined, parametric regression is preferred over nonparametric regression. However, where an appropriate model cannot be determined, nonparametric regression is preferred. It was found that both linear regression and nonparametric regression gave very similar regional relationships for annual maximum floods from New Brunswick, Canada. It was also found that nonparametric regression can be useful as a screening tool able to detect data deficient relationships.
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