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Journal articles on the topic 'Least absolute deviations (Statistics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 January 2023

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1

Sudermann-Merx, Nathan, and Steffen Rebennack. "Leveraged least trimmed absolute deviations." OR Spectrum 43, no. 3 (2021): 809–34. http://dx.doi.org/10.1007/s00291-021-00627-y.

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AbstractThe design of regression models that are not affected by outliers is an important task which has been subject of numerous papers within the statistics community for the last decades. Prominent examples of robust regression models are least trimmed squares (LTS), where the k largest squared deviations are ignored, and least trimmed absolute deviations (LTA) which ignores the k largest absolute deviations. The numerical complexity of both models is driven by the number of binary variables and by the value k of ignored deviations. We introduce leveraged least trimmed absolute deviations (

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2

MORGENTHALER, STEPHAN. "Least-absolute-deviations fits for generalized linear models." Biometrika 79, no. 4 (1992): 747–54. http://dx.doi.org/10.1093/biomet/79.4.747.

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3

Ziegelmann, Flavio A. "A Local Linear Least-Absolute-Deviations Estimator of Volatility." Communications in Statistics - Simulation and Computation 37, no. 8 (2008): 1543–64. http://dx.doi.org/10.1080/03610910802244398.

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4

Ciuperca, Gabriela. "Penalized least absolute deviations estimation for nonlinear model with change-points." Statistical Papers 52, no. 2 (2009): 371–90. http://dx.doi.org/10.1007/s00362-009-0236-6.

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5

Vazler, Ivan, Kristian Sabo, and Rudolf Scitovski. "Weighted Median of the Data in Solving Least Absolute Deviations Problems." Communications in Statistics - Theory and Methods 41, no. 8 (2012): 1455–65. http://dx.doi.org/10.1080/03610926.2010.539750.

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6

Mathew, Thomas, and Kenneth Nordström. "Least squares and least absolute deviation procedures in approximately linear models." Statistics & Probability Letters 16, no. 2 (1993): 153–58. http://dx.doi.org/10.1016/0167-7152(93)90160-k.

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7

McKean, Joseph W., and Gerald L. Sievers. "Coefficients of determination for least absolute deviation analysis." Statistics & Probability Letters 5, no. 1 (1987): 49–54. http://dx.doi.org/10.1016/0167-7152(87)90026-5.

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8

Pan, Baoguo, Min Chen, Yan Wang, and Wei Xia. "Weighted least absolute deviations estimation for ARFIMA time series with finite or infinite variance." Journal of the Korean Statistical Society 44, no. 1 (2015): 1–11. http://dx.doi.org/10.1016/j.jkss.2014.04.001.

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9

Tyrsin, A. N. "Robust construction of regression models based on the generalized least absolute deviations method." Journal of Mathematical Sciences 139, no. 3 (2006): 6634–42. http://dx.doi.org/10.1007/s10958-006-0380-7.

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10

Chan, Ngai Hang, and Liang Peng. "Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors." Biometrika 92, no. 2 (2005): 477–84. http://dx.doi.org/10.1093/biomet/92.2.477.

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11

Ling, Shiqing. "Self-weighted least absolute deviation estimation for infinite variance autoregressive models." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67, no. 3 (2005): 381–93. http://dx.doi.org/10.1111/j.1467-9868.2005.00507.x.

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12

Wang, Hongxia, Jinguan Lin, and Jinde Wang. "Local Linear Estimation for Spatiotemporal Models Based on Least Absolute Deviation." Communications in Statistics - Theory and Methods 44, no. 7 (2013): 1508–22. http://dx.doi.org/10.1080/03610926.2013.771744.

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13

Wang, Xinghui, Huilong Wang, Hongrui Wang, and Shuhe Hu. "Asymptotic inference of least absolute deviation estimation for AR(1) processes." Communications in Statistics - Theory and Methods 49, no. 4 (2018): 809–26. http://dx.doi.org/10.1080/03610926.2018.1549252.

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14

Silva, Lana Mirian Santos da, Luiz Carlos Estraviz Rodriguez, José Vicente Caixeta Filho, and Simone Carolina Bauch. "Fitting a taper function to minimize the sum of absolute deviations." Scientia Agricola 63, no. 5 (2006): 460–70. http://dx.doi.org/10.1590/s0103-90162006000500007.

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Multiple product inventories of forests require accurate estimates of the diameter, length and volume of each product. Taper functions have been used to precisely describe tree form, once they provide estimates for the diameter at any height or the height at any diameter. This study applied a goal programming technique to estimate the parameters of two taper functions to describe individual tree forms. The goal programming formulation generates parameters that minimize total absolute deviations (MOTAD). These parameters generated by the MOTAD method were compared to those of ordinary least squ

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15

Zhu, Qianqian, Ruochen Zeng, and Guodong Li. "Bootstrap Inference for Garch Models by the Least Absolute Deviation Estimation." Journal of Time Series Analysis 41, no. 1 (2019): 21–40. http://dx.doi.org/10.1111/jtsa.12474.

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16

Caner, Mehmet. "A NOTE ON LEAST ABSOLUTE DEVIATION ESTIMATION OF A THRESHOLD MODEL." Econometric Theory 18, no. 3 (2002): 800–814. http://dx.doi.org/10.1017/s0266466602183113.

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This paper develops the limit law for the least absolute deviation estimator of the threshold parameter in linear regression. In this respect, we extend the literature of threshold models. The existing literature considers only the least squares estimation of the threshold parameter (see Chan, 1993, Annals of Statistics 21, 520–533; Hansen, 2000, Econometrica 68, 575–605). This result is useful because in the case of heavy-tailed errors there is an efficiency loss resulting from the use of least squares. Also, for the first time in the literature, we derive the limit law for the likelihood rat

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17

Abdullahi, Ibrahim, and Abubakar Yahaya. "Analysis of quantile regression as alternative to ordinary least squares." International Journal of Advanced Statistics and Probability 3, no. 2 (2015): 138. http://dx.doi.org/10.14419/ijasp.v3i2.4686.

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<p>In this article, an alternative to ordinary least squares (OLS) regression based on analytical solution in the Statgraphics software is considered, and this alternative is no other than quantile regression (QR) model. We also present goodness of fit statistic as well as approximate distributions of the associated test statistics for the parameters. Furthermore, we suggest a goodness of fit statistic called the least absolute deviation (LAD) coefficient of determination. The procedure is well presented, illustrated and validated by a numerical example based on publicly available datase

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18

Wu, Rongning, and Richard A. Davis. "Least absolute deviation estimation for general autoregressive moving average time-series models." Journal of Time Series Analysis 31, no. 2 (2010): 98–112. http://dx.doi.org/10.1111/j.1467-9892.2009.00648.x.

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19

Wang, Lihong, and Jinde Wang. "The limiting behavior of least absolute deviation estimators for threshold autoregressive models." Journal of Multivariate Analysis 89, no. 2 (2004): 243–60. http://dx.doi.org/10.1016/j.jmva.2004.02.006.

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20

Wu, Rongning. "Least absolute deviation estimation for general ARMA time series models with infinite variance." Statistica Sinica 21, no. 2 (2011): 779. http://dx.doi.org/10.5705/ss.2011.035a.

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21

Catanzaro, Denys, and James C. Taylor. "The scaling of dispersion and correlation: A comparison of least-squares and absolute-deviation statistics." British Journal of Mathematical and Statistical Psychology 49, no. 1 (1996): 171–88. http://dx.doi.org/10.1111/j.2044-8317.1996.tb01081.x.

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22

Smit, Merijn, and Konrad Kuijken. "Chasing the peak: optimal statistics for weak shear analyses." Astronomy & Astrophysics 609 (January 2018): A103. http://dx.doi.org/10.1051/0004-6361/201731410.

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Context. Weak gravitational lensing analyses are fundamentally limited by the intrinsic distribution of galaxy shapes. It is well known that this distribution of galaxy ellipticity is non-Gaussian, and the traditional estimation methods, explicitly or implicitly assuming Gaussianity, are not necessarily optimal. Aims. We aim to explore alternative statistics for samples of ellipticity measurements. An optimal estimator needs to be asymptotically unbiased, efficient, and robust in retaining these properties for various possible sample distributions. We take the non-linear mapping of gravitation

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23

Herce, Miguel A. "Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors." Econometric Theory 12, no. 1 (1996): 129–53. http://dx.doi.org/10.1017/s0266466600006472.

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In this paper we derive the asymptotic distribution of the least absolute deviations (LAD) estimator of the autoregressive parameter under the unit root hypothesis, when the errors are assumed to have finite variances, and present LAD-based unit root tests, which, under heavy-tailed errors, are expected to be more powerful than tests based on least squares. The limiting distribution of the LAD estimator is that of a functional of a bivariate Brownian motion, similar to those encountered in cointegrating regressions. By appropriately correcting for serial correlation and other distributional pa

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24

Zhao, Quanshui. "ASYMPTOTICALLY EFFICIENT MEDIAN REGRESSION IN THE PRESENCE OF HETEROSKEDASTICITY OF UNKNOWN FORM." Econometric Theory 17, no. 4 (2001): 765–84. http://dx.doi.org/10.1017/s0266466601174050.

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We consider a linear model with heteroskedasticity of unknown form. Using Stone's (1977, Annals of Statistics 5, 595–645) k nearest neighbors (k-NN) estimation approach, the optimal weightings for efficient least absolute deviation regression are estimated consistently using residuals from preliminary estimation. The reweighted least absolute deviation or median regression estimator with the estimated weights is shown to be equivalent to the estimator using the true but unknown weights under mild conditions. Asymptotic normality of the estimators is also established. In the finite sample case,

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25

Chen, Dan, and Xiangfeng Yang. "Maximum likelihood estimation for uncertain autoregressive model with application to carbon dioxide emissions." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 1391–99. http://dx.doi.org/10.3233/jifs-201724.

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The objective of uncertain time series analysis is to explore the relationship between the imprecise observation data over time and to predict future values, where these data are uncertain variables in the sense of uncertainty theory. In this paper, the method of maximum likelihood is used to estimate the unknown parameters in the uncertain autoregressive model, and the unknown parameters of uncertainty distributions of the disturbance terms are simultaneously obtained. Based on the fitted autoregressive model, the forecast value and confidence interval of the future data are derived. Besides,

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26

Li, Guodong, and Wai Keung Li. "Diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach." Biometrika 92, no. 3 (2005): 691–701. http://dx.doi.org/10.1093/biomet/92.3.691.

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27

Li, G., and W. K. Li. "Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity." Biometrika 95, no. 2 (2008): 399–414. http://dx.doi.org/10.1093/biomet/asn014.

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28

Lerspipatthananon, Wanida, and Peerayuth Charnsethikul. "USING COLUMN GENERATION TECHNIQUE TO ESTIMATE PROBABILITY STATISTICS IN TRANSITION MATRIX OF LARGE SCALE MARKOV CHAIN WITH LEAST ABSOLUTE DEVIATION CRITERIA." Journal of Mathematics and Statistics 10, no. 3 (2014): 331–38. http://dx.doi.org/10.3844/jmssp.2014.331.338.

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29

Krivulin, Nikolai. "Using Parameter Elimination to Solve Discrete Linear Chebyshev Approximation Problems." Mathematics 8, no. 12 (2020): 2210. http://dx.doi.org/10.3390/math8122210.

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We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the least maximum absolute deviation of errors. Such problems find application in the solution of overdetermined systems of linear equations that appear in many practical contexts. The least maximum absolute deviation estimator is used in regression analysis in statistics when the distribution of errors has bounded support. To derive a direct solution of the problem, we propose an algebraic approach based on a parameter elimination technique. As a key compone

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30

Wada, Kazumi, Keiichiro Sakashita, and Hiroe Tsubaki. "Robust Estimation for a Generalised Ratio Model." Austrian Journal of Statistics 50, no. 1 (2021): 74–87. http://dx.doi.org/10.17713/ajs.v50i1.994.

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It is known that data such as business sales and household income need data transformation prior to regression estimate as the data has a homoscedastic error. However, data transformations make the estimation of mean and total unstable. Therefore, the ratio model is often used for imputation in the field of official statistics to avoid the problem. Our study aims to robustify the estimator following the ratio model by means of M-estimation. Reformulation of the conventional ratio model with homoscedastic quasi-error term provides quasi-residuals which can be used as a measure of outlyingness a

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31

Khan, Naveed Ahmad, Muhammad Sulaiman, Carlos Andrés Tavera Romero, and Fawaz Khaled Alarfaj. "Numerical Analysis of Electrohydrodynamic Flow in a Circular Cylindrical Conduit by Using Neuro Evolutionary Technique." Energies 14, no. 22 (2021): 7774. http://dx.doi.org/10.3390/en14227774.

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This paper analyzes the mathematical model of electrohydrodynamic (EHD) fluid flow in a circular cylindrical conduit with an ion drag configuration. The phenomenon was modelled as a nonlinear differential equation. Furthermore, an application of artificial neural networks (ANNs) with a generalized normal distribution optimization algorithm (GNDO) and sequential quadratic programming (SQP) were utilized to suggest approximate solutions for the velocity, displacements, and acceleration profiles of the fluid by varying the Hartmann electric number (Ha2) and the strength of nonlinearity (α). ANNs

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32

Sullivan, Patrick W., Julia F. Slejko, Mark J. Sculpher, and Vahram Ghushchyan. "Catalogue of EQ-5D Scores for the United Kingdom." Medical Decision Making 31, no. 6 (2011): 800–804. http://dx.doi.org/10.1177/0272989x11401031.

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Background. The National Institute for Health and Clinical Excellence (NICE) has issued guidance on cost-effectiveness analyses, suggesting that preference-based health-related quality of life (HRQL) weights or utilities be based on UK community preferences, preferably using the EQ-5D; ideally all analyses would use the same system for deriving HRQL weights, to encourage consistency and comparability across analyses. Development of a catalogue of EQ-5D scores for a range of health conditions based on UK preferences would help achieve many of these goals. Objective. To provide a UK-based catalo

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33

Nyquist, Hans. "Least orthogonal absolute deviations." Computational Statistics & Data Analysis 6, no. 4 (1988): 361–67. http://dx.doi.org/10.1016/0167-9473(88)90076-x.

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34

Xia, Yan, Shuguo Pan, Xiaolin Meng, Wang Gao, and He Wen. "Robust Statistical Detection of GNSS Multipath Using Inter-Frequency C/N0 Differences." Remote Sensing 12, no. 20 (2020): 3388. http://dx.doi.org/10.3390/rs12203388.

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Multipath detection and mitigation are crucial issues for global navigation satellite system (GNSS) high-precision positioning. The multi-frequency carrier power-to-noise density ratio (C/N0)-based multipath detection technique has achieved good results in real-time static and low-dynamic applications, and shown better practicability because of the low computational load and the requirement for little additional hardware. However, the classic multipath detection method based on inter-frequency C/N0 differences directly employs the 3σ rule to determine the threshold without considering the dist

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35

Sokolovsky, K. V., A. Z. Bonanos, P. Gavras, et al. "The Hubble Catalog of Variables (HCV)." Proceedings of the International Astronomical Union 14, S339 (2017): 91–94. http://dx.doi.org/10.1017/s1743921318002296.

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AbstractThe Hubble Source Catalog (HSC) combines lists of sources detected on images obtained with the WFPC2, ACS and WFC3 instruments aboard the Hubble Space Telescope (HST) and now available in the Hubble Legacy Archive. The catalogue contains time-domain information for about two million of its sources detected using the same instrument and filter on at least five HST visits. The Hubble Catalog of Variables (HCV) aims to identify HSC sources showing significant brightness variations. A magnitude-dependent threshold in the median absolute deviation of photometric measurements (an outlier-res

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36

Powell, Roger, Eleanor C. R. Green, Estephany Marillo Sialer, and Jon Woodhead. "Robust isochron calculation." Geochronology 2, no. 2 (2020): 325–42. http://dx.doi.org/10.5194/gchron-2-325-2020.

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Abstract. The standard classical statistics approach to isochron calculation assumes that the distribution of uncertainties on the data arising from isotopic analysis is strictly Gaussian. This effectively excludes datasets that have more scatter from consideration, even though many appear to have age significance. A new approach to isochron calculations is developed in order to circumvent this problem, requiring only that the central part of the uncertainty distribution of the data defines a “spine” in the trend of the data. This central spine can be Gaussian but this is not a requirement. Th

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37

Håkansson, Nina, Claudia Adok, Anke Thoss, Ronald Scheirer, and Sara Hörnquist. "Neural network cloud top pressure and height for MODIS." Atmospheric Measurement Techniques 11, no. 5 (2018): 3177–96. http://dx.doi.org/10.5194/amt-11-3177-2018.

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Abstract. Cloud top height retrieval from imager instruments is important for nowcasting and for satellite climate data records. A neural network approach for cloud top height retrieval from the imager instrument MODIS (Moderate Resolution Imaging Spectroradiometer) is presented. The neural networks are trained using cloud top layer pressure data from the CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) dataset. Results are compared with two operational reference algorithms for cloud top height: the MODIS Collection 6 Level 2 height product and the cloud top temperature and height alg

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38

Jiang, Feng, Lin Du, Fan Yang, and Zi-Chen Deng. "Regularized least absolute deviation-based sparse identification of dynamical systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 1 (2023): 013103. http://dx.doi.org/10.1063/5.0130526.

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This work develops a regularized least absolute deviation-based sparse identification of dynamics (RLAD-SID) method to address outlier problems in the classical metric-based loss function and the sparsity constraint framework. Our method uses absolute derivation loss as a substitute of Euclidean loss. Moreover, a corresponding computationally efficient optimization algorithm is derived on the basis of the alternating direction method of multipliers due to the non-smoothness of both the new proposed loss function and the regularization term. Numerical experiments are performed to evaluate the e

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39

Santos, André Luiz Pinto dos, Guilherme Rocha Moreira, Cicero Carlos Ramos de Brito, et al. "Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences." Semina: Ciências Agrárias 39, no. 6 (2018): 2659. http://dx.doi.org/10.5433/1679-0359.2018v39n6p2659.

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This study aims to propose a method to generate growth and degrowth models using differential equations as well as to present a model based on the method proposed, compare it with the classic linear mathematical models Logistic, Von Bertalanffy, Brody, Gompertz, and Richards, and identify the one that best represents the mean growth curve. To that end, data on Undefined Breed (UB) goats and Santa Inês sheep from the works of Cavalcante et al. (2013) and Sarmento et al. (2006a), respectively, were used. Goodness-of-fit was measured using residual mean squares (RMS), Akaike information criterion

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40

Saha, Bikash Chandra, Joshuva Arockia Dhanraj, M. Sujatha, et al. "Investigating Rotor Conditions on Wind Turbines Using Integrating Tree Classifiers." International Journal of Photoenergy 2022 (June 9, 2022): 1–14. http://dx.doi.org/10.1155/2022/5389574.

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Renewable wind power is productive and feasible to manage the energy crisis and global warming. The wind turbine’s blades are the essential components. The dimension of wind turbine blades has been increased with blade sizes varying from approx. 25 m up to approx. 100 m or even greater with a specific purpose to increase energy efficiency. While wind turbine blades tend to be highly stressed by environmental conditions, the wind turbine blade must be constantly tested, inspected, and monitored for wind turbine blades safety monitoring. This research presents a methodology adaptation on machine

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41

Martin, R. Douglas, and Daniel Z. Xia. "Efficient bias robust regression for time series factor models." Journal of Asset Management 23, no. 3 (2022): 215–34. http://dx.doi.org/10.1057/s41260-022-00258-0.

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AbstractWe introduce a robust regression estimator for time series factor models called the mOpt estimator. This estimator minimizes the maximum bias due to outlier generating distribution deviations from a standard normal errors distribution model, and at the same time has a high normal distribution efficiency. We demonstrate the efficacy of the mOpt estimator in comparison with the non-robust least squares (LS) estimator in applications to both single factor and multifactor time series models. For the case of single factor CAPM models we compared mOpt and LS estimates for cross sections of l

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42

Lee, Chau-Kwor, and J. Keith Ord. "Discriminant Analysis Using Least Absolute Deviations." Decision Sciences 21, no. 1 (1990): 86–96. http://dx.doi.org/10.1111/j.1540-5915.1990.tb00318.x.

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43

Späth, H. "Clusterwise linear least absolute deviations regression." Computing 37, no. 4 (1986): 371–77. http://dx.doi.org/10.1007/bf02251095.

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44

Sigauke, Caston, Murendeni Nemukula, and Daniel Maposa. "Probabilistic Hourly Load Forecasting Using Additive Quantile Regression Models." Energies 11, no. 9 (2018): 2208. http://dx.doi.org/10.3390/en11092208.

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Short-term hourly load forecasting in South Africa using additive quantile regression (AQR) models is discussed in this study. The modelling approach allows for easy interpretability and accounting for residual autocorrelation in the joint modelling of hourly electricity data. A comparative analysis is done using generalised additive models (GAMs). In both modelling frameworks, variable selection is done using least absolute shrinkage and selection operator (Lasso) via hierarchical interactions. Four models considered are GAMs and AQR models with and without interactions, respectively. The AQR

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45

Kovalchuk, I. P., K. A. Lukianchuk, and V. A. Bogdanets. "Assessment of open source digital elevation models (SRTM-30, ASTER, ALOS) for erosion processes modeling." Journal of Geology, Geography and Geoecology 28, no. 1 (2019): 95–105. http://dx.doi.org/10.15421/111911.

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The relief has a major impact on the landscape`s hydrological, geomorphological and biological processes. Many geographic information systems used elevation data as the primary data for analysis, modeling, etc. A digital elevation model (DEM) is a modern representation of the continuous variations of relief over space in digital form. Digital Elevation Models (DEMs) are important source for prediction of soil erosion parameters. The potential of global open source DEMs (SRTM, ASTER, ALOS) and their suitability for using in modeling of erosion processes are assessed in this study. Shumsky distr

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46

Xue, Wei, Wensheng Zhang, and Gaohang Yu. "Least absolute deviations learning of multiple tasks." Journal of Industrial & Management Optimization 14, no. 2 (2018): 719–29. http://dx.doi.org/10.3934/jimo.2017071.

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47

Rogers, Alan J. "LEAST ABSOLUTE DEVIATIONS REGRESSION UNDER NONSTANDARD CONDITIONS." Econometric Theory 17, no. 4 (2001): 820–52. http://dx.doi.org/10.1017/s0266466601174074.

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Most work on the asymptotic properties of least absolute deviations (LAD) estimators makes use of the assumption that the common distribution of the disturbances has a density that is both positive and finite at zero. We consider the implications of weakening this assumption in a number of regression settings, primarily with a time series orientation. These models include ones with deterministic and stochastic trends, and we pay particular attention to the case of a simple unit root model. The way in which the conventional assumption on the error distribution is modified is motivated in part b

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48

Mokhtari, Mikaeel, Tofigh Allahviranloo, Mohammad Hassan Behzadi, and Farhad Hoseinzadeh Lotfi. "Introducing a trapezoidal interval type-2 fuzzy regression model." Journal of Intelligent & Fuzzy Systems 42, no. 3 (2022): 1381–403. http://dx.doi.org/10.3233/jifs-210340.

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The uncertainty is an important attribute about data that can arise from different sources including randomness and fuzziness, therefore in uncertain environments, especially, in modeling, planning, decision-making, and control under uncertainty, most data available contain some degree of fuzziness, randomness, or both, and at the same time, some of this data may be anomalous (outliers). In this regard, the new fuzzy regression approaches by creating a functional relationship between response and explanatory variables can provide efficient tools to explanation, prediction and possibly control

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49

Babu, Gutti Jogesh, and C. Radhakrishna Rao. "Expansions for statistics involving the mean absolute deviations." Annals of the Institute of Statistical Mathematics 44, no. 2 (1992): 387–403. http://dx.doi.org/10.1007/bf00058648.

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50

Li, Ta-Hsin. "On robust spectral analysis by least absolute deviations." Journal of Time Series Analysis 33, no. 2 (2011): 298–303. http://dx.doi.org/10.1111/j.1467-9892.2011.00760.x.

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