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Journal articles on the topic 'Finite mixture of quantile regression'

Author: Grafiati

Published: 22 February 2023

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1

Alfò, Marco, Nicola Salvati, and M. Giovanna Ranallli. "Finite mixtures of quantile and M-quantile regression models." Statistics and Computing 27, no. 2 (2016): 547–70. http://dx.doi.org/10.1007/s11222-016-9638-1.

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2

Tian, Yuzhu, Manlai Tang, and Maozai Tian. "A class of finite mixture of quantile regressions with its applications." Journal of Applied Statistics 43, no. 7 (2015): 1240–52. http://dx.doi.org/10.1080/02664763.2015.1094035.

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3

Kiliç Depren, Serpil. "DETERMINATION OF THE FACTORS AFFECTING STUDENTS’ SCIENCE ACHIEVEMENT LEVEL IN TURKEY AND SINGAPORE: AN APPLICATION OF QUANTILE REGRESSION MIXTURE MODEL." Journal of Baltic Science Education 19, no. 2 (2020): 247–60. http://dx.doi.org/10.33225/jbse/20.19.247.

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In the last decade, the usage of advanced statistical models is growing rapidly in many different disciplines. However, the Quantile Regression Mixture Model (QRMIX), which is a developed approach of the Finite Mixture Model (FMM), is an applicable new method in the educational literature. The aim of the proposed study was to determine factors affecting students' science achievement using the QRMIX approach. To reach this aim, data of the Programme for International Student Assessment (PISA) survey, which has been conducted by the Organization Economic for Co-Operation and Development (OECD) every 3 years, was used. Dataset used in the research is composed of 6,115 students from Singapore, which is the top-performer country among the participant countries, and 5,895 students from Turkey. The results showed that the factors affecting students' science achievement and its importance on the achievement differentiated according to the achievement levels of the students. In conclusion, it was revealed that Turkish students with the lowest science achievement level should be supported with home possessions, perceived feedback, and environmental awareness and Singaporean students with the lowest achievement level should be supported with perceived feedback, enjoyment of science, and epistemological beliefs. Keywords: finite mixture models, Programme for International Student Assessment, quantile regression mixture models, science performance.

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4

Del Sarto, Simone, Maria Francesca Marino, Maria Giovanna Ranalli, and Nicola Salvati. "Using finite mixtures of M-quantile regression models to handle unobserved heterogeneity in assessing the effect of meteorology and traffic on air quality." Stochastic Environmental Research and Risk Assessment 33, no. 7 (2019): 1345–59. http://dx.doi.org/10.1007/s00477-019-01687-x.

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5

Liu, Xi, Keming Yu, Qifa Xu, and Xueqing Tang. "Improved local quantile regression." Statistical Modelling 19, no. 5 (2018): 501–23. http://dx.doi.org/10.1177/1471082x18782057.

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We investigate a new kernel-weighted likelihood smoothing quantile regression method. The likelihood is based on a normal scale-mixture representation of asymmetric Laplace distribution (ALD). This approach enjoys the same good design adaptation as the local quantile regression ( Spokoiny et al., 2013 , Journal of Statistical Planning and Inference, 143, 1109–1129), particularly for smoothing extreme quantile curves, and ensures non-crossing quantile curves for any given sample. The performance of the proposed method is evaluated via extensive Monte Carlo simulation studies and one real data analysis.

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6

Chen, Colin. "A Finite Smoothing Algorithm for Quantile Regression." Journal of Computational and Graphical Statistics 16, no. 1 (2007): 136–64. http://dx.doi.org/10.1198/106186007x180336.

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7

Chernozhukov, Victor, Christian Hansen, and Michael Jansson. "Finite sample inference for quantile regression models." Journal of Econometrics 152, no. 2 (2009): 93–103. http://dx.doi.org/10.1016/j.jeconom.2009.01.004.

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8

Alhamzawi, Rahim, and Keming Yu. "Power Prior Elicitation in Bayesian Quantile Regression." Journal of Probability and Statistics 2011 (2011): 1–16. http://dx.doi.org/10.1155/2011/874907.

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We address a quantile dependent prior for Bayesian quantile regression. We extend the idea of the power prior distribution in Bayesian quantile regression by employing the likelihood function that is based on a location-scale mixture representation of the asymmetric Laplace distribution. The propriety of the power prior is one of the critical issues in Bayesian analysis. Thus, we discuss the propriety of the power prior in Bayesian quantile regression. The methods are illustrated with both simulation and real data.

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9

Kalantan, Zakiah I., and Jochen Einbeck. "Quantile-Based Estimation of the Finite Cauchy Mixture Model." Symmetry 11, no. 9 (2019): 1186. http://dx.doi.org/10.3390/sym11091186.

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Heterogeneity and outliers are two aspects which add considerable complexity to the analysis of data. The Cauchy mixture model is an attractive device to deal with both issues simultaneously. This paper develops an Expectation-Maximization-type algorithm to estimate the Cauchy mixture parameters. The main ingredient of the algorithm are appropriately weighted component-wise quantiles which can be efficiently computed. The effectiveness of the method is demonstrated through a simulation study, and the techniques are illustrated by real data from the fields of psychology, engineering and computer vision.

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10

Zhang, Zhengyu. "LOCAL PARTITIONED QUANTILE REGRESSION." Econometric Theory 33, no. 5 (2016): 1081–120. http://dx.doi.org/10.1017/s0266466616000293.

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In this paper, we consider the nonparametric estimation of a broad class of quantile regression models, in which the partially linear, additive, and varying coefficient models are nested. We propose for the model a two-stage kernel-weighted least squares estimator by generalizing the idea of local partitioned mean regression (Christopeit and Hoderlein, 2006, Econometrica 74, 787–817) to a quantile regression framework. The proposed estimator is shown to have desirable asymptotic properties under standard regularity conditions. The new estimator has three advantages relative to existing methods. First, it is structurally simple and widely applicable to the general model as well as its submodels. Second, both the functional coefficients and their derivatives up to any given order can be estimated. Third, the procedure readily extends to censored data, including fixed or random censoring. A Monte Carlo experiment indicates that the proposed estimator performs well in finite samples. An empirical application is also provided.

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11

Parente, Paulo M. D. C., and João M. C. Santos Silva. "Quantile Regression with Clustered Data." Journal of Econometric Methods 5, no. 1 (2016): 1–15. http://dx.doi.org/10.1515/jem-2014-0011.

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AbstractWe study the properties of the quantile regression estimator when data are sampled from independent and identically distributed clusters, and show that the estimator is consistent and asymptotically normal even when there is intra-cluster correlation. A consistent estimator of the covariance matrix of the asymptotic distribution is provided, and we propose a specification test capable of detecting the presence of intra-cluster correlation. A small simulation study illustrates the finite sample performance of the test and of the covariance matrix estimator.

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12

Eggers, Shoshannah, Moira Bixby, Stefano Renzetti, Paul Curtin, and Chris Gennings. "Human Microbiome Mixture Analysis Using Weighted Quantile Sum Regression." International Journal of Environmental Research and Public Health 20, no. 1 (2022): 94. http://dx.doi.org/10.3390/ijerph20010094.

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Studies of the health effects of the microbiome often measure overall associations by using diversity metrics, and individual taxa associations in separate analyses, but do not consider the correlated relationships between taxa in the microbiome. In this study, we applied random subset weighted quantile sum regression with repeated holdouts (WQSRSRH), a mixture method successfully applied to ‘omic data to account for relationships between many predictors, to processed amplicon sequencing data from the Human Microbiome Project. We simulated a binary variable associated with 20 operational taxonomic units (OTUs). WQSRSRH was used to test for the association between the microbiome and the simulated variable, adjusted for sex, and sensitivity and specificity were calculated. The WQSRSRH method was also compared to other standard methods for microbiome analysis. The method was further illustrated using real data from the Growth and Obesity Cohort in Chile to assess the association between the gut microbiome and body mass index. In the analysis with simulated data, WQSRSRH predicted the correct directionality of association between the microbiome and the simulated variable, with an average sensitivity and specificity of 75% and 70%, respectively, in identifying the 20 associated OTUs. WQSRSRH performed better than all other comparison methods. In the illustration analysis of the gut microbiome and obesity, the WQSRSRH analysis identified an inverse association between body mass index and the gut microbe mixture, identifying Bacteroides, Clostridium, Prevotella, and Ruminococcus as important genera in the negative association. The application of WQSRSRH to the microbiome allows for analysis of the mixture effect of all the taxa in the microbiome, while simultaneously identifying the most important to the mixture, and allowing for covariate adjustment. It outperformed other methods when using simulated data, and in analysis with real data found results consistent with other study findings.

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13

Bremnes, John Bjørnar. "Constrained Quantile Regression Splines for Ensemble Postprocessing." Monthly Weather Review 147, no. 5 (2019): 1769–80. http://dx.doi.org/10.1175/mwr-d-18-0420.1.

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Abstract Statistical postprocessing of ensemble forecasts is widely applied to make reliable probabilistic weather forecasts. Motivated by the fact that nature imposes few restrictions on the shape of forecast distributions, a flexible quantile regression method based on constrained spline functions (CQRS) is proposed and tested on ECMWF Ensemble Prediction System (ENS) wind speed forecasting data at 125 stations in Norway. First, it is demonstrated that constraining quantile functions to be monotone and bounded is preferable. Second, combining an ensemble quantile with the ensemble mean proved to be a good covariate for the respective quantile. Third, CQRS only needs to be applied to about 10 equidistant quantiles, while those between can be obtained by interpolation. A comparison of CQRS versus a mixture model of truncated and lognormal distributions showed slight overall improvements in quantile score (less than 1%), reliability, and to some extent also sharpness. For strong wind speed forecasts the quantile score was improved by up to 4.5% depending on lead time.

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14

Aloqaili, Murtadha Jaafar, and Rahim Alhamzawi. "Bayesian Composite Quantile Regression with Composite Group Bridge Penalty." NeuroQuantology 20, no. 2 (2022): 173–79. http://dx.doi.org/10.14704/nq.2022.20.2.nq22269.

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We study composite quantile regression (CQReg) with composite group bridge penalty for model selection and estimation. Compared to conventional mean regression, composite quantile regression (CQR) is an efficient and robust estimation approach. A simple and efficient algorithm was developed for posterior inference using a pseudo composite asymmetric Laplace distribution which can be formulated as a location-scale mixture of normals. The composite group bridge priors were formulated as a scale mixture of multivariate uniforms. We assess the performance of the proposed method using simulation studies, and demonstrate it with an air pollution data. Results indicated that our approach performs very well compared to the existing approaches.

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15

Chen, Liqiong, Antonio F. Galvao, and Suyong Song. "Quantile Regression with Generated Regressors." Econometrics 9, no. 2 (2021): 16. http://dx.doi.org/10.3390/econometrics9020016.

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This paper studies estimation and inference for linear quantile regression models with generated regressors. We suggest a practical two-step estimation procedure, where the generated regressors are computed in the first step. The asymptotic properties of the two-step estimator, namely, consistency and asymptotic normality are established. We show that the asymptotic variance-covariance matrix needs to be adjusted to account for the first-step estimation error. We propose a general estimator for the asymptotic variance-covariance, establish its consistency, and develop testing procedures for linear hypotheses in these models. Monte Carlo simulations to evaluate the finite-sample performance of the estimation and inference procedures are provided. Finally, we apply the proposed methods to study Engel curves for various commodities using data from the UK Family Expenditure Survey. We document strong heterogeneity in the estimated Engel curves along the conditional distribution of the budget share of each commodity. The empirical application also emphasizes that correctly estimating confidence intervals for the estimated Engel curves by the proposed estimator is of importance for inference.

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16

Balmert, Lauren C., Ruosha Li, Limin Peng, and Jong-Hyeon Jeong. "Quantile regression on inactivity time." Statistical Methods in Medical Research 30, no. 5 (2021): 1332–46. http://dx.doi.org/10.1177/0962280221995977.

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The inactivity time, or lost lifespan specifically for mortality data, concerns time from occurrence of an event of interest to the current time point and has recently emerged as a new summary measure for cumulative information inherent in time-to-event data. This summary measure provides several benefits over the traditional methods, including more straightforward interpretation yet less sensitivity to heavy censoring. However, there exists no systematic modeling approach to inferring the quantile inactivity time in the literature. In this paper, we propose a semi-parametric regression method for the quantiles of the inactivity time distribution under right censoring. The consistency and asymptotic normality of the regression parameters are established. To avoid estimation of the probability density function of the inactivity time distribution under censoring, we propose a computationally efficient method for estimating the variance–covariance matrix of the regression coefficient estimates. Simulation results are presented to validate the finite sample properties of the proposed estimators and test statistics. The proposed method is illustrated with a real dataset from a clinical trial on breast cancer.

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17

Lyden, Grace R., David M. Vock, Emily S. Barrett, Sheela Sathyanarayana, Shanna H. Swan, and Ruby HN Nguyen. "A permutation-based approach to inference for weighted sum regression with correlated chemical mixtures." Statistical Methods in Medical Research 31, no. 4 (2022): 579–93. http://dx.doi.org/10.1177/09622802211013578.

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There is a growing demand for methods to determine the effects that chemical mixtures have on human health. One statistical challenge is identifying true “bad actors” from a mixture of highly correlated predictors, a setting in which standard approaches such as linear regression become highly variable. Weighted Quantile Sum regression has been proposed to address this problem, through a two-step process where mixture component weights are estimated using bootstrap aggregation in a training dataset and inference on the overall mixture effect occurs in a held-out test set. Weighted Quantile Sum regression is popular in applied papers, but the reliance on data splitting is suboptimal, and analysts who use the same data for both steps risk inflating the Type I error rate. We therefore propose a modification of Weighted Quantile Sum regression that uses a permutation test for inference, which allows for weight estimation using the entire dataset and preserves Type I error. To minimize computational burden, we propose replacing the bootstrap with L1 or L2 penalization and describe how to choose the appropriate penalty given expert knowledge about a mixture of interest. We apply our method to a national pregnancy cohort study of prenatal phthalate exposure and child health outcomes.

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18

Elliott, Michael R., and Xi Xia. "Weighted Dirichlet Process Mixture Models to Accommodate Complex Sample Designs for Linear and Quantile Regression." Journal of Official Statistics 37, no. 1 (2021): 71–95. http://dx.doi.org/10.2478/jos-2021-0004.

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Abstract Standard randomization-based inference conditions on the data in the population and makes inference with respect to the repeating sampling properties of the sampling indicators. In some settings these estimators can be quite unstable; Bayesian model-based approaches focus on the posterior predictive distribution of population quantities, potentially providing a better balance between bias correction and efficiency. Previous work in this area has focused on estimation of means and linear and generalized linear regression parameters; these methods do not allow for a general estimation of distributional functions such as quantile or quantile regression parameters. Here we adapt an extended Dirichlet Process Mixture model that allows the DP prior to be a mixture of DP random basis measures that are a function of covariates. These models allow many mixture components when necessary to accommodate the sample design, but can shrink to few components for more efficient estimation when the data allow. We provide an application to the estimation of relationships between serum dioxin levels and age in the US population, either at the mean level (via linear regression) or across the dioxin distribution (via quantile regression) using the National Health and Nutrition Examination Survey.

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19

Lim, Jeong Youn, and Jong-Hyeon Jeong. "Cause-specific quantile residual life regression." Statistical Methods in Medical Research 26, no. 4 (2015): 1912–24. http://dx.doi.org/10.1177/0962280215592426.

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We propose a cause-specific quantile residual life regression where the cause-specific quantile residual life, defined as the inverse of the cumulative incidence function of the residual life distribution of a specific type of events of interest conditional on a fixed time point, is log-linear in observable covariates. The proposed test statistic for the effects of prognostic factors does not involve estimation of the improper probability density function of the cause-specific residual life distribution under competing risks. The asymptotic distribution of the test statistic is derived. Simulation studies are performed to assess the finite sample properties of the proposed estimating equation and the test statistic. The proposed method is illustrated with a real dataset from a clinical trial on breast cancer.

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20

Luo, S., and Shuxia Pang. "Empirical likelihood for quantile regression models with response data missing at random." Open Mathematics 15, no. 1 (2017): 317–30. http://dx.doi.org/10.1515/math-2017-0028.

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Abstract This paper studies quantile linear regression models with response data missing at random. A quantile empirical-likelihood-based method is proposed firstly to study a quantile linear regression model with response data missing at random. It follows that a class of quantile empirical log-likelihood ratios including quantile empirical likelihood ratio with complete-case data, weighted quantile empirical likelihood ratio and imputed quantile empirical likelihood ratio are defined for the regression parameters. Then, a bias-corrected quantile empirical log-likelihood ratio is constructed for the mean of the response variable for a given quantile level. It is proved that these quantile empirical log-likelihood ratios are asymptotically χ2 distribution. Furthermore, a class of estimators for the regression parameters and the mean of the response variable are constructed, and the asymptotic normality of the proposed estimators is established. Our results can be used directly to construct the confidence intervals (regions) of the regression parameters and the mean of the response variable. Finally, simulation studies are conducted to assess the finite sample performance and a real-world data set is analyzed to illustrate the applications of the proposed method.

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21

Hall, Peter, and Joel L. Horowitz. "Bandwidth Selection in Semiparametric Estimation of Censored Linear Regression Models." Econometric Theory 6, no. 2 (1990): 123–50. http://dx.doi.org/10.1017/s0266466600005089.

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Quantile and semiparametric M estimation are methods for estimating a censored linear regression model without assuming that the distribution of the random component of the model belongs to a known parametric family. Both methods require estimating derivatives of the unknown cumulative distribution function of the random component. The derivatives can be estimated consistently using kernel estimators in the case of quantile estimation and finite difference quotients in the case of semiparametric M estimation. However, the resulting estimates of derivatives, as well as parameter estimates and inferences that depend on the derivatives, can be highly sensitive to the choice of the kernel and finite difference bandwidths. This paper discusses the theory of asymptotically optimal bandwidths for kernel and difference quotient estimation of the derivatives required for quantile and semiparametric M estimation, respectively. We do not present a fully automatic method for bandwidth selection.

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22

Nortey, Ezekiel N. N., Reuben Pometsey, Louis Asiedu, Samuel Iddi, and Felix O. Mettle. "Anomaly Detection in Health Insurance Claims Using Bayesian Quantile Regression." International Journal of Mathematics and Mathematical Sciences 2021 (February 23, 2021): 1–11. http://dx.doi.org/10.1155/2021/6667671.

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Research has shown that current health expenditure in most countries, especially in sub-Saharan Africa, is inadequate and unsustainable. Yet, fraud, abuse, and waste in health insurance claims by service providers and subscribers threaten the delivery of quality healthcare. It is therefore imperative to analyze health insurance claim data to identify potentially suspicious claims. Typically, anomaly detection can be posited as a classification problem that requires the use of statistical methods such as mixture models and machine learning approaches to classify data points as either normal or anomalous. Additionally, health insurance claim data are mostly associated with problems of sparsity, heteroscedasticity, multicollinearity, and the presence of missing values. The analyses of such data are best addressed by adopting more robust statistical techniques. In this paper, we utilized the Bayesian quantile regression model to establish the relations between claim outcome of interest and subject-level features and further classify claims as either normal or anomalous. An estimated model component is assumed to inherently capture the behaviors of the response variable. A Bayesian mixture model, assuming a normal mixture of two components, is used to label claims as either normal or anomalous. The model was applied to health insurance data captured on 115 people suffering from various cardiovascular diseases across different states in the USA. Results show that 25 out of 115 claims (21.7%) were potentially suspicious. The overall accuracy of the fitted model was assessed to be 92%. Through the methodological approach and empirical application, we demonstrated that the Bayesian quantile regression is a viable model for anomaly detection.

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23

Breunig, Christoph. "SPECIFICATION TESTING IN NONPARAMETRIC INSTRUMENTAL QUANTILE REGRESSION." Econometric Theory 36, no. 4 (2020): 583–625. http://dx.doi.org/10.1017/s0266466619000288.

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There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model with endogenous regressors, key conditions are validity of instrumental variables and monotonicity of the model in a scalar unobservable variable. Under these conditions the nonseparable model is equivalent to an instrumental quantile regression model. A failure of the key conditions, however, makes instrumental quantile regression potentially inconsistent. This article develops a methodology for testing the hypothesis whether the instrumental quantile regression model is correctly specified. Our test statistic is asymptotically normally distributed under correct specification and consistent against any alternative model. In addition, test statistics to justify the model simplification are established. Finite sample properties are examined in a Monte Carlo study and an empirical illustration is provided.

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24

Yang, Fengkai, Ang Shan, and Haijing Yuan. "Gibbs sampling for mixture quantile regression based on asymmetric Laplace distribution." Communications in Statistics - Simulation and Computation 48, no. 5 (2018): 1560–73. http://dx.doi.org/10.1080/03610918.2017.1419258.

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25

Chen, Zhiyong, Minghui Chen, and Fangyu Ju. "Bayesian P-Splines Quantile Regression of Partially Linear Varying Coefficient Spatial Autoregressive Models." Symmetry 14, no. 6 (2022): 1175. http://dx.doi.org/10.3390/sym14061175.

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This paper deals with spatial data that can be modelled by partially linear varying coefficient spatial autoregressive models with Bayesian P-splines quantile regression. We evaluate the linear and nonlinear effects of covariates on the response and use quantile regression to present comprehensive information at different quantiles. We not only propose an empirical Bayesian approach of quantile regression using the asymmetric Laplace error distribution and employ P-splines to approximate nonparametric components but also develop an efficient Markov chain Monte Carlo technique to explore the joint posterior distributions of unknown parameters. Monte Carlo simulations show that our estimators not only have robustness for different spatial weight matrices but also perform better compared with quantile regression and instrumental variable quantile regression estimators in finite samples at different quantiles. Finally, a set of Sydney real estate data applications is analysed to illustrate the performance of the proposed method.

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26

Bottai, Matteo, and Giovanna Cilluffo. "Nonlinear parametric quantile models." Statistical Methods in Medical Research 29, no. 12 (2020): 3757–69. http://dx.doi.org/10.1177/0962280220941159.

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Quantile regression is widely used to estimate conditional quantiles of an outcome variable of interest given covariates. This method can estimate one quantile at a time without imposing any constraints on the quantile process other than the linear combination of covariates and parameters specified by the regression model. While this is a flexible modeling tool, it generally yields erratic estimates of conditional quantiles and regression coefficients. Recently, parametric models for the regression coefficients have been proposed that can help balance bias and sampling variability. So far, however, only models that are linear in the parameters and covariates have been explored. This paper presents the general case of nonlinear parametric quantile models. These can be nonlinear with respect to the parameters, the covariates, or both. Some important features and asymptotic properties of the proposed estimator are described, and its finite-sample behavior is assessed in a simulation study. Nonlinear parametric quantile models are applied to estimate extreme quantiles of longitudinal measures of respiratory mechanics in asthmatic children from an epidemiological study and to evaluate a dose–response relationship in a toxicological laboratory experiment.

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27

Dong, Alice X. D., Jennifer S. K. Chan, and Gareth W. Peters. "RISK MARGIN QUANTILE FUNCTION VIA PARAMETRIC AND NON-PARAMETRIC BAYESIAN APPROACHES." ASTIN Bulletin 45, no. 3 (2015): 503–50. http://dx.doi.org/10.1017/asb.2015.8.

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AbstractWe develop quantile functions from regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk margin and an overview of implied capital based on the historical volatility of a general insurers loss portfolio. Two modeling frameworks are considered based around parametric and non-parametric regression models which we develop specifically in this insurance setting. In the parametric framework, quantile functions are derived using several distributions including the flexible generalized beta (GB2) distribution family, asymmetric Laplace (AL) distribution and power-Pareto (PP) distribution. In these parametric model based quantile regressions, we detail two basic formulations. The first involves embedding the quantile regression loss function from the nonparameteric setting into the argument of the kernel of a parametric data likelihood model, this is well known to naturally lead to the AL parametric model case. The second formulation we utilize in the parametric setting adopts an alternative quantile regression formulation in which we assume a structural expression for the regression trend and volatility functions which act to modify a base quantile function in order to produce the conditional data quantile function. This second approach allows a range of flexible parametric models to be considered with different tail behaviors. We demonstrate how to perform estimation of the resulting parametric models under a Bayesian regression framework. To achieve this, we design Markov chain Monte Carlo (MCMC) sampling strategies for the resulting Bayesian posterior quantile regression models. In the non-parametric framework, we construct quantile functions by minimizing an asymmetrically weighted loss function and estimate the parameters under the AL proxy distribution to resemble the minimization process. This quantile regression model is contrasted to the parametric AL mean regression model and both are expressed as a scale mixture of uniform distributions to facilitate efficient implementation. The models are extended to adopt dynamic mean, variance and skewness and applied to analyze two real loss reserve data sets to perform inference and discuss interesting features of quantile regression for risk margin calculations.

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28

Chen, Bin, and Keying Ye. "Componentwise variable selection in finite mixture regression." Statistics and Its Interface 8, no. 2 (2015): 239–54. http://dx.doi.org/10.4310/sii.2015.v8.n2.a11.

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29

Liang, Jian, Kun Chen, Ming Lin, Changshui Zhang, and Fei Wang. "Robust finite mixture regression for heterogeneous targets." Data Mining and Knowledge Discovery 32, no. 6 (2018): 1509–60. http://dx.doi.org/10.1007/s10618-018-0564-z.

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30

Karlsson, Maria, and Thomas Laitila. "Finite mixture modeling of censored regression models." Statistical Papers 55, no. 3 (2013): 627–42. http://dx.doi.org/10.1007/s00362-013-0509-y.

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31

Zhao, Qiang, Chao Zhang, Jingjing Wu, and Xiuli Wang. "Robust and efficient estimation for nonlinear model based on composite quantile regression with missing covariates." AIMS Mathematics 7, no. 5 (2022): 8127–46. http://dx.doi.org/10.3934/math.2022452.

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<abstract><p>In this article, two types of weighted quantile estimators were proposed for nonlinear models with missing covariates. The asymptotic normality of the proposed weighted quantile average estimators was established. We further calculated the optimal weights and derived the asymptotic distributions of the correspondingly resulted optimal weighted quantile estimators. Numerical simulations and a real data analysis were conducted to examine the finite sample performance of the proposed estimators compared with other competitors.</p></abstract>

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32

Maswanganyi, Norman, Caston Sigauke, and Edmore Ranganai. "Prediction of Extreme Conditional Quantiles of Electricity Demand: An Application Using South African Data." Energies 14, no. 20 (2021): 6704. http://dx.doi.org/10.3390/en14206704.

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It is important to predict extreme electricity demand in power utilities as the uncertainties in the future of electricity demand distribution have to be taken into consideration to achieve the desired goals. The study focused on the prediction of extremely high conditional quantiles (between 0.95 and 0.9999) and extremely low quantiles (between 0.001 and 0.05) of electricity demand using South African data. The paper discusses a comparative analysis of the additive quantile regression model with an extremal mixture model and a nonlinear quantile regression model. The estimated quantiles at each level were then combined using the median approach. The comparisons were carried out using daily peak electricity demand data ranging from January 1997 to May 2014. Proper scoring rules were used to compare the three models, and the model with the smallest score was preferred. The results could be useful to system operators including decision-makers in power utility companies by giving insights and guidance for future electricity demand patterns. The prediction of extremely high quantiles of daily peak electricity demand could help system operators know the possible largest demand that will enable them to supply adequate electricity to consumers and shift demand to off-peak periods. The prediction of extreme conditional quantiles of daily peak electricity demand in the context of South Africa using additive quantile regression, nonlinear quantile regression, and extremal mixture models has not been performed previously to the best of our knowledge.

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Liu, Minzhao, Michael J. Daniels, and Michael G. Perri. "Quantile regression in the presence of monotone missingness with sensitivity analysis." Biostatistics 17, no. 1 (2015): 108–21. http://dx.doi.org/10.1093/biostatistics/kxv023.

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Abstract In this paper, we develop methods for longitudinal quantile regression when there is monotone missingness. In particular, we propose pattern mixture models with a constraint that provides a straightforward interpretation of the marginal quantile regression parameters. Our approach allows sensitivity analysis which is an essential component in inference for incomplete data. To facilitate computation of the likelihood, we propose a novel way to obtain analytic forms for the required integrals. We conduct simulations to examine the robustness of our approach to modeling assumptions and compare its performance to competing approaches. The model is applied to data from a recent clinical trial on weight management.

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Kurtuluş, Tolga, and Serpil Kılıç Depren. "Assessing the heterogeneity of social connectedness index via quantile regression mixture model." Pamukkale University Journal of Engineering Sciences 28, no. 4 (2022): 625–31. http://dx.doi.org/10.5505/pajes.2021.16446.

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Li, Jessie. "The Proximal Bootstrap for Finite-Dimensional Regularized Estimators." AEA Papers and Proceedings 111 (May 1, 2021): 616–20. http://dx.doi.org/10.1257/pandp.20211036.

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We propose a proximal bootstrap that can consistently estimate the limiting distribution of sqrt(n)-consistent estimators with nonstandardasymptotic distributions in a computationally efficient manner by formulating the proximal bootstrap estimator as the solution to aconvex optimization problem, which can have a closed-form solution for certain designs. This paper considers the application to finite-dimensionalregularized estimators, such as the lasso, l1-norm regularized quantile regression, l1-norm support vector regression, and trace regression via nuclear norm regularization.

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Wu, Yuanshan, and Guosheng Yin. "Cure rate quantile regression accommodating both finite and infinite survival times." Canadian Journal of Statistics 45, no. 1 (2016): 29–43. http://dx.doi.org/10.1002/cjs.11306.

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Zhang, Yichong, and Xin Zheng. "Quantile treatment effects and bootstrap inference under covariate‐adaptive randomization." Quantitative Economics 11, no. 3 (2020): 957–82. http://dx.doi.org/10.3982/qe1323.

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In this paper, we study the estimation and inference of the quantile treatment effect under covariate‐adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the inference of method (1), we show that the Wald test using a weighted bootstrap standard error underrejects. But for method (2), its asymptotic size equals the nominal level. We also show that, for both methods, the asymptotic size of the Wald test using a covariate‐adaptive bootstrap standard error equals the nominal level. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets.

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Kadiri, Nadia, Abbes Rabhi, Salah Khardani, and Fatima Akkal. "CLT for single functional index quantile regression under dependence structure." Acta Universitatis Sapientiae, Mathematica 13, no. 1 (2021): 45–77. http://dx.doi.org/10.2478/ausm-2021-0003.

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Abstract In this paper, we investigate the asymptotic properties of a nonparametric conditional quantile estimation in the single functional index model for dependent functional data and censored at random responses are observed. First of all, we establish asymptotic properties for a conditional distribution estimator from which we derive an central limit theorem (CLT) of the conditional quantile estimator. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.

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Zheng, John Xu. "A CONSISTENT NONPARAMETRIC TEST OF PARAMETRIC REGRESSION MODELS UNDER CONDITIONAL QUANTILE RESTRICTIONS." Econometric Theory 14, no. 1 (1998): 123–38. http://dx.doi.org/10.1017/s0266466698141051.

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This paper proposes a nonparametric, kernel-based test of parametric quantile regression models. The test statistic has a limiting standard normal distribution if the parametric quantile model is correctly specified and diverges to infinity for any misspecification of the parametric model. Thus the test is consistent against any fixed alternative. The test also has asymptotic power 1 against local alternatives converging to the null at proper rates. A simulation study is provided to evaluate the finite-sample performance of the test.

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Jones, P. N., and G. J. McLachlan. "FITTING FINITE MIXTURE MODELS IN A REGRESSION CONTEXT." Australian Journal of Statistics 34, no. 2 (1992): 233–40. http://dx.doi.org/10.1111/j.1467-842x.1992.tb01356.x.

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Khalili, Abbas, and Jiahua Chen. "Variable Selection in Finite Mixture of Regression Models." Journal of the American Statistical Association 102, no. 479 (2007): 1025–38. http://dx.doi.org/10.1198/016214507000000590.

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Shimizu, Taciana, Francisco Louzada, and Adriano Suzuki. "Finite mixture of compositional regression with gaussian errors." Revista Colombiana de Estadística 41, no. 1 (2018): 75–86. http://dx.doi.org/10.15446/rce.v41n1.63152.

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In this paper, we consider to evaluate the efficiency of volleyball players according to the performance of attack, block and serve, but considering the compositional structure of the data related to the fundaments. The finite mixture of regression models better fitted the data in comparison with the usual regression model. The maximum likelihood estimates are obtained via an EM algorithm. A simulation study revels that the estimates are closer to the real values, the estimators are asymptotically unbiased for the parameters. A real Brazilian volleyball dataset related to the efficiency of the players is considered for the analysis.

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Tang, Qingguo, and R. J. Karunamuni. "Robust variable selection for finite mixture regression models." Annals of the Institute of Statistical Mathematics 70, no. 3 (2017): 489–521. http://dx.doi.org/10.1007/s10463-017-0602-4.

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Kaplan, David M., and Yixiao Sun. "SMOOTHED ESTIMATING EQUATIONS FOR INSTRUMENTAL VARIABLES QUANTILE REGRESSION." Econometric Theory 33, no. 1 (2016): 105–57. http://dx.doi.org/10.1017/s0266466615000407.

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The moment conditions or estimating equations for instrumental variables quantile regression involve the discontinuous indicator function. We instead use smoothed estimating equations (SEE), with bandwidth h. We show that the mean squared error (MSE) of the vector of the SEE is minimized for some h > 0, leading to smaller asymptotic MSE of the estimating equations and associated parameter estimators. The same MSE-optimal h also minimizes the higher-order type I error of a SEE-based χ2 test and increases size-adjusted power in large samples. Computation of the SEE estimator also becomes simpler and more reliable, especially with (more) endogenous regressors. Monte Carlo simulations demonstrate all of these superior properties in finite samples, and we apply our estimator to JTPA data. Smoothing the estimating equations is not just a technical operation for establishing Edgeworth expansions and bootstrap refinements; it also brings the real benefits of having more precise estimators and more powerful tests.

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Wang, Shangshan, and Liming Xiang. "Two-layer EM algorithm for ALD mixture regression models: A new solution to composite quantile regression." Computational Statistics & Data Analysis 115 (November 2017): 136–54. http://dx.doi.org/10.1016/j.csda.2017.06.002.

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Gómez, Yolanda M., Diego I. Gallardo, Osvaldo Venegas, and Tiago M. Magalhães. "An Asymmetric Bimodal Double Regression Model." Symmetry 13, no. 12 (2021): 2279. http://dx.doi.org/10.3390/sym13122279.

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In this paper, we introduce an extension of the sinh Cauchy distribution including a double regression model for both the quantile and scale parameters. This model can assume different shapes: unimodal or bimodal, symmetric or asymmetric. We discuss some properties of the model and perform a simulation study in order to assess the performance of the maximum likelihood estimators in finite samples. A real data application is also presented.

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Qiu, Zhiping, Huijuan Ma, Jianwei Chen, and Gregg E. Dinse. "Quantile regression models for survival data with missing censoring indicators." Statistical Methods in Medical Research 30, no. 5 (2021): 1320–31. http://dx.doi.org/10.1177/0962280221995986.

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The quantile regression model has increasingly become a useful approach for analyzing survival data due to its easy interpretation and flexibility in exploring the dynamic relationship between a time-to-event outcome and the covariates. In this paper, we consider the quantile regression model for survival data with missing censoring indicators. Based on the augmented inverse probability weighting technique, two weighted estimating equations are developed and corresponding easily implemented algorithms are suggested to solve the estimating equations. Asymptotic properties of the resultant estimators and the resampling-based inference procedures are established. Finally, the finite sample performances of the proposed approaches are investigated in simulation studies and a real data application.

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Chen, Danqing, Jianbao Chen, and Shuangshuang Li. "Instrumental Variable Quantile Regression of Spatial Dynamic Durbin Panel Data Model with Fixed Effects." Mathematics 9, no. 24 (2021): 3261. http://dx.doi.org/10.3390/math9243261.

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This paper studies a quantile regression spatial dynamic Durbin panel data (SDDPD) model with fixed effects. Conventional fixed effects estimators of quantile regression specification are usually biased in the presentation of lagged response variables in spatial and time as regressors. To reduce this bias, we propose the instrumental variable quantile regression (IVQR) estimator with lagged covariates in spatial and time as instruments. Under some regular conditions, the consistency and asymptotic normalityof the estimators are derived. Monte Carlo simulations show that our estimators not only perform well in finite sample cases at different quantiles but also have robustness for different spatial weights matrices and for different disturbance term distributions. The proposed method is used to analyze the influencing factors of international tourism foreign exchange earnings of 31 provinces in China from 2011 to 2017.

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Kaplan, David. "Finite Mixture Dynamic Regression Modeling of Panel Data With Implications for Dynamic Response Analysis." Journal of Educational and Behavioral Statistics 30, no. 2 (2005): 169–87. http://dx.doi.org/10.3102/10769986030002169.

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This article considers the problem of estimating dynamic linear regression models when the data are generated from finite mixture probability density function where the mixture components are characterized by different dynamic regression model parameters. Specifically, conventional linear models assume that the data are generated by a single probability density function characterized by a single set of regression model parameters. However, when the true generating model is finite mixture density function, then estimation of conventional linear models under the assumption of a single density function may lead to erroneous conclusions. Instead, it may be desirable to estimate the regression model under the assumption that the data are derived from a finite mixture density function and to examine differences in the parameters of the model within each mixture component. Dynamic regression models and subsequent dynamic response analysis using dynamic multipliers are also likely to be affected by the existence of a finite mixture density because dynamic multipliers are functions of the regression model parameters. Utilizing finite mixture modeling applied to two real data examples, this article shows that dynamic responses to changes in exogenous variables can be quite different depending on the number and nature of underlying mixture components. Implications for substantive conclusions based on the use of dynamic multipliers is discussed.

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Thorson, James T., Ian J. Stewart, and André E. Punt. "Development and application of an agent-based model to evaluate methods for estimating relative abundance indices for shoaling fish such as Pacific rockfish (Sebastes spp.)." ICES Journal of Marine Science 69, no. 4 (2012): 635–47. http://dx.doi.org/10.1093/icesjms/fss003.

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Abstract Thorson, J. T., Stewart, I. J., and Punt, A. E. 2012. Development and application of an agent-based model to evaluate methods for estimating relative abundance indices for shoaling fish such as Pacific rockfish (Sebastes spp.). – ICES Journal of Marine Science, 69: 635–647. Many marine fish, including Pacific rockfish (Sebastes spp.), exhibit habitat-selective and shoaling behaviours, which can lead to imprecision when using survey data to estimate an annual index of stock abundance. We develop a spatial agent-based model (ABM) for Pacific rockfish, which generates data similar to those observed in existing bottom-trawl surveys and can represent various spatial and shoaling behaviours. We use the ABM to evaluate the performance of a model that uses mixture distribution methods to account for fish shoals and delta-methods to account for range expansion or contraction. This delta-mixture model is compared with conventional delta-generalized linear models (delta-GLMs) and a quantile regression delta-model. The delta-mixture increases precision by 15% relative to delta-GLMs in estimated abundance indices when shoaling behaviours are present, whereas precision is similar between delta-GLM and delta-mixture models when shoals are absent. The delta-quantile method has similar improvements over conventional delta-GLM methods, and the improved precision from delta-mixture and delta-quantile methods is decreased but not eliminated by decreased sampling intensities. These simulations represent the first evaluation of delta-mixture models for index standardization and show a substantial improvement over conventional delta-GLMs for shoaling species such as Pacific rockfish.

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