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Local Variable Selection In Varying Coefficients Regression Models
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Book Synopsis Local Variable Selection in Varying-coefficients Regression Models by :
Download or read book Local Variable Selection in Varying-coefficients Regression Models written by and published by . This book was released on 2015 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Varying coefficient regression is a flexible technique for modeling data where the coefficients are functions of some effect-modifying parameter, often time or location in a certain domain. Existing methods for variable selection in a varying coefficient context are mostly for global selection over the entire domain. Presented here is a new local adaptive grouped regularization (LAGR) method for local variable selection in spatially varying coefficient regression. LAGR selects the covariates that are associated with the response at any point in space, and simultaneously estimates the coefficients of those covariates through a kind of adaptive group Lasso. Oracle properties of the proposed method are established. The finite sample properties of LAGR are assessed in a simulation study and for illustration, the Boston housing price data set is analyzed. After the properties of estimation by the method of LAGR are established, the natural next step for statistical inference for the model parameters. The distribution of LASSO-type estimators (like LAGR) is a complicated mixture of a point mass at zero with a continuous density conditional on the estimate being nonzero. Because the Gaussian approximation is not workable in this case, it is common to use Monte Carlo methods such as the bootstrap to simulate the distribution of the coefficient estimates. A weighted likelihood bootstrap approach is developed for simulating the distribution of coefficients estimated by LAGR. This approach is new and is apparently the first uniformly-convergent bootstrap for the so-called "paired" nonparametric regression, where the locations, covariates, and response are iid samples from a joint distribution. The methods proposed in this dissertation are kernel smoothing methods for nonparametric regression. Any kernel smoothing method includes a bandwidth parameter, which we estimate by minimizing the Akaike Information Criterion (AIC). Then estimation and inference proceed conditional on the selected bandwidth. An empirical Bayes approach to marginal inference for the coefficients is proposed. The weighted likelihood bootstrap is used to simulate the distribution of bandwidth. The simulated distribution is interpreted as the posterior hyperprior in a mixture distribution for the coefficient estimates.
Book Synopsis Macroeconometrics and Time Series Analysis by : Steven Durlauf
Download or read book Macroeconometrics and Time Series Analysis written by Steven Durlauf and published by Springer. This book was released on 2016-04-30 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specially selected from The New Palgrave Dictionary of Economics 2nd edition, each article within this compendium covers the fundamental themes within the discipline and is written by a leading practitioner in the field. A handy reference tool.
Book Synopsis Shrinkage Estimation of the Varying Coefficient Model by : Hansheng Wang
Download or read book Shrinkage Estimation of the Varying Coefficient Model written by Hansheng Wang and published by . This book was released on 2008 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: The varying coefficient model is a useful extension of the linear regression model. Nevertheless, how to conduct variable selection for the varying coefficient model in a computationally efficient manner is poorly understood. To solve the problem, we propose here a novel method, which combines the ideas of the local polynomial smoothing (Fan and Zhang, 1999) and the shrinkage estimation (Tibshirani, 1996, LASSO). The new method can do nonparametric estimation and variable selection simultaneously. With a local constant estimator and the adaptive LASSO penalty, the new method can identify the true model consistently, and that the resulting estimator can be as efficient as the oracle estimator (Fan and Li, 2001). Numerical studies clearly confirm our theories. Extension to other shrinkage methods (e.g., the SCAD) and other smoothing methods (Zhang and Lin, 2003) is straightforward.
Book Synopsis Handbook of Bayesian Variable Selection by : Mahlet G. Tadesse
Download or read book Handbook of Bayesian Variable Selection written by Mahlet G. Tadesse and published by CRC Press. This book was released on 2021-12-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material
Book Synopsis Variable Selection by Regularization Methods for Generalized Mixed Models by : Andreas Groll
Download or read book Variable Selection by Regularization Methods for Generalized Mixed Models written by Andreas Groll and published by Cuvillier Verlag. This book was released on 2011-12-13 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: A regression analysis describes the dependency of random variables in the form of a functional relationship. One distinguishes between the dependent response variable and one or more independent influence variables. There is a variety of model classes and inference methods available, ranging from the conventional linear regression model up to recent non- and semiparametric regression models. The so-called generalized regression models form a methodically consistent framework incorporating many regression approaches with response variables that are not necessarily normally distributed, including the conventional linear regression model based on the normal distribution assumption as a special case. When repeated measurements are modeled in addition to fixed effects also random effects or coefficients can be included. Such models are known as Random Effects Models or Mixed Models. As a consequence, regression procedures are applicable extremely versatile and consider very different problems. In this dissertation regularization techniques for generalized mixed models are developed that are able to perform variable selection. These techniques are especially appropriate when many potential influence variables are present and existing approaches tend to fail. First of all a componentwise boosting technique for generalized linear mixed models is presented which is based on the likelihood function and works by iteratively fitting the residuals using weak learners. The complexity of the resulting estimator is determined by information criteria. For the estimation of variance components two approaches are considered, an estimator resulting from maximizing the profile likelihood, and an estimator which can be calculated using an approximative EM-algorithm. Then the boosting concept is extended to mixed models with ordinal response variables. Two different types of ordered models are considered, the threshold model, also known as cumulative model, and the sequential model. Both are based on the assumption that the observed response variable results from a categorized version of a latent metric variable. In the further course of the thesis the boosting approach is extended to additive predictors. The unknown functions to be estimated are expanded in B-spline basis functions, whose smoothness is controlled by penalty terms. Finally, a suitable L1-regularization technique for generalized linear models is presented, which is based on a combination of Fisher scoring and gradient optimization. Extensive simulation studies and numerous applications illustrate the competitiveness of the methods constructed in this thesis compared to conventional approaches. For the calculation of standard errors bootstrap methods are used.
Book Synopsis Variable Selection in Single Index Varying Coefficient Models with LASSO. by : Peng Wang
Download or read book Variable Selection in Single Index Varying Coefficient Models with LASSO. written by Peng Wang and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Single index varying coefficient model is a very attractive statistical model due to its ability to reduce dimensions and easy-of-interpretation. There are many theoretical studies and practical applications with it, but typically without features of variable selection, and no public software is available for solving it. Here we propose a new algorithm to fit the single index varying coefficient model, and to carry variable selection in the index part with LASSO. The core idea is a two-step scheme which alternates between estimating coefficient functions and selecting-and-estimating the single index. Both in simulation and in application to a Geoscience dataset, we showed that it works very well. We also presented our R package "sivcm" with the algorithm implemented and with ideas that can be extended beyond.
Book Synopsis Adaptive Varying-Coefficient Linear Models by : Zongwu Cai
Download or read book Adaptive Varying-Coefficient Linear Models written by Zongwu Cai and published by . This book was released on 2008 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Varying-coefficient linear models arise from multivariate nonparametric regression, nonlinear time series modelling and forecasting, functional data analysis, longitudinal data analysis, and others. It has been a common practice to assume that the vary-coefficients are functions of a given variable which is often called an index. A frequently asked question is which variable should be used as the index. In this paper, we explore the class of the varying-coefficient linear models in which the index is unknown and is estimated as a linear combination of regression and/or other variables. This will enlarge the modelling capacity substantially. We search for the index such that the derived varying-coefficient model provides the best approximation to the underlying unknown multi-dimensional regression function in the least square sense. The search is implemented through the newly proposed hybrid backfitting algorithm. The core of the algorithm is the alternative iteration between estimating the index through a one-step scheme and estimating coefficient functions through a one-dimensional local linear smoothing. The generalised cross-validation method for choosing bandwidth is efficiently incorporated into the algorithm. The locally significant variables are selected in terms of the combined use of t-statistic and Akaike information criterion. We further extend the algorithm for the models with two indices. Simulation shows that the proposed methodology has appreciable flexibility to model complex multivariate nonlinear structure and is practically feasible with average modern computers. The methods are further illustrated through the Canadian mink-muskrat data in 1925-1994 and the pound/dollar exchange rates in 1974-1983.
Book Synopsis The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics by : Jeffrey Racine
Download or read book The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics written by Jeffrey Racine and published by Oxford University Press. This book was released on 2014-04 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, edited by Jeffrey Racine, Liangjun Su, and Aman Ullah, contains the latest research on nonparametric and semiparametric econometrics and statistics. Chapters by leading international econometricians and statisticians highlight the interface between econometrics and statistical methods for nonparametric and semiparametric procedures.
Book Synopsis Nonlinear Time Series by : Jianqing Fan
Download or read book Nonlinear Time Series written by Jianqing Fan and published by Springer Science & Business Media. This book was released on 2008-09-11 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book that integrates useful parametric and nonparametric techniques with time series modeling and prediction, the two important goals of time series analysis. Such a book will benefit researchers and practitioners in various fields such as econometricians, meteorologists, biologists, among others who wish to learn useful time series methods within a short period of time. The book also intends to serve as a reference or text book for graduate students in statistics and econometrics.
Book Synopsis Variable Selection in Varying Multi-Index Coefficient Models with Applications to Gene-Environmental Interactions by : Shunjie Guan
Download or read book Variable Selection in Varying Multi-Index Coefficient Models with Applications to Gene-Environmental Interactions written by Shunjie Guan and published by . This book was released on 2017 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantile Regression in Heteroscedastic Varying Coefficient Models by : Mohammed Abdulkerim Ibrahim
Download or read book Quantile Regression in Heteroscedastic Varying Coefficient Models written by Mohammed Abdulkerim Ibrahim and published by . This book was released on 2018 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis ROBUST JOINT MEAN-COVARIANCE M by : Xueying Zheng
Download or read book ROBUST JOINT MEAN-COVARIANCE M written by Xueying Zheng and published by Open Dissertation Press. This book was released on 2017-01-26 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Robust Joint Mean-covariance Model Selection and Time-varying Correlation Structure Estimation for Dependent Data" by Xueying, Zheng, 郑雪莹, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In longitudinal and spatio-temporal data analysis, repeated measurements from a subject can be either regional- or temporal-dependent. The correct specification of the within-subject covariance matrix cultivates an efficient estimation for mean regression coefficients. In this thesis, robust estimation for the mean and covariance jointly for the regression model of longitudinal data within the framework of generalized estimating equations (GEE) is developed. The proposed approach integrates the robust method and joint mean-covariance regression modeling. Robust generalized estimating equations using bounded scores and leverage-based weights are employed for the mean and covariance to achieve robustness against outliers. The resulting estimators are shown to be consistent and asymptotically normally distributed. Robust variable selection method in a joint mean and covariance model is considered, by proposing a set of penalized robust generalized estimating equations to estimate simultaneously the mean regression coefficients, the generalized autoregressive coefficients and innovation variances introduced by the modified Cholesky decomposition. The set of estimating equations select important covariate variables in both mean and covariance models together with the estimating procedure. Under some regularity conditions, the oracle property of the proposed robust variable selection method is developed. For these two robust joint mean and covariance models, simulation studies and a hormone data set analysis are carried out to assess and illustrate the small sample performance, which show that the proposed methods perform favorably by combining the robustifying and penalized estimating techniques together in the joint mean and covariance model. Capturing dynamic change of time-varying correlation structure is both interesting and scientifically important in spatio-temporal data analysis. The time-varying empirical estimator of the spatial correlation matrix is approximated by groups of selected basis matrices which represent substructures of the correlation matrix. After projecting the correlation structure matrix onto the space spanned by basis matrices, varying-coefficient model selection and estimation for signals associated with relevant basis matrices are incorporated. The unique feature of the proposed model and estimation is that time-dependent local region signals can be detected by the proposed penalized objective function. In theory, model selection consistency on detecting local signals is provided. The proposed method is illustrated through simulation studies and a functional magnetic resonance imaging (fMRI) data set from an attention deficit hyperactivity disorder (ADHD) study. DOI: 10.5353/th_b5089970 Subjects: Robust statistics Estimation theory Generalized estimating equations
Book Synopsis Robust Nonparametric and Semiparametric Modeling by : Bo Kai
Download or read book Robust Nonparametric and Semiparametric Modeling written by Bo Kai and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, several new statistical procedures in nonparametric and semiparametric models are proposed. The concerns of the research are efficiency, robustness and sparsity. In Chapter 3, we propose complete composite quantile regression (CQR) procedures for estimating both the regression function and its derivatives in fully nonparametric regression models by using local smoothing techniques. The CQR estimator was recently proposed by Zou and Yuan (2008) for estimating the regression coefficients in the classical linear regression model. The asymptotic theory of the proposed estimator was established. We show that, compared with the classical local linear least squares estimator, the new method can significantly improve the estimation efficiency of the local linear least squares estimator for commonly used non-normal error distributions, and at the same time, the loss in efficiency is at most 8.01% in the worst case scenario. In Chapter 4, we further consider semiparametric models. The complexity of semiparametric models poses new challenges to parametric inferences and model selection that frequently arise from real applications. We propose new robust inference procedures for the semiparametric varying-coefficient partially linear model. We first study a quantile regression estimate for the nonparametric varying-coefficient functions and the parametric regression coefficients. To improve efficiency, we further develop a composite quantile regression procedure for both parametric and nonparametric components. To achieve sparsity, we develop a variable selection procedure for this model to select significant variables. We study the sampling properties of the resulting quantile regression estimate and composite quantile regression estimate. With proper choices of penalty functions and regularization parameters, we show the proposed variable selection procedure possesses the oracle property in the terminology of Fan and Li (2001). In Chapter 5, we propose a novel estimation procedure for varying coefficient models based on local ranks. By allowing the regression coefficients to change with certain covariates, the class of varying coefficient models offers a flexible semiparametric approach to modeling nonlinearity and interactions between covariates. Varying coefficient models are useful nonparametric regression models and have been well studied in the literature. However, the performance of existing procedures can be adversely influenced by outliers. The new procedure provides a highly efficient and robust alternative to the local linear least squares method and can be conveniently implemented using existing R software packages. We study the sample properties of the proposed procedure and establish the asymptotic normality of the resulting estimate. We also derive the asymptotic relative efficiency of the proposed local rank estimate to the local linear estimate for the varying coefficient model. The gain of the local rank regression estimate over the local linear regression estimate can be substantial. We further develop nonparametric inferences for the rank-based method. Monte Carlo simulations are conducted to access the finite sample performance of the proposed estimation procedure. The simulation results are promising and consistent with our theoretical findings. All the proposed procedures are supported by intensive finite sample simulation studies and most are illustrated with real data examples.
Book Synopsis Subset Selection in Regression by : Alan Miller
Download or read book Subset Selection in Regression written by Alan Miller and published by CRC Press. This book was released on 2002-04-15 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1990, the first edition of Subset Selection in Regression filled a significant gap in the literature, and its critical and popular success has continued for more than a decade. Thoroughly revised to reflect progress in theory, methods, and computing power, the second edition promises to continue that tradition. The author ha
Book Synopsis Fuzzy Regression Analysis by : Janusz Kacprzyk
Download or read book Fuzzy Regression Analysis written by Janusz Kacprzyk and published by Physica. This book was released on 1992-08-27 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression analysis is a relatively simple yet extremely useful and widely employed tool for determining relationship between some variables on the basis of some observed values taken by these variables. Fuzzy regression analysis has been recently deviced to accomodate in the framework of regression analysis vaguely specified data which are omnipresent in many applications, notably in all areas where human judgements are used. Fuzzy sets theory provides here proper tools. This book is a collection of papers written by virtually all major contributors to fuzzy regression. Its main issue is that vague, imprecise, etc. data may now be used in regression analysis. This is new. Apart from this it gives an extensive coverage of the whole field of fuzzy regression, both in a strictly mathematical and applicational perspective. Most approaches are algorithmic, and can be readily implemented. Information on software is provided.
Book Synopsis Practical Statistics for Data Scientists by : Peter Bruce
Download or read book Practical Statistics for Data Scientists written by Peter Bruce and published by "O'Reilly Media, Inc.". This book was released on 2017-05-10 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical methods are a key part of of data science, yet very few data scientists have any formal statistics training. Courses and books on basic statistics rarely cover the topic from a data science perspective. This practical guide explains how to apply various statistical methods to data science, tells you how to avoid their misuse, and gives you advice on what's important and what's not. Many data science resources incorporate statistical methods but lack a deeper statistical perspective. If you’re familiar with the R programming language, and have some exposure to statistics, this quick reference bridges the gap in an accessible, readable format. With this book, you’ll learn: Why exploratory data analysis is a key preliminary step in data science How random sampling can reduce bias and yield a higher quality dataset, even with big data How the principles of experimental design yield definitive answers to questions How to use regression to estimate outcomes and detect anomalies Key classification techniques for predicting which categories a record belongs to Statistical machine learning methods that “learn” from data Unsupervised learning methods for extracting meaning from unlabeled data
Book Synopsis Alternative Methods of Variable Selection in Linear Regression Models for Incomplete Multivariate Normal Data by : Xiaowei Yang
Download or read book Alternative Methods of Variable Selection in Linear Regression Models for Incomplete Multivariate Normal Data written by Xiaowei Yang and published by . This book was released on 2002 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:
