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Robust Adaptively Weighted Estimators For Regression Models
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Book Synopsis Robust Adaptively Weighted Estimators for Regression Models by : Wei Tu
Download or read book Robust Adaptively Weighted Estimators for Regression Models written by Wei Tu and published by . This book was released on 2015 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis introduces a new class of robust estimators for regression models. Specifically, a class of weighted least square estimators under linear regression models is introduced in Chapter 2, with a continuous adaptive weight function computed using the Kolmogorov-Smirnov statistic. Asymptotic properties, such as consistency and asymptotic normality, of the proposed estimator are established under the model. Simulation studies show that the proposed estimator attains almost full efficiency and have a better robustness properties than the initial estimators for finite sample sizes. An application to a real contaminated dataset shows that it's comparable to other robust estimators in practice. In Chapter 3, a class of weighted maximum likelihood estimators under logistic regression models is introduced, again with a continuous adaptive weight function computed using Mahalanobis distances of exploratory variables. Asymptotic consistency of the proposed estimator is proved under the model, and finite-sample properties are also studied by simulation. In simulation studies, it is observed that the proposed estimator is almost as efficient as the maximum likelihood estimator under the model, and under point-mass contamination models, the proposed estimator shows a comparable robustness. This is also verified in an application to a real data set. Chapter 4 contains some concluding remarks and future directions.
Book Synopsis Efficient Robust Estimation of Regression Models by : Pavel Čížek
Download or read book Efficient Robust Estimation of Regression Models written by Pavel Čížek and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Adaptive Robust Regression Approaches in Data Analysis and Their Applications by : Zongjun Zhang
Download or read book Adaptive Robust Regression Approaches in Data Analysis and Their Applications written by Zongjun Zhang and published by . This book was released on 2015 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we proposed several novel Adaptive Robust Approaches. The main purpose of the proposed adaptive robust approaches is: (a) To facilitate the decision on whether it is more pertinent to use a robust or a standard technique. (b) To provide an easy but relatively safe alternative to robust approaches without too much struggle about how to choose one among a variety of robust approaches and how to select the parameters (such as trimming portion, tuning constant). The proposed adaptive robust regression approaches are constructed by combining regular robust regressions (such as M-estimators/ LTS) with application of optimization procedure and characteristics of data in terms of tail weight index(TWI) and normality test. Three main adaptive robust regression approaches are proposed and the related algorithms are also implemented in programs (SAS MACROS and S-PLUS application): (1) Adaptive Robust M-Estimator with optimal tuning constant based on the empirical distribution function (EDF) of the standardized absolute residuals. The algorithm is similar to standard IRWLS, but the TWI and normality test of residuals are investigated to adjust the tuning constant in each iteration within iterative re-weighted least square algorithm (IRWLS) loop. The adaptive approach is implemented in SAS macro %BIWREG()(with Parameter ADAPT=TW).(2) Adaptive Robust M-Estimator with optimal tuning constant based on minimizing the asymptotic variance estimate. Two different algorithms are proposed and compared. The adaptive approaches are implemented in SAS macro %BIWREG(). One is statically adaptive approach (with Parameter ADAPT=AV_S) in which the optimal tuning constant is obtained through many IRWLS processes. The other is dynamically adaptive approach (with Parameter ADAPT=AV_D).(3) Least adaptively trimmed sum of squares estimators with adjusted cut-off (denoted as LATS_AC). The proposed approach is implemented in the Menu-driven application (Adaptive LTS Regression V.1 in S-Plus). The proposed adaptive robust approaches were demonstrated in both extensive simulation studies and application examples.
Book Synopsis Efficient Robust Estimation of Time-series Regression Models by : Pavel Čížek
Download or read book Efficient Robust Estimation of Time-series Regression Models written by Pavel Čížek and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modern Methods for Robust Regression by : Robert Andersen
Download or read book Modern Methods for Robust Regression written by Robert Andersen and published by SAGE. This book was released on 2008 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering an in-depth treatment of robust and resistant regression, this volume takes an applied approach and offers readers empirical examples to illustrate key concepts.
Book Synopsis Robust and Efficient Adaptive Estimation of Binary-choice Regression Models by : Pavel Čižek
Download or read book Robust and Efficient Adaptive Estimation of Binary-choice Regression Models written by Pavel Čižek and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applied Adaptive Statistical Methods by : Thomas W. O'Gorman
Download or read book Applied Adaptive Statistical Methods written by Thomas W. O'Gorman and published by SIAM. This book was released on 2004-01-01 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive statistical tests, developed over the last 30 years, are often more powerful than traditional tests of significance, but have not been widely used. To date, discussions of adaptive statistical methods have been scattered across the literature and generally do not include the computer programs necessary to make these adaptive methods a practical alternative to traditional statistical methods. Until recently, there has also not been a general approach to tests of significance and confidence intervals that could easily be applied in practice. Modern adaptive methods are more general than earlier methods and sufficient software has been developed to make adaptive tests easy to use for many real-world problems. Applied Adaptive Statistical Methods: Tests of Significance and Confidence Intervals introduces many of the practical adaptive statistical methods developed over the last 10 years and provides a comprehensive approach to tests of significance and confidence intervals. It shows how to make confidence intervals shorter and how to make tests of significance more powerful by using the data itself to select the most appropriate procedure.
Book Synopsis Essays on Robust Model Selection and Model Averaging for Linear Models by : Le Chang
Download or read book Essays on Robust Model Selection and Model Averaging for Linear Models written by Le Chang and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model selection is central to all applied statistical work. Selecting the variables for use in a regression model is one important example of model selection. This thesis is a collection of essays on robust model selection procedures and model averaging for linear regression models. In the first essay, we propose robust Akaike information criteria (AIC) for MM-estimation and an adjusted robust scale based AIC for M and MM-estimation. Our proposed model selection criteria can maintain their robust properties in the presence of a high proportion of outliers and the outliers in the covariates. We compare our proposed criteria with other robust model selection criteria discussed in previous literature. Our simulation studies demonstrate a significant outperformance of robust AIC based on MM-estimation in the presence of outliers in the covariates. The real data example also shows a better performance of robust AIC based on MM-estimation. The second essay focuses on robust versions of the "Least Absolute Shrinkage and Selection Operator" (lasso). The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty term mean that the adaptive lasso achieves the oracle property. In this essay, we propose an extension of the adaptive lasso named the Tukey-lasso. By using Tukey's biweight criterion, instead of squared loss, the Tukey-lasso is resistant to outliers in both the response and covariates. Importantly, we demonstrate that the Tukey-lasso also enjoys the oracle property. A fast accelerated proximal gradient (APG) algorithm is proposed and implemented for computing the Tukey-lasso. Our extensive simulations show that the Tukey-lasso, implemented with the APG algorithm, achieves very reliable results, including for high-dimensional data where p>n. In the presence of outliers, the Tukey-lasso is shown to offer substantial improvements in performance compared to the adaptive lasso and other robust implementations of the lasso. Real data examples further demonstrate the utility of the Tukey-lasso. In many statistical analyses, a single model is used for statistical inference, ignoring the process that leads to the model being selected. To account for this model uncertainty, many model averaging procedures have been proposed. In the last essay, we propose an extension of a bootstrap model averaging approach, called bootstrap lasso averaging (BLA). BLA utilizes the lasso for model selection. This is in contrast to other forms of bootstrap model averaging that use AIC or Bayesian information criteria (BIC). The use of the lasso improves the computation speed and allows BLA to be applied even when the number of variables p is larger than the sample size n. Extensive simulations confirm that BLA has outstanding finite sample performance, in terms of both variable and prediction accuracies, compared with traditional model selection and model averaging methods. Several real data examples further demonstrate an improved out-of-sample predictive performance of BLA.
Book Synopsis Robust Estimation with Discrete Explanatory Variables by : Pavel Cizek
Download or read book Robust Estimation with Discrete Explanatory Variables written by Pavel Cizek and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The least squares estimator is probably the most frequently used estimation method in regression analysis. Unfortunately, it is also quite sensitive to data contamination and model misspecification. Although there are several robust estimators designed for parametric regression models that can be used in place of least squares, these robust estimators cannot be easily applied to models containing binary and categorical explanatory variables. Therefore, I design a robust estimator that can be used for any linear regression model no matter what kind of explanatory variables the model contains. Additionally, I propose an adaptive procedure that maximizes the efficiency of the proposed estimator for a given data set while preserving its robustness.
Book Synopsis Robust High-dimensional Data Analysis Using a Weight Shrinkage Rule by : Bin Luo
Download or read book Robust High-dimensional Data Analysis Using a Weight Shrinkage Rule written by Bin Luo and published by . This book was released on 2016 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In high-dimensional settings, a penalized least squares approach may lose its efficiency in both estimation and variable selection due to the existence of either outliers or heteroscedasticity. In this thesis, we propose a novel approach to perform robust high-dimensional data analysis in a penalized weighted least square framework. The main idea is to relate the irregularity of each observation to a weight vector and obtain the outlying status data-adaptively using a weight shrinkage rule. By usage of L-1 type regularization on both the coefficients and weight vectors, the proposed method is able to perform simultaneous variable selection and outliers detection efficiently. Eventually, this procedure results in estimators with potentially strong robustness and non-asymptotic consistency. We provide a unified link between the weight shrinkage rule and a robust M-estimation in general settings. We also establish the non-asymptotic oracle inequalities for the joint estimation of both the regression coefficients and weight vectors. These theoretical results allow the number of variables to far exceed the sample size. The performance of the proposed estimator is demonstrated in both simulation studies and real examples."--Abstract from author supplied metadata.
Book Synopsis Robust Statistics for Signal Processing by : Abdelhak M. Zoubir
Download or read book Robust Statistics for Signal Processing written by Abdelhak M. Zoubir and published by Cambridge University Press. This book was released on 2018-11-08 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understand the benefits of robust statistics for signal processing using this unique and authoritative text.
Book Synopsis Robust and Multivariate Statistical Methods by : Mengxi Yi
Download or read book Robust and Multivariate Statistical Methods written by Mengxi Yi and published by Springer Nature. This book was released on 2023-04-19 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent developments in multivariate and robust statistical methods. Featuring contributions by leading experts in the field it covers various topics, including multivariate and high-dimensional methods, time series, graphical models, robust estimation, supervised learning and normal extremes. It will appeal to statistics and data science researchers, PhD students and practitioners who are interested in modern multivariate and robust statistics. The book is dedicated to David E. Tyler on the occasion of his pending retirement and also includes a review contribution on the popular Tyler’s shape matrix.
Book Synopsis Adaptive L1 Regularized Second-order Least Squares Method for Model Selection by : Lin Xue
Download or read book Adaptive L1 Regularized Second-order Least Squares Method for Model Selection written by Lin Xue and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second-order least squares (SLS) method in regression model proposed by Wang (2003, 2004) is based on the first two conditional moments of the response variable given the observed predictor variables. Wang and Leblanc (2008) show that the SLS estimator (SLSE) is asymptotically more efficient than the ordinary least squares estimator (OLSE) if the third moment of the random error is nonzero. We apply the SLS method to variable selection problems and propose the adaptively weighted L1 regularized SLSE (L1-SLSE). The L1-SLSE is robust against the shape of error distributions in variable selection problems. Finite sample simulation studies show that the L1-SLSE is more efficient than L1-OLSE in the case of asymmetric error distributions. A real data application with L1-SLSE is presented to demonstrate the usage of this method.
Book Synopsis Strong Consistency of the Least Squares Estimator in Regression Models with Adaptive Learning by : Norbert Christopeit
Download or read book Strong Consistency of the Least Squares Estimator in Regression Models with Adaptive Learning written by Norbert Christopeit and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust and Efficient Regression by : Qi Zheng
Download or read book Robust and Efficient Regression written by Qi Zheng and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This dissertation aims to address two problems in regression analysis. One problem is the model selection and robust parameter estimation in high dimensional linear regressions. The other is concerning developing a robust and efficient estimator in nonparametric regressions. In Chapter 1, we introduce the robust and efficient regression analysis, discuss those two interesting problems and our motivations, and present several exciting results. We propose a novel robust penalized method for high dimensional linear regression in Chapter 2. Asymptotic properties are established and a data-driven procedure is developed to select adaptive penalties. We show it is the very first estimator to achieve desired oracle properties with certainty for high dimensional linear regression. Extensive simulations have been conducted and demonstrate the usefulness of the new technique. A new local polynomial nonparametric regression is developed in Chapter 3. It minimizes a convex combination of several weighted loss functions simultaneously. The optimal weights are selected by a proposed procedure and adapt to the tails of the error distribution resulting in a procedure which is both robust and resistant. The asymptotic properties have been investigated. We show the resulting estimators are at least as efficient as those provided by existing procedures, but can be much more efficient for many distributions. Its excellent finite sample performance is presented through simulations under a variety of settings. A real data analysis exhibits the usefulness of the proposed methodology.
Book Synopsis The Weighted Bootstrap by : Philippe Barbe
Download or read book The Weighted Bootstrap written by Philippe Barbe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: INTRODUCTION 1) Introduction In 1979, Efron introduced the bootstrap method as a kind of universal tool to obtain approximation of the distribution of statistics. The now well known underlying idea is the following : consider a sample X of Xl ' n independent and identically distributed H.i.d.) random variables (r. v,'s) with unknown probability measure (p.m.) P . Assume we are interested in approximating the distribution of a statistical functional T(P ) the -1 nn empirical counterpart of the functional T(P) , where P n := n l:i=l aX. is 1 the empirical p.m. Since in some sense P is close to P when n is large, n • • LLd. from P and builds the empirical p.m. if one samples Xl ' ... , Xm n n -1 mn • • P T(P ) conditionally on := mn l: i =1 a • ' then the behaviour of P m n,m n n n X. 1 T(P ) should imitate that of when n and mn get large. n This idea has lead to considerable investigations to see when it is correct, and when it is not. When it is not, one looks if there is any way to adapt it.
Book Synopsis Adaptive Regression by : Yadolah Dodge
Download or read book Adaptive Regression written by Yadolah Dodge and published by Springer Science & Business Media. This book was released on 2012-10-01 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: While there have been a large number of estimation methods proposed and developed for linear regression, none has proved good for all purposes. This text focuses on the construction of an adaptive combination of two estimation methods so as to help users make an objective choice and combine the desirable properties of two estimators.
