Linear regression is an important area of statistics, theoretical or applied. There have been a large number of estimation methods proposed and developed for linear regression. Each has its own competitive edge but none is good for all purposes. This manuscript focuses on construction of an adaptive combination of two estimation methods. The purpose of such adaptive methods is to help users make an objective choice and to combine desirable properties of two estimators.

This volume collects authoritative contributions on analytical methods and mathematical statistics. The methods presented include resampling techniques; the minimization of divergence; estimation theory and regression, eventually under shape or other constraints or long memory; and iterative approximations when the optimal solution is difficult to achieve. It also investigates probability distributions with respect to their stability, heavy-tailness, Fisher information and other aspects, both asymptotically and non-asymptotically. The book not only presents the latest mathematical and statistical methods and their extensions, but also offers solutions to real-world problems including option pricing. The selected, peer-reviewed contributions were originally presented at the workshop on Analytical Methods in Statistics, AMISTAT 2015, held in Prague, Czech Republic, November 10-13, 2015.

The second edition of Robust Statistical Methods with R provides a systematic treatment of robust procedures with an emphasis on new developments and on the computational aspects. There are many numerical examples and notes on the R environment, and the updated chapter on the multivariate model contains additional material on visualization of multivariate data in R. A new chapter on robust procedures in measurement error models concentrates mainly on the rank procedures, less sensitive to errors than other procedures. This book will be an invaluable resource for researchers and postgraduate students in statistics and mathematics. Features * Provides a systematic, practical treatment of robust statistical methods * Offers a rigorous treatment of the whole range of robust methods, including the sequential versions of estimators, their moment convergence, and compares their asymptotic and finite-sample behavior * The extended account of multivariate models includes the admissibility, shrinkage effects and unbiasedness of two-sample tests * Illustrates the small sensitivity of the rank procedures in the measurement error model * Emphasizes the computational aspects, supplies many examples and illustrations, and provides the own procedures of the authors in the R software on the book's website

Robust and nonparametric statistical methods have their foundation in fields ranging from agricultural science to astronomy, from biomedical sciences to the public health disciplines, and, more recently, in genomics, bioinformatics, and financial statistics. These disciplines are presently nourished by data mining and high-level computer-based algorithms, but to work actively with robust and nonparametric procedures, practitioners need to understand their background. Explaining the underpinnings of robust methods and recent theoretical developments, Methodology in Robust and Nonparametric Statistics provides a profound mathematically rigorous explanation of the methodology of robust and nonparametric statistical procedures. Thoroughly up-to-date, this book Presents multivariate robust and nonparametric estimation with special emphasis on affine-equivariant procedures, followed by hypotheses testing and confidence sets Keeps mathematical abstractions at bay while remaining largely theoretical Provides a pool of basic mathematical tools used throughout the book in derivations of main results The methodology presented, with due emphasis on asymptotics and interrelations, will pave the way for further developments on robust statistical procedures in more complex models. Using examples to illustrate the methods, the text highlights applications in the fields of biomedical science, bioinformatics, finance, and engineering. In addition, the authors provide exercises in the text.

Robust and nonparametric statistical methods have their foundation in fields ranging from agricultural science to astronomy, from biomedical sciences to the public health disciplines, and, more recently, in genomics, bioinformatics, and financial statistics. These disciplines are presently nourished by data mining and high-level computer-based algorithms, but to work actively with robust and nonparametric procedures, practitioners need to understand their background. Explaining the underpinnings of robust methods and recent theoretical developments, Methodology in Robust and Nonparametric Statistics provides a profound mathematically rigorous explanation of the methodology of robust and nonparametric statistical procedures. Thoroughly up-to-date, this book Presents multivariate robust and nonparametric estimation with special emphasis on affine-equivariant procedures, followed by hypotheses testing and confidence sets Keeps mathematical abstractions at bay while remaining largely theoretical Provides a pool of basic mathematical tools used throughout the book in derivations of main results The methodology presented, with due emphasis on asymptotics and interrelations, will pave the way for further developments on robust statistical procedures in more complex models. Using examples to illustrate the methods, the text highlights applications in the fields of biomedical science, bioinformatics, finance, and engineering. In addition, the authors provide exercises in the text.

The second edition of Robust Statistical Methods with R provides a systematic treatment of robust procedures with an emphasis on new developments and on the computational aspects. There are many numerical examples and notes on the R environment, and the updated chapter on the multivariate model contains additional material on visualization of multivariate data in R. A new chapter on robust procedures in measurement error models concentrates mainly on the rank procedures, less sensitive to errors than other procedures. This book will be an invaluable resource for researchers and postgraduate students in statistics and mathematics. Features * Provides a systematic, practical treatment of robust statistical methods * Offers a rigorous treatment of the whole range of robust methods, including the sequential versions of estimators, their moment convergence, and compares their asymptotic and finite-sample behavior * The extended account of multivariate models includes the admissibility, shrinkage effects and unbiasedness of two-sample tests * Illustrates the small sensitivity of the rank procedures in the measurement error model * Emphasizes the computational aspects, supplies many examples and illustrations, and provides the own procedures of the authors in the R software on the book's website

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.

This volume collects authoritative contributions on analytical methods and mathematical statistics. The methods presented include resampling techniques; the minimization of divergence; estimation theory and regression, eventually under shape or other constraints or long memory; and iterative approximations when the optimal solution is difficult to achieve. It also investigates probability distributions with respect to their stability, heavy-tailness, Fisher information and other aspects, both asymptotically and non-asymptotically. The book not only presents the latest mathematical and statistical methods and their extensions, but also offers solutions to real-world problems including option pricing. The selected, peer-reviewed contributions were originally presented at the workshop on Analytical Methods in Statistics, AMISTAT 2015, held in Prague, Czech Republic, November 10-13, 2015.