Analytical Methods in Statistics

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.

Features new results in estimation theory, hypothesis testing and regression, including quantile regression and divergence minimization Elaborates on analytical properties of probability distributions and resampling techniques Presents robust and nonparametric inference under shape constraints and inference for weakly dependent data Collates the latest contributions by experts in the field Includes supplementary material: sn.pub/extras

Autorentext

Jaromír Antoch is a full professor at the Charles University in Prague. His research interests include statistical computing, simulations, change point detection, robust and nonparametric statistics, industrial statistics and applications. He was chairman of the European Regional Section of the International Association for Statistical Computing (IASC) Board of Directors, president of IASC and council member of the International Statistical Institute.

Jana Jureková is a full professor at the Charles University in Prague. She has published over 130 papers in leading journals and coauthored 5 monographs. She has worked on relationships and behavior of robust estimators and nonparametric procedures since the 1970s. She has worked as a visiting professor in Belgium, France, Italy, Switzerland and the USA. She is elected member of the International Statistical Institute, fellow of the Institute of Mathematical Statistics, member of the Bernoulli Society Council and of the ASA Noether's Award Committee.

Matú Maciak is an assistant professor at the Charles University in Prague. His research work focuses on nonparametric estimation methods, change point detection and robustness. Recently he elaborated contemporary ideas in sparse fitting via convex optimization atomic pursuit and lasso. He also gained experience during his stays at the University of Alberta in Edmonton, Hasselt University and the University of Hamburg.

Michal Peta is an assistant professor at the Charles University in Prague. His research interests include asymptotic methods for weak dependence, resampling methods, panel data, nonparametric regression, and errors-in-variables modeling. In the recent years, he has been developing the statistical methodology for non-life insurance. Michal Peta has utilized the skills gained during his PhD and postdoctoral stays (Hasselt University, University of Hamburg, HU Berlin, University of Alberta) to contribute to applied fields.

Inhalt

Preface.- A Weighted Bootstrap Procedure for Divergence Minimization Problems (Michel Broniatowski).- Asymptotic Analysis of Iterated 1-step Huber-skip M-estimators with Varying Cut-offs (Xiyu Jiao and Bent Nielsen).-Regression Quantile and Averaged Regression Quantile Processes (Jana Jureková).- Stability and Heavy-tailness (Lev B. Klebanov).- Smooth Estimation of Error Distribution in Nonparametric Regression under Long Memory (Hira L. Koul and Lihong Wang).- Testing Shape Constrains in Lasso Regularized Joinpoint Regression (Matú Maciak).- Shape Constrained Regression in Sobolev Spaces with Application to Option Pricing (Michal Peta and Zdenk Hlávka).- On Existence of Explicit Asymptotically Normal Estimators in Non-Linear Regression Problems (Alexander Sakhanenko).- On the Behavior of the Risk of a LASSO-Type Estimator (Silvelyn Zwanzig and M. Rauf Ahmad).