Parametric Statistical Change Point Analysis

Parametric Statistical Change Point Analysis
Author: Jie Chen
Publisher: Springer Science & Business Media
Total Pages: 190
Release: 2013-11-11
Genre: Mathematics
ISBN: 1475731310

Recently there has been a keen interest in the statistical analysis of change point detec tion and estimation. Mainly, it is because change point problems can be encountered in many disciplines such as economics, finance, medicine, psychology, geology, litera ture, etc. , and even in our daily lives. From the statistical point of view, a change point is a place or time point such that the observations follow one distribution up to that point and follow another distribution after that point. Multiple change points problem can also be defined similarly. So the change point(s) problem is two fold: one is to de cide if there is any change (often viewed as a hypothesis testing problem), another is to locate the change point when there is a change present (often viewed as an estimation problem). The earliest change point study can be traced back to the 1950s. During the fol lowing period of some forty years, numerous articles have been published in various journals and proceedings. Many of them cover the topic of single change point in the means of a sequence of independently normally distributed random variables. Another popularly covered topic is a change point in regression models such as linear regres sion and autoregression. The methods used are mainly likelihood ratio, nonparametric, and Bayesian. Few authors also considered the change point problem in other model settings such as the gamma and exponential.

Nonparametric Methods in Change Point Problems

Nonparametric Methods in Change Point Problems
Author: E. Brodsky
Publisher: Springer Science & Business Media
Total Pages: 228
Release: 1993-01-31
Genre: Mathematics
ISBN: 9780792321224

The explosive development of information science and technology puts in new problems involving statistical data analysis. These problems result from higher re quirements concerning the reliability of statistical decisions, the accuracy of math ematical models and the quality of control in complex systems. A new aspect of statistical analysis has emerged, closely connected with one of the basic questions of cynergetics: how to "compress" large volumes of experimental data in order to extract the most valuable information from data observed. De tection of large "homogeneous" segments of data enables one to identify "hidden" regularities in an object's behavior, to create mathematical models for each seg ment of homogeneity, to choose an appropriate control, etc. Statistical methods dealing with the detection of changes in the characteristics of random processes can be of great use in all these problems. These methods have accompanied the rapid growth in data beginning from the middle of our century. According to a tradition of more than thirty years, we call this sphere of statistical analysis the "theory of change-point detection. " During the last fifteen years, we have witnessed many exciting developments in the theory of change-point detection. New promising directions of research have emerged, and traditional trends have flourished anew. Despite this, most of the results are widely scattered in the literature and few monographs exist. A real need has arisen for up-to-date books which present an account of important current research trends, one of which is the theory of non parametric change--point detection.

Bayesian Time Series Models

Bayesian Time Series Models
Author: David Barber
Publisher: Cambridge University Press
Total Pages: 432
Release: 2011-08-11
Genre: Computers
ISBN: 0521196760

The first unified treatment of time series modelling techniques spanning machine learning, statistics, engineering and computer science.

Limit Theorems in Change-Point Analysis

Limit Theorems in Change-Point Analysis
Author: Miklós Csörgö
Publisher: John Wiley & Sons
Total Pages: 448
Release: 1997-12-29
Genre: Mathematics
ISBN:

Change-point problems arise in a variety of experimental and mathematical sciences, as well as in engineering and health sciences. This rigorously researched text provides a comprehensive review of recent probabilistic methods for detecting various types of possible changes in the distribution of chronologically ordered observations. Further developing the already well-established theory of weighted approximations and weak convergence, the authors provide a thorough survey of parametric and non-parametric methods, regression and time series models together with sequential methods. All but the most basic models are carefully developed with detailed proofs, and illustrated by using a number of data sets. Contains a thorough survey of: The Likelihood Approach Non-Parametric Methods Linear Models Dependent Observations This book is undoubtedly of interest to all probabilists and statisticians, experimental and health scientists, engineers, and essential for those working on quality control and surveillance problems. Foreword by David Kendall

A Parametric Approach to Nonparametric Statistics

A Parametric Approach to Nonparametric Statistics
Author: Mayer Alvo
Publisher: Springer
Total Pages: 277
Release: 2018-10-12
Genre: Mathematics
ISBN: 3319941534

This book demonstrates that nonparametric statistics can be taught from a parametric point of view. As a result, one can exploit various parametric tools such as the use of the likelihood function, penalized likelihood and score functions to not only derive well-known tests but to also go beyond and make use of Bayesian methods to analyze ranking data. The book bridges the gap between parametric and nonparametric statistics and presents the best practices of the former while enjoying the robustness properties of the latter. This book can be used in a graduate course in nonparametrics, with parts being accessible to senior undergraduates. In addition, the book will be of wide interest to statisticians and researchers in applied fields.

Sequential Analysis

Sequential Analysis
Author: Alexander Tartakovsky
Publisher: CRC Press
Total Pages: 600
Release: 2014-08-27
Genre: Mathematics
ISBN: 1439838216

Sequential Analysis: Hypothesis Testing and Changepoint Detection systematically develops the theory of sequential hypothesis testing and quickest changepoint detection. It also describes important applications in which theoretical results can be used efficiently. The book reviews recent accomplishments in hypothesis testing and changepoint detecti

Density Ratio Estimation in Machine Learning

Density Ratio Estimation in Machine Learning
Author: Masashi Sugiyama
Publisher: Cambridge University Press
Total Pages: 343
Release: 2012-02-20
Genre: Computers
ISBN: 0521190177

This book introduces theories, methods and applications of density ratio estimation, a newly emerging paradigm in the machine learning community.

Change-Point Analysis in Nonstationary Stochastic Models

Change-Point Analysis in Nonstationary Stochastic Models
Author: Boris Brodsky
Publisher: CRC Press
Total Pages: 286
Release: 2016-12-12
Genre: Mathematics
ISBN: 1315350955

This book covers the development of methods for detection and estimation of changes in complex systems. These systems are generally described by nonstationary stochastic models, which comprise both static and dynamic regimes, linear and nonlinear dynamics, and constant and time-variant structures of such systems. It covers both retrospective and sequential problems, particularly theoretical methods of optimal detection. Such methods are constructed and their characteristics are analyzed both theoretically and experimentally. Suitable for researchers working in change-point analysis and stochastic modelling, the book includes theoretical details combined with computer simulations and practical applications. Its rigorous approach will be appreciated by those looking to delve into the details of the methods, as well as those looking to apply them.