+612 9045 4394
 
CHECKOUT
Nonparametric Methods in Change Point Problems : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - B.E. Brodsky

Nonparametric Methods in Change Point Problems

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

Hardcover Published: 31st January 1993
ISBN: 9780792321224
Number Of Pages: 210

Share This Book:

Hardcover

RRP $423.99
$293.75
31%
OFF
or 4 easy payments of $73.44 with Learn more
Ships in 7 to 10 business days

Other Available Editions (Hide)

  • Paperback View Product Published: 6th December 2010
    $213.24

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.

`... excellent monograph ... highly recommended ... as a graduate-level textbook on the subject, as well as an outstanding source of information for everyone doing research in these and related areas of random processes and mathematical statistics.' Mathematical Reviews, 95d

Preface
Introduction: Goals and problems of change-point detection
Preliminary considerationsp. 1
Auxiliary results from the theory of random processes and mathematical statisticsp. 1
Mixing conditionsp. 1
The Wiener process and some functionals related to itp. 2
Weak convergencep. 4
Martingales. Markov's moments. Wald's identityp. 7
General approach to change-point detection. Reduction to the basic-problemp. 8
State-of-the-art reviewp. 11
A posteriori methods of change-point detectionp. 13
Sequential methods of change-point detectionp. 24
A posteriori change-point problemsp. 36
Formulation of problems. Assumptionsp. 36
Auxiliary resultsp. 40
Decision rules and methods of estimation. Limit theoremsp. 53
Inequalitiesp. 73
Asymptotic analysis of a posteriori change-point detection methodsp. 80
Sequential change-point detection problemsp. 95
A nonparametric method of sequential change-point detectionp. 96
Nonparametric versions of different sequential change-point methods and their asymptotic propertiesp. 102
Cumulative Sum (CUSUM) methodp. 102
The Girshik-Rubin-Shiryaev (GRSh) methodp. 107
The exponential smoothing methodp. 111
"Moving-sample" methods of detectionp. 113
Asymptotic comparative analysis of sequential nonparametric change-point detection methodsp. 120
The main inequalityp. 120
CUSUM and GRSh methodsp. 122
Exponential smoothing and moving sample methodsp. 136
Comparative study of change-point detection methodsp. 137
The asymptotically optimal linear moving-sample methodp. 141
Disorder detection of random fieldsp. 151
Formulation of the problemp. 151
Methods of detection of the parametric disorder regionsp. 152
Methods of detection of the nonparametric disorder regionsp. 161
Binary problemp. 161
General problemp. 164
Applications of nonparametric change-point detection methodsp. 169
Detection of homogenous and non-homogenous segments in large historical textsp. 169
Detection of collisionless shock waves. Statistical analysis of space datap. 178
Analysis of geophysical datap. 180
Proofs, new results and technical detailsp. 183
The algorithm and the program package for a posteriori change-point detection VERDIA (short overview)p. 195
Referencesp. 199
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792321224
ISBN-10: 0792321227
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 210
Published: 31st January 1993
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 1.91
Weight (kg): 0.5