In this post we will see Problems in Mathematical Statistics by
G. I. Ivchenko, Yu. I. Medvedev and A. V. Chistyakov
This problem book covers all the traditional topics in modern statistical theory and is designed for students at technical colleges and universities who have mathematical statistics as an obligatory course. The problems are mostly analytical. The student is asked to prove the validity or an assertion or carry out an investigation. This will help him grasp the main aspects of mathematical statistics. Some of the problems are more difficult and can be used as individual assignments for course papers. We have included problems on computer simulation of random variables in order to obtain the data for statistical interpretation. Any “theoretical” problem which contains a statistical algorithm for data analysis can be used (with the appropriate (practically infinite) choice of the model parameters ) to formulate a “practical” problem. At the first stage the original data should be simulated using either published tables of random numbers or special computer programs. Then, by interpreting these “experimental” results according to the algorithm in question, the student can compare the theoretical hypothesis with the original parameters which are known as they were used when the sample was simulated. All the problems differ in complexity. More difficult problems are marked with an asterisk and may require a significant effort on the part of the reader. Problems that cannot be reduced to standard algorithms are answered in detail or hints are given.
Each chapter contains the basic notions, assertions, and formulas from the respective theoretical section. The statistical tables at the end of the book will help the reader obtain numerical results. The list of distributions will help him choose problems on different aspects of the same model.
This book was translated from the Russian by Elena Troshneva. The book was published by first Mir Publishers in 1991.This makes it one of the last books to see the light of publication under Mir.
All credits to the original uploader.
DJVU | 3.8 MB | Pages: 282 | OCR | Cover
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Table of Contents
Theory and Problems 7
Principles of Statistical Description. Sampling Characteristics and
Their Distributions 7
Estimation and Distribution of Parameters 37
Estimators and their General Properties 45
Optimum Estimators 56
Maximum Likelihood estimates 66
Confidence Estimation 71
Tests of Statistical Hypotheses 79
Goodness of Fit Tests 87
A Choice Between Two Simple Hypotheses 96
Composite Hypotheses 99
Tests of Hypotheses and Confidence Estimation l01
Likelihood Ratio Test 102
Various Problems 104
Linear, Regression and the Least Squares Method 107
Decision Functions 119
Statistics of Stationary Sequences 131
Answers and Solutions 137
List of Distributions 277