Ivchenko G., Medvedev Y., Chtstyakov A. Problems in mathematical statistics

Moscow: Mir Publishers, 1991. — 279 p.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 of 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 probfems 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.Theory and Problems
Principles of Statistical Description. Sampling
Characteristics and Their' Distributions
Estimation of Distribution Parameters
Estimators and Their General Properties
Optimum Estimators
Maximum Likelihood Estimates
Confidence Estimation
Tests of Statistical Hypotheses
Goodness of Fit Tests
A Choice Between TVro Simple Hypotheses
Composite Hypotheses
Tests of Hypotheses and Confidence Estimation
Likelihood Ratio lest
Various Problems
Linear Regression and the Least Squares Metbod
Decision-Functions
Statistics of Stationary Sequences
Answers and SolutionsAppendix

List of Distributions
Bibliography