(Математическая статистика - Chapman & Hall/CRC, 2000).
This book is intended as a textbook (or reference) for a full year Master’s level (or senior level undergraduate) course in mathematical statistics aimed at students in statistics, biostatistics, and related fields.
Contents:
Introduction to Probability.
Random experiments.
Probability measures.
Conditional probability and independence.
Random variables.
Transformations of random variables.
Expected values.
Problems and complements.
Random vectors and joint distributions.
Introduction.
Discrete and continuous random vectors.
Conditional distributions and expected values.
Distribution theory for Normal samples.
Poisson processes.
Generating random variables.
Problems and complements.
Convergence of Random Variables.
Introduction.
Convergence in probability and distribution.
Weak Law ofLarg e Numbers.
Proving convergence in distribution.
Central Limit Theorems.
Some applications.
Convergence with probability 1.
Problems and complements.
Principles of Point Estimation.
Introduction.
Statistical models.
Sufficiency.
Point estimation.
The substitution principle.
Influence curves.
Standard errors and their estimation.
Asymptotic relative efficiency.
he jackknife.
Problems and complements.
Likelihood-Based Estimation.
Introduction.
The likelihood function.
The likelihood principle.
Asymptotic theory for MLEs.
Misspecified models.
Non-parametric maximum likelihood estimation.
Numerical computation ofMLE s.
Bayesian estimation.
Problems and complements.
Optimality in Estimation.
Introduction.
Decision theory.
Minimum variance unbiased estimation.
The Cram?er-Rao lower bound.
Asymptotic efficiency.
Problems and complements.
Interval Estimation and Hypothesis Testing.
Confidence intervals and regions.
Highest posterior density regions.
Hypothesis testing.
Likelihood ratio tests.
Other issues.
Problems and complements.
Linear and Generalized Linear Model.
Linear models.
Estimation in linear models.
Hypothesis testing in linear models.
Non-normal errors.
Generalized linear models.
Quasi-Likelihood models.
Problems and complements.
Goodness-of-Fit.
Introduction.
Tests based on the Multinomial distribution.
Smooth goodness-of-fit tests.
Problems and complements.
This book is intended as a textbook (or reference) for a full year Master’s level (or senior level undergraduate) course in mathematical statistics aimed at students in statistics, biostatistics, and related fields.
Contents:
Introduction to Probability.
Random experiments.
Probability measures.
Conditional probability and independence.
Random variables.
Transformations of random variables.
Expected values.
Problems and complements.
Random vectors and joint distributions.
Introduction.
Discrete and continuous random vectors.
Conditional distributions and expected values.
Distribution theory for Normal samples.
Poisson processes.
Generating random variables.
Problems and complements.
Convergence of Random Variables.
Introduction.
Convergence in probability and distribution.
Weak Law ofLarg e Numbers.
Proving convergence in distribution.
Central Limit Theorems.
Some applications.
Convergence with probability 1.
Problems and complements.
Principles of Point Estimation.
Introduction.
Statistical models.
Sufficiency.
Point estimation.
The substitution principle.
Influence curves.
Standard errors and their estimation.
Asymptotic relative efficiency.
he jackknife.
Problems and complements.
Likelihood-Based Estimation.
Introduction.
The likelihood function.
The likelihood principle.
Asymptotic theory for MLEs.
Misspecified models.
Non-parametric maximum likelihood estimation.
Numerical computation ofMLE s.
Bayesian estimation.
Problems and complements.
Optimality in Estimation.
Introduction.
Decision theory.
Minimum variance unbiased estimation.
The Cram?er-Rao lower bound.
Asymptotic efficiency.
Problems and complements.
Interval Estimation and Hypothesis Testing.
Confidence intervals and regions.
Highest posterior density regions.
Hypothesis testing.
Likelihood ratio tests.
Other issues.
Problems and complements.
Linear and Generalized Linear Model.
Linear models.
Estimation in linear models.
Hypothesis testing in linear models.
Non-normal errors.
Generalized linear models.
Quasi-Likelihood models.
Problems and complements.
Goodness-of-Fit.
Introduction.
Tests based on the Multinomial distribution.
Smooth goodness-of-fit tests.
Problems and complements.