Statistical Theory and Inference
Statistical Theory and Inference By David Olive
2014 | 448 Pages | ISBN: 3319049712 | PDF | 4 MB
This
text is for a one semester graduate course in statistical theory and
covers minimal and complete sufficient statistics, maximum likelihood
estimators, method of moments, bias and mean square error, uniform
minimum variance estimators and the Cramer-Rao lower bound, an
introduction to large sample theory, likelihood ratio tests and
uniformly most powerful tests and the Neyman Pearson Lemma. A major goal
of this text is to make these topics much more accessible to students
by using the theory of exponential families.Exponential families,
indicator functions and the support of the distribution are used
throughout the text to simplify the theory. More than 50 ``brand name"
distributions are used to illustrate the theory with many examples of
exponential families, maximum likelihood estimators and uniformly
minimum variance unbiased estimators. There are many homework problems
with over 30 pages of solutions.
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