This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.
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Transformations and Expectations
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acceptance apply approximation assume asymptotic Bayes binomial bound calculate called Chapter complete compute conditional confidence interval confidence set constant construct continuous converges coverage defined Definition denote depend derived discussed distribution equal error Example Exercise exists expected experiment exponential expression fact Figure Find function fx(x given gives hence hypothesis independent Inequality inference integral interested interval joint pdf known least Let X1 likelihood limit loss marginal mean measure method minimal normal Note observed obtain parameter Poisson population possible Principle prior probability problem proof properties prove random sample random variables region regression reject relationship result sample mean satisfies sequence Show similar situation space squared sufficient statistic Suppose Theorem transformation true Type unbiased estimator usually variance vector verify versus write