Statistical InferenceThomson Learning, 2002 - 660 páginas 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. |
Índice
Probability Theory | 1 |
Transformations and Expectations | 47 |
Common Families of Distributions | 85 |
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acceptance region ancillary statistic ANOVA approximation asymptotic Bayes estimator best unbiased estimator bivariate bootstrap calculate conditional confidence interval confidence set Continuation of Example converges coverage probability defined Definition denote derived equivariant Exercise exponential family Find finite fx(x gamma given H₁ hypothesis independent Inequality inference integral interval estimator joint pdf least squares Lemma Let X1 level a test likelihood function Likelihood Principle linear M-estimator mean and variance method Miscellanea Mx(t observed order statistics parameter pdf or pmf Poisson population problem proof random sample random variable random vector regression reject relationship risk function sample space satisfies Section Show sufficient statistic Suppose Theorem transformation Type I Error unbiased estimator verify versus H1 X₁ Xn be iid Y₁ θο μο μχ σ² ΣΧ