## Statistical InferenceThis 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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### Contents

Probability Theory | 1 |

Transformations and Expectations | 47 |

Common Families of Distributions | 85 |

Copyright | |

14 other sections not shown

### Common terms and phrases

acceptance region algorithm ancillary statistic ANOVA approximation assumptions asymptotic Bayes estimator best unbiased estimator bivariate bootstrap calculate compute confidence interval confidence set constant Continuation of Example converges coverage probability defined Definition denote density derived equal equations equivariant error Exercise exponential family finite fx(x fx{x gamma given hence Inequality inference integral interval estimator joint pdf least squares Lemma Let Xi level a test likelihood function Likelihood Principle linear M-estimator marginal distribution maximum mean and variance median method of moments minimal sufficient statistic Miscellanea observed obtain order statistics pdf or pmf point estimator Poisson Poisson(A population power function problem proof properties prove random sample random variable random vector regression relationship risk function sample mean sample space satisfies Section sequence Show sufficient statistic Suppose Theorem transformation Type I Error unbiased estimator verify Xn be iid