## Introduction to mathematical statisticsThis classic book retains its outstanding ongoing features and continues to provide readers with excellent background material necessary for a successful understanding of mathematical statistics. Chapter topics cover classical statistical inference procedures in estimation and testing, and an in-depth treatment of sufficiency and testing theory—including uniformly most powerful tests and likelihood ratios. Many illustrative examples and exercises enhance the presentation of material throughout the book. For a more complete understanding of mathematical statistics. |

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### Contents

3 | 16 |

Unbiasedness Consistency and Limiting Distributions | 25 |

Multivariate Distributions | 73 |

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approximate assume asymptotic best critical region complete sufficient statistic compute conditional pdf conﬁdence interval Consider continuous random variable continuous type critical region deﬁned deﬁnition degrees of freedom denote a random determine discussed equal equation Example Exercise ﬁnd ﬁnite ﬁrst ﬁxed gamma distribution given Hence hypothesis H0 independent random variables inequality integral joint pdf Let the random Let X1 likelihood function likelihood ratio test linear marginal pdf matrix median MVUE noncentral normal distribution null observations obtain order statistics p-value pdf f pdf of Y1 pdf or pmf Poisson distribution power function probability density functions proof quadratic form random sample random vector reject H0 respectively sample mean sample space satisﬁes sequence Show signiﬁcance level simple hypothesis statistic for 9 sufficient statistic Suppose t-test test statistic Theorem unbiased estimator variance 02 versus H1 Wilcoxon X1 and X2 zero elsewhere