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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Page 204
... Theorem ( 1.10.3 ) . An illustration of this is given in the following proof . To emphasize the fact that we are working with sequences of random variables , we may place a subscript n on random variables , like X to read Xn . = Theorem ...
... Theorem ( 1.10.3 ) . An illustration of this is given in the following proof . To emphasize the fact that we are working with sequences of random variables , we may place a subscript n on random variables , like X to read Xn . = Theorem ...
Page 220
... theorem that will be proved in the next section . 4.3.17 . Using Exercise 4.3.16 , find the limiting distribution of √ ( √√n − 1 ) . 4.3.18 . Let Y1 < Y2 < ... < Yn be the order statistics of a random sample ( see Section 5.2 ) from ...
... theorem that will be proved in the next section . 4.3.17 . Using Exercise 4.3.16 , find the limiting distribution of √ ( √√n − 1 ) . 4.3.18 . Let Y1 < Y2 < ... < Yn be the order statistics of a random sample ( see Section 5.2 ) from ...
Page 704
... Theorem asymptotic normality of mles , 325 Asymptotic Power Lemma , 524 Basu's theorem , 412 Bayes ' theorem , 25 Boole's Inequality , 19 Central Limit Theorem , 220 n - variate , 229 Chebyshev's inequality , 69 Cochran's Theorem , 511 ...
... Theorem asymptotic normality of mles , 325 Asymptotic Power Lemma , 524 Basu's theorem , 412 Bayes ' theorem , 25 Boole's Inequality , 19 Central Limit Theorem , 220 n - variate , 229 Chebyshev's inequality , 69 Cochran's Theorem , 511 ...
Contents
Some Elementary Statistical Inferences | 5 |
Multivariate Distributions | 73 |
Some Special Distributions | 133 |
Copyright | |
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Other editions - View all
Introduction to Mathematical Statistics Robert V. Hogg,Joseph W. McKean,Allen Thornton Craig No preview available - 2005 |
Introduction to Mathematical Statistics Robert V. Hogg,Hogg,Joseph W. McKean,Allen T. Craig No preview available - 2013 |
Common terms and phrases
approximate asymptotic Bayes bootstrap C₁ C₂ chi-square distribution compute conditional pdf confidence interval Consider continuous random variable continuous type correlation coefficient critical region defined degrees of freedom denote a random determine discrete random variable discrete type discussed equal equation Example Exercise Find Fx(x gamma distribution given H₁ Hence independent random variables inequality integral joint pdf Let the random Let X1 Let Y₁ likelihood function linear marginal pdf matrix median MVUE normal distribution observations obtain order statistics p-value P(C₁ p₁ pdf f(x pdf of Y₁ Poisson distribution Proof random sample random variables X1 random vector respectively result S-PLUS sample mean sample space sequence Show significance level subsets sufficient statistic Suppose t-distribution test statistic Theorem unbiased estimator Wilcoxon X₁ X1 and X2 Y₁ Y₂ zero elsewhere σ²