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 307
... Consider the algorithm for a two sample bootstrap test given in Section 5.9.2 . ( a ) Rewrite the algorithm for the bootstrap test based on the difference in medi- ans . ( b ) Consider the data in Example 5.9.2 . By substituting the ...
... Consider the algorithm for a two sample bootstrap test given in Section 5.9.2 . ( a ) Rewrite the algorithm for the bootstrap test based on the difference in medi- ans . ( b ) Consider the data in Example 5.9.2 . By substituting the ...
Page 523
... consider the behavior of a test under a sequence of local alternatives . In this section , we will often take 000 in hypotheses ( 10.2.2 ) . As noted before expression ( 10.2.9 ) , this is without loss of generality . For the hypotheses ...
... consider the behavior of a test under a sequence of local alternatives . In this section , we will often take 000 in hypotheses ( 10.2.2 ) . As noted before expression ( 10.2.9 ) , this is without loss of generality . For the hypotheses ...
Page 576
... consider a rank correlation coefficient based on a general score function . Let ( X1 , Y1 ) , ( X2 , Y2 ) , ... , ( Xn , Yn ) be a random sample from a bivariate continuous cdf F ( x , y ) . Let a ( i ) = p ( i / ( n + 1 ) ) where Σa ...
... consider a rank correlation coefficient based on a general score function . Let ( X1 , Y1 ) , ( X2 , Y2 ) , ... , ( Xn , Yn ) be a random sample from a bivariate continuous cdf F ( x , y ) . Let a ( i ) = p ( i / ( n + 1 ) ) where Σa ...
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