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 505
... matrix A is idempotent if A2 = In Section 9.1 , we have already met some idempotent matrices . For example , the matrix I J of Example 9.8.1 is idempotent . Idempotent matrices possess some important characteristics . Suppose A is an ...
... matrix A is idempotent if A2 = In Section 9.1 , we have already met some idempotent matrices . For example , the matrix I J of Example 9.8.1 is idempotent . Idempotent matrices possess some important characteristics . Suppose A is an ...
Page 507
... matrix , B is an m × k matrix , and C is a k × n matrix , then tr ( ABC ) = tr ( BCA ) = tr ( CAB ) . ( c ) If A is a square matrix and if I is an orthogonal matrix , use the result of Part ( a ) to show that tr ( г'AF ) = trA . ( d ) A ...
... matrix , B is an m × k matrix , and C is a k × n matrix , then tr ( ABC ) = tr ( BCA ) = tr ( CAB ) . ( c ) If A is a square matrix and if I is an orthogonal matrix , use the result of Part ( a ) to show that tr ( г'AF ) = trA . ( d ) A ...
Page 650
... matrix onto the space VF VR . Proof : Let UR be an o.n. basis matrix for VR and let [ UR : U2 ] be an extension of it to an o.n. basis matrix for VF . Then clearly U2 is a basis matrix for VF VR and U2U2 is the projection matrix onto VF ...
... matrix onto the space VF VR . Proof : Let UR be an o.n. basis matrix for VR and let [ UR : U2 ] be an extension of it to an o.n. basis matrix for VF . Then clearly U2 is a basis matrix for VF VR and U2U2 is the projection matrix onto VF ...
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