Statistical InferenceDiscusses both theoretical statistics and the practical applications of the theoretical developments. Includes a large numer of exercises covering both theory and applications. |
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Page 169
... denote multiple variates . Thus , we write X to denote the random variables X1 , ... , Xn , and x to denote the sample x1 , .. Xn . = The random vector X ( X1 , ... , Xn ) has a sample space that is a subset of R " . If ( X1 , ... , Xn ) ...
... denote multiple variates . Thus , we write X to denote the random variables X1 , ... , Xn , and x to denote the sample x1 , .. Xn . = The random vector X ( X1 , ... , Xn ) has a sample space that is a subset of R " . If ( X1 , ... , Xn ) ...
Page 246
... denote multiple variates , so X denotes the random variables X1 , ... , Xn , and denotes the sample 1 , ... , n . Any statistic , T ( X ) , defines a form of data reduction or data summary . An experimenter who uses only the observed ...
... denote multiple variates , so X denotes the random variables X1 , ... , Xn , and denotes the sample 1 , ... , n . Any statistic , T ( X ) , defines a form of data reduction or data summary . An experimenter who uses only the observed ...
Page 461
... denoted by . Thus the model is a set { ƒ ( x | 0 ) : 0 € } where each f ( x0 ) is a pdf or pmf on X. After the data X = x are observed , a decision regarding is made . The set of allowable decisions is the action space , denoted by A ...
... denoted by . Thus the model is a set { ƒ ( x | 0 ) : 0 € } where each f ( x0 ) is a pdf or pmf on X. After the data X = x are observed , a decision regarding is made . The set of allowable decisions is the action space , denoted by A ...
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Common terms and phrases
a₁ acceptance region ancillary statistic ANOVA approximation Bayes estimator Bayes rule best unbiased estimator binomial calculate conditional confidence interval confidence set constant coverage probability decision rule defined definition denote derived equal Example Exercise exponential Find Fx(x given hence hypothesis testing independent Inequality inference integral interval estimator joint pdf Lemma Let X1 level a test likelihood function Likelihood Principle linear loss function mean and variance method minimal sufficient statistic minimax Neyman-Pearson Lemma normal observed oneway ANOVA parameter pdf or pmf point estimation population power function Proof prove random sample random variable regression rejection region risk function sample mean sample points sample space satisfies Section Show sufficient statistic Suppose Theorem Type I Error UMP level unbiased estimator verify versus H₁ Xn be iid Y₁ zero σ²