## 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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ancillary statistic ANOVA approximation Basu's Theorem Bayes estimator best unbiased estimator binomial distribution calculate compute conditional distribution confidence interval confidence set consider constant converges coverage probability decision rule defined definition degrees of freedom denote derived equal Example Exercise expected exponential family Find finite Fx(x gamma given hence hypothesis testing independent random variables Inequality inference integral joint pdf Lemma level a test likelihood function Likelihood Principle linear location-scale family marginal distribution marginal pdf mean and variance minimal sufficient statistic minimax Mx(t negative binomial normal distribution Note observed obtain order statistics parameter pdf or pmf Poisson Poisson(A population probability distribution problem Proof properties prove random sample random vector regression relationship risk function sample mean sample points sample space satisfies Show Sufficiency Principle sufficient statistic Suppose Theorem transformation values verify versus H Xn be iid zero