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Minimum Variance Unbiased Estimation
Simultaneous Estimation of Several Parameters
Consistent Asymptotically Normal Estimators
Method of Maximum Likelihood
Tests of HypothesesI
asymptotic distribution asymptotic variance Cauchy distribution conditional distribution consider consistent estimator Cramer family critical region CRLB defined denote depend determine distribution with pdf error Example exists exponential distribution exponential with mean Fisher information Fisher information matrix hypotheses implies independent interval joint pdf Laplace large sample level a test likelihood equation log L(x M-optimal maximum likelihood method of moments minimal sufficient statistic MP test multinomial distribution MVUE N-P lemma normal Note null hypothesis observed obtain order statistic parameter exponential family Pareto distribution pdf belonging pdf f(x Pearson percentile pivotal quantity Poisson Poisson distribution power function probability problem random sample Rao-Blackwellization regularity conditions reject H0 SELCI solution test is given testing H0 Theorem transformation type I error UMP level unbiased estimator variance covariance matrix vector valued zero otherwise