A text that stresses the general concepts of the theory of statistics Theoretical Statistics provides a systematic statement of the theory of statistics, emphasizing general concepts rather than mathematical rigor. Chapters 1 through 3 provide an overview of statistics and discuss some of the basic philosophical ideas and problems behind statistical procedures. Chapters 4 and 5 cover hypothesis testing with simple and null hypotheses, respectively. Subsequent chapters discuss non-parametrics, interval estimation, point estimation, asymptotics, Bayesian procedure, and deviation theory. Student familiarity with standard statistical techniques is assumed.
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Pure significance tests
simple null hypotheses
composite null hypotheses
Point estimation 250
Bibliographic notes 272
Further results and exercises 459
alternative analysis ancillary statistic apply approach approximation arbitrary argument asymptotically normal Bayes Bayesian bution calculation Chapter chi-squared distribution components conditional distribution conﬁdence confidence limits confidence region consider consistent corresponding critical region decision rule defined degrees of freedom denote depend derived discussion distri efficient score equivalent Example expected utility exponential family ﬁrst fY(y given independent large-sample likelihood function likelihood principle likelihood ratio locally most powerful m.l. ratio maximal invariant methods multivariate normal distribution nuisance parameters null hypothesis observations obtained optimal order statistics parameter space parameter values particular permutation point estimation Poisson distribution possible posterior distribution powerful test principle prior density prior distribution probability procedure properties random variables ratio test regression risk function sample Section signiﬁcance significance test similar regions simple situation squared error sufficient statistic Suppose test statistic theorem theory transformations unbiased estimate uniformly most powerful unknown parameters vector Yn are i.i.d. zero