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最大似然估计量分布的一个公式AI 解读

Abstract A simple formula for the conditional distribution of the maximum likelihood estimator given a maximal ancillary statistic is discussed and exemplified. The formula is generally accurate to order $ O(n^{-1}) $ or even $ O(n^{-{3}/{2}}) $, and for many important models it is, in fact, exact. After some preliminary discussion of the formula and of certain relevant aspects of likelihood, the formula is used to motivate the definition of a modified profile likelihood…

最大似然估计量分布的一个公式AI 解读

A simple formula for the conditional distribution of the maximum likelihood estimator given a maximal ancillary statistic is discussed and exemplified. The formula is generally accurate to order O(n−θθl) or even O(n−θθ3/2), and for many important models it is, in fact, exact. After some preliminary discussion of the formula and of certain relevant aspects of likelihood, the formula is used to motivate the definition of a modified profile likelihood whose inferential…

Edgeworth 与鞍点近似及其统计应用AI 解读

Summary A simple exposition is given of Edgeworth and saddle-point approximations for some univariate, multivariate and conditional distributions. The application of these approximations to some problems of conditional statistical inference within the exponential family is illustrated. Examples connected with the time-dependent Poisson process, the von Mises distribution and with bioassay are among those studied in a little detail. Some general results are derived about…

满指数族似然函数的因子分解AI 解读

Summary Examples are presented of full exponential families for which the likelihood function factorizes into a product of functions in such a way that each of the factor functions depends on a subparameter only and these subparameters vary independently of each other. A number of results are then discussed, concerning the key case of just two factors, one being the marginal likelihood for a statistic u, the other the conditional likelihood given u. Any statistic u which…

可信度推断AI 解读

Summary A scheme for inference—plausibility theory—is proposed. It parallels likelihood theory, the analogue of the likelihood function L(ω) = p(t; ω) being the plausibility function π(ω) = p(t; ω)/supt p(t; ω), but likelihood and plausibility throw light on different aspects of the evidence in the data t. The ordinate test for significance (which rejects for small values of the probability (density) function, of a simple hypothesis), the maximum ordinate estimate (which…

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