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对称性下t统计量尾概率的最优阶不等式
An inequality for the tail probabilites of the t statistic under the hypotheses of independence and symmetry is presented and is shown to yield bounds for the upper quantiles that approach those of the normal (and hence the smallest of such bounds possible) as the corresponding upper tail area tends to 0.
局部最强序贯 t 检验的一个候选方案
A sequential t test is presented based on a simple function of the usual student t statistic. This function is shown to possess the martingale property that, conditional on previous observations, the expectation of a future increment is zero. This property facilitates calculation of error probabilities and expected sample sizes, so that the resulting test is relatively straightforward to use. It is argued that this test behaves in a manner similar to that of the locally most…
正态均值混合分布的估计及其在复合决策问题中的应用
A procedure for estimating the mixing distribution for a normal mean is presented. The estimator is shown to be consistent regardless of the mixing distribution, and it is suggested that the estimation techniques may be applied in a similar manner to estimate mixing distributions for a wide class of location parameter families. Implied marginal density and derivative estimates for the normal case are shown to be consistent, converging at near-optimal rates. In addition,…
非参数 t 临界值表的界
A simple inequality for bounding the tail probabilities of normalized sums of independent, symmetric random variables is used to produce bounds on the tail probabilities of the usual Student t statistic under the same hypothesis. The relative difference between the resulting t scores and the usual ones is shown to be asymptotically negligible as the sample size increases and the tail probability decreases to zero. As an example, a table of upper 0·025 cutoff bounds is given…