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局部备择假设下基于似然的 p 值分布AI 解读

We consider inference on a scalar parameter of interest in the presence of a nuisance parameter, using a likelihood-based statistic which is asymptotically normally distributed under the null hypothesis. Higher-order expansions are used to compare the repeated sampling distribution, under a general contiguous alternative hypothesis, of |$p$|-values calculated from the asymptotic normal approximation to the null sampling distribution of the statistic with the distribution of |…

标量参数的方差稳定化AI 解读

Summary We present a variance stabilizing transformation for inference about a scalar parameter that is estimated by a function of a multivariate M-estimator. The transformation proposed is automatic, computationally simple and can be applied quite generally. Though it is based on an intuitive notion and entirely empirical, the transformation is shown to have an appropriate justification in providing variance stabilization when viewed from both parametric and nonparametric…

构造双重自助法置信区间时插值的重要性AI 解读

Summary We show that, in the context of double-bootstrap confidence intervals, linear interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Intervals that are indistinguishable in terms of coverage error with theoretical, infinite simulation, double-bootstrap confidence intervals may be obtained at substantially less computational expense than by using the standard Monte Carlo…

标准化统计量分布函数的估计AI 解读

Summary For estimating the distribution of a standardized statistic, the bootstrap estimate is known to be local asymptotic minimax. Various computational techniques have been developed to improve on the simulation efficiency of uniform resampling, the standard Monte Carlo approach to approximating the bootstrap estimate. Two new approaches are proposed which give accurate yet simple approximations to the bootstrap estimate. The second of the approaches even improves the…

SUMMARY A version of the sequential probability ratio test for testing simultaneously a set of nested hypotheses is developed. This procedure is then applied to define a sequential procedure of sampling at the inner level of the two nested levels of resampling required by Monte Carlo construction of an iterated bootstrap percentile method confidence interval. The sequential resampling scheme reduces very significantly the computational demands of construction of the iterated…

迭代 Bootstrap 置信区间的渐近近似AI 解读

An iterated bootstrap confidence interval requires an additive correction to be made to the nominal coverage level of an uncorrected interval. Such correction is usually performed using a computationally intensive Monte Carlo simulation involving two nested levels of bootstrap sampling. Asymptotic expansions of the required correction and the iterated interval endpoints are used to provide two new computationally efficient methods for constructing an approximation to the…

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快速且准确的近似双重自助法置信区间AI 解读

We propose two new methods for the construction of approximate iterated bootstrap confidence intervals. Our methods follow a saddlepoint approach, but employ approximate rather than exact solutions to the nonlinear saddlepoint equations that arise in applying that technique. The main advantages of the new techniques are that they yield confidence intervals with high coverage accuracy in small- to moderately-sized samples and that they achieve this accuracy with very…