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非标准条件下基于 M 估计量的 Bootstrap 置信域AI 解读

Suppose that a confidence region is desired for a subvector $\theta $ of a multidimensional parameter $\xi =(\theta ,\psi )$, based on an M-estimator $\hat{\xi }_{n}=(\hat{\theta }_{n},\hat{\psi }_{n})$ calculated from a random sample of size $n$. Under nonstandard conditions $\hat{\xi }_{n}$ often converges at a nonregular rate $r_{n}$, in which case consistent estimation of the distribution of $r_{n}(\hat{\theta }_{n}-\theta )$, a pivot commonly chosen for confidence…

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 |…

总体分位数的校准插值置信区间AI 解读

Beran & Hall's (1993) simple linear interpolation provides a very convenient approach for constructing nonparametric confidence intervals for population quantiles based on a random sample of size n. We show that the coverage error of the interpolated interval, which is of order O(n−1), can be improved upon by calibrating the nominal coverage level. Three distinct methods of calibration are considered. The analytical and Monte Carlo methods succeed in reducing the order of…

总体分位数的迭代平滑自助法置信区间AI 解读

This paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap-t confidence intervals for population quantiles, and establishes the optimal kernel bandwidths at various stages of the smoothing procedures. The conventional smoothed bootstrap and bootstrap-t methods have been known to yield one-sided coverage errors of orders O(n−1/2) and o(n−2/3), respectively, for intervals based on the sample quantile of a…

一类 m out of n Bootstrap 置信区间AI 解读

Summary It is widely known that bootstrap failure can often be remedied by using a technique known as the ‘m out of n’ bootstrap, by which a smaller number, m say, of observations are resampled from the original sample of size n. In successful cases of the bootstrap, the m out of n bootstrap is often deemed unnecessary. We show that the problem of constructing nonparametric confidence intervals is an exceptional case. By considering a new class of m out of n bootstrap…

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…