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客观贝叶斯、条件推断与有符号平方根似然比统计量AI 解读

Bayesian properties of the signed root likelihood ratio statistic are analysed. Conditions for first-order probability matching are derived by the examination of the Bayesian posterior and frequentist means of this statistic. Second-order matching conditions are shown to arise from matching of the Bayesian posterior and frequentist variances of a mean-adjusted version of the signed root statistic. Conditions for conditional probability matching in ancillary statistic models…

指数族中的客观贝叶斯与条件推断AI 解读

Objective Bayes methodology is considered for conditional frequentist inference about a canonical parameter in a multi-parameter exponential family. A condition is derived under which posterior Bayes quantiles match the conditional frequentist coverage to a higher-order approximation in terms of the sample size. This condition is on the model, not on the prior, and it ensures that any first-order probability matching prior in the unconditional sense automatically yields…

指数族推断中无条件参数自助法的条件性质AI 解读

Higher-order inference about a scalar parameter in the presence of nuisance parameters can be achieved by bootstrapping, in circumstances where the parameter of interest is a component of the canonical parameter in a full exponential family. The optimal test, which is approximated, is a conditional one based on conditioning on the sufficient statistic for the nuisance parameter. A bootstrap procedure that ignores the conditioning is shown to have desirable conditional…

蒙特卡洛近似对双重 Bootstrap 置信区间覆盖误差的影响AI 解读

Summary A double-bootstrap confidence interval must usually be approximated by a Monte Carlo simulation, consisting of two nested levels of bootstrap sampling. We provide an analysis of the coverage accuracy of the interval which takes account of both the inherent bootstrap and Monte Carlo errors. The analysis shows that, by a suitable choice of the number of resamples drawn at the inner level of bootstrap sampling, we can reduce the order of coverage error. We consider also…

L1回归估计量分布的解析与自助法近似AI 解读

Edgeworth and bootstrap approximations to estimator distributions in L1 regression are described. Analytic approximations based on Edgeworth expansions that mix lattice and nonlattice components and allow for an intercept term in the regression are developed under mild conditions, which do not even require a density for the error distribution. Under stronger assumptions on the error distribution, the Edgeworth expansion assumes a simpler form. Bootstrap approximations are…

摘要暂缺

学生化均值的鞍点近似及其 Bootstrap 应用AI 解读

A saddlepoint technique is used to approximate to the density and tail probability of the studentized mean of a random sample. The motivation was to replace bootstrapping of the studentized mean in the way Davison & Hinkley (1988) used the saddlepoint approximation for the unstudentized mean. The method involves first obtaining a bivariate saddlepoint approximation, then, after a nonlinear transformation, integrating out an unwanted variable either numerically or by a…

学生化均值的鞍点近似及其自助法应用AI 解读

A saddlepoint technique is used to approximate to the density and tail probability of the studentized mean of a random sample. The motivation was to replace bootstrapping of the studentized mean in the way Davison & Hinkley (1988) used the saddlepoint approximation for the unstudentized mean. The method involves first obtaining a bivariate saddlepoint approximation, then, after a nonlinear transformation, integrating out an unwanted variable either numerically or by a…

平滑 Bootstrap 的替代方法AI 解读

SUMMARY Bootstrap estimation of simple population functionals is considered. The smoothed bootstrap (Efron, 1979, 1982) is compared with an alternative estimation procedure based on resampling ideas of Kendall and Kendall (1980). Specific examples of the estimation problem are considered, showing that the competing estimators may display different qualitative behaviours.

Bootstrap偏差AI 解读

Use of the bootstrap in estimation of the sampling distribution of a pivot is considered for two simple situations. It is shown by a simulation study that in each case the bootstrap is noticeably biased for small sample sizes. The techniques of computer algebra are used to obtain an exact assessment of the bias in both problems and an approximate theoretical analysis based on saddlepoint approximation is presented.

关于相关系数自助法的说明AI 解读

Smoothed bootstrap estimation of the sampling standard deviation of the variance-stabilized correlation coefficient is reconsidered. An approximation to the mean squared error of the bootstrap estimator is obtained and an empirical procedure for choosing the degree of smoothing in the bootstrap estimation is presented. Performance of the procedure is examined in a simulation study.

相关系数自助法估计的一则札记AI 解读

Smoothed bootstrap estimation of the sampling standard deviation of the variance-stabilized correlation coefficient is reconsidered. An approximation to the mean squared error of the bootstrap estimator is obtained and an empirical procedure for choosing the degree of smoothing in the bootstrap estimation is presented. Performance of the procedure is examined in a simulation study.

Bootstrap：是否应当平滑？AI 解读

The bootstrap and smoothed bootstrap are considered as alternative methods of estimating properties of unknown distributions such as the sampling error of parameter estimates. Criteria are developed for determining whether it is advantageous to use the smoothed bootstrap rather than the standard bootstrap. Key steps in the argument leading to these criteria include the study of the estimation of linear functionals of distributions and the approximation of general functionals…