Abstract

Nonparametric two-stage procedures to construct fixed-width confidence intervals are studied to quantify uncertainty. It is shown that the validity of the random central limit theorem (RCLT) accompanied by a consistent and asymptotically unbiased estimator of the asymptotic variance already guarantees consistency and first-order as well as second-order efficiency of the two-stage procedures. This holds under the common asymptotics where the length of the confidence interval tends toward 0 as well as under the novel proposed high-confidence asymptotics where the confidence level tends toward 1. The approach is motivated by and applicable to data analysis from distributed big data with nonnegligible costs of data queries. The following problems are discussed: Fixed-width intervals for the mean, for a projection when observing high-dimensional data, and for the common mean when using nonlinear common mean estimators under order constraints. The procedures are investigated by simulations and illustrated by a real data analysis.

摘要

研究了用于构造固定宽度置信区间的非参数两阶段过程，以量化不确定性。结果表明，随机中心极限定理（RCLT）的有效性以及渐近方差的一致且渐近无偏估计量已经保证了两阶段程序的一致性以及一阶和二阶效率。这在置信区间的长度趋于0的常见渐近性以及置信度趋向于1的新提出的高置信渐近性的情况下成立。不可忽略的数据查询成本。讨论了以下问题：均值的固定宽度间隔，用于观察高维数据时的投影，对于在阶数约束下使用非线性公共均值估计器的公共均值。该程序通过仿真进行研究，并通过实际数据分析进行说明。