High-confidence Nonparametric Fixed-Width Uncertainty Intervals and Applications to Projected High-Dimensional Data and Common Mean Estimation
Sequential Analysis(2019)
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.
MoreTranslated text
Key words
Big data,data science,high-dimensional data,jackknife,sequential analysis,sequential sampling
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined