Consistency of the jackknife-after-bootstrap variance estimator for the bootstrap quantiles of a studentized statistic

Studentized U-quantile processes under dependence with applications to change-point analysis

Many popular robust estimators are $U$-quantiles, most notably the Hodges-Lehmann location estimator and the $Q_n$ scale estimator. We prove a functional central limit theorem for the sequential $U$-quantile process without any moment assumptions and under weak short-range dependence conditions. We further devise an estimator for the long-run variance and show its consistency, from which the convergence of the studentized version of the sequential $U$-quantile process to a standard Brownian motion follows. This result can be used to construct CUSUM-type change-point tests based on $U$-quantile…

用于半参数推断的V折刀切法：方差估计、置信区间和同时置信带

The V-fold jackknife for semiparametric inference: variance estimation, confidence intervals, and simultaneous confidence bands

研究针对半参数推断开发V折刀切法，它计算高效且理论合理，仅需V次留一法重拟合，利用伪值经验离散度量化不确定性，给出有效置信区间和同时置信带，扩展理论到特定估计量，模拟证实其可靠推断。

Jackknife Model Averaging for Composite Quantile Regression

Model averaging considers the model uncertainty and is an alternative to model selection. In this paper, we propose a frequentist model averaging estimator for composite quantile regressions. In recent years, research on these topics has been added as a separate method, but no study has investigated them in combination. We apply a delete-one cross-validation method to estimate the model weights, and prove that the jackknife model averaging estimator is asymptotically optimal in terms of minimizing out-of-sample composite final prediction error. Simulations are conducted to demonstrate the good…

CLT 与 Edgeworth 展开：m-out-of-n 自助法对学生化中位数估计量的应用

CLT and Edgeworth Expansion for m-out-of-n Bootstrap Estimators of The Studentized Median

本文为 m-out-of-n 自助法估计样本分位数建立了无参数保证，证明中心极限定理并给出 Edgeworth 展开与 Berry-Esseen 界，且应用于 MCMC 和 MDP 等现代任务。

Predictive inference with the jackknife+

This paper introduces the jackknife+, which is a novel method for constructing predictive confidence intervals. Whereas the jackknife outputs an interval centered at the predicted response of a test point, with the width of the interval determined by the quantiles of leave-one-out residuals, the jackknife+ also uses the leave-one-out predictions at the test point to account for the variability in the fitted regression function. Assuming exchangeable training samples, we prove that this crucial modification permits rigorous coverage guarantees regardless of the distribution of the data points, …

Jackknife Partially Linear Model Averaging for the Conditional Quantile Prediction

Estimating the conditional quantile of the interested variable with respect to changes in the covariates is frequent in many economical applications as it can offer a comprehensive insight. In this paper, we propose a novel semiparametric model averaging to predict the conditional quantile even if all models under consideration are potentially misspecified. Specifically, we first build a series of non-nested partially linear sub-models, each with different nonlinear component. Then a leave-one-out cross-validation criterion is applied to choose the model weights. Under some regularity conditio…