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The Infinitesimal Jackknife is a general method for estimating variances of parametric models, and more recently also for some ensemble methods. In this paper we extend the Infinitesimal Jackknife to estimate the covariance between any two…

Machine Learning · Statistics 2022-09-02 Indrayudh Ghosal , Yunzhe Zhou , Giles Hooker

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…

Statistics Theory · Mathematics 2022-06-08 Jing Lv

We use the jackknife to bias correct the log-periodogram regression(LPR) estimator of the fractional parameter in a stationary fractionally integrated model. The weights for the jackknife estimator are chosen in such a way that bias…

Methodology · Statistics 2020-10-19 Kanchana Nadarajah , Gael M Martin , Donald S Poskitt

We study the variability of predictions made by bagged learners and random forests, and show how to estimate standard errors for these methods. Our work builds on variance estimates for bagging proposed by Efron (1992, 2012) that are based…

Machine Learning · Statistics 2014-04-01 Stefan Wager , Trevor Hastie , Bradley Efron

Linear mixed-effects models are widely used in analyzing repeated measures data, including clustered and longitudinal data, where inferences of both fixed effects and variance components are of importance. Unlike the fixed effect inference…

Methodology · Statistics 2022-08-31 J. Zhang , W. Guo , J. S. Carpenter , Andrew Leroux , K. R. Merikangas , N. G. Martin , I. B. Hickie , H. Shou , H. Li

Empirical likelihood method has been applied to dependent observations by Monti (1997) through the Whittle's estimation method. Similar asymptotic distribution of the empirical likelihood ratio statistic for stationary time series has been…

Methodology · Statistics 2016-03-01 Ramadha D. Piyadi Gamage , Wei Ning , Arjun K. Gupta

Ensemble learning is widely used in applications to make predictions in complex decision problems---for example, averaging models fitted to a sequence of samples bootstrapped from the available training data. While such methods offer more…

Methodology · Statistics 2020-11-13 Byol Kim , Chen Xu , Rina Foygel Barber

Conformal regression provides prediction intervals with global coverage guarantees, but often fails to capture local error distributions, leading to non-homogeneous coverage. We address this with a new adaptive method based on rescaling…

Machine Learning · Computer Science 2023-06-01 Nicolas Deutschmann , Mattia Rigotti , Maria Rodriguez Martinez

We consider an empirical likelihood framework for inference for a statistical model based on an informative sampling design. Covariate information is incorporated both through the weights and the estimating equations. The estimator is based…

Methodology · Statistics 2019-05-03 Sanjay Chaudhuri , Mark S. Handcock

The frequentist variability of Bayesian posterior expectations can provide meaningful measures of uncertainty even when models are misspecified. Classical methods to asymptotically approximate the frequentist covariance of Bayesian…

Methodology · Statistics 2024-06-28 Ryan Giordano , Tamara Broderick

Conformal prediction methods enjoy strong theoretical and empirical predictive inference performance, provided the data is exchangeable, and predictors are trained in a memoryless fashion. However, these assumptions and constraints are…

Machine Learning · Statistics 2026-05-29 Hanyang Jiang , Rina Foygel Barber , Ashwin Pananjady , Yao Xie

Inferential models (IMs) are data-dependent, imprecise-probabilistic structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncertainty quantification for inference and on its reliability…

Statistics Theory · Mathematics 2026-05-01 Ryan Martin , Shih-Ni Prim , Jonathan Williams

We develop a concept of weak identification in linear IV models in which the number of instruments can grow at the same rate or slower than the sample size. We propose a jackknifed version of the classical weak identification-robust…

Econometrics · Economics 2021-10-06 Anna Mikusheva , Liyang Sun

This paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain. Unlike the frequency domain empirical likelihood (FDEL) methodology for time series (on a regular grid), the formulation of…

Statistics Theory · Mathematics 2015-03-18 Soutir Bandyopadhyay , Soumendra N. Lahiri , Daniel J. Nordman

The error or variability of machine learning algorithms is often assessed by repeatedly re-fitting a model with different weighted versions of the observed data. The ubiquitous tools of cross-validation (CV) and the bootstrap are examples…

Methodology · Statistics 2020-02-10 Ryan Giordano , Will Stephenson , Runjing Liu , Michael I. Jordan , Tamara Broderick

We prove ratio-consistency of the jackknife variance estimator, and certain variants, for a broad class of generalized U-statistics whose variance is asymptotically dominated by their H\'ajek projection, with the classical fixed-order case…

Statistics Theory · Mathematics 2025-09-17 Jakob R. Juergens

In the literature, quite a few measures have been proposed for quantifying the deviation of a probability distribution from symmetry. The most popular of these skewness measures are based on the third centralized moment and on quantiles.…

Statistics Theory · Mathematics 2019-08-23 Andreas Eberl , Bernhard Klar

Empirical likelihood method has been applied to short-memory time series models by Monti (1997) through the Whittle's estimation method. Yau (2012) extended this idea to long-memory time series models. Asymptotic distributions of the…

Methodology · Statistics 2016-04-22 Ramadha D. Piyadi Gamage , Wei Ning , Arjun K. Gupta

Sequential trial emulation (STE) is an approach to estimating causal treatment effects by emulating a sequence of target trials from observational data. In STE, inverse probability weighting is commonly utilised to address time-varying…

Methodology · Statistics 2025-07-10 Juliette M. Limozin , Shaun R. Seaman , Li Su

Energy distance is a statistical distance between the distributions of random variables, which characterizes the equality of the distributions. Utilizing the energy distance, we develop a nonparametric test for the diagonal symmetry, which…

Methodology · Statistics 2019-08-20 Yongli Sang , Xin Dang