Related papers: Credible intervals and bootstrap confidence interv…
We consider the nonparametric multivariate isotonic regression problem, where the regression function is assumed to be nondecreasing with respect to each predictor. Our goal is to construct a Bayesian credible interval for the function…
We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…
Bootstrap smoothed (bagged) estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. Efron, 2014, derived a widely applicable formula for a delta method approximation to the standard…
This paper introduces new methods for constructing prediction intervals using quantile-based techniques. The procedures are developed for both classical (homoscedastic) autoregressive models and modern quantile autoregressive models. They…
In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate $n^{1/3}$. The Grenander estimator, the nonparametric maximum…
Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this…
In modern experimental science, there is a common problem of estimating the coefficients of a linear regression in a context where the variables of interest cannot be observed simultaneously. When there is a categorical variable that is…
Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice.…
A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is…
The bootstrap is a versatile inference method that has proven powerful in many statistical problems. However, when applied to modern large-scale models, it could face substantial computation demand from repeated data resampling and model…
Predictive inference under a general regression setting is gaining more interest in the big-data era. In terms of going beyond point prediction to develop prediction intervals, two main threads of development are conformal prediction and…
Bootstrap inference is a powerful tool for obtaining robust inference for quantiles and difference-in-quantiles estimators. The computationally intensive nature of bootstrap inference has made it infeasible in large-scale experiments. In…
This paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap-t confidence intervals for population quantiles, and establishes the optimal kernel bandwidths at various…
We study an AMOC time series model with an abrupt change in the mean and dependent errors that fulfill certain mixing conditions. We obtain confidence intervals for the unknown change-point via bootstrapping methods. Precisely we use a…
Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…
The age of big data has produced data sets that are computationally expensive to analyze and store. Algorithmic leveraging proposes that we sample observations from the original data set to generate a representative data set and then…
In this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a…
We consider the problem of finding confidence intervals for the risk of forecasting the future of a stationary, ergodic stochastic process, using a model estimated from the past of the process. We show that a bootstrap procedure provides…