Related papers: Error estimation in the method of quasi-optimal we…

Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…

In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction…

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use…

A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…

Cross-validation is a widely-used technique to estimate prediction error, but its behavior is complex and not fully understood. Ideally, one would like to think that cross-validation estimates the prediction error for the model at hand, fit…

Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. The conventional approach of model building…

One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…

Measurement error arises through a variety of mechanisms. A rich literature exists on the bias introduced by covariate measurement error and on methods of analysis to address this bias. By comparison, less attention has been given to errors…

We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of…

The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…

In healthcare applications, predictive uncertainty has been used to assess predictive accuracy. In this paper, we demonstrate that predictive uncertainty estimated by the current methods does not highly correlate with prediction error by…

Conformal prediction (CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We…

This paper analyzes several different biases that emerge from the (possibly) low-precision nonparametric ingredient in a semiparametric model. We show that both the variance part and the bias part of the nonparametric ingredient can lead to…

Assessing sensitivity to unmeasured confounding is an important step in observational studies, which typically estimate effects under the assumption that all confounders are measured. In this paper, we develop a sensitivity analysis…

Parameter estimates in misspecified models converge to pseudo-true parameter values, which minimize a population objective function. Pseudo-true values often differ from quantities of economic interest, raising questions of how, if at all,…

Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal…

In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple…

We consider the problem of efficient inference of the Average Treatment Effect in a sequential experiment where the policy governing the assignment of subjects to treatment or control can change over time. We first provide a central limit…

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…