Related papers: Optimal Nuisance Function Tuning for Estimating a …
The accuracy of a diagnostic test is typically characterised using the receiver operating characteristic (ROC) curve. Summarising indexes such as the area under the ROC curve (AUC) are used to compare different tests as well as to measure…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…
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…
We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted…
We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property…
We consider the problem of finding tuned regularized parameter estimators for linear models. We start by showing that three known optimal linear estimators belong to a wider class of estimators that can be formulated as a solution to a…
In many problems, a sensible estimator of a possibly multivariate monotone function may itself fail to be monotone. We study the correction of such an estimator obtained via projection onto the space of functions monotone over a finite grid…
The consistency of doubly robust estimators relies on consistent estimation of at least one of two nuisance regression parameters. In moderate to large dimensions, the use of flexible data-adaptive regression estimators may aid in achieving…
We propose a new procedure for inference on optimal treatment regimes in the model-free setting, which does not require to specify an outcome regression model. Existing model-free estimators for optimal treatment regimes are usually not…
We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in…
Constructing confidence intervals for the value of an (unknown) optimal treatment policy is a fundamental problem in causal inference. Insight into the optimal policy value can guide the development of reward-maximizing, individualized…
In precision medicine, one of the most important problems is estimating the optimal individualized treatment rules (ITR), which typically involves recommending treatment decisions based on fully observed individual characteristics of…
We establish a general statistical optimality theory for estimation problems where the target parameter is a linear functional of an unknown nuisance component that must be estimated from data. This formulation covers many causal and…
In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as…
Many causal estimands, such as average treatment effects under unconfoundedness, can be written as continuous linear functionals of an unknown regression function. We study a weighting estimator that sets weights by a minimax procedure:…
This study introduces a debiasing method for regression estimators, including high-dimensional and nonparametric regression estimators. For example, nonparametric regression methods allow for the estimation of regression functions in a…
Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which…
We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved…
This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation…