Related papers: Augmented Minimax Linear Estimation
Two popular approaches for relating correlated measurements of a non-Gaussian response variable to a set of predictors are to fit a marginal model using generalized estimating equations and to fit a generalized linear mixed model by…
This work aims to give non-asymptotic results for estimating the first principal component of a multivariate random process. We first define the covariance function and the covariance operator in the multivariate case. We then define a…
This paper presents a state estimation approach for an uncertain linear equation with a non-invertible operator in Hilbert space. The approach addresses linear equations with uncertain deterministic input and noise in the measurements,…
We consider inference procedures, conditional on an observed ancillary statistic, for regression coefficients under a linear regression setup where the unknown error distribution is specified nonparametrically. We establish conditional…
We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…
One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
In this work we study the semi-supervised framework of confidence set classification with controlled expected size in minimax settings. We obtain semi-supervised minimax rates of convergence under the margin assumption and a H{\"o}lder…
We propose a functional accelerated failure time model to characterize effects of both functional and scalar covariates on the time to event of interest, and provide regularity conditions to guarantee model identifiability. For efficient…
Many important quantities of interest are only partially identified from observable data: the data can limit them to a set of plausible values, but not uniquely determine them. This paper develops a unified framework for covariate-assisted…
The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient…
Let $Y\in\R^n$ be a random vector with mean $s$ and covariance matrix $\sigma^2P_n\tra{P_n}$ where $P_n$ is some known $n\times n$-matrix. We construct a statistical procedure to estimate $s$ as well as under moment condition on $Y$ or…
We delve into the estimation of the functional coefficients and inference for varying coefficient model. Applying Laguerre series, we develop an estimator for the vector of functional coefficients that attains asymptotically optimal…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
In applications it is common that the exact form of a conditional expectation is unknown and having flexible functional forms can lead to improvements. Series method offers that by approximating the unknown function based on $k$ basis…
Inference problems with incomplete observations often aim at estimating population properties of unobserved quantities. One simple way to accomplish this estimation is to impute the unobserved quantities of interest at the individual level…
In this article, we propose a penalized high dimensional semiparametric model average quantile prediction approach that is robust for forecasting the conditional quantile of the response. We consider a two-step estimation procedure. In the…
Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…
We propose a model averaging approach, combined with a partition and matching method to estimate the conditional average treatment effects under heteroskedastic error settings. The proposed approach has asymptotic optimality and consistency…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…