Related papers: Robust Optimal Designs when Missing Data Happen at…
Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found…
Selective prediction, where a model has the option to abstain from making a decision, is crucial for machine learning applications in which mistakes are costly. In this work, we focus on distributional regression and introduce a framework…
We study multivariate linear regression under Gaussian covariates in two settings, where data may be erased or corrupted by an adversary under a coordinate-wise budget. In the incomplete data setting, an adversary may inspect the dataset…
The subject of this work is two treatment groups random coefficient regression models, in which observational units receive some group-specific treatments. We provide A- and D-optimality criteria for the estimation of the fixed parameter…
This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…
Modern empirical work in Regression Discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment effect…
In this paper optimal experimental designs for inverse quadratic regression models are determined. We consider two different parameterizations of the model and investigate local optimal designs with respect to the $c$-, $D$- and…
Many existing methods for constructing optimal split-plot designs, such as D-optimal designs, only focus on minimizing the variances and covariances of the estimation for the fitted model. However, the underlying true model is usually…
We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to…
We consider the equivalent problems of estimating the residual variance, the proportion of explained variance $\eta$ and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand…
Optimal designs for generalized linear models require a prior knowledge of the regression parameters. At certain values of the parameters we propose particular assumptions which allow to derive a locally optimal design for a model without…
This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some of covariates. The target is a marginal location parameter which is given through an $M-$functional.…
This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the…
Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard…
In our paper, we focus on robust variable selection for missing data and measurement error. Missing data and measurement errors can lead to confusing data distribution. We propose an exponential loss function with a tuning parameter to…
We construct confidence sets for the regression function in nonparametric binary regression with an unknown design density. These confidence sets are adaptive in $L^2$ loss over a continuous class of Sobolev type spaces. Adaptation holds in…
Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…
We study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings. Our sharp lower bounds shed light on the possibility (or impossibility) of adapting…
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of…
We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…