Related papers: Functional Adaptive Huber Linear Regression

This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We…

We consider the problem of estimating the value l({\phi}) of a linear functional, where the structural function {\phi} models a nonparametric relationship in presence of instrumental variables. We propose a plug-in estimator which is based…

In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…

Estimating linear regression using least squares and reporting robust standard errors is very common in financial economics, and indeed, much of the social sciences and elsewhere. For thick tailed predictors under heteroskedasticity this…

We propose simultaneous mean-variance regression for the linear estimation and approximation of conditional mean functions. In the presence of heteroskedasticity of unknown form, our method accounts for varying dispersion in the regression…

In performative Reinforcement Learning (RL), an agent faces a policy-dependent environment: the reward and transition functions depend on the agent's policy. Prior work on performative RL has studied the convergence of repeated retraining…

Our goal is to develop a Bayesian model averaging technique in linear regression models that accommodates heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in the presence of…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…

Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…

Beta regression models are widely used for modeling continuous data limited to the unit interval, such as proportions, fractions, and rates. The inference for the parameters of beta regression models is commonly based on maximum likelihood…

We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…

This paper introduces new empirical process tools for analyzing a broad class of statistical learning models under heavy-tailed noise and complex function classes. Our primary contribution is the derivation of two Dudley-type maximal…

We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal components based estimator for the…

Consider semiparametric estimation where a doubly robust estimating function for a low-dimensional parameter is available, depending on two working models. With high-dimensional data, we develop regularized calibrated estimation as a…

Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric…

We consider new formulations and methods for sparse quantile regression in the high-dimensional setting. Quantile regression plays an important role in many applications, including outlier-robust exploratory analysis in gene selection. In…

We develop a Fisher-consistent redescending robust estimator for the spatial scalar-on-function regression model, where a scalar response depends on both a functional predictor and a spatial autoregressive lag. Existing estimation…

Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…

We introduce a new model of linear regression for random functional inputs taking into account the first order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our…