Related papers: Confidence sets for nonparametric wavelet regressi…
We consider the problem of constructing honest and adaptive confidence sets in Lp-loss (with p>=1 and p < infinity) over sets of Sobolev-type classes, in the setting of non-parametric Gaussian regression. The objective is to adapt the…
In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…
We consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened, that is, less precise or contaminated predictors. Specifically, while…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions…
In a linear regression model of fixed dimension $p \leq n$, we construct confidence regions for the unknown parameter vector based on the Lasso estimator that uniformly and exactly hold the prescribed in finite samples as well as in an…
We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as $Z$-functionals. Our approach combines self-normalized statistics with a test…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
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 study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a…
A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by…
This paper addresses the problem of regularity properties of functions represented as an expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov norm with probability 1. Such representations are used to…
In order to certify performance and safety, feedback control requires precise characterization of sensor errors. In this paper, we provide guarantees on such feedback systems when sensors are characterized by solving a supervised learning…
We consider the statistical problem of estimating constituent curves from observations of their aggregated curves, referred to as \textit{aggregated functional data}, in models with strictly positive random errors following a Gamma…
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, 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…