Related papers: Estimating a Function and Its Derivatives Under a …

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique…

This paper develops theory for feasible estimators of finite-dimensional parameters identified by general conditional quantile restrictions, under much weaker assumptions than previously seen in the literature. This includes instrumental…

We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $n$, the smoothing spline estimator can be expressed as a linear combination of $n$ basis functions,…

We propose an inference procedure for estimators defined by mathematical programming problems, focusing on the important special cases of linear programming (LP) and quadratic programming (QP). In these settings, the coefficients in both…

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…

The problem of testing hypothesis that a density function has no more than $\mu$ derivatives versus it has more than $\mu$ derivatives is considered. For a solution, the $L^2$ norms of wavelet orthogonal projections on some orthogonal…

We consider the problem of estimating smooth integrated functionals of a monotone nonincreasing density $f$ on $[0,\infty)$ using the nonparametric maximum likelihood based plug-in estimator. We find the exact asymptotic distribution of…

We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression…

Let $X^{(n)}$ be an observation sampled from a distribution $P_{\theta}^{(n)}$ with an unknown parameter $\theta,$ $\theta$ being a vector in a Banach space $E$ (most often, a high-dimensional space of dimension $d$). We study the problem…

We propose a new method for estimating the minimizer $\boldsymbol{x}^*$ and the minimum value $f^*$ of a smooth and strongly convex regression function $f$ from the observations contaminated by random noise. Our estimator $\boldsymbol{z}_n$…

Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…

Over the past decades, the concept "partial smoothness" has been playing as a powerful tool in several fields involving nonsmooth analysis, such as nonsmooth optimization, inverse problems and operation research, etc. The essence of partial…

In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…

We consider the regression model with errors-in-variables where we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f(X)+\xi, Z=X+\sigma\epsilon$, involving independent and unobserved random variables $X,\xi,\epsilon$. The density $g$ of…

This paper discusses the problem of estimating a stochastic signal from nonlinear uncertain observations with time-correlated additive noise described by a first-order Markov process. Random deception attacks are assumed to be launched by…

We consider the problem of optimizing the sum of a smooth, nonconvex function for which derivatives are unavailable, and a convex, nonsmooth function with easy-to-evaluate proximal operator. Of particular focus is the case where the smooth…

In practice, data often contain discrete variables. But most of the popular nonparametric estimation methods have been developed in a purely continuous framework. A common trick among practitioners is to make discrete variables continuous…

When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…

This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…

The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…