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Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…
This study introduces a debiasing method for regression estimators, including high-dimensional and nonparametric regression estimators. For example, nonparametric regression methods allow for the estimation of regression functions in a…
We study counterfactual regression, which aims to map input features to outcomes under hypothetical scenarios that differ from those observed in the data. This is particularly useful for decision-making when adapting to sudden shifts in…
Regressing a scalar response on a random function is nowadays a common situation. In the nonparametric setting, this paper paves the way for making the local linear regression based on a projection approach a prominent method for solving…
Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for non Euclidean data. Circular data is a classic example, but so is data in…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
Estimating function inference is indispensable for many common point process models where the joint intensities are tractable while the likelihood function is not. In this paper we establish asymptotic normality of estimating function…
For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…
We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression…
In a nonparametric instrumental regression model, we strengthen the conventional moment independence assumption towards full statistical independence between instrument and error term. This allows us to prove identification results and…
This paper derives limit properties of nonparametric kernel regression estimators without requiring existence of density for regressors in $\mathbb{R}^{q}.$ In functional regression limit properties are established for multivariate…
We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…
Existing identification and estimation methods for semiparametric sample selection models rely heavily on exclusion restrictions. However, it is difficult in practice to find a credible excluded variable that has a correlation with…
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
Uniform asymptotic confidence bands for a multivariate regression function in an inverse regression model with a convolution-type operator are constructed. The results are derived using strong approximation methods and a limit theorem for…
Suppose that $n$ statistical units are observed, each following the model $Y(x_j)=m(x_j)+ \epsilon(x_j),\, j=1,...,N,$ where $m$ is a regression function, $0 \leq x_1 <...<x_N \leq 1$ are observation times spaced according to a sampling…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only…
This paper explores the identification and estimation of nonseparable panel data models. We show that the structural function is nonparametrically identified when it is strictly increasing in a scalar unobservable variable, the conditional…