Related papers: Sharp Debiasing for Smooth Functional Estimation i…

We study the non-parametric estimation of the value ${\theta}(f )$ of a linear functional evaluated at an unknown density function f with support on $R_+$ based on an i.i.d. sample with multiplicative measurement errors. The proposed…

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…

In this paper the notion of an abstract square function (estimate) is introduced as an operator X to gamma (H; Y), where X, Y are Banach spaces, H is a Hilbert space, and gamma(H; Y) is the space of gamma-radonifying operators. By the…

In this paper, we propose a new regularization technique called "functional SCAD". We then combine this technique with the smoothing spline method to develop a smooth and locally sparse (i.e., zero on some sub-regions) estimator for the…

In this paper, we present a stochastic gradient algorithm for minimizing a smooth objective function that is an expectation over noisy cost samples, and only the latter are observed for any given parameter. Our algorithm employs a gradient…

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,…

Let $X$ be a centered Gaussian random variable in a separable Hilbert space ${\mathbb H}$ with covariance operator $\Sigma.$ We study a problem of estimation of a smooth functional of $\Sigma$ based on a sample $X_1,\dots ,X_n$ of $n$…

The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…

Given a smooth function $f$, we develop a general approach to turn Monte Carlo samples with expectation $m$ into an unbiased estimate of $f(m)$. Specifically, we develop estimators that are based on randomly truncating the Taylor series…

We study distribution-free nonparametric regression following a notion of average smoothness initiated by Ashlagi et al. (2021), which measures the "effective" smoothness of a function with respect to an arbitrary unknown underlying…

We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth…

We deal with the problem of gradient estimation for stochastic differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. Stochastic smoothing conventionally perturbs the input of a…

Consider an open set $\mathbb{D}\subseteq\mathbb{R}^n$, equipped with a probability measure $\mu$. An important characteristic of a smooth function $f:\mathbb{D}\rightarrow\mathbb{R}$ is its \emph{second-moment matrix} $\Sigma_{\mu}:=\int…

We study the convergence of $Z$-estimators $\widehat \theta(\eta)\in \mathbb R^p$ for which the objective function depends on a parameter $\eta$ that belongs to a Banach space $\mathcal H$. Our results include the uniform consistency over…

We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…

We characterize the class of separable Banach spaces $X$ such that for every continuous function $f:X\to\mathbb{R}$ and for every continuous function $\epsilon:X\to\mathbb(0,+\infty)$ there exists a $C^1$ smooth function $g:X\to\mathbb{R}$…

Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…

Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of…

We consider a spatial functional linear regression, where a scalar response is related to a square integrable spatial functional process. We use a smoothing spline estimator for the functional slope parameter and establish a finite sample…

This work extends local linear regression to Banach space-valued time series for estimating smoothly varying means and their derivatives in non-stationary data. The asymptotic properties of both the standard and bias-reduced Jackknife…