Related papers: Minimax Estimation of Quadratic Fourier Functional…
For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the…
This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…
The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…
We investigate nonparametric estimation of sliced inverse regression (SIR) via the $k$-nearest neighbors approach with a kernel. An estimator of the covariance matrix of the conditional expectation of the explanatory random vector given the…
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…
In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of $p$-values under the null hypothesis and the other component $f$ is…
We provide a means of computing and estimating the asymptotic distributions of statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in…
This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…
Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…
This article investigates the eigenspectrum of the inner product-type kernel matrix $\sqrt{p} \mathbf{K}=\{f( \mathbf{x}_i^{\sf T} \mathbf{x}_j/\sqrt{p})\}_{i,j=1}^n $ under a binary mixture model in the high dimensional regime where the…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
We study the asymptotic error of score-based diffusion model sampling in large-sample scenarios from a non-parametric statistics perspective. We show that a kernel-based score estimator achieves an optimal mean square error of…
We discuss bilinear estimates of tempered distributions in the Fourier restriction spaces for the two-dimensional Sch\"odinger equation whose principal part is the d'Alembertian. We prove that the bilinear estimates hold if and only if the…
Non-parametric estimation of a convex discrete distribution may be of interest in several applications, such as the estimation of species abundance distribution in ecology. In this paper we study the least squares estimator of a discrete…
This paper considers the partially functional linear model (PFLM) where all predictive features consist of a functional covariate and a high dimensional scalar vector. Over an infinite dimensional reproducing kernel Hilbert space, the…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…
Covariate shift occurs when the distribution of input features differs between the training and testing phases. In covariate shift, estimating an unknown function's moment is a classical problem that remains under-explored, despite its…
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…