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A new approach to $L_2$-consistent estimation of a general density functional using $k$-nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function $f$ of the densities…

Statistics Theory · Mathematics 2022-03-14 J. Jon Ryu , Shouvik Ganguly , Young-Han Kim , Yung-Kyun Noh , Daniel D. Lee

The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…

Methodology · Statistics 2025-11-27 Ioannis Kalogridis , Stanislav Nagy

Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…

Machine Learning · Computer Science 2022-03-22 Nhat Ho , Koulik Khamaru , Raaz Dwivedi , Martin J. Wainwright , Michael I. Jordan , Bin Yu

This survey provides a self-contained account of $M$-estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying $M$-functionals and discuss their weak continuity and differentiability. This is…

Statistics Theory · Mathematics 2015-03-20 Lutz Duembgen , Markus Pauly , Thomas Schweizer

Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…

Statistics Theory · Mathematics 2022-01-14 Qin Fang , Shaojun Guo , Xinghao Qiao

Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…

Methodology · Statistics 2019-10-08 Vitaliy Oryshchenko , Richard J. Smith

Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…

Statistics Theory · Mathematics 2008-12-18 Ismael Castillo , Jean-Michel Loubes

Faithful representations of atomic environments and general models for regression can be harnessed to learn electron densities that are close to the ground state. One of the applications of data-derived electron densities is to orbital-free…

Materials Science · Physics 2019-03-01 Andrew T. Fowler , Chris J. Pickard , James A. Elliott

When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In…

Chemical Physics · Physics 2007-05-23 A. Daniel Boese , Jan M. L. Martin , Nicholas C. Handy

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

Information Theory · Computer Science 2021-11-29 Georg Pichler , Pablo Piantanida , Günther Koliander

We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function…

Statistics Theory · Mathematics 2022-08-23 Timothée Mathieu

For studies in reliability, biometry, and survival analysis, the length-biased distribution is often well-suited for certain natural sampling plans. In this paper, we study the strong uniform consistency of two nonparametric estimators for…

Methodology · Statistics 2025-09-22 Vaishnavi Pavithradas , Rajesh G

In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a…

Methodology · Statistics 2020-12-21 Meng Yuan , Chunlin Wang , Boxi Lin , Pengfei Li

Statistical dependence measures like mutual information is ideal for analyzing autoencoders, but it can be ill-posed for deterministic, static, noise-free networks. We adopt the variational (Gaussian) formulation that makes dependence among…

Machine Learning · Computer Science 2026-03-24 Bo Hu , Jose C Principe

Based on a quantum mechanical approach, we investigate moment- (or M-) indeterminate probability densities by way of the characteristic function and self-adjoint operators. The approach leads to new methods to construct classes of…

Probability · Mathematics 2023-02-14 Patrick Loughlin , Leon Cohen

We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For…

Statistics Theory · Mathematics 2016-03-30 Shashank Singh , Barnabás P óczos

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes $\{(Y_{i},\underline{X}_{i})\}$. We establish a strong uniform consistency rate for the Bahadur representation of…

Statistics Theory · Mathematics 2007-11-29 Efang Kong , Oliver Linton , Yingcun Xia

We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of…

Methodology · Statistics 2024-10-07 Pratim Guha Niyogi , Ping-Shou Zhong

Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…

Machine Learning · Statistics 2018-03-13 Dangna Li , Kun Yang , Wing Hung Wong

We propose a novel sampling-based federated learning framework for statistical inference on M-estimators with non-smooth objective functions, which frequently arise in modern statistical applications such as quantile regression and AUC…

Methodology · Statistics 2025-05-06 Xiudi Li , Lu Tian , Tianxi Cai