English
Related papers

Related papers: Estimation Error: Distribution and Pointwise Limit…

200 papers

It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…

Statistics Theory · Mathematics 2021-01-08 Alexander Goldenshluger , Taeho Kim

Many practical problems are related to the pointwise estimation of dis- tribution functions when data contains measurement errors. Motivation for these problems comes from diverse fields such as astronomy, reliability, quality control,…

Methodology · Statistics 2012-02-21 I. Dattner , B. Reiser

Noise-contrastive estimation (NCE) is a statistically consistent method for learning unnormalized probabilistic models. It has been empirically observed that the choice of the noise distribution is crucial for NCE's performance. However,…

Machine Learning · Computer Science 2021-10-22 Bingbin Liu , Elan Rosenfeld , Pradeep Ravikumar , Andrej Risteski

We consider a stochastic optimization problem involving two random variables: a context variable $X$ and a dependent variable $Y$. The objective is to minimize the expected value of a nonlinear loss functional applied to the conditional…

Optimization and Control · Mathematics 2026-03-16 Noel Smith , Andrzej Ruszczynski

Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…

Information Theory · Computer Science 2010-04-21 Dongning Guo , Yihong Wu , Shlomo Shamai , Sergio Verdu

A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…

Methodology · Statistics 2022-09-15 Chao Ma , Lexing Ying

For normal canonical models with $X \sim N_p(\theta, \sigma^{2} I_{p}), \;\; S^{2} \sim \sigma^{2}\chi^{2}_{k}, \;{independent}$, we consider the problem of estimating $\theta$ under scale invariant squared error loss $\frac{\|d-\theta…

Statistics Theory · Mathematics 2012-04-30 Othmane Kortbi , Éric Marchand

Accurately forecasting the probability distribution of phenomena of interest is a classic and ever more widespread goal in statistics and decision theory. In comparison to point forecasts, probabilistic forecasts aim to provide a more…

Statistics Theory · Mathematics 2025-05-05 Erez Buchweitz , João Vitor Romano , Ryan J. Tibshirani

We propose a new approach for estimating the parameters of a probability distribution. It consists on combining two new methods of estimation. The first is based on the definition of a new distance measuring the difference between…

Methodology · Statistics 2008-12-30 Ahmed Guellil , Tewfik Kernane

We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…

Statistics Theory · Mathematics 2020-11-18 Jasper C. H. Lee , Paul Valiant

We consider the problem of regression learning for deterministic design and independent random errors. We start by proving a sharp PAC-Bayesian type bound for the exponentially weighted aggregate (EWA) under the expected squared empirical…

Applications · Statistics 2012-06-27 Arnak Dalalyan , Alexandre B. Tsybakov

We consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened, that is, less precise or contaminated predictors. Specifically, while…

Statistics Theory · Mathematics 2008-12-18 Aurore Delaigle , Peter Hall , Hans-Georg Müller

A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…

Probability · Mathematics 2021-09-14 Jaromir Sant , Paul A. Jenkins , Jere Koskela , Dario Spano

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…

Econometrics · Economics 2021-12-08 Koen Jochmans , Martin Weidner

This work proposes a Bayesian rule based on the mixture of a point mass function at zero and the logistic distribution to perform wavelet shrinkage in nonparametric regression models with stationary errors (with short or long-memory…

Methodology · Statistics 2024-04-24 Alex Rodrigo dos S. Sousa , Mauricio Zevallos

Expected improvement (EI) is one of the most widely used acquisition functions in Bayesian optimization (BO). Despite its proven success in applications for decades, important open questions remain on the theoretical convergence behaviors…

Machine Learning · Statistics 2025-02-13 Jingyi Wang , Haowei Wang , Nai-Yuan Chiang , Cosmin G. Petra

An approximate maximum likelihood method of estimation of diffusion parameters $(\vartheta,\sigma)$ based on discrete observations of a diffusion $X$ along fixed time-interval $[0,T]$ and Euler approximation of integrals is analyzed. We…

Statistics Theory · Mathematics 2018-08-21 Miljenko Huzak

A key problem in the theory of meta-learning is to understand how the task distributions influence transfer risk, the expected error of a meta-learner on a new task drawn from the unknown task distribution. In this paper, focusing on fixed…

Machine Learning · Statistics 2021-06-15 Mikhail Konobeev , Ilja Kuzborskij , Csaba Szepesvári

Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable…

Statistics Theory · Mathematics 2013-07-19 Susanne M. Schennach

Huber loss, its asymmetric variants and their associated functionals (here named Huber functionals) are studied in the context of point forecasting and forecast evaluation. The Huber functional of a distribution is the set of minimizers of…

Statistics Theory · Mathematics 2022-02-17 Robert J. Taggart