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We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…

Statistics Theory · Mathematics 2026-02-10 Jiming Jiang , Matt P. Wand , Swarnadip Ghosh

This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…

Statistics Theory · Mathematics 2007-11-30 Jean-Yves Brua

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

Statistics Theory · Mathematics 2012-11-26 Stefano Favaro , Antonio Lijoi , Igor Prünster

Discontinuity in density functions is of economic importance and interest. For instance, in studies on regression discontinuity designs, discontinuity in the density of a running variable suggests violation of the no-manipulation…

Statistics Theory · Mathematics 2016-08-02 Benedikt Funke , Masayuki Hirukawa

Modelling the first-order intensity function is one of the main aims in point process theory, and it has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate.…

Methodology · Statistics 2018-07-03 M. I. Borrajo , W. González-Manteiga , M. D. Martínez-Miranda

We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…

Statistics Theory · Mathematics 2025-01-17 Cristina Butucea , Alexander Meister , Angelika Rohde

The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper (2007) for estimation of unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk. It…

Statistics Theory · Mathematics 2008-12-18 Leonid Galtchouk , Serguey Pergamenshchikov

It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a…

Methodology · Statistics 2023-06-14 Aaron Hudson

Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…

Statistics Theory · Mathematics 2017-10-16 Jana Jankova , Sara van de Geer

The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are as follows: (1) the study is nonasymptotic, that is, the sample size is fixed and does not…

Statistics Theory · Mathematics 2013-03-06 Vladimir Spokoiny

Contrary to standard statistical models, unnormalised statistical models only specify the likelihood function up to a constant. While such models are natural and popular, the lack of normalisation makes inference much more difficult. Here…

Computation · Statistics 2014-12-01 Simon Barthelmé , Nicolas Chopin

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

Statistics Theory · Mathematics 2024-05-16 Lucas Reding , Andrés F. López-Lopera , François Bachoc

Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the…

Methodology · Statistics 2017-12-29 Achmad Choiruddin , Jean-François Coeurjolly , Frédérique Letué

We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…

Statistics Theory · Mathematics 2022-07-04 Teppei Ogihara

We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…

Probability · Mathematics 2018-05-28 Igor Honoré , Stephane Menozzi , Gilles Pagès

We construct uniform and point-wise asymptotic confidence sets for the single edge in an otherwise smooth image function which are based on rotated differences of two one-sided kernel estimators. Using methods from M-estimation, we show…

Statistics Theory · Mathematics 2019-03-26 Viktor Bengs , Matthias Eulert , Hajo Holzmann

In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…

Statistics Theory · Mathematics 2017-11-01 Zuofeng Shang , Guang Cheng

In this paper we study the consistency of different bootstrap procedures for constructing confidence intervals (CIs) for the unique jump discontinuity (change-point) in an otherwise smooth regression function in a stochastic design setting.…

Statistics Theory · Mathematics 2011-01-06 Emilio Seijo , Bodhisattva Sen

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

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…

Statistics Theory · Mathematics 2022-12-29 Bryon Aragam , Ruiyi Yang