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One-step ahead prediction for the multinomial model is considered. The performance of a predictive density is evaluated by the average Kullback-Leibler divergence from the true density to the predictive density. Asymptotic approximations of…

Statistics Theory · Mathematics 2021-05-27 Fumiyasu Komaki

Given a random sample from a distribution with density function that depends on an unknown parameter $\theta$, we are interested in accurately estimating the true parametric density function at a future observation from the same…

Statistics Theory · Mathematics 2009-09-29 Mihaela Aslan

We consider estimating the predictive density under Kullback-Leibler loss in an $\ell_0$ sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable…

Statistics Theory · Mathematics 2015-06-04 Gourab Mukherjee , Iain M. Johnstone

We study predictive density estimation under Kullback-Leibler loss in $\ell_0$-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. A surprise is the…

Statistics Theory · Mathematics 2017-08-01 Gourab Mukherjee , Iain M. Johnstone

We consider the problem of predictive density estimation under Kullback-Leibler loss in a high-dimensional Gaussian model with exact sparsity constraints on the location parameters. We study the first order asymptotic minimax risk of Bayes…

Statistics Theory · Mathematics 2019-05-24 Ujan Gangopadhyay , Gourab Mukherjee

This paper discusses predictive densities under the Kullback--Leibler loss for high-dimensional Poisson sequence models under sparsity constraints. Sparsity in count data implies zero-inflation. We present a class of Bayes predictive…

Statistics Theory · Mathematics 2020-09-08 Keisuke Yano , Ryoya Kaneko , Fumiyasu Komaki

This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this…

Probability · Mathematics 2017-06-26 Yulong Lu , Andrew M. Stuart , Hendrik Weber

We consider estimating the predictive density under Kullback-Leibler loss in a high-dimensional Gaussian model. Decision theoretic properties of the within-family prediction error -- the minimal risk among estimates in the class…

Statistics Theory · Mathematics 2012-12-04 Gourab Mukherjee , Iain M. Johnstone

In this work, we are concerned with the estimation of the predictive density of a Gaussian random vector where both the mean and the variance are unknown. In such a context, we prove the inadmissibility of the best equivariant predictive…

Statistics Theory · Mathematics 2014-05-27 Aurélie Boisbunon , Yuzo Maruyama

This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…

Statistics Theory · Mathematics 2014-11-03 Lucien Birgé

We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter $\theta \in \mathbb{R}^d$, and which include multivariate skew normal…

Statistics Theory · Mathematics 2022-02-02 Pankaj Bhagwat , Eric Marchand

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 this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…

Methodology · Statistics 2018-07-13 Denis Belomestny , Alexander Goldenshluger

Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the…

Statistics Theory · Mathematics 2012-01-24 Florian Gach , Benedikt M. Pötscher

This paper deals with the problem of estimating predictive densities of a matrix-variate normal distribution with known covariance matrix. Our main aim is to establish some Bayesian predictive densities related to matricial shrinkage…

Statistics Theory · Mathematics 2017-04-03 Hisayuki Tsukuma , Tatsuya Kubokawa

Let $X| \mu \sim N_p(\mu,v_xI)$ and $Y| \mu \sim N_p(\mu,v_yI)$ be independent p-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on only observing $X=x$, we consider the problem of obtaining a predictive…

Statistics Theory · Mathematics 2007-06-13 Edward I. George , Feng Liang , Xinyi Xu

Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…

Statistics Theory · Mathematics 2012-03-22 Lee Dicker

We discuss the finite sample theoretical properties of online predictions in non-stationary time series under model misspecification. To analyze the theoretical predictive properties of statistical methods under this setting, we first…

Statistics Theory · Mathematics 2023-06-21 Kōsaku Takanashi , Kenichiro McAlinn

In this study, simultaneous predictive distributions for independent Poisson observables were considered and the performance of predictive distributions was evaluated using the Kullback-Leibler (K-L) loss. This study proposes a class of…

Statistics Theory · Mathematics 2024-02-13 Xiao Li

We study minimax convergence rates of nonparametric density estimation in the Huber contamination model, in which a proportion of the data comes from an unknown outlier distribution. We provide the first results for this problem under a…

Statistics Theory · Mathematics 2021-09-08 Ananya Uppal , Shashank Singh , Barnabas Poczos
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