Related papers: Admissible predictive density estimation

In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a Kullback-Leibler type loss for a single model maximum likelihood estimate.…

This paper investigates estimation of the mean vector under invariant quadratic loss for a spherically symmetric location family with a residual vector with density of the form $ f(x,u)=\eta^{(p+n)/2}f(\eta\{\|x-\theta\|^2+\|u\|^2\}) $,…

The Bayesian predictive density has complex representation and does not belong to any finite-dimensional statistical model except for in limited situations. In this paper, we introduce its simple approximate representation employing its…

This paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the Kullback--Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and…

In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and in particular consider unbalanced settings. First, the problem of estimating multiple negative multinomial parameter vectors…

This paper considers estimation of the predictive density for a normal linear model with unknown variance under alpha-divergence loss for -1 <= alpha <= 1. We first give a general canonical form for the problem, and then give general…

The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…

We consider the problem of estimating the joint distribution $P$ of $n$ independent random variables within the Bayes paradigm from a non-asymptotic point of view. Assuming that $P$ admits some density $s$ with respect to a given reference…

This paper addresses the problem of an efficient predictive density estimation for the density $q(\|y-\theta\|^2)$ of $Y$ based on $X \sim p(\|x-\theta\|^2)$ for $y, x, \theta \in \mathbb{R}^d$. The chosen criteria are integrated $L_1$ loss…

Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…

We consider Bayesian shrinkage predictions for the Normal regression problem under the frequentist Kullback-Leibler risk function. Firstly, we consider the multivariate Normal model with an unknown mean and a known covariance. While the…

Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability…

Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…

In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…

Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated $L_2$ and $L_1$ losses. Our findings relate to a $p-$variate…

We evaluate priors by the second order asymptotic behavior of the corresponding estimators.Under certain regularity conditions, the risk differences between efficient estimators of parameters taking values in a domain D, an open connected…

We consider here estimation of an unknown probability density s belonging to L2(mu) where mu is a probability measure. We have at hand n i.i.d. observations with density s and use the squared L2-norm as our loss function. The purpose of…

Let $Y$ be a Gaussian vector whose components are independent with a common unknown variance. We consider the problem of estimating the mean $\mu$ of $Y$ by model selection. More precisely, we start with a collection…

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…

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…