On predictive density estimation with additional information

Parameter estimation with additional information

Admissible Predictive Density Estimation

Let X|μ ∼ Np(μ,vxI ) and Y |μ ∼ Np(μ,vyI ) be independent pdimensional multivariate normal vectors with common unknown mean μ. Based on observing X = x, we consider the problem of estimating the true predictive density p(y|μ) of Y under expected Kullback–Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Baye...

Information Geometric Density Estimation

We investigate kernel density estimation where the kernel function varies from point to point. Density estimation in the input space means to find a set of coordinates on a statistical manifold. This novel perspective helps to combine efforts from information geometry and machine learning to spawn a family of density estimators. We present example models with simulations. We discuss the princip...

Predictive Density Estimation for Multiple Regression

Suppose we observe X ∼ Nm(Aβ, σI) and would like to estimate the predictive density p(y | β) of a future Y ∼ Nn(Bβ, σI). Evaluating predictive estimates p̂(y | x) by KullbackLeibler loss, we develop and evaluate Bayes procedures for this problem. We obtain general sufficient conditions for minimaxity and dominance of the “noninformative” uniform prior Bayes procedure. We extend these results to ...

Exact Minimax Predictive Density Estimation and MDL

The problems of predictive density estimation with Kullback-Leibler loss, optimal universal data compression for MDL model selection, and the choice of priors for Bayes factors in model selection are interrelated. Research in recent years has identified procedures which are minimax for risk in predictive density estimation and for redundancy in universal data compression. Here, after reviewing ...