Kubokawa, Tatsuya; Marchand, Éric; Strawderman, William E. On predictive density estimation for location families under integrated absolute error loss. (English) Zbl 1382.62011 Bernoulli 23, No. 4B, 3197-3212 (2017). The paper considers the problem of estimating a \(d\)-dimensional unimodal spherically symmetric density and establishes the existence of a clear relationship between a predictive density estimation problem and a point estimation. It is proved that for the class of log-concave densities a scale expansion, which is induced by a predictive density estimator \(q(x,y)=c^{-1}q(e c^{-1})\), \(e=xy-x\), performs better, in terms of the integrated absolute error loss than a plug-in rule under certain conditions on \( c\). A set of 9 theorems, corollaries and lemmata are proved for sustaining the claims. They are illustrated by discussing some examples. Reviewer: Carlos Narciso Bouza Herrera (Habana) Cited in 8 Documents MSC: 62G07 Density estimation 62F10 Point estimation 62C15 Admissibility in statistical decision theory 62H12 Estimation in multivariate analysis 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) Keywords:concave loss; dominance; frequentist risk; inadmissibility; plug-in; predictive density PDFBibTeX XMLCite \textit{T. Kubokawa} et al., Bernoulli 23, No. 4B, 3197--3212 (2017; Zbl 1382.62011) Full Text: DOI Euclid