Statistics and Its Interface

Volume 7 (2014)

Number 4

Special Issue on Modern Bayesian Statistics (Part I)

Guest Editor: Ming-Hui Chen (University of Connecticut)

Bayesian nonparametric density estimation for doubly-truncated data

Pages: 455 – 463

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n4.a3

Authors

Yuhui Chen (Department of Statistics, University of South Carolina, Columbia, S.C., U.S.A.)

Timothy Hanson (Department of Statistics, University of South Carolina, Columbia, S.C., U.S.A.)

Abstract

A Bayesian nonparametric density estimator is presented for doubly-truncated data. The estimator is based on a Pólya tree prior, and readily extended to truncated regression. The approach nicely blends a standard parametric normal fit with the nonparametric maximum likelihood estimator. Since the density is directly modeled, a standard likelihood approach applies; inference is efficiently obtained through an adaptiveMarkov chain Monte Carlo and no manual tuning is required. The estimator is broadly illustrated on simulated data, the quasar luminosity data of Efron and Petrosian (1999), times of cancer diagnosis considered in Moreira and Uña-Álvarez (2012), and the AIDS induction time data of Lagakos, Barraj, and De Gruttola (1988).

Keywords

Pólya tree, regression, truncation

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