## The Annals of Statistics

### Consistent and Robust Bayes Procedures for Location Based on Partial Information

#### Abstract

We consider Bayes procedures for a location parameter $\theta$ that are robust with respect to the shape of the distribution $F$ of the data. The case where $F$ is fixed (nonrandom) and the case where $F$ has a Dirichlet distribution are both treated. The procedures are based on the posterior distributions of the location parameter given the partial information contained in a robust estimate of location. We show consistency and asymptotic normality of the procedures and give instances where the Bayes procedure based on the full sample diverges while the Bayes procedures based on partial information converges and is asymptotically normal. Finally, we show that robust confidence procedures can be given a Bayesian interpretation.

#### Article information

Source
Ann. Statist., Volume 18, Number 1 (1990), 443-453.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347510

Digital Object Identifier
doi:10.1214/aos/1176347510

Mathematical Reviews number (MathSciNet)
MR1041403

Zentralblatt MATH identifier
0701.62043

JSTOR
links.jstor.org

Subjects
Primary: 62A15
Secondary: 62E20: Asymptotic distribution theory

#### Citation

Doksum, Kjell A.; Lo, Albert Y. Consistent and Robust Bayes Procedures for Location Based on Partial Information. Ann. Statist. 18 (1990), no. 1, 443--453. doi:10.1214/aos/1176347510. https://projecteuclid.org/euclid.aos/1176347510