Akademisk avhandling

som för avläggande av filosofie
doktorsexamen

vid Stockholms universitet

offentligen försvaras i

hörsal 1, hus A Södra huset,
Frescati

fredagen den 12 juni 1992 kl 10.00

av

**Raul Cano**

fil lic

Statistiska institutionen

Stockholms universitet

**ABSTRACT**

The efficiency of the Bayesian bootstrap is treated for large and small samples from infinite and finite populations. The Bayesian bootstrap is compared with nonparametric and parametric Bayesian methods in the infinite case, for large samples and considering the mean and truncation functionals. It is shown that in this case, all these methods give the same results in a first order asymptotical sense. However, when the Bayesian bootstrap is compared with a parametric method in the truncation case, a inefficiency is detected. An expression of this inefficiency is given in terms of the Fisher information. A method to measure the bootstrap efficiency for small samples is proposed and its feasibility is illustrated. Some ways of improving this efficiency are considered. In the finite case, known results of the Bayesian approach are summarized. The Bayesian bootstrap feasibility is demonstrated by means of a real-life estimation problem. Next, the Bayesian bootstrap in the presence of outliers is also investigated. Some alternative methods based on the Bayesian bootstrap resampling technique are also considered. The efficiencey of all these methods with respect to a parametric Bayesian method is studied in a simulated lognormal population. Finally, the Bayesian bootstrap and modified versions of the previous methods are compared in a population generated from real data.

ISBN 91-7153-024-x

*Last update: 990916/CE*