Weak Convergence for Nonparametric Bayes Estimators Based on Beta Processes in the Random Censorship Model

Title & Authors
Weak Convergence for Nonparametric Bayes Estimators Based on Beta Processes in the Random Censorship Model
Hong, Jee-Chang;

Abstract
Hjort(1990) obtained the nonparametric Bayes estimator $\small{\^{F}_{c,a}}$ of $\small{F_0}$ with respect to beta processes in the random censorship model. Let $\small{X_1,{\cdots},X_n}$ be i.i.d. $\small{F_0}$ and let $\small{C_1,{\cdot},\;C_n}$ be i.i.d. G. Assume that $\small{F_0}$ and G are continuous. This paper shows that {$\small{\^{F}_{c,a}}$(u){\|}0 < u < T} converges weakly to a Gaussian process whenever T < $\small{\infty}$ and $\~{F}_0({\tau})\;<\;1$.
Keywords
Nonparametric Bayes estimator;Compact differentiability;Delta method;
Language
English
Cited by
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