• Journal of the Korean Statistical Society
• /
• v.30 no.3
• /
• pp.481-498
• /
• 2001

Empirical Bayes procedure of nonparametric estiamtion of cumulative hazard rates based on censored data is considered using the beta process priors of Hjort(1990). Beta process priors with unknown parameters are used for cumulative hazard rates. Empirical Bayes estimators are suggested and asymptotic optimality is proved. Our result generalizes that of Susarla and Van Ryzin(1978) in the sensor that (i) the cumulative hazard rate induced by a Dirichlet process is a beta process, (ii) our empirical Bayes estimator does not depend on the censoring distribution while that of Susarla and Van Ryzin(1978) does, (iii) a class of estimators of the hyperprameters is suggested in the prior distribution which is assumed known in advance in Susarla and Van Ryzin(1978). This extension makes the proposed empirical Bayes procedure more applicable to real dta sets.

• Communications for Statistical Applications and Methods
• /
• v.12 no.3
• /
• pp.545-556
• /
• 2005

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

• Journal of the Korean Statistical Society
• /
• v.34 no.3
• /
• pp.235-244
• /
• 2005

In recent years, theoretical properties of Bayesian nonparametric survival models have been studied and the conclusion is that although there are pathological cases the popular prior processes have the desired asymptotic properties, namely, the posterior consistency and the Bernstein-von Mises theorem. In this study, through a simulation experiment, we study the finite sample properties of the Bayes estimator and compare it with the frequentist estimators. To our surprise, we conclude that in most situations except that the prior is highly concentrated at the true parameter value, the Bayes estimator performs worse than the frequentist estimators.

• The Pure and Applied Mathematics
• /
• v.5 no.2
• /
• pp.123-132
• /
• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• Communications for Statistical Applications and Methods
• /
• v.14 no.1
• /
• pp.111-119
• /
• 2007

In this paper, we develop a nonparametric Bayesian methodology of estimating an unknown distribution function F at the given survival time with current status data under the assumption of Dirichlet process prior on F. We compare our algorithm with the nonparametric maximum likelihood estimator through application to simulated data and real data.

• Journal of the Korean Statistical Society
• /
• v.33 no.2
• /
• pp.191-202
• /
• 2004

The paper considers nonparametric empirical Bayes estimation of residual survival function at age t using a Dirichlet process prior V(a). Empirical Bayes estimators are proposed for the case where both the function ${\alpha}$(0, $\chi$] and the size a(R$\^$+/) are unknown. It is shown that the proposed empirical Bayes estimators are asymptotically optimal at a rate n$\^$-1/, where n is the number of past data available for the present estimation problem. Therefore, the result of Lahiri and Park (1988) in which a(R$\^$+/) is assumed to be known and a rate n$\^$-1/ is achieved, is extended to a(R$\^$+/) unknown case.

• Proceedings of the Korean Statistical Society Conference
• /
• 2002.05a
• /
• pp.1-5
• /
• 2002

We consider the problem of optimal bandwidth choice for nonparametric classification, based on kernel density estimators, where the problem of interest is distinguishing between two univariate distributions. When the densities intersect at a single point, optimal bandwidth choice depends on curvatures of the densities at that point. The problem of empirical bandwidth selection and classifying data in the tails of a distribution are also addressed.