Communications for Statistical Applications and Methods

  • 제12권3호
  • /
  • Pages.545-556
  • /
  • 2005
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

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

  • 발행 : 2005.12.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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 $\~{F}_0({\tau})\;<\;1$.

키워드

참고문헌

  1. Billingsley, P. (1986). Probability and Measure. John Wiley & Son. New York
  2. Doksum, K. (1974). Tailfree and neutral random probabilities and their posterior distributions. Ann. Probability 2 183-201 https://doi.org/10.1214/aop/1176996703
  3. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. statist. 1 209-230 https://doi.org/10.1214/aos/1176342360
  4. Ferguson, T. S. and Phadia, E. G. (1979). Bayesian nonparametric estimation based one censored data. Ann. Statist. 7 163-186 https://doi.org/10.1214/aos/1176344562
  5. Gill, R. D. (1989). Non- and Semi-parametric maximum likelihood estimators and the von Mises method (Part I). Scand. J. Statist. 16 97-128
  6. Gill, R. D. (994). Lectures on probability theory. Springer-Verlag. New York
  7. Gill, R. D. and Johansen, S. (1990). A survey of product-integration with a view toward application in survival analysis. Ann. Statist. 18 1501-1555 https://doi.org/10.1214/aos/1176347865
  8. Hjort, N. L. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Ann. Statist. 18 1259-1294 https://doi.org/10.1214/aos/1176347749
  9. Susarla, V. and Van Ryzin, J. (1976). Nonparametric Bayesian estimation of survival curve from incomplete observations. J. Amer. Statist. Assoc. 61 897-902
  10. Susarla, V. and Van Ryzin, J. (1978). Large sample theory for a Bayesian nonparametric survival curve estimator based on censored samples. Ann. Statist. 6 755-768 https://doi.org/10.1214/aos/1176344250
  11. Van der Vaart, A. W. and Wellner, J. A. (1996). Weak convergence and Empirical processes. Springer-Verlag. New York