Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expansion is close to the exact distribut...Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expansion is close to the exact distribution of the Studentized product-limit estimator with a remainder of On(su-1/2).展开更多
Let X<sub>1</sub>,X<sub>2</sub>,…, Y<sub>1</sub>,Y<sub>2</sub>,…, T<sub>1</sub>,T<sub>2</sub>,…be independent random variables such thatX<s...Let X<sub>1</sub>,X<sub>2</sub>,…, Y<sub>1</sub>,Y<sub>2</sub>,…, T<sub>1</sub>,T<sub>2</sub>,…be independent random variables such thatX<sub>i</sub> are real-valued and have a common continuous distribution function F. Y<sub>i</sub> are extendedreal-valued and have a common distribution G and T<sub>i</sub> are extended real-valued and have acommon distribution funtion D. The nonparametric maximum likelihood estimator of Fbased on X<sub>1</sub>,…, X<sub>n</sub> is the empirical distribution function F<sub>n</sub>.展开更多
Let S(s,t) be the bivariate survival function.Let Sn(s,t) be the bivariate product limit estimator proposed by Campbell and Foldes.The one-term Edgeworth expansion for Sn(s,t) is established by expressing logSn(s,t)-l...Let S(s,t) be the bivariate survival function.Let Sn(s,t) be the bivariate product limit estimator proposed by Campbell and Foldes.The one-term Edgeworth expansion for Sn(s,t) is established by expressing logSn(s,t)-logS(s,t) as U-statistics,which admits one-term Edgeworth expansion plus some remainders with sufficient accuracy.展开更多
文摘Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expansion is close to the exact distribution of the Studentized product-limit estimator with a remainder of On(su-1/2).
基金Project supported by the National Natural Science Foundation of China.
文摘Let X<sub>1</sub>,X<sub>2</sub>,…, Y<sub>1</sub>,Y<sub>2</sub>,…, T<sub>1</sub>,T<sub>2</sub>,…be independent random variables such thatX<sub>i</sub> are real-valued and have a common continuous distribution function F. Y<sub>i</sub> are extendedreal-valued and have a common distribution G and T<sub>i</sub> are extended real-valued and have acommon distribution funtion D. The nonparametric maximum likelihood estimator of Fbased on X<sub>1</sub>,…, X<sub>n</sub> is the empirical distribution function F<sub>n</sub>.
基金Project supported by the Postdoctoral Science Foundation of China.
文摘Let S(s,t) be the bivariate survival function.Let Sn(s,t) be the bivariate product limit estimator proposed by Campbell and Foldes.The one-term Edgeworth expansion for Sn(s,t) is established by expressing logSn(s,t)-logS(s,t) as U-statistics,which admits one-term Edgeworth expansion plus some remainders with sufficient accuracy.
