In this paper we study semiparametric estimators of the survival function and the cumulative hazard function based on left truncated and right censored data. Weak representations of the two estimators are derived, whi...In this paper we study semiparametric estimators of the survival function and the cumulative hazard function based on left truncated and right censored data. Weak representations of the two estimators are derived, which are valid up to a given order statistic of the observations.展开更多
Skorokhod's representation theorem states that if on a Polish space,there is a weakly convergent sequence of probability measures μnw→μ0,as n →∞,then there exist a probability space(Ω,F,P) and a sequence of ...Skorokhod's representation theorem states that if on a Polish space,there is a weakly convergent sequence of probability measures μnw→μ0,as n →∞,then there exist a probability space(Ω,F,P) and a sequence of random elements Xnsuch that Xn→ X almost surely and Xnhas the distribution function μn,n = 0,1,2,... We shall extend the Skorokhod representation theorem to the case where if there are a sequence of separable metric spaces Sn,a sequence of probability measures μnand a sequence of measurable mappings n such that μnn-1w→μ0,then there exist a probability space(Ω,F,P) and Sn-valued random elements Xndefined on Ω,with distribution μnand such that n(Xn) → X0 almost surely. In addition,we present several applications of our result including some results in random matrix theory,while the original Skorokhod representation theorem is not applicable.展开更多
基金This research is supported by National Natural Science Foundation of China（10471140 and 10571169）.
文摘In this paper we study semiparametric estimators of the survival function and the cumulative hazard function based on left truncated and right censored data. Weak representations of the two estimators are derived, which are valid up to a given order statistic of the observations.
基金supported by the Fundamental Research Funds for the Central UniversitiesProgram for Changjiang Scholars and Innovative Research Team in UniversityNational Natural Science Foundation of China(Grant Nos.11301063 and 11171057)
文摘Skorokhod's representation theorem states that if on a Polish space,there is a weakly convergent sequence of probability measures μnw→μ0,as n →∞,then there exist a probability space(Ω,F,P) and a sequence of random elements Xnsuch that Xn→ X almost surely and Xnhas the distribution function μn,n = 0,1,2,... We shall extend the Skorokhod representation theorem to the case where if there are a sequence of separable metric spaces Sn,a sequence of probability measures μnand a sequence of measurable mappings n such that μnn-1w→μ0,then there exist a probability space(Ω,F,P) and Sn-valued random elements Xndefined on Ω,with distribution μnand such that n(Xn) → X0 almost surely. In addition,we present several applications of our result including some results in random matrix theory,while the original Skorokhod representation theorem is not applicable.
