The generalized maximum likelihood estimate (GMLE) assumptions are studied for four product-limit estimates (PLE): Censoring PLE (Kaplan-Meier estimate), truncation PLE, censoring-truncation PLE, and the degenerated PLE - the empirical distribution function. This paper shows that all the PLE's are also the GMLE's even if they are derived from partial likelihoods by natural parameterization techniques. However, a counter example is given to show that Kiefer Wolfowitz's assumption (1956) for consistency of GMLE can hardly be satisfied for undominated case.
- generalized maximum likelihood estimate
- product-limit estimate
ASJC Scopus subject areas
- Statistics and Probability