TITLE:
On the Convergence of Observed Partial Likelihood under Incomplete Data with Two Class Possibilities
AUTHORS:
Tomoyuki Sugimoto
KEYWORDS:
Cox’s Regression Model; Logistic Regression Model; Incomplete Binary Data; Partial Likelihood; Partial-Sum Processes; Profile Likelihood
JOURNAL NAME:
Open Journal of Statistics,
Vol.4 No.2,
February
27,
2014
ABSTRACT: In this paper, we discuss
the theoretical validity of the observed partial likelihood (OPL) constructed
in a Coxtype model under
incomplete data with two class possibilities, such as missing binary
covariates, a cure-mixture model or doubly censored data. A main result is
establishing the asymptotic convergence of the OPL. To reach this result, as it
is difficult to apply some standard tools in the survival analysis, we develop
tools for weak convergence based on partial-sum processes. The result of the
asymptotic convergence shown here indicates that a suitable order of the number
of Monte Carlo trials is less than the square of the sample size. In addition,
using numerical examples, we investigate how the asymptotic properties
discussed here behave in a finite sample.