Statistics and Data Science Seminar
Prof. Hanxiang Peng
Indiana University - Purdue University Indianapolis
Asymptotics of Maximum Partial Likelihood Estimators in General Semiparametric Multiplicative Hazard Models Under First Order Differentiability
Abstract: In this talk, we discuss the asymptotic properties
of a semiparametric multiplicative hazard model when the
relative risk is expressed as a first order continuously
differentiable parametric function. We show that the log-
the partial likelihood function of the model is locally
concave for an arbitrary continuously differentiable relative
risk under suitable conditions. Then we derive the
existence and uniqueness of the MPLE and show consistency.
Using the convexity lemma and characterization of minimizers,
we demonstrate that the MPLE of the parameter is asymptotically
normal. As an application, we exhibit that the MPLE of the
parameter in a model in which the log- the relative risk is
expressed as a free-knot spline with knots in covariates uniquely
exists in a neighborhood of the true parameter value and is
consistent and asymptotically normal. In particular, we derive the
asymptotic normality of the MPLE of the parameter in a model in
which the log- relative risk is expressed as a free-knot
quadratic spline which has first order continuous derivative.
Wednesday November 11, 2009 at 3:00 PM in SEO 636