Statistica Sinica 18(2008), 1153-1163
A PSEUDO-LIKELIHOOD
ESTIMATION METHOD FOR
NONHOMOGENEOUS GAMMA PROCESS MODEL WITH
RANDOM EFFECTS
Xiao Wang
University of Maryland
Abstract: We study a semiparametric
pseudo-likelihood inference for nonhomogeneous Gamma process with
random effects for degradation data. The setting for degradation
data is one in which 
independent subjects, each with a
nonhomogeneous Gamma process, are observed at possible different
times. The random effects are used to represent heterogeneity of
degradation paths. To obtain the maximum pseudo-likelihood
estimator, we use the Pool Adjacent Violators Algorithm. We study
the asymptotic properties for this estimator. A simulation study is
conducted to validate the method and its application is illustrated
by using degradation data of a civil engineering structure to
estimate its reliability.
Key words
and phrases: Degradation data, empirical process, greatest convex
minorant, pseudo-likelihood, profile likelihood, Gamma process.