Statistica Sinica 22 (2012), 47-68
doi:http://dx.doi.org/10.5705/ss.2010.161
ANALYSIS ON CENSORED
QUANTILE RESIDUAL LIFE
MODEL VIA
SPLINE SMOOTHING
Yanyuan Ma and Ying Wei
Texas A&M University and Columbia
University
Abstract: We propose a general class of quantile
residual life models, where a
specific quantile of the residual life time, conditional on an
individual has survived up to time 
, is a function of
certain covariates with their coefficients varying
over time. The varying coefficients are assumed to be smooth unspecified
functions of .
We propose to estimate the coefficient functions using spline
approximation. Incorporating the spline representation directly into
a set of unbiased estimating equations, we obtain a one-step
estimation procedure, and we show that this leads to a uniformly
consistent estimator. To obtain further computational
simplification, we
propose a two-step estimation approach in which we estimate the coefficients on a series of
time points first, and follow this with spline smoothing. We compare
the two methods in terms of their asymptotic efficiency and
computational complexity. We further develop inference tools to
test the significance of the covariate effect on residual life.
The finite sample performance of the estimation and testing
procedures are further illustrated through numerical experiments. We
also apply the methods to a data set from
a neurological study.
Key words and phrases: Censored data,
nonparametric regression, quantile regression, residual life,
spline.