Special Colloquium
Yehua Li
Department of Statistics, Texas A&M University
Nonparametric Estimation of Correlation Functions In Longitudinal And Spatial Data, With Application To Colon Carcinogenesis Experiments
Abstract: In longitudinal and spatial studies, observations at a
particular time or location within one subject could have complicated
structures, e.g. vectors or even functions.
Measurements within the same subject usually demonstrate strong
correlations that are stationary in time or distance lags. The times or
locations of these data being sampled may not be homogeneous. We propose a
nonparametric estimator of the correlation function in such data, using
kernel methods. We show that the proposed estimator has a pointwise
asymptotic normal distribution, when the number of subjects is fixed and
the number of vectors or functions within each subject goes to infinity.
Based on the asymptotic theory, we propose a weighted block bootstrapping
method in making inferences on the correlation function, where the weights
account for the inhomogeneity of the distribution of the times or
locations. The method is applied to a data set from a colon carcinogenesis
study, in which colonic crypts were sampled from a piece of colon segment
from each of the 12 rats in the experiment and the expression level of
p27, an important cell cycle protein, was then measured for each cell
within the sampled crypts. A simulation study is also provided to illustrate
the numerical performance of the proposed method.
Thursday January 26, 2006 at 4:00 PM in SEO 636