  In environmental health research, it is of interest to understand the effect
of the neighborhood environment on health. Researchers have shown a protective
association between green space around a person's residential address and
depression outcomes. In measuring exposure to green space, distance buffers are
often used. However, buffer distances differ across studies. Typically, the
buffer distance is determined by researchers a priori. It is unclear how to
identify an appropriate buffer distance for exposure assessment. To address
geographic uncertainty problem for exposure assessment, we present a domain
selection algorithm based on the penalized functional linear Cox regression
model. The theoretical properties of our proposed method are studied and
simulation studies are conducted to evaluate finite sample performances of our
method. The proposed method is illustrated in a study of associations of green
space exposure with depression and/or antidepressant use in the Nurses' Health
Study.
