1999 Aug 09 (Mon), 10:30 AM
Chinese Academy of Sciences and The University of
In this paper, a covariate marked empirical process is defined. Stute's
(1997) method of nonparametric principal component decomposition, as a
basis of creating tests, can be applied componentwise. The tests based on
the process only involve one-dimensional projections of the covariate and
do not need local smoothing techniques. Hence the curse of dimensionality
is largely avoided. Furthermore,in contrast with the case that Stute,
Manteiga and Quindimil (1998) investigated,it is shown that in our case,
the classical bootstrap is consistent but the wild bootstrap is
inconsistent. A variant of the wild bootstrap is suggested, which is
consistent. A simulation study is performed to show how the test works.
In addition to formal testing, residuals versus covariates along the most
interesting projection direction are plotted to demonstrate how the plots
can be used for model checking in multivariate cases.