Statistica Sinica
7(1997), 1155-1169
M-TYPE SMOOTHING SPLINES IN NONPARAMETRIC
AND SEMIPARAMETRIC REGRESSION MODELS
Jiti Gao and Peide Shi
Queensland University of Technology and Beijing University
Abstract:
Consider the regression model
Yi=g(ti)+ei
for
i=1,...,n.
Here
,and H
is a specified class of continuous functions from T
to R.
Based on a
finite series
expansion 
of g,
an M-estimate
of g
is constructed,
and the asymptotic normality of the estimate is investigated. Meanwhile, a test
statistic
for testing
H0:g(.)=g0(.)
(a known function) is discussed. We
also
consider M-estimates for semiparametric regression models and show that
they are
consistent and asymptotically normal.
Key words and phrases:
Asymptotic normality, M-estimation,
nonparametotic regression model, semiparametric regression model, spline
smoothing technique.