THURSDAY, October 23rd, 2008 at 4.10pm,
MSB 1147 (Colloquium Room)
Refreshments: 3.30pm, MSB 4110 (Statistics
Lounge)
Title: Testing for Linearity of
the Nonparametric Component of a Partially Linear Model
Abstract:
The nonparametric component in a partially linear
model is estimated by a linear combination of fixed-knot cubic B-splines with a second-order difference
penalty on the adjacent B-spline
coefficients. The resulting penalized least-squares estimator is used to
construct two Wald-type spline-based test statistics for the null hypothesis of
the linearity of the nonparametric function. When the number of knots is fixed,
the limiting distribution of the first test statistic is the distribution of a
linear combination of independent chi-squared random variables, each with one
degree of freedom, under the null hypothesis. The smoothing parameter is
determined by specifying a value for the asymptotically expected value of the
test statistic under the null hypothesis. When the number of knots is fixed and
under the null hypothesis, the second test statistic asymptotically has a
chi-squared distribution with K = q + 2 degrees of freedom, where q is the number of knots used for
estimation. The power performances of the two proposed tests are investigated
via simulation experiments, and the practicality of the proposed methodology is
illustrated using a real-life data set.
