Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
, 50 (3), 675-687

Estimation in Partially Linear Models and Numerical Comparisons

Affiliations

Estimation in Partially Linear Models and Numerical Comparisons

Hua Liang. Comput Stat Data Anal.

Abstract

Partially linear models with local kernel regression are popular non-parametric techniques. However, bandwidth selection in the models is a puzzling topic that has been addressed in literature with the use of undersmoothing and regular smoothing. In an attempt to address the strategy of bandwidth selection, we review profile-kernel based and backfitting methods for partially linear models, and justify why undersmoothing is necessary for backfitting method and why the "optimal" bandwidth works out for profile-kernel based method. We suggest a general computation strategy for estimating nonparametric functions. We also employ the penalized spline method for partially linear models and conduct intensive simulation experiments to explore the numerical performance of the penalized spline method, profile and backfitting methods. A real example is analyzed with the three methods.

Figures

Figure 1
Figure 1
Box plots of the estimates (N=500 simulation runs) for backfitting (back), profile, and penalized spline (PS) methods for homogeneous errors. Upper panel: the first element of β; lower panel: the second element of β. The long horizontal lines are the true values.
Figure 2
Figure 2
Estimated curves of the nonparametric components for simulated data. The true curve is shown as an unbroken line and the curves estimated with backfitting, profile, and penalized spline methods are shown by dotted, dashed, long-dashed lines, respectively.
Figure 3
Figure 3
Relation between log-earnings and labor-market experience.
Figure 4
Figure 4
Penalized spline estimates of the nonparametric component from real data with different numbers of knots.

Similar articles

See all similar articles

Cited by 2 PubMed Central articles

LinkOut - more resources

Feedback