A KERNEL-BASED METHOD FOR ESTIMATING ADDITIVE PARTIALLY LINEAR MODELS

In this paper we propose a kernel-based method for estimating addi- tive partially linear models. Our method makes use of the partially linear model structure at the initial stage when estimating the individual nonparametric compo- nents. Monte Carlo simulations show that our proposed estimator performs quite well for moderate sample sizes. In addition, we provide a consistent estimator for the asymptotic variance of the estimator of the parameter in the linear part of the model, where the linear component variable can be discrete or continuous. This facilitates inferential procedures based on our proposed estimator for the finite di- mensional parameter. Our result also leads to a simple identification condition for the finite dimensional parameter.

[1]  Jens Perch Nielsen,et al.  An optimization interpretation of integration and back‐fitting estimators for separable nonparametric models , 1998 .

[2]  W. Newey,et al.  Kernel Estimation of Partial Means and a General Variance Estimator , 1994, Econometric Theory.

[3]  C. J. Stone,et al.  Additive Regression and Other Nonparametric Models , 1985 .

[4]  Jianqing Fan.  Local Linear Regression Smoothers and Their Minimax Efficiencies , 1993 .

[5]  P. Speckman.  Kernel smoothing in partial linear models , 1988 .

[6]  Dag Tjøstheim,et al.  Nonparametric Identification of Nonlinear Time Series: Projections , 1994 .

[7]  David Ruppert,et al.  Fitting a Bivariate Additive Model by Local Polynomial Regression , 1997 .

[8]  Stefan Sperlich,et al.  Estimation of Derivatives for Additive Separable Models , 1999 .

[9]  Lijian Yang,et al.  DIRECT ESTIMATION IN AN ADDITIVE MODEL WHEN THE COMPONENTS ARE PROPORTIONAL , 2002 .

[10]  W. Härdle,et al.  Estimation and Variable Selection in Additive Nonparametric Regression Models , 1995 .

[11]  Qi Li,et al.  EFFICIENT ESTIMATION OF ADDITIVE PARTIALLY LINEAR MODELS , 2000 .

[12]  R. Tibshirani,et al.  Generalized Additive Models , 1991 .

[13]  Jianqing Fan,et al.  Generalized Partially Linear Single-Index Models , 1997 .

[14]  Oliver Linton,et al.  Miscellanea Efficient estimation of additive nonparametric regression models , 1997 .

[15]  Anton Schick,et al.  Root-n-consistent and efficient estimation in semiparametric additive regression models , 1996 .

[16]  Gary Chamberlain,et al.  Efficiency Bounds for Semiparametric Regression , 1992 .

[17]  P. Robinson.  ROOT-N-CONSISTENT SEMIPARAMETRIC REGRESSION , 1988 .

[18]  Wolfgang Härdle,et al.  Direct estimation of low-dimensional components in additive models , 1998 .

[19]  O. Linton,et al.  A kernel method of estimating structured nonparametric regression based on marginal integration , 1995 .

[20]  Dag Tjøstheim,et al.  NONPARAMETRIC ESTIMATION AND TESTING OF INTERACTION IN ADDITIVE MODELS , 2002, Econometric Theory.

[21]  W. Wong,et al.  Profile Likelihood and Conditionally Parametric Models , 1992 .

[22]  C. J. Stone,et al.  The Dimensionality Reduction Principle for Generalized Additive Models , 1986 .

[23]  Enno Mammen,et al.  The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions , 1999 .

[24]  Jianqing Fan.  Design-adaptive Nonparametric Regression , 1992 .