EFFICIENT ESTIMATION OF ADDITIVE PARTIALLY LINEAR MODELS

I consider the problem of estimating an additive partially linear model using general series estimation methods with polynomial and splines as two leading cases. I show that the finite-dimensional parameter is identified under weak conditions. I establish the root-n-normality result for the finite-dimensional parameter in the linear part of the model and show that it is asymptotically more efficient than a semiparametric estimator that ignores the additive structure. When the error is conditional homoskedastic, my finite-dimensional parameter estimator reaches the semiparametric efficiency bound. Efficient estimation when the error is conditional heteroskedastic is also discussed.

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

[2]  J. Stock.  Nonparametric Policy Analysis , 1989 .

[3]  Xiaotong Shen,et al.  Sieve extremum estimates for weakly dependent data , 1998 .

[4]  W. J. Hall,et al.  Information and Asymptotic Efficiency in Parametric-Nonparametric Models , 1983 .

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

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

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

[8]  A. Ronald Gallant,et al.  On the asymptotic normality of Fourier flexible form estimates , 1991 .

[9]  Stephen G. Donald,et al.  Series estimation of semilinear models , 1994 .

[10]  W. Newey,et al.  Convergence rates and asymptotic normality for series estimators , 1997 .

[11]  A semiparametric efficiency bound of a disequilibrium model without observed regime , 1994 .

[12]  D. Cox.  Approximation of Least Squares Regression on Nested Subspaces , 1988 .

[13]  Brian J. Eastwood,et al.  Adaptive Rules for Seminonparametric Estimators That Achieve Asymptotic Normality , 1991, Econometric Theory.

[14]  G. Lorentz.  Approximation of Functions , 1966 .

[15]  D. Andrews.  Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models , 1991 .

[16]  Whitney K. Newey,et al.  Adaptive estimation of regression models via moment restrictions , 1988 .

[17]  Spiridon Penev,et al.  On shape-preserving probabilistic wavelet approximators , 1997 .

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

[19]  G. Chamberlain.  Asymptotic efficiency in semi-parametric models with censoring , 1986 .

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

[21]  Peter Craven,et al.  Smoothing noisy data with spline functions , 1978 .

[22]  R. Eubank,et al.  The asymptotic average squared error for polynomial regression , 1993 .

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

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

[25]  Joel L. Horowitz,et al.  NONPARAMETRIC ESTIMATION OF A GENERALIZED ADDITIVE MODEL WITH AN UNKNOWN LINK FUNCTION , 2001 .

[26]  L. Hansen,et al.  Efficiency bounds implied by multiperiod conditional moment restrictions , 1988 .

[27]  S. Cosslett.  Efficiency Bounds for Distribution-free Estimators of the Binary , 1987 .

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

[29]  Ker-Chau Li,et al.  Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set , 1987 .

[30]  D. Andrews,et al.  Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality , 1990, Econometric Theory.