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\noindent Statistica Sinica {\bf 13}(2003), 739-762

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\centerline{\large\bf A KERNEL-BASED METHOD FOR ESTIMATING}
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\centerline{\large\bf ADDITIVE PARTIALLY LINEAR MODELS}
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\author{Yanqin Fan and Qi Li}
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\centerline{\it Vanderbilt University and Texas A {\rm \&} M University}
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\begin{quotation}
\noindent {\it Abstract:}
   In this paper we propose a kernel-based method for
  estimating additive partially linear models. Our method makes use
  of the partially linear model structure at the initial stage when
  estimating the individual nonparametric components.
   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 dimensional parameter. Our result
   also leads to a simple identification condition for the finite
   dimensional parameter.\par
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\noindent {\it Key words and phrases:}
 Additive partially linear model,
   finite sample efficiency, identification,
   kernel smoother, simulations.\par
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