Nonparametric regression estimation with general parametric error covariance

  • Authors:

  • Carlos Martins-Filho;Feng Yao

  • Affiliations:

  • Department of Economics, Oregon State University, Ballard Hall 303, Corvallis, OR 97331-3612, USA;Department of Economics, West Virginia University, P.O. Box 6025, Morgantown, WV 26506-6025, USA

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2009

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Abstract

The asymptotic distribution for the local linear estimator in nonparametric regression models is established under a general parametric error covariance with dependent and heterogeneously distributed regressors. A two-step estimation procedure that incorporates the parametric information in the error covariance matrix is proposed. Sufficient conditions for its asymptotic normality are given and its efficiency relative to the local linear estimator is established. We give examples of how our results are useful in some recently studied regression models. A Monte Carlo study confirms the asymptotic theory predictions and compares our estimator with some recently proposed alternative estimation procedures.