Asymptotics for partly linear regression with dependent samples and ARCH errors: consistency with rates |
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Authors: | LU Zudi IGijbels |
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Institution: | 1. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China 2. Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium |
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Abstract: | Partly linear regression model is useful in practice, but little is investigated in the literature to adapt it to the real
data which are dependent and conditionally heteroscedastic. In this paper, the estimators of the regression components are
constructed via local polynomial fitting and the large Sample properties are explored. Under certain mild regularities, the
conditions are obtained to ensure that the estimators of the nonparametric component and its derivatives are consistent up
to the convergence rates which are optimal in the i. i. d. case, and the estimator of the parametric component is root-n consistent with the same rate as for parametric model. The technique adopted in the proof differs from that used and corrects
the errors in the reference by Hamilton and Truong under i. i. d. samples. |
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Keywords: | ARCH (GARCH) errors dependent samples local polynomial fitting convergence rates partly linear model root-n consistency |
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