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Moment consistency of estimators in partially linear models under NA samples

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Abstract

Consider the heteroscedastic regression model Y (j)(x in , t in ) = t in βg(x in ) + σ in e (j)(x in ), 1 ≤ j ≤ m, 1 ≤ i ≤ n, where \({\sigma_{in}^{2}=f(u_{in})}\), (x in , t in , u in ) are fixed design points, β is an unknown parameter, g(·) and f(·) are unknown functions, and the errors {e (j)(x in )} are mean zero NA random variables. The moment consistency for least-squares estimators and weighted least-squares estimators of β is studied. In addition, the moment consistency for estimators of g(·) and f(·) is investigated.

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Correspondence to Xingcai Zhou.

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This research was supported by the Anhui Province College Excellent Young Talents Fund Project of China (No. 2009SQRZ176ZD) and the National Natural Science Foundation of China (10871001).

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Zhou, X., Liu, X. & Hu, S. Moment consistency of estimators in partially linear models under NA samples. Metrika 72, 415–432 (2010). https://doi.org/10.1007/s00184-009-0260-5

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  • DOI: https://doi.org/10.1007/s00184-009-0260-5

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