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CLT of wavelet estimator in semiparametric model with correlated errors

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Abstract

This paper considers the semiparametric regression model y i = x i β+g(t i )+V i (1 ≤ i ≤ n), where (x i , t i ) are known design points, β is an unknown slope parameter, g(·) is an unknown function, the correlated errors \(V_i = \sum\nolimits_{j = - \infty }^\infty {c_j e_{i - j} } \) with \(\sum\nolimits_{j = - \infty }^\infty {|c_j |} < \infty \), and e i are negatively associated random variables. Under appropriate conditions, the authors study the asymptotic normality for wavelet estimators of β and g(·). A simulation study is undertaken to investigate finite sample behavior of the estimators.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, 200092, China

    Sili Niu

  2. Department of Mathematics and Physics, Henan University of Urban Construction, Pingdingshan, 467044, China

    Yamei Liu

Authors
  1. Sili Niu
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  2. Yamei Liu
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Correspondence to Sili Niu.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 10871146.

This paper was recommended for publication by Editor Guohua ZOU.

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Niu, S., Liu, Y. CLT of wavelet estimator in semiparametric model with correlated errors. J Syst Sci Complex 25, 567–581 (2012). https://doi.org/10.1007/s11424-012-0166-6

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  • DOI: https://doi.org/10.1007/s11424-012-0166-6

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