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Asymptotic normality of wavelet estimator in heteroscedastic model with α-mixing errors

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Abstract

Consider heteroscedastic regression model Y ni = g(x ni ) + σ ni ɛ ni (1 ≤ i ≤ n), where σ 2 ni = f(u ni ), the design points (x ni , u ni ) are known and nonrandom, g(·) and f(·) are unknown functions defined on closed interval [0, 1], and the random errors {ɛ ni , 1 ≤ i ≤ n} are assumed to have the same distribution as {ξ i , 1 ≤ i ≤ n}, which is a stationary and α-mixing time series with Eξ i = 0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g(·) and f(·). Finite sample behavior of the estimators is investigated via simulations, too.

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Authors and Affiliations

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

    Hanying Liang

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  1. Hanying Liang
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Correspondence to Hanying Liang.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 10871146 and the Grant MTM2008-03129 from the Spanish Ministry of Science and Innovation.

This paper was recommended for publication by Editor Guohua ZOU.

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Liang, H. Asymptotic normality of wavelet estimator in heteroscedastic model with α-mixing errors. J Syst Sci Complex 24, 725–737 (2011). https://doi.org/10.1007/s11424-010-8354-8

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  • DOI: https://doi.org/10.1007/s11424-010-8354-8

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