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Heteroscedasticity Detection and Estimation with Quantile Difference Method

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Abstract

When dealing with regression analysis, heteroscedasticity is a problem that the authors have to face with. Especially if little information can be got in advance, detection of heteroscedasticity as well as estimation of statistical models could be even more difficult. To this end, this paper proposes a quantile difference method (QDM) that can effectively estimate the heteroscedastic function. This method, being completely free from the estimation of mean regression function, is simple, robust and easy to implement. Moreover, the QDM method enables the detection of heteroscedasticity without any restrictions on error terms, consequently being widely applied. What is worth mentioning is that based on the proposed approach estimators of both mean regression function and heteroscedastic function can be obtained. In the end, the authors conduct some simulations to examine the performance of the proposed methods and use a real data to make an illustration.

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Authors and Affiliations

  1. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou, 730020, China

    Wentao Xia

  2. School of Statistics, University of International Business and Economics, Beijing, 100029, China

    Wei Xiong

  3. Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, 100872, China

    Maozai Tian

Authors
  1. Wentao Xia
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  2. Wei Xiong
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  3. Maozai Tian
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Corresponding author

Correspondence to Maozai Tian.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11271368, the Major Program of Beijing Philosophy and Social Science Foundation of China under Grant No. 15ZDA17, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20130004110007, the Key Program of National Philosophy and Social Science Foundation under Grant No. 13AZD064, the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China under Grant No. 15XNL008, and the Project of Flying Apsaras Scholar of Lanzhou University of Finance & Economics.

This paper was recommended for publication by Editor SUN Liuquan.

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Xia, W., Xiong, W. & Tian, M. Heteroscedasticity Detection and Estimation with Quantile Difference Method. J Syst Sci Complex 29, 511–530 (2016). https://doi.org/10.1007/s11424-015-3161-x

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  • DOI: https://doi.org/10.1007/s11424-015-3161-x

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