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Estimating conditional means with heavy tails

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  • Peng, Liang
  • Yao, Qiwei

Abstract

When a conditional distribution has an infinite variance, commonly employed kernel smoothing methods such as local polynomial estimators for the conditional mean admit non-normal limiting distributions (Hall et al., 2002). This complicates the related inference as the conventional tests and confidence intervals based on asymptotic normality are no longer applicable, and the standard bootstrap method often fails. By utilizing the middle part of data nonparametrically and the tail parts parametrically based on extreme value theory, this paper proposes a new estimation method for conditional means, resulting in asymptotically normal estimators even when the conditional distribution has infinite variance. Consequently the standard bootstrap method could be employed to construct, for example, confidence intervals regardless of the tail heaviness. The same idea can be applied to estimating the difference between a conditional mean and a conditional median, which is a useful measure in data exploratory analysis.

Suggested Citation

  • Peng, Liang & Yao, Qiwei, 2017. "Estimating conditional means with heavy tails," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 14-22.
    • Handle: RePEc:eee:stapro:v:127:y:2017:i:c:p:14-22
    DOI: 10.1016/j.spl.2017.03.023
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    References listed on IDEAS

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    1. Peter Hall & Liang Peng & Qiwei Yao, 2002. "Prediction and nonparametric estimation for time series with heavy tails," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(3), pages 313-331, May.
    2. Peng, Liang, 2001. "Estimating the mean of a heavy tailed distribution," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 255-264, April.
    3. Goedele Dierckx & Yuri Goegebeur & Armelle Guillou, 2014. "Local robust and asymptotically unbiased estimation of conditional Pareto-type tails," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 330-355, June.
    4. Necir, Abdelhakim & Meraghni, Djamel, 2009. "Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 49-58, August.
    5. Hall, Peter & Peng, Liang & Yao, Qiwei, 2002. "Prediction and nonparametric estimation for time series with heavy tails," LSE Research Online Documents on Economics 6086, London School of Economics and Political Science, LSE Library.
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