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Asymptotic normality for L1-norm kernel estimator of conditional median under association dependence

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  • Lin, Zhengyan
  • Li, Degui

Abstract

Let be a set of observations from a stationary jointly associated process and [theta](x) be the conditional median, that is, . We consider the problem of estimating [theta](x) based on the L1-norm kernel and establish asymptotic normality of the resulting estimator [theta]n(x).

Suggested Citation

  • Lin, Zhengyan & Li, Degui, 2007. "Asymptotic normality for L1-norm kernel estimator of conditional median under association dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1214-1230, July.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:6:p:1214-1230
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    References listed on IDEAS

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    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
    3. Xiang, Xiaojing, 1996. "A Kernel Estimator of a Conditional Quantile," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 206-216, November.
    4. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    5. Roussas, George G., 2000. "Asymptotic normality of the kernel estimate of a probability density function under association," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 1-12, October.
    6. Zhou, Yong & Liang, Hua, 2000. "Asymptotic Normality for L1 Norm Kernel Estimator of Conditional Median under [alpha]-Mixing Dependence," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 136-154, April.
    7. Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 459-470, September.
    8. Masry, Elias, 2003. "Local polynomial fitting under association," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 330-359, August.
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    Cited by:

    1. Lin, Wei & Cai, Zongwu & Li, Zheng & Su, Li, 2015. "Optimal smoothing in nonparametric conditional quantile derivative function estimation," Journal of Econometrics, Elsevier, vol. 188(2), pages 502-513.
    2. Laksaci, Ali & Lemdani, Mohamed & Ould-Sad, Elias, 2009. "A generalized L1-approach for a kernel estimator of conditional quantile with functional regressors: Consistency and asymptotic normality," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1065-1073, April.

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