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Asymptotic Normality for L1 Norm Kernel Estimator of Conditional Median under [alpha]-Mixing Dependence

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  • Zhou, Yong
  • Liang, Hua

Abstract

Let (X1, Y1), (X2, Y2), ..., be d+1 dimensional random vectors which are distributed as (X, Y). Let [theta](x) be the conditional median, that is, [theta](x)=inf{y: P(Y[less-than-or-equals, slant]y | X=x)[greater-or-equal, slanted]1/2}. We consider the problem of estimating [theta](x) from the data (X1, Y1), ..., (Xn, Yn) which are [alpha]-mixing dependence. L1-norm kernel estimators of conditional median of weakly dependent random variables are proposed and the asymptotic normality of the resulting estimators is derived.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:73:y:2000:i:1:p:136-154
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    References listed on IDEAS

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    1. Masry, E., 1993. "Asymptotic Normality for Deconvolution Estimators of Multivariate Densities of Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 47-68, January.
    2. Greblicki, Wlodzimierz & Pawlak, Miroslaw, 1987. "Necessary and sufficient consistency conditions for a recursive kernel regression estimate," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 67-76, October.
    3. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
    4. Masry, Elias, 1993. "Strong consistency and rates for deconvolution of multivariate densities of stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 47(1), pages 53-74, August.
    5. Xiang, Xiaojing, 1996. "A Kernel Estimator of a Conditional Quantile," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 206-216, November.
    6. Collomb, Gérard & Härdle, Wolfgang, 1986. "Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 77-89, October.
    7. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    8. Fan, Jianqing & Masry, Elias, 1992. "Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 237-271, November.
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    Cited by:

    1. Han-Ying Liang & Jacobo Uña-Álvarez, 2011. "Asymptotic properties of conditional quantile estimator for censored dependent observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 267-289, April.
    2. Han-Ying Liang & Jacobo Uña-Álvarez, 2012. "Empirical likelihood for conditional quantile with left-truncated and dependent data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 765-790, August.
    3. Marc Hallin & Catherine Vermandele & Bas J. M. Werker, 2008. "Semiparametrically efficient inference based on signs and ranks for median‐restricted models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 389-412, April.
    4. 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.
    5. Liang, Han-Ying & de Ua-lvarez, Jacobo, 2009. "A Berry-Esseen type bound in kernel density estimation for strong mixing censored samples," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1219-1231, July.
    6. 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.
    7. Dabo-Niang, Sophie & Thiam, Baba, 2010. "Robust quantile estimation and prediction for spatial processes," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1447-1458, September.

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