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Nonlinear wavelet density estimation with data missing at random when covariates are present

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  • Yu-Ye Zou
  • Han-Ying Liang
  • Jing-Jing Zhang

Abstract

In this paper, we construct the nonlinear wavelet estimator of a density with data missing at random when covariables are present, and provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. Unlike for kernel estimators, the MISE expression of the wavelet-based estimator still holds when the density function is piecewise smooth. Also, the asymptotic normality of the estimator is established. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Yu-Ye Zou & Han-Ying Liang & Jing-Jing Zhang, 2015. "Nonlinear wavelet density estimation with data missing at random when covariates are present," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 967-995, November.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:8:p:967-995
    DOI: 10.1007/s00184-015-0536-x
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    References listed on IDEAS

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    1. Wangli Xu & Xu Guo, 2013. "Nonparametric checks for varying coefficient models with missing response at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 459-482, May.
    2. Wei Yu & Cuizhen Niu & Wangli Xu, 2014. "An empirical likelihood inference for the coefficient difference of a two-sample linear model with missing response data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 675-693, July.
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    5. Liang, Han-Ying & de Uña-Álvarez, Jacobo, 2011. "Wavelet estimation of conditional density with truncated, censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 448-467, March.
    6. Wangli Xu & Lixing Zhu, 2013. "Testing the adequacy of varying coefficient models with missing responses at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 53-69, January.
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    Cited by:

    1. Xu, Hong-Xia & Fan, Guo-Liang & Chen, Zhen-Long, 2017. "Hypothesis tests in partial linear errors-in-variables models with missing response," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 219-229.
    2. Yu-Ye Zou & Han-Ying Liang, 2020. "CLT for integrated square error of density estimators with censoring indicators missing at random," Statistical Papers, Springer, vol. 61(6), pages 2685-2714, December.

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