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On multivariate kernel estimation for samples from weighted distributions

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  • Ahmad, Ibrahim A.

Abstract

Data from multivariate weighted distributions appear in such cases as missing data, damaged data, sociological or economic data. Multivariate kernel density estimation is discussed for these data where its mean square error (pointwise and integrated) is derived and for an important and common special case, its mean absolute error is outlined. The analogous problem dealing with regression estimation is presented.

Suggested Citation

  • Ahmad, Ibrahim A., 1995. "On multivariate kernel estimation for samples from weighted distributions," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 121-129, February.
    • Handle: RePEc:eee:stapro:v:22:y:1995:i:2:p:121-129
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    Cited by:

    1. de Uña-Álvarez, Jacobo, 2003. "Large sample results under biased sampling when covariables are present," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 287-293, July.
    2. Colin Wu & Andrew Mao, 1996. "Minimax kernels for density estimation with biased data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 451-467, September.
    3. Wu, Colin O., 1997. "A Cross-Validation Bandwidth Choice for Kernel Density Estimates with Selection Biased Data," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 38-60, April.
    4. Ying Qing Chen, 2010. "Semiparametric Regression in Size-Biased Sampling," Biometrics, The International Biometric Society, vol. 66(1), pages 149-158, March.
    5. Wu, Colin O., 1997. "The effects of kernel choices in density estimation with biased data," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 373-383, June.
    6. Junke Kou & Youming Liu, 2018. "Wavelet regression estimations with strong mixing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 667-688, December.
    7. J. Cristóbal & J. Ojeda & J. Alcalá, 2004. "Confidence bands in nonparametric regression with length biased data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(3), pages 475-496, September.
    8. Yogendra P. Chaubey & Christophe Chesneau & Fabien Navarro, 2017. "Linear wavelet estimation of the derivatives of a regression function based on biased data," Working Papers 2017-70, Center for Research in Economics and Statistics.

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