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Bandwidth selection for kernel density estimation with doubly truncated data

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  • Moreira, C.
  • Van Keilegom, I.

Abstract

Several bandwidth selection procedures for kernel density estimation of a random variable that is sampled under random double truncation are introduced and compared. The motivation is based on the fact that this type of incomplete data is often encountered in astronomy and medicine. The considered bandwidth selection procedures are appropriate modifications of the normal reference rule, the least squares cross-validation procedure, two types of plug-in procedures, and a bootstrap based method. The methods are first shown to work from a theoretical point of view. A simulation study is then carried out to assess the finite sample behavior of these five bandwidth selectors. The use of the various practical bandwidth selectors are illustrated by means of data regarding the luminosity of quasars in astronomy.

Suggested Citation

  • Moreira, C. & Van Keilegom, I., 2013. "Bandwidth selection for kernel density estimation with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 107-123.
    • Handle: RePEc:eee:csdana:v:61:y:2013:i:c:p:107-123
    DOI: 10.1016/j.csda.2012.11.017
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    Cited by:

    1. Pao-sheng Shen & Yi Liu, 2019. "Pseudo maximum likelihood estimation for the Cox model with doubly truncated data," Statistical Papers, Springer, vol. 60(4), pages 1207-1224, August.
    2. Achim Dörre & Chung-Yan Huang & Yi-Kuan Tseng & Takeshi Emura, 2021. "Likelihood-based analysis of doubly-truncated data under the location-scale and AFT model," Computational Statistics, Springer, vol. 36(1), pages 375-408, March.
    3. Ya-Hsuan Hu & Takeshi Emura, 2015. "Maximum likelihood estimation for a special exponential family under random double-truncation," Computational Statistics, Springer, vol. 30(4), pages 1199-1229, December.
    4. Takeshi Emura & Ya-Hsuan Hu & Yoshihiko Konno, 2017. "Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation," Statistical Papers, Springer, vol. 58(3), pages 877-909, September.

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