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Logspline Density Estimation under Censoring and Truncation

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  • Ja‐Yong Koo
  • Charles Kooperberg
  • Jinho Park

Abstract

ABSTRACT. In this paper we consider logspline density estimation for data that may be left‐truncated or right‐censored. For randomly left‐truncated and right‐censored data the product‐limit estimator is known to be a consistent estimator of the survivor function, having a faster rate of convergence than many density estimators. The product‐limit estimator and B‐splines are used to construct the logspline density estimate for possibly censored or truncated data. Rates of convergence are established when the log‐density function is assumed to be in a Besov space. An algorithm involving a procedure similar to maximum likelihood, stepwise knot addition, and stepwise knot deletion is proposed for the estimation of the density function based upon sample data. Numerical examples are used to show the finite‐sample performance of inference based on the logspline density estimation.

Suggested Citation

  • Ja‐Yong Koo & Charles Kooperberg & Jinho Park, 1999. "Logspline Density Estimation under Censoring and Truncation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 87-105, March.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:1:p:87-105
    DOI: 10.1111/1467-9469.00139
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    Cited by:

    1. Christian Schellhase & Göran Kauermann, 2012. "Density estimation and comparison with a penalized mixture approach," Computational Statistics, Springer, vol. 27(4), pages 757-777, December.
    2. Bak, Kwan-Young & Jhong, Jae-Hwan & Lee, JungJun & Shin, Jae-Kyung & Koo, Ja-Yong, 2021. "Penalized logspline density estimation using total variation penalty," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    3. Patrick Marsh, "undated". "Nonparametric Likelihood Ratio Tests," Discussion Papers 00/56, Department of Economics, University of York.

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