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A-Spline Regression for Fitting a Nonparametric Regression Function with Censored Data

Author

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  • Ersin Yılmaz

    (Mugla Sitki Kocman University, Faculty of Science, Statistics, Muğla 48000, Turkey)

  • Syed Ejaz Ahmed

    (Faculty of Science, Mathematics and Statistics, Brock University, Niagara Region, St. Catharines, ON L2S 3A1, Canada)

  • Dursun Aydın

    (Mugla Sitki Kocman University, Faculty of Science, Statistics, Muğla 48000, Turkey)

Abstract

This paper aims to solve the problem of fitting a nonparametric regression function with right-censored data. In general, issues of censorship in the response variable are solved by synthetic data transformation based on the Kaplan–Meier estimator in the literature. In the context of synthetic data, there have been different studies on the estimation of right-censored nonparametric regression models based on smoothing splines, regression splines, kernel smoothing, local polynomials, and so on. It should be emphasized that synthetic data transformation manipulates the observations because it assigns zero values to censored data points and increases the size of the observations. Thus, an irregularly distributed dataset is obtained. We claim that adaptive spline (A-spline) regression has the potential to deal with this irregular dataset more easily than the smoothing techniques mentioned here, due to the freedom to determine the degree of the spline, as well as the number and location of the knots. The theoretical properties of A-splines with synthetic data are detailed in this paper. Additionally, we support our claim with numerical studies, including a simulation study and a real-world data example.

Suggested Citation

  • Ersin Yılmaz & Syed Ejaz Ahmed & Dursun Aydın, 2020. "A-Spline Regression for Fitting a Nonparametric Regression Function with Censored Data," Stats, MDPI, vol. 3(2), pages 1-17, May.
    • Handle: RePEc:gam:jstats:v:3:y:2020:i:2:p:11-136:d:364587
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    References listed on IDEAS

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    2. Anouar El Ghouch & Ingrid Van Keilegom, 2008. "Non‐parametric Regression with Dependent Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 228-247, June.
    3. Florian Frommlet & Grégory Nuel, 2016. "An Adaptive Ridge Procedure for L0 Regularization," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-23, February.
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    5. Clifford M. Hurvich & Jeffrey S. Simonoff & Chih‐Ling Tsai, 1998. "Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 271-293.
    6. Kohler, Michael & Máthé, Kinga & Pintér, Márta, 2002. "Prediction from Randomly Right Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 73-100, January.
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