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Asymptotic properties of the maximum smoothed partial likelihood estimator in the change‐plane Cox model

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  • Shota Takeishi

Abstract

The change‐plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the finite‐dimensional parameter. Particularly, the convergence rate, not to mention the asymptotic distribution, has not been fully characterized for the general model where classification is based on multiple covariates. To bridge this theoretical gap, this study proposes a maximum smoothed partial likelihood estimator and establishes the following asymptotic properties. First, it shows that the convergence rate for the classification parameter can be arbitrarily close to n−1$$ {n}^{-1} $$ up to a logarithmic factor under a certain condition on covariates and the choice of tuning parameter. Given this convergence rate result, it also establishes the asymptotic normality for the regression parameter.

Suggested Citation

  • Shota Takeishi, 2023. "Asymptotic properties of the maximum smoothed partial likelihood estimator in the change‐plane Cox model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1503-1531, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1503-1531
    DOI: 10.1111/sjos.12642
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    References listed on IDEAS

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    1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    2. Ping Yu & Xiaodong Fan, 2021. "Threshold Regression With a Threshold Boundary," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 953-971, October.
    3. Susan Wei & Michael R Kosorok, 2018. "The change-plane Cox model," Biometrika, Biometrika Trust, vol. 105(4), pages 891-903.
    4. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    5. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, Enero-Abr.
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