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Restoration of Monotonicity Respecting in Dynamic Regression

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  • Yijian Huang

Abstract

Dynamic regression models, including the quantile regression model and Aalen’s additive hazards model, are widely adopted to investigate evolving covariate effects. Yet lack of monotonicity respecting with standard estimation procedures remains an outstanding issue. Advances have recently been made, but none provides a complete resolution. In this article, we propose a novel adaptive interpolation method to restore monotonicity respecting, by successively identifying and then interpolating nearest monotonicity-respecting points of an original estimator. Under mild regularity conditions, the resulting regression coefficient estimator is shown to be asymptotically equivalent to the original. Our numerical studies have demonstrated that the proposed estimator is much more smooth and may have better finite-sample efficiency than the original as well as, when available as only in special cases, other competing monotonicity-respecting estimators. Illustration with a clinical study is provided.

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  • Yijian Huang, 2017. "Restoration of Monotonicity Respecting in Dynamic Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 613-622, April.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:518:p:613-622
    DOI: 10.1080/01621459.2016.1149070
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    1. Neocleous, Tereza & Portnoy, Stephen, 2008. "On monotonicity of regression quantile functions," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1226-1229, August.
    2. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
    3. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275.
    5. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    6. Holger Dette & Stanislav Volgushev, 2008. "Non‐crossing non‐parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627, July.
    7. Yijian Huang & Limin Peng, 2009. "Accelerated Recurrence Time Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 636-648, December.
    8. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    9. Yijian Huang, 2013. "Fast Censored Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 789-806, December.
    10. Peng, Limin & Huang, Yijian, 2008. "Survival Analysis With Quantile Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 637-649, June.
    11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    12. J. P. Fine, 2004. "Temporal process regression," Biometrika, Biometrika Trust, vol. 91(3), pages 683-703, September.
    13. Jing Qian & Limin Peng, 2010. "Censored quantile regression with partially functional effects," Biometrika, Biometrika Trust, vol. 97(4), pages 839-850.
    14. Limin Peng & Yijian Huang, 2007. "Survival analysis with temporal covariate effects," Biometrika, Biometrika Trust, vol. 94(3), pages 719-733.
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    Cited by:

    1. Ziyi Li & Yijian Huang & Dattatraya Patil & Martin G. Sanda, 2023. "Covariate adjustment in continuous biomarker assessment," Biometrics, The International Biometric Society, vol. 79(1), pages 39-48, March.
    2. J. E. Soh & Yijian Huang, 2021. "A varying-coefficient model for gap times between recurrent events," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 437-459, July.

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