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Robust accelerated failure time regression

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  • Locatelli, Isabella
  • Marazzi, Alfio
  • Yohai, Victor J.

Abstract

Robust estimators for accelerated failure time models with asymmetric (or symmetric) error distribution and censored observations are proposed. It is assumed that the error model belongs to a log-location-scale family of distributions and that the mean response is the parameter of interest. Since scale is a main component of mean, scale is not treated as a nuisance parameter. A three steps procedure is proposed. In the first step, an initial high breakdown point S estimate is computed. In the second step, observations that are unlikely under the estimated model are rejected or down weighted. Finally, a weighted maximum likelihood estimate is computed. To define the estimates, functions of censored residuals are replaced by their estimated conditional expectation given that the response is larger than the observed censored value. The rejection rule in the second step is based on an adaptive cut-off that, asymptotically, does not reject any observation when the data are generated according to the model. Therefore, the final estimate attains full efficiency at the model, with respect to the maximum likelihood estimate, while maintaining the breakdown point of the initial estimator. Asymptotic results are provided. The new procedure is evaluated with the help of Monte Carlo simulations. Two examples with real data are discussed.

Suggested Citation

  • Locatelli, Isabella & Marazzi, Alfio & Yohai, Victor J., 2011. "Robust accelerated failure time regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 874-887, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:874-887
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    References listed on IDEAS

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    1. Zeng, Donglin & Lin, D.Y., 2007. "Efficient Estimation for the Accelerated Failure Time Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1387-1396, December.
    2. Marazzi, Alfio & Villar, Ana J. & Yohai, Victor J., 2009. "Robust Response Transformations Based on Optimal Prediction," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 360-370.
    3. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    4. Kim, Jin Seon & Yum, Bong-Jin, 2008. "Selection between Weibull and lognormal distributions: A comparative simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 477-485, December.
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    1. Sanjoy K. Sinha, 2019. "Robust estimation in accelerated failure time models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 52-78, January.
    2. Jad Beyhum & Ingrid Keilegom, 2023. "Robust censored regression with $$\ell _1$$ ℓ 1 -norm regularization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 146-162, March.

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