Regular Variation and the Identification of Generalized Accelerated Failure-Time Models

J.H. Abbring, G. Ridder

Research output: Working paperDiscussion paperOther research output

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Abstract

Ridder (1990) provides an identification result for the Generalized Accelerated Failure-Time (GAFT) model. We point out that Ridder's proof of this result is incomplete, and provide an amended proof with an additional necessary and sufficient condition that requires that a function varies regularly at zero and infinity. We also give more readily interpretable sufficient conditions on the tails of the error distribution or the asymptotic behavior of the transformation of the dependent variable. The sufficient conditions are shown to encompass all previous results on the identification of the Mixed Proportional Hazards (MPH) model. Thus, this paper not only clarifies, but also unifies the literature on the non-parametric identification of the GAFT and MPH models.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages30
Volume2011-135
Publication statusPublished - 2011

Publication series

NameCentER Discussion Paper
Volume2011-135

Fingerprint

Accelerated Failure Time Model
Regular Variation
Proportional Hazards Model
Sufficient Conditions
Nonparametric Identification
Failure Time
Tail
Asymptotic Behavior
Infinity
Vary
Necessary Conditions
Dependent
Zero

Keywords

  • duration analysis
  • identifiability
  • Mixed Proportional Hazards model
  • regular variation

Cite this

Abbring, J. H., & Ridder, G. (2011). Regular Variation and the Identification of Generalized Accelerated Failure-Time Models. (CentER Discussion Paper; Vol. 2011-135). Tilburg: Econometrics.
Abbring, J.H. ; Ridder, G. / Regular Variation and the Identification of Generalized Accelerated Failure-Time Models. Tilburg : Econometrics, 2011. (CentER Discussion Paper).
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Abbring, JH & Ridder, G 2011 'Regular Variation and the Identification of Generalized Accelerated Failure-Time Models' CentER Discussion Paper, vol. 2011-135, Econometrics, Tilburg.

Regular Variation and the Identification of Generalized Accelerated Failure-Time Models. / Abbring, J.H.; Ridder, G.

Tilburg : Econometrics, 2011. (CentER Discussion Paper; Vol. 2011-135).

Research output: Working paperDiscussion paperOther research output

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N2 - Ridder (1990) provides an identification result for the Generalized Accelerated Failure-Time (GAFT) model. We point out that Ridder's proof of this result is incomplete, and provide an amended proof with an additional necessary and sufficient condition that requires that a function varies regularly at zero and infinity. We also give more readily interpretable sufficient conditions on the tails of the error distribution or the asymptotic behavior of the transformation of the dependent variable. The sufficient conditions are shown to encompass all previous results on the identification of the Mixed Proportional Hazards (MPH) model. Thus, this paper not only clarifies, but also unifies the literature on the non-parametric identification of the GAFT and MPH models.

AB - Ridder (1990) provides an identification result for the Generalized Accelerated Failure-Time (GAFT) model. We point out that Ridder's proof of this result is incomplete, and provide an amended proof with an additional necessary and sufficient condition that requires that a function varies regularly at zero and infinity. We also give more readily interpretable sufficient conditions on the tails of the error distribution or the asymptotic behavior of the transformation of the dependent variable. The sufficient conditions are shown to encompass all previous results on the identification of the Mixed Proportional Hazards (MPH) model. Thus, this paper not only clarifies, but also unifies the literature on the non-parametric identification of the GAFT and MPH models.

KW - duration analysis

KW - identifiability

KW - Mixed Proportional Hazards model

KW - regular variation

M3 - Discussion paper

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BT - Regular Variation and the Identification of Generalized Accelerated Failure-Time Models

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Abbring JH, Ridder G. Regular Variation and the Identification of Generalized Accelerated Failure-Time Models. Tilburg: Econometrics. 2011. (CentER Discussion Paper).