### Abstract

Notions of monotone ordering with respect to continuous covariates in duration data regression models have recently been discussed, and tests for the proportional hazards model against such alternatives have been developed (Bhattacharjee and Das, 2002). Such monotone/ ordered departures are common in applications, and provide useful additional information about the nature of covariate dependence. In this paper, we describe methods for estimating hazard regression models when such monotone departures are known to hold. In particular, it is shown how the histogram sieve estimators (Murphy and Sen, 1991) in this setup can be smoothed and order restricted estimation performed using biased bootstrap techniques like adaptive bandwidth kernel estimators (Brockmann et. al., 1993; Schucany, 1995) or data tilting (Hall and Huang, 2001). The performance of the methods is compared using simulated data, and their use is illustrated with applications from biomedicine and economic duration data.

Original language | English |
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Place of Publication | Cambridge |

Publisher | University of Cambridge |

Publication status | Published - 2003 |

### Publication series

Name | Cambridge Working Papers in Economics |
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### Keywords

- proportional hazards
- ordered restricted inference
- age-varying covariate effects
- biased bootstrap
- data tilting
- adaptive bandwidth selection
- histogram sieve estimator

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## Cite this

Bhattacharjee, A. (2003).

*Estimation in hazard regression models under ordered departures from proportionality*. (Cambridge Working Papers in Economics). University of Cambridge. http://ideas.repec.org/p/cam/camdae/0337.html