Efficient Estimation in a Nonproportional Hazards Model

  • Filia Vonta
Chapter

Abstract

A nonproportional hazards regression model is considered in which the structural parameter is the vector of regression coefficients and the nuisance parameter is a vector of arbitrarily high dimension. The asymptotic distribution as well as the efficiency and consistency of jointly, implicitly defined estimators of the structural and nuisance parameters of the model are established.

Keywords

Asymptotic Distribution Consistent Estimator Nuisance Parameter Efficient Estimation Preliminary Estimator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Begun, J. M., Hall, W. J., Huang, W. M., and Wellner, J. A. (1983), “Information and asymptotic efficiency in parametric–nonparametric models”, Ann. Statist., 11, 432–452.MathSciNetMATHCrossRefGoogle Scholar
  2. Clayton, D. and Cuzick, J. (1985), “Multivariate generalizations of the proportional hazards model (with discussion)”, J. Roy. Statist. Soc., A 148, 82–117.Google Scholar
  3. Clayton, D. and Cuzick, J. (1986), “The semiparametric Pareto model for regression analysis of survival times”, Papers on Semiparametric Models,MS-R8614, 19–31, Centrum voor Wiskunde en Informatica, Amsterdam.Google Scholar
  4. Cox, D. R. (1972), “Regression models and life tables”, J. Roy. Statist. Soc., B 34, 187–202.Google Scholar
  5. Cox, D. R. (1975), “Partial Likelihood”, Biometrika, 62, 269–276.MathSciNetMATHCrossRefGoogle Scholar
  6. Huber, P. J. (1967), “The behavior of maximum likelihood estimates under nonstandard conditions”, Proc. Fifth Berkeley Sympos. Math. Statist. Probab., 1, 221–233.Google Scholar
  7. Jennrich, R. I. (1969), “Asymptotic properties of non-linear least squares estimators”, An.n. Math. Statist., 40, 633–643.Google Scholar
  8. Slud, E. V. (1982), “Consistency and efficiency of inferences with the partial likelihood”, Biometrika, 69, 547–552.MathSciNetMATHCrossRefGoogle Scholar
  9. Vonta, F. (1992), “Efficient estimation of a structural parameter in a nonproportional hazards model in the two-sample problem”, Ph.D. Dissertation, University of Maryland.Google Scholar
  10. Vonta, F. (1993), “Efficient estimation in a nonproportional hazards model in survival analysis”, Submitted to Scandin. J. of Statist.Google Scholar
  11. Vonta, F. (1994), “An algorithmic procedure for efficient estimation in a nonproportional hazards model”, Preprint.Google Scholar
  12. Wong, W. H. (1986), “Theory of partial likelihood”, Ann. Statist., 14, 88–123.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Filia Vonta
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of CyprusNicosiaCyprus

Personalised recommendations