Selecting a semi-parametric estimator by the expected log-likelihood

Liquet, Benoit and Commenges, Daniel (2005). Selecting a semi-parametric estimator by the expected log-likelihood. In Probability, statistics and modelling in public health (pp. 332-349) New York, NY, United States: Springer US. doi:10.1007/0-387-26023-4_22


Author Liquet, Benoit
Commenges, Daniel
Title of chapter Selecting a semi-parametric estimator by the expected log-likelihood
Title of book Probability, statistics and modelling in public health
Place of Publication New York, NY, United States
Publisher Springer US
Publication Year 2005
Sub-type Chapter in textbook
DOI 10.1007/0-387-26023-4_22
ISBN 9780387260228
9780387260235
Start page 332
End page 349
Total pages 18
Language eng
Abstract/Summary A criterion for choosing an estimator in a family of semi-parametric estimators from incomplete data is proposed. This criterion is the expected observed log-likelihood (ELL). Adapted versions of this criterion in case of censored data and in presence of explanatory variables are exhibited. We show that likelihood cross-validation (LCV) is an estimator of ELL and we exhibit three bootstrap estimators. A simulation study considering both families of kernel and penalized likelihood estimators of the hazard function (indexed on a smoothing parameter) demonstrates good results of LCV and a bootstrap estimator called ELLbboot. When using penalized likelihood an approximated version of LCV also performs very well. The use of these estimators of ELL is exemplified on the more complex problem of choosing between stratified and unstratified proportional hazards models. An example is given for modeling the effect of sex and educational level on the risk of developing dementia.
Keyword Bootstrap
Cross-validation
Kullback-Leibler information
Proportional hazard model
Semi-parametric
Smoothing
Q-Index Code BX
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Book Chapter
Collection: School of Mathematics and Physics
 
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Created: Thu, 19 Sep 2013, 12:21:48 EST by Kay Mackie on behalf of School of Mathematics & Physics