The Annals of Statistics

Semiparametric likelihood ratio inference

S. A. Murphy and A. W. van der Vaart

Full-text: Open access

Abstract

Likelihood ratio tests and related confidence intervals for a real parameter in the presence of an infinite dimensional nuisance parameter are considered. In all cases, the estimator of the real parameter has an asymptotic normal distribution. However, the estimator of the nuisance parameter may not be asymptotically Gaussian or may converge to the true parameter value at a slower rate than the square root of the sample size. Nevertheless the likelihood ratio statistic is shown to possess an asymptotic chi-squared distribution. The examples considered are tests concerning survival probabilities based on doubly censored data, a test for presence of heterogeneity in the gamma frailty model, a test for significance of the regression coefficient in Cox's regression model for current status data and a test for a ratio of hazards rates in an exponential mixture model. In both of the last examples the rate of convergence of the estimator of the nuisance parameter is less than the square root of the sample size.

Article information

Source
Ann. Statist. Volume 25, Number 4 (1997), 1471-1509.

Dates
First available: 9 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1031594729

Mathematical Reviews number (MathSciNet)
MR1463562

Digital Object Identifier
doi:10.1214/aos/1031594729

Zentralblatt MATH identifier
0928.62036

Subjects
Primary: 62G15: Tolerance and confidence regions 62G20: Asymptotic properties 62F25: Tolerance and confidence regions

Keywords
Least favorable submodel profile likelihood confidence interval

Citation

Murphy, S. A.; van der Vaart, A. W. Semiparametric likelihood ratio inference. The Annals of Statistics 25 (1997), no. 4, 1471--1509. doi:10.1214/aos/1031594729. http://projecteuclid.org/euclid.aos/1031594729.


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