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December 2001 Likelihood Ratio Tests for Monotone Functions
Moulinath Banerjee, Jon A. Wellner
Ann. Statist. 29(6): 1699-1731 (December 2001). DOI: 10.1214/aos/1015345959


We study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function.The likelihood ratio test for this hypothesis is derived in the particular case of interval censoring (or current status data)and its limiting distribution is obtained. The limiting distribution is that of the integral of the difference of the squared slope processes corresponding to a canonical version of the problem involving Brownian motion $+t^2$ and greatest convex minorants thereof. Inversion of the family of tests yields pointwise confidence intervals for the unknown distribution function.We also study the behavior of the statistic under local and fixed alternatives.


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Moulinath Banerjee. Jon A. Wellner. "Likelihood Ratio Tests for Monotone Functions." Ann. Statist. 29 (6) 1699 - 1731, December 2001.


Published: December 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1043.62037
MathSciNet: MR1891743
Digital Object Identifier: 10.1214/aos/1015345959

Primary: 62G05
Secondary: 60G15 , 62E20

Keywords: asymptotic distribution , Brownian motion , constrained estimation , fixed alternatives , Gaussian process , greatest convex minorant , interval censoring , Kullback-Leibler discrepancy , least squares , likelihood ratio , local alternatives , monotone function , slope processes

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 6 • December 2001
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