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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Contiguity and irreconcilable nonstandard asymptotics of statistical tests

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Author(s):
Sen, Pranab K. [1, 2] ; Pedroso-de-Lima, Antonio C. [3]
Total Authors: 2
Affiliation:
[1] Univ N Carolina, Dept Biostat, Chapel Hill, NC 27599 - USA
[2] Univ N Carolina, Dept Stat & Operat Res, Chapel Hill, NC 27599 - USA
[3] Univ Sao Paulo, Dept Stat, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 3
Document type: Journal article
Source: BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 25, n. 3, p. 444-470, NOV 2011.
Web of Science Citations: 2
Abstract

Wald-type test statistics based on asymptotically normally distributed estimators (not necessarily maximum likelihood estimation or best asymptotically normal) provides an easy access to have tests for statistical hypotheses, far beyond the parametric paradigms. The methodological perspectives rest on a basic consistent asymptotic normal (CAN) condition which is interrelated to the well-known local asymptotic normality (LAN) condition. Contiguity of probability measures facilitates the C(L)AN condition in a relatively easier way. For many regular families of distributions, when statistical hypotheses do not involve nonstandard constraints, verification of contiguity of probability measures is facilitated by the well-known LeCam's First Lemma {[}see Hajek, Sidak and Sen Theory of Rank Tests (1999), Chapter 7]. For nonregular families, though contiguity may hold under different setups, CAN estimators are not fully exploitable in the Wald type testing theory. This simple feature is illustrated by a two-parameter exponential model. Guided by this simple example, mixture of distributions are appraised in the context of Wald-type tests and the so-called (chi) over bar (2)- and (E) over bar -test theory is thoroughly appraised. A general result on counter examples is presented in detail. (AU)

FAPESP's process: 10/05967-9 - Contiguity of probability measures for the gamma frailty Cox model
Grantee:Antonio Carlos Pedroso de Lima
Support type: Scholarships abroad - Research