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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Contiguity and irreconcilable nonstandard asymptotics of statistical tests

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Autor(es):
Sen, Pranab K. [1, 2] ; Pedroso-de-Lima, Antonio C. [3]
Número total de Autores: 2
Afiliação do(s) autor(es):
[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
Número total de Afiliações: 3
Tipo de documento: Artigo Científico
Fonte: BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 25, n. 3, p. 444-470, NOV 2011.
Citações Web of Science: 2
Resumo

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)

Processo FAPESP: 10/05967-9 - Contiguidade de medidas de probabilidade para o modelo de Cox com fragilidade gama
Beneficiário:Antonio Carlos Pedroso de Lima
Linha de fomento: Bolsas no Exterior - Pesquisa