Noncentral Convergence of Wald's Large-Sample Test Statistic in Exponential Families
Stroud, T. W. F.
Ann. Statist., Tome 1 (1973) no. 2, p. 161-165 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
It is shown that under very mild assumptions Wald's large-sample test statistic (quadratic form based on unrestricted maximum likelihood estimators) converges to noncentral chi-square under a sequence of local alternatives of the order $n^{-\frac{1}{2}}$, when the family of distributions is assumed to be of exponential type. This eliminates, for these families, the necessity of invoking the strict regularity conditions of Wald for the purpose of justifying the asymptotic distribution.
Publié le : 1973-01-14
Classification:  
@article{1193342393,
     author = {Stroud, T. W. F.},
     title = {Noncentral Convergence of Wald's Large-Sample Test Statistic in Exponential Families},
     journal = {Ann. Statist.},
     volume = {1},
     number = {2},
     year = {1973},
     pages = { 161-165},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1193342393}
}

Stroud, T. W. F. Noncentral Convergence of Wald's Large-Sample Test Statistic in Exponential Families. Ann. Statist., Tome 1 (1973) no. 2, pp.  161-165. http://gdmltest.u-ga.fr/item/1193342393/