Let $Z_1, Z_2, \cdots$ be i.i.d. standard normal variables. Results are obtained which relate to the tail behavior as $x \rightarrow \infty$ of distributions of the form $F(x) = P\{\sum^\infty_{k=1}\lambda_k\lbrack(Z_k + a_k)^2 - 1\rbrack \leqslant x\}$. For test statistics which have such limiting distributions $F$, asymptotic relative efficiency measures are discussed. One of these is the limiting approximate Bahadur efficiency. Applications are to tests of fit and tests of symmetry.
@article{1176344895,
author = {Gregory, Gavin G.},
title = {On Efficiency and Optimality of Quadratic Tests},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 116-131},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344895}
}
Gregory, Gavin G. On Efficiency and Optimality of Quadratic Tests. Ann. Statist., Tome 8 (1980) no. 1, pp. 116-131. http://gdmltest.u-ga.fr/item/1176344895/