@article{Burgio_Nikitin_1998, title={Goodness-of-fit tests for normal distribution of order p and their asymptotic effìciency}, volume={58}, url={https://rivista-statistica.unibo.it/article/view/1082}, DOI={10.6092/issn.1973-2201/1082}, abstractNote={This paper deals with the Bahadur local efficiency of the parametric score test and of the Kolmogorov, Cramér-von Mises and Chapman-Moses non parametric tests to verify the null hypothesis Ho Teta= 0 agains the alternative Hl: Teta &gt; 0, being Teta the centrality parameter of a p normal distribution. Bahadur efficiency is calculated with respect to the theoretical upper bound for exact slopes given in terms of Kullback-Leibler information numbers. It is analytically, numerically and graphically shown that the score test is locally optimal for all p &gt;= 1 whereas the non parametric tests behave very differently for large p and p close to 1. As a matter of fact, for large p their efficiency decreases approxi-mately as 1/p, but for p close to 1 they are serious competitors of the score test. For instance, the Kolmogorov test is for p= 1 locally optimal in the Bahadur sense.}, number={2}, journal={Statistica}, author={Burgio, Giuseppe and Nikitin, Yakov}, year={1998}, month={Jan.}, pages={213–230} }