ASYMPTOTIC BOUND ON THE CHARACTERISTIC FUNCTION OF SIGNED LINEAR SERIAL RANK STATISTICS

M’HAMMED KADRI^{1} AND KHALID RIFI^{2}

1Département de Mathématiques et Informatique, Faculté des Sciences Dhar Mahraz, Fès, Morocco 2Ecole Normale Supérieure, B. P. 5206, Bensouda, Fès, Morocco

(Received August 10, 1999; revised October 16, 2000)

Abstract. This work establishes an asymptotic bound on the characteristic function of signed linear serial rank statistics. The result is obtained under rather general conditions including the important case of van der Waerden scores. It generalizes the result of Seoh (1983, Ph.D. Thesis, Department of Mathematics, Indiana University) and constitutes an essential step to the elaboration of Berry-Esséen’s bounds and the establishment of Edgeworth expansions. These statistics constitute a natural tool for testing the hypothesis of white noise with a symmetrical (unspecified) distribution in comparison to other alternative hypothesis of serial dependence.

Key words and phrases: Berry-Esséen bounds, characteristic function, Edgeworth expansions, signed serial rank statistics, time series.