Abstract. We deduce a partial version of the KMT (1975) inequality for coupling the uniform empirical process with a sequence of Brownian bridges via the construction used by Csörgő and Révész (CsR) (1978) for their similar coupling of the uniform quantile process with another sequence of Brownian bridges. These constructions are pivoted on the KMT (1975, 1976) inequalities for approximating partial sums by a Wiener process (Brownian motion).

AMS Subject Classification (1991): 60F17, 60F15, 60G50, 62G30

Keyword(s): Empirical and quantile processes, Brownian bridge approximations, Hungarian construction

Received January 8, 2007, and in revised form March 6, 2007. (Registered under 5970/2009.)