STRONG APPROXIMATION OF THE QUANTILE PROCESSES AND ITS APPLICATIONS UNDER STRONG MIXING PROPERTIES

[摘要] Given some regularity conditions on the distribution F(.) of a random X(1), ..., X(n) emanating from a strictly stationary sequence of random variables satisfying a strong mixing condition, it is shown that the sequence of quantile processes {n(1/2)f(F-1(s))(F-n(-1)(s)-F-1(s)); 0<1} behaves like a sequence of Brownian bridges {B-n(s); 0<1}. The latter is then utilized to construct (i) simultaneous bounds for the unknown quantile function F-1(s), and (ii) a tolerance interval for predicting a future observation. Some numerical investigations of the results are also discussed. (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-01

[关键词] STRONG MIXING;EMPIRICAL PROCESS;QUANTILE PROCESS;PREDICTION INTERVAL