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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:51

Article

FOTOPOULOS, SB ; AHN, SK

关键词: STRONG MIXING;    EMPIRICAL PROCESS;    QUANTILE PROCESS;    PREDICTION INTERVAL;   

DOI  :  10.1006/jmva.1994.1047

来源: Elsevier

【 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.

【 授权许可】

Free