Taconis-Haantjes, E.

condition proof t h e theorem probability representation distribution quantile bahadur sample r e m result sequence note t h ghosh variable function sample quantiles distribution function lemma theorem 2 order sample p-quantile p-quantile uniform order statistics elselien taconis-haantje probability 1 distribution function f --~oo statistic lauren n /loglogn n --~oo elselien taconis-haantjes binomial distribution l __<i order statistics integer iterated logarithm theorem 1 l ~ i g n 4 case i f t ~= ~/-~ g n b n / 2 n i c process l ~_k p r e n v ~ n hoeffding ~ ~ b e n t show t h assumption theorem 2. proof normality sample p ~-quantile ~=f l /4w t h r g e t elselien taconis-haantjes 306 v 4 1 sample quantiles laurens p ~ 2 n ~ b k e e.g t lim zsup uniform r ~v p neighbourhood n e b i /2-~log n elselien taconis-haantjes j elselien taconis-haantjes f condition t <b kiefer t theorem i