## Approximate distributions of order statistics: with applications to nonparametric statistics |

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absolutely continuous applied Assume asymptotic normality bootstrap Borel sets central order statistics co(F common d.f. conditional distribution Corollary defined Denote derivatives distributed r.v.'s distributions of order domain of attraction Example expansion of length extreme value d.f. extreme value theory Frechet function given Hellinger distance holds i.i.d. random variables implies inequality joint density joint distribution largest order statistics Lemma limit theorem Markov kernel maximum Mises Moreover nonparametric normal distribution Notice obtain P(Ye Pareto d.f. polynomials positive integer probability measure proof of Theorem prove q-quantile random vectors Reiss rth order statistic sample maxima sample median sample q.f. sample quantiles scale parameter Section signed measures single order statistic standard exponential r.v.'s standard normal underlying d.f. uniform distribution uniform r.v.'s uniformly unimodal upper bound Ur:n variables with common variational distance w.r.t. the variational weak convergence Weibull densities Xi:n Xn:n Xr:n Xs:n yields zero