In this note, we derive a Gaussian Central Limit Theorem for the sample quantiles based on identically distributed but possibly dependent random variables with explicit convergence rate. Our approach is based on converting the problem to a sum of indicator random variables, applying Stein's method for local dependence, and bounding the distance between two normal distributions. We also generalize this approach to the joint convergence of sample quantiles with an explicit convergence rate.
翻译:在本说明中,我们根据分布相同但可能具有依赖性的随机变量以及明确的趋同率,为抽样的四分位数得出高西亚中央限制理论。 我们的方法是将问题转换成指标随机变量的总和,对本地依赖性采用施泰因的方法,并限制两种正常分布之间的距离。 我们还将这一方法推广到样本四分位数与明确的趋同率的联合趋同率。