A Space-Efficient Recursive Procedure for Estimating a Quantile of an Unknown Distribution
A Space-Efficient Recursive Procedure for Estimating a Quantile of an Unknown Distribution
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用于估计未知分布的分位数的节省空间的递归过程
DOI：
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发表时间：
1983
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通讯作者：
L. Tierney
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文献类型：
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作者：
L. Tierney
考虑基于n个观测值的随机样本计算未知总体的百分位数或分位数的估计值的问题。通过将这个问题视为随机逼近中的一个问题，我们得到了一个估计量，它只需要少量的直接访问存储空间，不随样本大小的增加。我们表明，一个简单的随机近似估计的修改版本具有相同的大样本行为的样本分位数，它具有最小的渐近方差之间的所有合理的估计。修改后的程序也产生了估计的渐近方差的估计。一些模拟结果表明，所提出的估计器表现良好，在中等规模的样本。
Consider the problem of computing an estimate of a percentile or quantile of an unknown population based on a random sample of n observations. By viewing this problem as a problem in stochastic approximation, we obtain an estimator that requires only a small amount of direct access storage space that does not increase with the sample size. We show that a modified version of the simple stochastic approximation estimator has the same large-sample behavior as the sample quantile, which has the smallest asymptotic variance among all reasonable estimators. The modified procedure also yields an estimate of the asymptotic variance of the estimator. Some simulation results are presented to show that the proposed estimator performs well in samples of moderate size.