Estimating Quantile Sensitivities
成果类型：
Article
署名作者：
Hong, L. Jeff
署名单位：
Hong Kong University of Science & Technology
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1080.0531
发表日期：
2009
页码：
118-130
关键词：
摘要：
Quantiles of a random performance serve as important alternatives to the usual expected value. They are used in the financial industry as measures of risk and in the service industry as measures of service quality. To manage the quantile of a performance, we need to know how changes in the input parameters affect the output quantiles, which are called quantile sensitivities. In this paper, we show that the quantile sensitivities can be written in the form of conditional expectations. Based on the conditional-expectation form, we first propose an infinitesimal-perturbation-analysis (IPA) estimator. The IPA estimator is asymptotically unbiased, but it is not consistent. We then obtain a consistent estimator by dividing data into batches and averaging the IPA estimates of all batches. The estimator satisfies a central limit theorem for the i.i.d. data, and the rate of convergence is strictly slower than n(-1/3). The numerical results show that the estimator works well for practical problems.