文章基本信息

标题：Nonparametric confidence intervals for conditional quantiles with large-dimensional covariates
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作者：Laurent Gardes
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2020
卷号：14
期号：1
页码：661-701
DOI：10.1214/20-EJS1678
语种：English
出版社：Institute of Mathematical Statistics
摘要：The first part of the paper is dedicated to the construction of a $\gamma$ - nonparametric confidence interval for a conditional quantile with a level depending on the sample size. When this level tends to 0 or 1 as the sample size increases, the conditional quantile is said to be extreme and is located in the tail of the conditional distribution. The proposed confidence interval is constructed by approximating the distribution of the order statistics selected with a nearest neighbor approach by a Beta distribution. We show that its coverage probability converges to the preselected probability $\gamma $ and its accuracy is illustrated on a simulation study. When the dimension of the covariate increases, the coverage probability of the confidence interval can be very different from $\gamma $. This is a well known consequence of the data sparsity especially in the tail of the distribution. In a second part, a dimension reduction procedure is proposed in order to select more appropriate nearest neighbors in the right tail of the distribution and in turn to obtain a better coverage probability for extreme conditional quantiles. This procedure is based on the Tail Conditional Independence assumption introduced in (Gardes, Extremes, pp. 57–95, 18(3), 2018).
关键词：Extreme conditional quantiles; confidence interval; dimension reduction