文章基本信息

标题：Monotone least squares and isotonic quantiles
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作者：Alexandre Mösching ; Lutz Dümbgen
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：24-49
DOI：10.1214/19-EJS1659
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider bivariate observations $(X_{1},Y_{1}),\ldots,(X_{n},Y_{n})$ such that, conditional on the $X_{i}$, the $Y_{i}$ are independent random variables. Precisely, the conditional distribution function of $Y_{i}$ equals $F_{X_{i}}$, where $(F_{x})_{x}$ is an unknown family of distribution functions. Under the sole assumption that $x\mapsto F_{x}$ is isotonic with respect to stochastic order, one can estimate $(F_{x})_{x}$ in two ways.
关键词：Regression quantiles; stochastic order; uniform consistency