Linear Functions of Concomitants of Order Statistics with Application to Nonparametric Estimation of a Regression Function
研究了次序统计量伴随量的线性函数的渐近正态性，并利用这些统计量构造了条件期望等条件量的相合估计，对非参数回归估计有参考价值。
Abstract Let (Xi , Yi )(i = 1, 2, …, n) be independent identically distributed as (X, Y). Then the rth ordered X variate is denoted by Xr:n and the associated Y variate, the concomitant of the rth order statistic, by Y [r:n]. This paper considers statistics of the form and more generally of the form , where J is a bounded smooth function and may depend on n. Under certain regularity conditions, the asymptotic normality of these statistics is established. These statistics are used to construct consistent estimators of various conditional quantities, for example E(Y | X = x), P(Y ∈ A | X = x) and var(Y | X = x). Key Words: Concomitants of order statisticsAsymptotic normalityConsistent estimationRegression function