Linear Functions of Concomitants of Order Statistics with Application to Nonparametric Estimation of a Regression Function
Shie‐Shien Yang · Journal of the American Statistical Association · 1981
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).