Estimating the error distribution function in nonparametric regression


Consider the nonparametric regression model Y = r(Z) + ε, where the covariate Z and the error ε are independent, and ε has mean zero, finite variance σ and density f . We observe independent copies (Y1, Z1), . . . , (Yn, Zn) of (Y, Z) and want to estimate the distribution function F of ε. If the regression function r were known, we could use the empirical… (More)