Canadian Journal of Statistics

Nonparametric two‐step regression estimation when regressors and error are dependent

Journal Article


This paper considers estimation of the function g in the model Yt = g(Xt ) + ϵt when E(ϵt|Xt) ≠ 0 with nonzero probability. We assume the existence of an instrumental variable Zt that is independent of ϵt, and of an innovation ηt = XtE(Xt|Zt). We use a nonparametric regression of Xt on Zt to obtain residuals ηt, which in turn are used to obtain a consistent estimator of g. The estimator was first analyzed by Newey, Powell & Vella (1999) under the assumption that the observations are independent and identically distributed. Here we derive a sample mean‐squared‐error convergence result for independent identically distributed observations as well as a uniform‐convergence result under time‐series dependence.

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