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

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Abstract

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 = Xt - E(Xt|Zt). We use a nonparametric regression of Xt on Zt to obtain residuals η̂t, 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.

Original languageEnglish (US)
Pages (from-to)289-300
Number of pages12
JournalCanadian Journal of Statistics
Volume28
Issue number2
DOIs
StatePublished - Jun 2000

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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