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This paper examines the local linear regression (LLR) estimate of theconditional distribution function $F(y|x)$. We derive three uniform convergenceresults: the uniform bias expansion, the uniform convergence rate, and theuniform asymptotic linear representation. The uniformity in the above resultsis with respect to both $x$ and $y$ and therefore has not previously beenaddressed in the literature on local polynomial regression. Such uniformconvergence results are especially useful when the conditional distributionestimator is the first stage of a semiparametric estimator. We demonstrate theusefulness of these uniform results with two examples: the stochasticequicontinuity condition in $y$, and the estimation of the integratedconditional distribution function.

Uniform Convergence Results for the Local Linear Regression Estimation of the Conditional Distribution