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An estimator of the derivative of the nonparametric covariate function is derived first, and the nonparametric function estimator is then obtained by integrating the derivative estimator. Uniform consistency rates and pointwise asymptotic normality are obtained for the local derivative estimator under some regularity conditions. Moreover, the baseline function estimator is shown to be uniformly consistent. Demonstration of the asymptotic results strongly relies on the modern empirical theory, which generally does not require the Poisson assumption. Simulation studies also illustrate that the local derivative estimator performs well in a finite\u2010sample regardless of whether the Poisson assumption holds. 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