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The density weighted average derivative (DWAD) of a regression function is acanonical parameter of interest in economics. Classical first-order largesample distribution theory for kernel-based DWAD estimators relies on tuningparameter restrictions and model assumptions leading to an asymptotic linearrepresentation of the point estimator. Such conditions can be restrictive, andthe resulting distributional approximation may not be representative of theunderlying sampling distribution of the statistic of interest, in particularnot being robust to bandwidth choices. Small bandwidth asymptotics offers analternative, more general distributional approximation for kernel-based DWADestimators that allows for, but does not require, asymptotic linearity. Theresulting inference procedures based on small bandwidth asymptotics were foundto exhibit superior finite sample performance in simulations, but no formaltheory justifying that empirical success is available in the literature.Employing Edgeworth expansions, this paper shows that small bandwidthasymptotics lead to inference procedures with demonstrable superiorhigher-order distributional properties relative to procedures based onasymptotic linear approximations.

Higher-order Refinements of Small Bandwidth Asymptotics for Density-Weighted Average Derivative Estimators