Bandwidth choice for average derivative estimation. (English) Zbl 0781.62044

Härdle, W.; Hart, J.; Marron, J. S.; Tsybakov, A. B.

J. Am. Stat. Assoc. 87, No. 417, 218-226 (1992).

Summary: The average derivative is the expected value of the derivative of a regression function. Kernel methods have been proposed as a means of estimating this quantity. The problem of bandwidth selection for these kernel estimators is addressed here. Asymptotic representations are found for the variance and squared bias. These are compared with each other to find an insightful representation for a bandwidth optimizing terms of lower order than \(n^{-1}\). It is interesting that, for dimensions greater than 1, negative kernels have to be used to prevent domination of bias terms in the asymptotic expression of the mean squared error. The extent to which the theoretical conclusions apply in practice is investigated in an economical example related to the so-called “law of demand”.

MSC:

62G07	Density estimation
65C99	Probabilistic methods, stochastic differential equations

Keywords:

bandwidth optimization; asymptotic representations; law of demand; bandwidth selection; kernel estimators; variance; squared bias; negative kernels