BANDWIDTH CHOICE FOR AVERAGE DERIVATIVE ESTIMATION

• 成果类型: Article
• 署名作者: HARDLE, W; HART, J; MARRON, JS; TSYBAKOV, AB
• 署名单位: Texas A&M University System; Texas A&M University College Station; University of North Carolina; University of North Carolina Chapel Hill; Russian Academy of Sciences
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2290472
• 发表日期: 1992
• 页码: 218-226
• 关键词: regression

摘要

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.