A DCp Criterion for Nonparametric First Derivative Estimation

• Activity Number: 198 - SPEED: Nonparametric Statistics: Estimation, Testing, and Modeling
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 11:35 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sisheng Liu* and Richard Charnigo and Cidambi Srinivasan
• Companies: Fred Hutchinson Cancer Research Center and University of Kentucky and University of Kentucky
• Keywords: Nonparametric derivative estimation; tuning parameter selection; random design points

Abstract

Nonparametric derivative estimation depends on tuning parameter selection. For example, the performance of kernel regression and local polynomial regression will depend on the bandwidth h. The spline smooth regression depends on the penalty parameter \lambda. We propose a DCp criterion for general nonparametric first derivative estimation. Our motivation comes from a more general setting with random designed points and non-constant error variance since the derivative estimation with random covariates are common and pivotal in Econometrics. We justify Dcp criterion both theoretically and by simulation. Moreover, we illustrate a potential application of DCp criterion by an example in Economics.