Bootstrapping the Partial Linear Model

• Activity Number: 463
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Megan Heyman*+ and Snigdhansu Chatterjee
• Companies: and University of Minnesota
• Keywords: bootstrap ; partially linear model ; high dimension

Abstract

In the classical partial linear model, a response is modeled as a linear combination of a finite number of variables and an unknown smooth function of one variable. However, the smooth function becomes problematic when attempting to bootstrap standard errors for the model. Thus, we propose approximating the unknown smooth function by an orthonormal basis (for example, polynomial) in order to produce consistent bootstrap estimators. Therefore, for any fixed number of basis coefficients, the conditional distribution of the errors given the data is biased from 0. We show that as the number of basis coefficients is allowed to tend toward infinity at an appropriate rate (with respect to the number of observations), the least squares estimator is consistent. More importantly, we explore the consistency of type E and R estimators, from Liu and Singh (1992 Annals of Statistics, Vol. 20, pages 370-384). Simulation results are provided.