On Sample Size for Nonparametric Regression and Partial Linear Models

• Activity Number: 295
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Li-Shan Huang*+ and Hsiao-Hsian Gao
• Companies: National Tsing Hua University and National Tsing Hua University
• Keywords: sample size ; nonparametric regression ; partial linear model ; local polynomial regression ; smoothing methods ; curve fitting

Abstract

Non- and semi-parametric regression models have received considerable attention in statistics with a wide range of applications. However, to our knowledge, sample size calculations for non- and semi-parametric models have not been discussed in the literature. This paper examines the sample size required for a curve estimated by local polynomial regression to achieve significance based on the F-tests investigated in Huang and Chen (2008) for univariate nonparametric regression and in Huang and Davidson (2010) for partial linear models. We describe explicit procedures for power/sample size calculation based on these two tests. Real-data examples are provided to demonstrate the use of the procedures. Simulation results indicate that the proposed methods are conservative and the empirical power is often larger than the desired power.