Regression Analysis for Linear Models with Functional Responses

Abstract

Linear models where the response is a function, but the predictors are vectors are considered. A functional F test for choosing among two nested functional linear models is developed. Its null distribution is derived and a convenient approximation is presented. A simulation study is conducted to compare the size and power of the test to some competing tests. A simple way to test individual predictors is presented. Studentized residuals, jackknife residuals and Cook statistics are defined to detect outliers and highly influential points. Chi-square Q-Q plots are proposed to check for the assumption of independent Gaussian errors. The methodology is illustrated with some data from Ergonomics.