Optimal Designs for Discriminating Between Functional Linear Models

• Activity Number: 307
• Type: Invited
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Verity Fisher*+ and David Woods
• Companies: University of Southampton and University of Southampton
• Keywords: T-optimality ; functional data

Abstract

Improvements in online measuring and monitoring have facilitated an increase in the number of observations that can be taken on each experimental unit in many industrial and scientific experiments. It is often a reasonable assumption that the data for each experimental unit are generated by an unknown smooth function and interest is then in how changes to the levels of the controllable factors influence the shape of these functions. Often a semi-parametric model is assumed for the response, with relatively simple polynomial models describing the factor effects. That is, the functional response from each unit is described by a linear combination of functional parameters, leading to a functional linear model.

Methods are presented for the design of experiments when the aim is to discriminate between two functional linear models. We develop an extension of the T-optimality criterion to functional data and present some properties of the resulting designs. The methodology is motivated by a wear study from Tribology and assessed via simulation studies to calculate the power of the resulting analyses.