Analysis of Aggregated Functional Data from Mixed Populations with Application to Energy Consumption

• Activity Number: 470
• Type: Invited
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Nancy Heckman* and Amanda Lenzi and Camila de Souza and Ronaldo Dias and Nancy Garcia
• Companies: The University of British Columbia and Technical University of Denmark and The University of British Columbia and University of Campinas and University of Campinas
• Keywords: functional data analysis ; aggregated data ; nonparametric regression ; energy consumption

Abstract

Efficient energy distribution requires understanding energy consumption patterns of different types of consumers. However, obtaining individual-level consumption information is often either not possible or too expensive. More readily available are data from aggregations of energy use, that is, from sums of individuals' energy use. The sum is over individuals falling within a range of consumer classes, such as residential and commercial. We consider analysis of such data when information on the exact number of individuals of each class may be incorrect, due to self-reporting inaccuracies. We develop a maximum likelihood methodology to estimate the expected energy use of each class as a function of time and the true number of consumers in each class. We model individual level energy consumption via random regression coefficients and a B-spline basis. We model reported consumer class counts using probabilities of individual-level misreporting.