Methodological Development of Functional Data Analysis, with Applications

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Modern data sets require statistical methodology beyond that of univariate and multivariate analyses: they require Functional Data Analysis (FDA), where each individual generates data from some continuous process, observed with error. My proposal focuses on several areas of FDA.METHODS WITH LATENT VARIABLES WITH RELATION TO ENERGY CONSUMPTION. In the first project I develop methods to analyze hourly power consumption data from a group of buildings, where each building has a different (known) number of air conditioners. The amount of energy used depends on the number of air conditioners that are in use, which is unknown. In the second project, a hydro-electric company has data in several neighbourhoods on the total energy consumption as a function of time, along with the reported number of several consumer types (eg residential, small business). However the reported number is often not equal to the actual number. The goal is to estimate the number of consumer types in each neighbourhood, along with the "typical usage curve" for each consumer type.THE USE OF DIFFERENTIAL OPERATORS IN FDA. Differential operators have a long history in the analysis of functional data. They appear in penalties, with resulting methodology having an elegant way to stochastic processes and to Bayes estimation. Differential operators are also used explicitly in modeling. I will develop these connections, in order to obtain a more unified and model-based approach.FDA IN ANIMAL BREEDING AND EVOLUTIONARY BIOLOGY. In this application, the underlying genetic structure of the continuous process is important for successful and profitable animal breeding and for understanding the forces and consequences of natural selection. This genetic structure can be estimated via data from dependent individuals with known pedigree. I will develop new methods and compare new and existing methods for studying genetic structure.