PhD Dissertation Abstracts: 2016
Statistics PhD Alumni 2016:
ADVISERS: Alexander Aue, Prabir Burman
TITLE: Spatio-temporal Modeling and Predictions of House Prices in San Jose
ABSTRACT: House prices are of interest to the general public and government agencies for many reasons. The complexity and practicality of house price modeling have attracted many researchers. In this talk, the dependence structure in time and space, among houses using over 130 thousand house price observations in San Jose from 1991 to 2012, are explored. Innovative spline methods are utilized to build a forecasting model incorporating both hedonic, spatial and temporal information. The use of splines greatly reduces the number of variables needed in the model without sacrificing for precision. Moreover, the recession period (2008--2010) was given special care because it behaved differently from the rest of the 22 year time period. The proposed model uses both repeat sales and single sale transactions, and is able to produce an overall price index for the whole region, as well as predictions for individual houses. The final model, which includes an autoregressive spatio-temporal error term, is shown to have better predictive abilities than other competing methods in the literature.
Alexander Petersen (2016)
ADVISER: Hans-Georg Mueller
TITLE: Transformation Methods for Density Functions and Covariance Matrices in Functional Data Analysis.
ABSTRACT: Transformations for constrained data are used widely in statistical methodology. In functional data analysis, one frequently encounters complex objects with non-linear properties for which transformations can be usefully applied. As a first illustration, functional data that are non-negative and have a constrained integral can be considered as samples of one-dimensional probability density functions. Because densities do not live in a vector space, common methods of functional data analysis are not applicable. Instead, we propose to first transform the probability densities into a Hilbert space of functions through a continuous and invertible map, and then apply standard linear methods. A second example is given by multivariate functional data recorded for a sample of subjects on a common domain, where one is often interested in the covariance between pairs of the component functions. We generalize the straightforward approach of integrating the pointwise covariance matrices over the functional time domain by introducing Fr\'echet integrals which, in analogy to Fr\'echet means, depend on the metric chosen for the space of covariance matrices. This generalization is motivated by the class of power transformations on covariance matrices and associated metrics. Some asymptotic results on optimal metric selection will be presented. The proposed transformation methods for densities and functional covariance are illustrated by functional connectivity analyses of fMRI data.