STATISTICAL METHODS FOR ADVANCED ECONOMETRIC MODELS WITH APPLICATIONS TO VEHICLE HOLDING AND SPEED QUANTILES DISTRIBUTION

This dissertation proposes statistical methods to formulate, estimate and apply complex transportation models. Two main problems are part of the analyses conducted and presented in this dissertation. The first method solves an econometric problem and is concerned with the joint estimation of models that contain both discrete and continuous decision variables. The use of ordered models along with a regression is proposed and their effectiveness is evaluated with respect to unordered models. Procedure to calculate and optimize the log-likelihood functions of both discrete-continuous approaches are derived, and difficulties associated with the estimation of unordered models explained. Numerical approximation methods based on the Genz algortithm are implemented in order to solve the multidimensional integral associated with the unordered modeling structure. The problems deriving from the lack of smoothness of the probit model around the maximum of the log-likelihood function, which makes the optimization and the calculation of standard deviations very difficult, are carefully analyzed. A methodology to perform out-of-sample validation in the context of a joint model is proposed. Comprehensive numerical experiments have been conducted on both simulated and real data. In particular, the discrete-continuous models are estimated and applied to vehicle ownership and use models on data extracted from the 2009 National Household Travel Survey. The second part of this work offers a comprehensive statistical analysis of free-flow speed distribution; the method is applied to data collected on a sample of roads in Italy. A linear mixed model that includes speed quantiles in its predictors is estimated. Results show that there is no road effect in the analysis of free-flow speeds, which is particularly important for model transferability. A very general framework to predict random effects with few observations and incomplete access to model covariates is formulated and applied to predict the distribution of free-flow speed quantiles. The speed distribution of most road sections is successfully predicted; jack-knife estimates are calculated and used to explain why some sections are poorly predicted. Eventually, this work contributes to the literature in transportation modeling by proposing econometric model formulations for discrete-continuous variables, more efficient methods for the calculation of multivariate normal probabilities, and random effects models for free-flow speed estimation that takes into account the survey design. All methods are rigorously validated on both real and simulated data.

TRADITION AND INNOVATION: ANALYSIS AND PERFORMANCE OF SELECTED COMPOSITIONS FOR VIOLONCELLO BY HEITOR VILLA-LOBOS

Brazilian composer Heitor Villa-Lobos (1887-1959) began his musical career as a cellist. When he was only twelve years old, it became imperativeupon the sudden and untimely death of his fatherthat the young Villa-Lobos earn money as a cellist to provide financial support for his mother and sisters. Villa-Lobos's intimate relationship with the cello eventually inspired him to compose great music for this instrument. This dissertation explores both the diversity of compositional technique and the evolution of style found in the music for cello written by Villa-Lobos. The project consists of two recorded recital performances and a written document exploring and analyzing those pieces. In the study of the music of Villa-Lobos, it is of great interest to consider the music's traditional European elements in combination (or even juxtaposition) with its imaginative and sometimes wildly innovative Brazilian character. His early works were greatly influenced by European Romantic composers such as Robert Schumann, Frédéric Chopin, and the virtuoso cellist/composer David Popper (whom Villa-Lobos idolized). Later, Villa-Lobos flourished in a newfound compositional independence and moved away from Euro-romanticism and toward the folk music of his Brazilian homeland. It is intriguing to experience this transition through an exploration of his cello compositions. The works examined and performed in this dissertation project are chosen from among the extensive number of Villa-Lobos's cello compositions and are his most important works for cello with piano, cello with another instrument, and cello with orchestra. The chosen works demonstrate the evolving range and combination of characteristic elements found in Villa-Lobos's compositional repertoire.