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.

SEMIPARAMETRIC METHODS IN THE ESTIMATION OF TAIL PROBABILITIES AND EXTREME QUANTILES

In quantitative risk analysis, the problem of estimating small threshold exceedance probabilities and extreme quantiles arise ubiquitously in bio-surveillance, economics, natural disaster insurance actuary, quality control schemes, etc. A useful way to make an assessment of extreme events is to estimate the probabilities of exceeding large threshold values and extreme quantiles judged by interested authorities. Such information regarding extremes serves as essential guidance to interested authorities in decision making processes. However, in such a context, data are usually skewed in nature, and the rarity of exceedance of large threshold implies large fluctuations in the distribution's upper tail, precisely where the accuracy is desired mostly. Extreme Value Theory (EVT) is a branch of statistics that characterizes the behavior of upper or lower tails of probability distributions. However, existing methods in EVT for the estimation of small threshold exceedance probabilities and extreme quantiles often lead to poor predictive performance in cases where the underlying sample is not large enough or does not contain values in the distribution's tail. In this dissertation, we shall be concerned with an out of sample semiparametric (SP) method for the estimation of small threshold probabilities and extreme quantiles. The proposed SP method for interval estimation calls for the fusion or integration of a given data sample with external computer generated independent samples. Since more data are used, real as well as artificial, under certain conditions the method produces relatively short yet reliable confidence intervals for small exceedance probabilities and extreme quantiles.