Supervisors info:
Μελιγκοτσίδου Λουκία, Επίκουρη Καθηγήτρια, Τμήμα Μαθηματικών, ΕΚΠΑ
Μπουρνέτας Απόστολος, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Τρέβεζας Σάμης, Λέκτορας, Τμήμα Μαθηματικών, ΕΚΠΑ
Summary:
This dissertation is concerned with Classical and Bayesian theory for the threshold regression model with one or two threshold variables. Threshold regression models have a wide variety of applications, mainly in the field of econometrics, and belong to the family of regression models with structural breaks that were introduced by Quandt (1960). In the literature most of the interest is focused on the discontinuous Threshold Regression Models, because of the non-standard asymptotic distribution of the statistical functions of the threshold parameters. Among others, we will examine this particular issue not only in theoretical but also in a more applied level.
Estimating the model parameters and obtaining asymptotic distributions of the respective estimators concentrates most of the interest in the area of Regression Analysis. The main goal is the construction of confidence intervals and hypotheses testing regarding the significance of each parameter. From the scope of Bayesian analysis, it is of great importance to take advantage of all the available information in order to define the prior distribution and finally get the posterior. The computation of the posterior distribution is a procedure that becomes more complex as the number of parameters increases, since it demands the calculation of composite integrals and the utilization of simulation techniques when the former is not applicable. Such methods are the Markov Chain Monte Carlo (MCMC) algorithms and a special case of them, the Gibb's sampler. All these methods are presented extensively in this dissertation and cover a wide variety of regression models.
Although the estimation of a model's parameters is the primary objective for a statistician, the selection of the most appropriate model for a given dataset comes first. Therefore, model comparison is the first step that one needs to do for precise and complete inference results. In essence, this is a hypotheses test that concerns the kind of relationship between the dependent variable and the explanatories, namely the type of model. Such tests are accomplished from the scope of Classical theory by using appropriate statistical tools, such as the LR statistic, and from the scope of Bayesian theory with the computation of each model's posterior probability. Having selected, either way, the most appropriate model, shall one proceed to statistical inference regarding its parameters.
