Diagnostic analysis in generalized extreme value nonlinear regression models

Abstract

In this dissertation, we consider an important class of regression models, namely: the class of generalized extreme value nonlinear regression models. Such models are commonly used in many fields to model extremal events. The main model foundations involve extreme value theory, which provides underlying laws for scenarios in which the data may contain atypical observations which results from the phenomenon of interest and not the result of measurement or recording error. In particular, we develop residual based diagnostic analysis, local influence analysis, generalized Cook’s distance and generalized leverage for the generalized extreme value nonlinear regression model. Since the expected value of the dependent variable is determined by the two parameters that index the distribution, we model each parameter separately and also both parameters jointly, thus considering three possible scenarios. Additionally, we present a model misspecification test that can be used to determine whether the fitted model is incorrectly specified. We provide Monte Carlo simulation results on the finite sample behavior of the test. The results show that the test performs well both in terms of size and power. The size simulations were performed by generating the data from the postulated model whereas in the power simulations the fitted model is different from that used for data generation. The local influence analysis is carried out using three different perturbation schemes. We show that the diagnostic procedures that focus on the scale parameter are typically less stable and more computationally challenging than that on the other model parameter. We also propose two residuals for use with the model: the standardized and deviance residuals. Empirical applications based on simulated and observed data are presented and discussed. All numerical results were obtained using the Julia programming language.