Parametric and Non-Parametric Regression Models with Applications to Climate Change

Abstract

In this dissertation we have studied the climate factors that contribute to climate change using univariate and multivariate parametric methods as well as nonparametric models. In this study, we have three major contributions. First, the extent of mountain glaciers around the globe and their responses to climate factors are investigated using multivariate methods and we have proposed a predictive model to estimate the mountain glacier response to climate factors. Second, we have addressed the important problem of bandwidth selection in presence of correlated noise in nonparametric regression analysis. We have proposed a denoising method based on an ensemble bandwidth optimization where an adaptive bandwidth chooses the optimal bandwidth for each data point by maximizing the signal to noise ratio. The proposed denoising method is evaluated by running several hundreds of Monte Carlo simulations for various signals corrupted with different types of noise including white Gaussian noise and correlated noise. Third, since most of the observed climate factors are corrupted with the correlated noise, we applied the proposed denoising method to the observed climate factors, and located the representative features including peaks and change points and investigated the correlation of these factors as well as environmental events.