Nonparametric Methods For Functional Regression With Multiple Responses

Nonparametric functional regression is of considerable importance due to its impact on the development of data analysis in a number of elds, least cost and saving time. In this thesis, we focus on nonparametric functional regression and its extensions, and its application to functional data. We rst review nonparametric functional regression, followed by a detailed discussion about model structures, semi-metrics and kernel functions. Secondly, we extend the independent response model to multivariate response variables with functional covariates. Our model uses the K-Nearest Neighbour function with automatic bandwidth selection by a cross-validation procedure, and where the closeness between functional data is measured via semi-metrics. Then, in the third topic, we use the principal component analysis to decorrelate multivariate response variables. After that, in the fourth topic, we add new results to the nonparametric functional regression when the covariate is functional and the response is multivariate in nature with di erent bandwidths for di erent responses, and where the correlation among di erent responses is taken into account with di erent bandwidths for di erent responses. Our model uses the kernel function with automatic bandwidth selection via a cross-validation procedure and semi-metrics as a measure of the proximity between functional data. Finally, we extend the univariate functional responses to the multivariate case and then take the correlation between di erent functional responses into account. The e ectiveness of the proposed models is illustrated through simulated instances. The proposed methods are then applied to functional data and, through our numerical outcomes, we improve the results as compared with the various methods reported in the literature.