Dynamic modeling for functional data

The first part of this thesis proposes a measure for heteroscedascity for functional data in the Hilbert space L²[0,1] equipped with a particular inner product using a distance function on the kernel of the associated covariance function. This results in a closed form expression for the minimal distance of the observed functional data to the nearest homoscedasctic process. We develop an estimator for this measure which, under particular conditions on the observed data, converges to a zero mean normal distribution with a closed form variance if the hypothesis of homoscedascity holds. We propose bootstrap estimation to make the estimating the variance computationally tractable and investigate the accuracy and performance of the proposed methods on numerical simulations and a real data case study. This method is further extended theoretically to the cases of precise hypotheses of heteroscedascity and testing on surrogate variables. The second part of this thesis considers the variable selection problem in a functional logistic regression setting, the proposed methodology being adapting the group lasso penalty. The problem of low incidence rate it considered and handled using a bias reduced maximized incidence approach instead of the classic maximum likelihood estimator. Some theoretical results are established and block co-ordinate gradient descent algorithms are implemented to study the methodology in numerical simulations. As a result of these numerical simulations and the fact that the group lasso is not selection consistent, an adaptive group lasso is studied via numerical simulation for the functional logistic framework.

Author

• Cameron, James

• adaptive group LASSO
• functional data analysis
• group LASSO
• heteroscedascity

Identifier

hdl:1920/14015

OAI identifier oai:identifier

oai:MARS:1920/14015