Physical Sciences and Mathematics Commons^™

Testing And Estimation For Functional Data With Applications To Magnetometer Records, Inga Maslova

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The functional linear model, Y_n = ψX_n + ε_n, with functional response and explanatory variables is considered. A simple test of the nullity of ψ based on the principal component decomposition is proposed. The test statistic has asymptotic chi-squared distribution, which is also an excellent approximation in finite samples. The methodology is applied to data from terrestrial magnetic observatories.

In recent years, the interaction of the auroral substorms with the equatorial and mid-latitude currents has been the subject of extensive research. We introduce a new statistical technique that allows us to test at a specified …

Smoothing Parameter Selection For A Class Of Semiparametric Linear Models, Philip T. Reiss, R. Todd Ogden

Philip T. Reiss

Spline-based approaches to nonparametric and semiparametric regression, as well as to regression of scalar outcomes on functional predictors, entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized. In this paper we demonstrate that the equations determining two popular methods for smoothing parameter selection, generalized cross-validation and restricted maximum likelihood, share a similar form that allows us to prove several results common to both, and to derive a condition under which they yield identical values. These ideas are illustrated by application of functional principal component regression, a method for regressing scalars on functions, to …