Browsing by Subject "Delta method"
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Item Asymptotic Limiting Distributions for Functional Regression Model(2011-05) Wang, Eliza; Ruymgaart, Frits; Hadjicostas, Petros; Trindade, A. AlexandreIn this dissertation, we are interested in the functional regression model, with infinite dimensional parameter in a Hilbert space as the regression function. Estimating the parameter involves the regularization and smoothing. The asymptotic normality for the regression function estimator is derived in detail and several linear hypotheses are discussed.Item Perturbations of Operators with Application to Testing Equality of Covariance Operators.(2011-07) Kaphle, Krishna; Ruymgaart, Frits; Allen, Linda J. S.; Hadjicostas, PetrosThe generalization of multivariate statistical procedures to infinite dimension naturally requires extra theoretical work. In this dissertation, we will focus on testing the equality of covariance operators. We derive a procedure from the Union Intersection principle in conjunction with a Likelihood Ratio test. This procedure leads to a statistic which is the largest eigenvalue of a product of operators. We generalize this procedure by using a test statistic that is based on the first $m \in \mathbb{N}$ largest eigenvalues. Perturbation theory of operators and functional calculus of covariance operators are extensively used to derieve the required asymptotics. It is shown that the power of the test is improved with inclusion of more eigenvalues. We perform simulations to corroborate the testing procedure, using samples from two Gaussian distributions.