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The paper develops a comprehensive asymptotic theory for the estimation of a change– point in the mean function of functional observations. We consider both the case of a constant change size, and the case of a change whose size approaches zero, as the sample size tends to infinity. We show how the limit distribution of a suitably defined change– point(More)
We study the almost sure convergence of the Bartlett estimator for the asymp-totic variance of the sample mean of a stationary weekly dependent process. We also study the a. s. behavior of this estimator in the case of long-range dependent observations. In the weakly dependent case, we establish conditions under which the estimator is strongly consistent.(More)
AMS subject classifiactions: 62H15 62H25 Keywords: Functional data Change in mean Increasing dimension Normal approximation Principal components a b s t r a c t Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the(More)
To my family Acknowledgements The meaning of life for me is experiencing new things and learning from them. Enrolling in the Ph.D. program has enabled me to gain invaluable experiences along the way. Though only my name appears on the cover of this dissertation, many people have helped me to produce it. I am indebted to all of them: it would not have been(More)