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Estimating The Coefficients Of A Linear Differential Operator, Maria Ivette Barraza

Open Access Theses & Dissertations

Principal Differential Analysis (PDA; Ramsay, 1996) is used to obtain low dimensional representations of functional data, where each observation is represented as a curve. PDA seeks to identify a Linear Differential Operator (LDO) L = ω0I + ω 1D + ... + ωmDm, where I denotes the identity function and D j the jth derivative, that satisfies as closely as possible that Lx = 0 for each functional observation x. A theorem from analysis establishes that the coefficients of the LDO are in the Sobolev space, and thus can be approximated by B-splines. Current PDA software used to estimate the …