Principal differential analysis: incorporating covariates with kernel smoothers
Principal Differential Analysis is a statistical technique which suggests that a given set of functional data curves can be annihilated completely when an estimated linear differential operator (LDO) is applied (Coddington & Levinson). The novelty of residuals as forcing functions is introduced in PDA. ^ This thesis builds on PDA with covariates by Jin et al, 2012 by dropping the assumption that the coefficients of the linear differential operator are a product of a function in t and v; the equivalent kernel is used to estimate the coefficient functions at target values. Incorporating covariates with kernel smoothers leads to two approaches: global PDA (equivalent kernel set to 1) and local PDA. Cross-validation, which is critical for finding the optimal smoothing parameter is considered for λ and b using the leave-one-out definition of cross-validation and an ad hoc approach to cross-validation. ^ The data-set for analysis are the Lip Data from Ramsay and Silverman and the CAEP curves for children with normal hearing. Applications to this method (PDA incorporating covariates with kernel smoothers) suggests a theoretical assistance in determining the optimal age for a cochlear implant since the null space basis functions for the low dimensional approximation to the curves are computed for each target age.^
Dodoo, Christopher Alfred, "Principal differential analysis: incorporating covariates with kernel smoothers" (2013). ETD Collection for University of Texas, El Paso. AAI1545156.