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Abstract:
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In this talk, we introduce a new estimation method for sufficient dimension reduction with functional and longitudinal covariates in a fully nonparametric and gradient-based way. Under this approach, only smoothness conditions of population parameter functions are required. Thus, our proposal still works well when the linearity condition is violated, which is commonly used in the popular inverse regression methods. A reproducing kernel approach is used to study the conditional expectation given infinite-dimensional covariates. Moreover, all the parameter functions involved in our proposal can be successfully estimated through classical nonparametric smoothing when the trajectories of covariates are only sparsely observed. The resulting estimator is obtained by a functional principal component analysis method, which is easily implemented in practice.
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