Abstract
Functional data is a common and important type in econometrics and has been easier and easier to collect in the big data era. To improve estimation accuracy and reduce forecast risks with functional data, in this paper, we propose a novel cross-validation model averaging method for generalized functional linear model where the scalar response variable is related to a random function predictor by a link function. We establish asymptotic theoretical result on the optimality of the weights selected by our method when the true model is not in the candidate model set. Our simulations show that the proposed method often performs better than the commonly used model selection and averaging methods. We also apply the proposed method to Beijing second-hand house price data.
Highlights
In recent years, functional data have been increasingly popular in many scientific areas
For generalized functional linear model designed for the case where the scalar response is nonlinearly dependent on functional explanatory variables, model averaging is a good alternative to model selection that may lead to instability in variable selection or coefficient estimation caused by randomness of the data collection and so on
We proposed a model averaging approach under the framework of the generalized functional linear model
Summary
Functional data have been increasingly popular in many scientific areas. Proposed a model averaging estimator based on Mallows’ criterion for partial functional linear models whose response is a scalar and the predictors are a random vector and some functional variables. For generalized functional linear model designed for the case where the scalar response is nonlinearly dependent on functional explanatory variables, model averaging is a good alternative to model selection that may lead to instability in variable selection or coefficient estimation caused by randomness of the data collection and so on. We consider model averaging methods for GFLM to capture the nonlinear characteristics hidden in the data and to reduce the prediction errors and risks. The contributions of this article are threefold: We first adopt FPCA to reduce the dimensions as it provides a parsimonious representation of functional data, and present a novel model averaging procedure based on leave-one-out cross-validation criterion (CV). Proofs of theoretical results are provided in Appendix A and B
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