Predictive Functional Linear Models with Diverging Number of Semiparametric Single-Index Interactions
| Autor: | Naisyin Wang, Raymond J. Carroll, Yanghui Liu, Yehua Li |
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| Rok vydání: | 2023 |
| Předmět: |
Functional principal component analysis
Statistics::Theory Economics and Econometrics Sequence Multivariate statistics Applied Mathematics 05 social sciences Linear model Nonparametric statistics 01 natural sciences Statistics::Machine Learning 010104 statistics & probability Dimension (vector space) Component (UML) 0502 economics and business Statistics Statistics::Methodology 0101 mathematics 050205 econometrics Mathematics Parametric statistics |
| Zdroj: | Journal of econometrics. 230(2) |
| ISSN: | 0304-4076 |
| Popis: | When predicting crop yield using both functional and multivariate predictors, the prediction performances benefit from the inclusion of the interactions between the two sets of predictors. We assume the interaction depends on a nonparametric, single-index structure of the multivariate predictor and reduce each functional predictor’s dimension using functional principal component analysis (FPCA). Allowing the number of FPCA scores to diverge to infinity, we consider a sequence of semiparametric working models with a diverging number of predictors, which are FPCA scores with estimation errors. We show that the parametric component of the model is root-n consistent and asymptotically normal, the overall prediction error is dominated by the estimation of the nonparametric interaction function, and justify a CV-based procedure to select the tuning parameters. |
| Databáze: | OpenAIRE |
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