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Register a new userModel Averaging Estimation for Partially Linear Functional Score Models
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Added by
Shishi Liu
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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This paper is concerned with model averaging estimation for partially linear functional score models. These models predict a scalar response using both parametric effect of scalar predictors and non-parametric effect of a functional predictor. Within this context, we develop a Mallows-type criterion for choosing weights. The resulting model averaging estimator is proved to be asymptotically optimal under certain regularity conditions in terms of achieving the smallest possible squared error loss. Simulation studies demonstrate its superiority or comparability to information criterion score-based model selection and averaging estimators. The proposed procedure is also applied to two real data sets for illustration. That the components of nonparametric part are unobservable leads to a more complicated situation than ordinary partially linear models (PLM) and a different theoretical derivation from those of PLM.
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We consider averaging a number of candidate models to produce a prediction of lower risk in the context of partially linear functional additive models. These models incorporate the parametric effect of scalar variables and the additive effect of a functional variable to describe the relationship between a response variable and regressors. We develop a model averaging scheme that assigns the weights by minimizing a cross-validation criterion. Under the framework of model misspecification, the resulting estimator is proved to be asymptotically optimal in terms of the lowest possible square error loss for prediction. Also, simulation studies and real data analysis demonstrate the good performance of our proposed method.
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