• 论文 •

### 部分函数线性模型的模型平均方法

1. 1. 中国科学院数学与系统科学研究院, 北京 100190; 2. 中国科学院大学,北京 100049;3. 首都师范大学数学科学学院,北京 100048
• 出版日期:2018-07-25 发布日期:2018-10-12

ZHU Rong,ZOU Guohua, ZHANG Xinyu. Optimal Model Averaging Estimation for Partial Functional Linear Models[J]. Journal of Systems Science and Mathematical Sciences, 2018, 38(7): 777-800.

### Optimal Model Averaging Estimation for Partial Functional Linear Models

ZHU Rong 1,2 ,ZOU Guohua 3 ,ZHANG Xinyu1

1. 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190; 2. University of Chinese Academy of Sciences, Beijing 100049; 3. School of Mathematical Sciences, Capital Normal University, Beijing 100048
• Online:2018-07-25 Published:2018-10-12

In this paper, we propose a model averaging method for the partial functional linear models (PFLM), which are designed for the case that the scalar response is related to a vector of random variables and some function-valued random variables as predictor variables. % First, we use a conventional spectral decomposition for the covariance functions, and linearize the PFLM with inner product of the functional variables and the eigenfunctions. The least squares estimators are obtained by the candidate linearized models. % Then, we propose an optimal weight choice criterion for the PFLM, which is based on the Mallows' criterion proposed by Hansen (2007) and derive the asymptotic optimality of the model average estimators. % Besides, we also prove the asymptotic optimality of the model average estimators under the case which only two special candidate models are considered. % The proposed method is illustrated with a simulation study, and is applied to the data set of near infrared reflection (NIR) spectra of meat samples and corn samples.

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