部分线性函数多项式模型的联合探测

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部分线性函数多项式模型的联合探测张涛¹, 万艳玲², 王智文³1. 广西科技大学理学院, 柳州 545006;
2. 广西科技大学社会科学学院, 柳州 545006;
3. 广西科技大学计算机科学与通讯工程学院, 柳州 545006 Joint Detection for Partial Linear Functional Polynomial Model ZHANG Tao¹, WAN Yanling², WANG Zhiwen³1. School of Science, Guangxi University of Science and Technology, Liuzhou 545006, China;
2. School of Social Sciences, Guangxi University of Science and Technology, Liuzhou 545006, China;
3. School of Computer Science and Communication Engineering, Guangxi University of Science and Technology, Liuzhou 545006, China

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摘要本文提出了一个新的部分线性函数多项式回归模型，该模型中响应变量依赖于一个p阶函数多项式和一些非函数型数据的协变量.函数多项式模型、函数线性模型和部分函数线性模型是该模型的特殊情形.本文提出了一个模型探测方法，它能同时探测部分线性函数多项式回归模型中哪些阶是重要的以及哪些非函数型变量是重要的.提出的方法能相合地识别真实的模型并有好的预测表现.数值模拟能清晰地证实我们的理论结果.

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收稿日期: 2015-03-08

PACS:

O212.7

基金资助:国家自然科学基金（11561006，61462008），广西高校科学技术研究项目（KY2015YB171），柳州市科学技术研究项目（2016C050205），以及广西科技大学创新团队项目（gxkjdx201504）资助.

引用本文:

张涛, 万艳玲, 王智文. 部分线性函数多项式模型的联合探测[J]. 应用数学学报, 2018, 41(1): 110-123. ZHANG Tao, WAN Yanling, WANG Zhiwen. Joint Detection for Partial Linear Functional Polynomial Model. Acta Mathematicae Applicatae Sinica, 2018, 41(1): 110-123.

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[1]	王亚飞, 杜江, 张忠占. 相依误差下部分函数型线性模型的估计[J]. 应用数学学报, 2017, 40(1): 49-65.
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