Abstract
With the rapid development of information technology, data information also presents the Characteristics of diversity. Meanwhile more and more datum are presented in the form of functions. Therefore, functional data has become the focus of researchers. Functional data analysis has also proved to be of great value in the fields of biology, medicine and metrology. A partially functional linear regression model is proposed for the regression cases in which the response variables are scalar types and the predictive variables are both variable types and functional types. For the functional predictive variables, we use the functional principal component analysis method to reduce the dimension of the functional data.The least square method is used to calculate the estimate of parameters.With the improvement of people's living standard, people pay more and more attention to health. And an increasing number of people are eager to live a healthy life and keep healthy. Healthy and comfortable sleep has become a topic of increasing concern to researchers. Using data from PhysioNet Databases on activity and sleep in healthy people for this study, we found that the predicted variables in the model could well explain the response variables. The application of partially functional linear model is further extended.
Highlights
With the rapid development of information technology, data information presents the Characteristics of diversity
Using data from PhysioNet Databases on activity and sleep in healthy people for this study, we found that the predicted variables in the model could well explain the response variables
[1] RAMSAY J O, When the data are functions [J]
Summary
With the rapid development of information technology, data information presents the Characteristics of diversity. 摘要:随着信息技术的迅速发展,数据信息也呈现出多元化的特点,越来越多的数据以函数的形式呈现出来。因此, 函数型数据成为广大研究者们关注的焦点。函数型数据分析也被证实在生物学、医学、计量学等领域有很大的应用价 值。针对响应变量是标量型、预测变量既有变量型又有函数型的回归情形,提出了一种部分函数型线性回归模型。针 对函数型预测变量,我们采用函数型主成分分析法,对函数型数据进行降维;并采用最小二乘法求得参数估计。随着 人民生活水平的提高,人们对于健康的重视不断提升,越来越多的人迫切地想得到健康的生活,保持身体的健康状态。 健康与舒适的睡眠日益成为广大研究者关注的话题。我们通过应用PhysioNet Databases中提供的有关健康人活动与睡眠 的数据进行了研究,研究结果可以看出此模型中的预测变量可以很好的解释响应变量。部分函数型线性模型的应用得 到了进一步的推广。 {( ) ( ) ( ) } X i1 (t1 ), t1 ∈T1 , Xi2 (t2 ) ,t2 ∈T2 ,⋯, Xid (td ) , td ∈Td , Zi ,Yi ( ) ( ) 变量 Xij tj 和参数函数 β j t j 可以展开为: 数型的混合协变量之间的线性关系[3]。Shin提出一个基于 函数型主成分分析的估计方法并且研究了它的渐近性质[4]。 Shin and Lee分别采用函数型主成分分析法和Tikhonov正则 ∑∑ d p ξijk β jk + ZiTγ + εi ,i = 1, 2,⋯, n
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