Least absolute relative error estimation for functional quadratic multiplicative model. Issue 19 (1st October 2016)

• Record Type: Journal Article
• Authors: Zhang, Tao; Zhang, Qingzhao; Li, Naixiong
• Is Part Of: Communications in statistics. Volume 45:Issue 19(2016)
• Page Start: 5802
• Page End: 5817
• Publication Date: 2016-10-01
• Subjects: Consistency -- Functional principal components -- Functional quadratic multiplicative model -- Least absolute relative error.; 62N02; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.950748
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: As an alternative to the functional quadratic model due to Yao and Müller (2010 ), we consider a functional quadratic multiplicative model. This multiplicative model provides a useful alternative when the relative error is considered for analyzing data with positive responses. The existing work for functional models are mainly based on absolute errors. The commonly used least squares criterion is just such an example. In many practical applications, however, people concern on the size of relative error rather than that of error itself. Therefore, the estimation procedure based on least absolute relative errors, which is proposed by Chen et al. (2010 ) for the linear multiplicative model, is developed for functional quadratic multiplicative model. The asymptotic behaviors of the proposed estimators are established. Some simulation studies show that the estimation procedure has good prediction performance. Moreover, a real data set is analyzed for illustrating the proposed methods.