We consider the problem of constructing functional regression models for scalar responses and functional predictors, using Gaussian basis functions along with the technique of regularization. An advantage of our regularized Gaussian basis expansions to functional data analysis is that it creates a much more flexible instrument for transforming each individual's observations into functional form. In constructing functional regression models there remains the problem of how to determine the number of basis functions and an appropriate value of a regularization parameter. We present model selection criteria for evaluating models estimated by the method of regularization in the context of functional regression models. The proposed functional regression models are applied to Canadian temperature data. Monte Carlo simulations are conducted to examine the efficiency of our modeling strategies. The simulation results show that the proposed procedure performs well especially in terms of flexibility and stable estimates.

Yuko Araki

Sadanori Konishi

Shuichi Kawano

Hidetoshi Matsui

Annals of the Institute of Statistical Mathematics

统计数学研究所年鉴（AISM）旨在为统计学家之间的公开交流提供一个论坛，并促进统计学作为一门科学的进步，使人类能够处理信息以应对不确定性。它发表高质量的论文，为统计科学的理论、计算和/或方法论方面提供新的视角。重点放在（A）以真实数据为动力的新方法的开发，（B）统一理论的开发，以及（C）现有方法和理论的分析和改进。

The Annals of the Institute of Statistical Mathematics aims to provide a forum for open communication among statisticians and to promote the advancement of statistics as a science, enabling humanity to handle information in the face of uncertainty. It publishes high-quality papers that offer new perspectives on the theoretical, computational, and methodological aspects of statistical science. The focus is on (A) the development of new methods driven by real data, (B) the development of unified theories, and (C) the analysis and improvement of existing methods and theories.

《Annals of the Institute of Statistical Mathematics》旨在为统计学家之间提供一个公开交流的论坛，促进统计学作为一门科学的发展，以帮助人们处理不确定性的信息。期刊发表高质量的论文，为统计科学的理论、计算和方法论提供新的视角。重点关注：（A）基于真实数据的新方法开发；（B）统一理论的发展；（C）对现有方法和理论的分析与改进。

Category	Quartile
数学	4
数学, 统计学与概率论	4

Functional regression modeling via regularized Gaussian basis expansions

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Journal Info

Category	Quartile
STATISTICS & PROBABILITY	3