Methods for Scalar-on-Function Regression

被引：122

作者：

Reiss, Philip T. ^{[1
,2
,3
]}

Goldsmith, Jeff ^{[4
]}

Shang, Han Lin ^{[5
]}

Ogden, R. Todd ^{[4
,6
]}

机构：

[1] NYU, Sch Med, Dept Child & Adolescent Psychiat, New York, NY 10003 USA

[2] NYU, Sch Med, Dept Populat Hlth, New York, NY 10003 USA

[3] Univ Haifa, Dept Stat, Haifa, Israel

[4] Columbia Univ, Mailman Sch Publ Hlth, Dept Stat, New York, NY USA

[5] Australian Natl Univ, Res Sch Finance Actuarial Studies & Stat, Canberra, ACT, Australia

[6] New York State Psychiat Inst & Hosp, New York, NY USA

来源：

INTERNATIONAL STATISTICAL REVIEW | 2017年 / 85卷 / 02期

基金：

美国国家卫生研究院;

关键词：

Functional additive model; functional generalised linear model; functional linear model; functional polynomial regression; functional single-index model; non-parametric functional regression; BAYESIAN BANDWIDTH ESTIMATION; GENERALIZED LINEAR-MODELS; TIME-SERIES PREDICTION; LIKELIHOOD RATIO TESTS; NONPARAMETRIC REGRESSION; ADDITIVE-MODELS; PRINCIPAL; SELECTION; COMPONENTS; DIMENSIONALITY;

D O I：

10.1111/insr.12163

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images and so onare considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorising the basic model types as linear, non-linear and non-parametric. We discuss publicly available software packages and illustrate some of the procedures by application to a functional magnetic resonance imaging data set.

引用

页码：228 / 249

页数：22

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