Preprint Review Version 1 Preserved in Portico This version is not peer-reviewed

A Literature Review of Semi-functional Partial Linear Regression Models

Version 1 : Received: 15 November 2021 / Approved: 17 November 2021 / Online: 17 November 2021 (15:21:19 CET)

How to cite: Fayaz, M. A Literature Review of Semi-functional Partial Linear Regression Models. Preprints 2021, 2021110310 (doi: 10.20944/preprints202111.0310.v1). Fayaz, M. A Literature Review of Semi-functional Partial Linear Regression Models. Preprints 2021, 2021110310 (doi: 10.20944/preprints202111.0310.v1).

Abstract

Background: In the functional data analysis (FDA), the hybrid or mixed data are scalar and functional datasets. The semi-functional partial linear regression model (SFPLR) is one of the first semiparametric models for the scalar response with hybrid covariates. Various extensions of this model are explored and summarized. Methods: Two first research articles, including “semi-functional partial linear regression model”, and “Partial functional linear regression” have more than 300 citations in Google Scholar. Finally, only 106 articles remained according to the inclusion and exclusion criteria such as 1) including the published articles in the ISI journals and excluding 2) non-English and 3) preprints, slides, and conference papers. We use the PRISMA standard for systematic review. Results: The articles are categorized into the following main topics: estimation procedures, confidence regions, time series, and panel data, Bayesian, spatial, robust, testing, quantile regression, varying Coefficient Models, Variable Selection, Single-index model, Measurement error, Multiple Functions, Missing values, Rank Method and Others. There are different applications and datasets such as the Tecator dataset, air quality, electricity consumption, and Neuroimaging, among others. Conclusions: SFPLR is one of the most famous regression modeling methods for hybrid data that has a lot of extensions among other models.

Keywords

Functional Data Analysis (FDA); Hybrid Data; Semi-Functional Partial Linear Regression Model (SFPLR); Partial Functional Linear Regression; Literature Review

Subject

MATHEMATICS & COMPUTER SCIENCE, Probability and Statistics

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