Xiao, W. orcid.org/0000-0002-9553-2581, Li, S. and Liu, H. orcid.org/0000-0002-3442-1722 (2023) Generalized Partially Functional Linear Model with Unknown Link Function. Axioms, 12 (12). 1089. ISSN 2075-1680
Abstract
In existing models with an unknown link function, the issue of predictors containing both multiple functional data and multiple scalar data has not been studied. To fill this gap, we propose a generalized partially functional linear model, which not only models the relationship between multiple scalar and functional predictors and responses, but also automatically estimates the link function. Specifically, we use the functional principal component analysis method to reduce the dimensionality of functional predictors, estimate the regression coefficients using the maximum likelihood estimation method, estimate the link function using the method of local linear regression, iteratively obtain the final estimator, and establish the asymptotic normality of the estimator. The asymptotic normality is illustrated through simulation experiments. Finally, the proposed model is applied to study the influence of environmental, economic, and medical levels on life expectancy in China. In the study, functional predictors are the daily air quality index, temperature, and humidity of 58 cities in 2020, and scalar predictors are GDP and the number of beds in hospitals. The experimental results indicate that the unknown link function model has a smaller prediction error and better performance than both the model with the known link function and the model without a link function.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
Keywords: | functional data analysis; unknown link function; generalized functional linear model average life expectancy |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 01 Dec 2023 14:13 |
Last Modified: | 01 Dec 2023 14:13 |
Status: | Published |
Publisher: | MDPI |
Identification Number: | 10.3390/axioms12121089 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:206070 |