A Penalized Least Squares Estimation of Fourier Series Semiparametric Regression Theory, Simulation, and Application

Ihsan Amri; Nur Chamidah; Toha Saifudin; Budi Lestari; Dursun Aydin; Febrian Rohim

doi:10.19139/soic-2310-5070-3139

A Penalized Least Squares Estimation of Fourier Series Semiparametric Regression Theory, Simulation, and Application

Ihsan Amri Universitas Muhammadiyah Semarang https://orcid.org/0009-0004-7978-8773
Nur Chamidah Airlangga University http://orcid.org/0000-0003-1592-4671
Toha Saifudin Airlangga University https://orcid.org/0000-0002-6716-3096
Budi Lestari Universitas Jember https://orcid.org/0009-0005-1978-8613
Dursun Aydin Mu˘gla Sıtkı Koc¸man University https://orcid.org/0000-0001-8393-1270
Febrian Rohim Universitas Muhammadiyah Semarang

DOI: https://doi.org/10.19139/soic-2310-5070-3139

Keywords: Estimation, Fourier Series Semiparametric Regression Model, Penalized Least Square, Generalized Cross Validation, Mean Average Percentage Error

Abstract

In regression analysis, a functional relationship between response and predictor variables sometimes follows a semiparametric regression model that is constructed by parametric and nonparametric components where its nonparametric component is a function of time which will be approximated by a Fourier Series. In this study, we develop a penalized least square smoothing technique for estimating a Fourier Series Semiparametric Regression (FSSR) model. The penalized least square is very good to use when generalized cross validation method cannot choose really good parameters due to over-fitting effect in the model is ignored. We also provide numerical example through a simulation study, and apply the proposed method to real data for predicting temperature of earth surface based on relative humidity. The results show that the estimated FSSR model results MAPE value of 1.068% . This means that the obtained model has a highly accuracy category as a prediction model

Published

2026-02-20

How to Cite

Amri, I., Chamidah, N., Saifudin, T., Lestari, B., Aydin, D., & Rohim, F. (2026). A Penalized Least Squares Estimation of Fourier Series Semiparametric Regression Theory, Simulation, and Application. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-3139

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Research Articles

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