Mathematics and Statistics 12(1): 69-79, 2024 http://www.hrpub.org
DOI: 10.13189/ms.2024.120110
Functional Continuum Regression Approach to Wavelet
Transformation Data in a Non-Invasive Glucose
Measurement Calibration Model
Ismah Ismah
1
, Erfiani
2
, Aji Hamim Wigena
2
, Bagus Sartono
2,*
1
Department of Mathematics Education, Universitas Muhammadiyah Jakarta, Indonesia
2
Department of Statistics, IPB University, Indonesia
Received May 5, 2023; Revised December 11, 2023; Accepted January 17, 2024
Cite This Paper in the Following Citation Styles
(a): [1] Ismah Ismah, Erfiani, Aji Hamim Wigena, Bagus Sartono , "Functional Continuum Regression Approach to
Wavelet Transformation Data in a Non-Invasive Glucose Measurement Calibration Model," Mathematics and Statistics,
Vol. 12, No. 1, pp. 69 - 79, 2024. DOI: 10.13189/ms.2024.120110.
(b): Ismah Ismah, Erfiani, Aji Hamim Wigena, Bagus Sartono (2024). Functional Continuum Regression Approach to
Wavelet Transformation Data in a Non-Invasive Glucose Measurement Calibration Model. Mathematics and Statistics,
12(1), 69 - 79. DOI: 10.13189/ms.2024.120110.
Copyright©2024 by authors, all rights reserved. Authors agree that this article remains permanently open access under the
terms of the Creative Commons Attribution License 4.0 International License
Abstract Functional data has a data structure with large
dimensions and is a broad source of information, but it is
very possible that there are problems in analyzing
functional data. Functional continuum regression is an
alternative method that can be used to overcome
calibration modeling with functional data. This study
aimed to determine the robustness of Functional continuum
regression in overcoming multicollinearity problems or the
number of independent variables greater than the number
of observations, with functional data. The research method
used in this study is the analysis of the Functional
continuum regression method on the results of the Wavelet
transform of blood glucose measurements with
noninvasive techniques in the calibration model, and
making comparisons with non-functional methods, namely
Principal component regression, partial least square
regression, least square regression, and functional method
namely functional regression. The results of the analysis
using the five methods obtained the root mean square error
prediction (RMSEP), the correlation between the observed
data and the estimated observation data, and the mean
absolute error (MAE). The results of the analysis can be
said that reduction methods such as Functional continuum
regression, Principal component regression, and partial
least square regression are superior methods when used
when multicollinearity occurs or the number of
independent variables is greater than the number of
observations. In the case of functional data analysis, the
application of Functional continuum regression is better
because it does not eliminate data patterns. Thus it can be
said that Functional continuum regression is an effective
approach in analyzing calibration models which generally
have functional data, and there are several problems which
include multicollinearity or the number of independent
variables is greater than the number of observations.
Keywords Functional Continuum Regression, Weight
Function, Calibration Model, Wavelet Transform
1. Introduction
Data in the field of statistics is a raw material that is
processed in order to obtain one or more important
information quantitatively or qualitatively about a situation.
The traditional statistical approach is generally used for
data that is in the form of a single or non-function, but for
data that is in the form of a function or continuous, the
traditional statistical approach is considered inappropriate
because it cannot provide information relevant to the form
of a function. Grenander and Karhunen [1] introduced
functional data analysis as an alternative approach to
analyzing functional data. Ramsay and Silverman [2]