Mathematics and Statistics Vol. 12(1), pp. 69 - 79
DOI: 10.13189/ms.2024.120110
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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

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

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[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). APA Format:
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.