Performance Analysis of Robust Functional Continuum Regression to Handle Outliers
Abstract
Robust functional continuum regression (RFCR) is an innovation as a development of functional continuum regression that can be applied to functional data and is resistant to outliers. The resistance of RFCR depends on the applied weighting function. This study aims to evaluate the RFCR performance to handle outliers. We propose the various weighting functions in this evaluation, i.e., Huber, Hampel, Ramsay, and Tukey (Bisquare), which do not eliminate or give zero weight to observed data identified as outliers. This contribution is essential to determining the appropriate RFCR method without eliminating the outlier data. The result shows that the RFCR performance with the Huber weighting function is better than the others, based on the goodness of fit, consisting of the root means square error of prediction (RMSEP), the correlation between the actual data and the model, and the mean absolute error (MAE).
Keywords: functional data analysis; Huber weighted function; Hampel weighted function; Ramsay weighted function; Tukey (Bisquare) weighted function.
Abstrak
Regresi kontinum fungsional kekar (RFCR) merupakan inovasi yang merupakan pengembangan dari regresi kontinum fungsional yang dapat diaplikasikan pada data fungsional dan tahan terhadap outlier. Resistansi RFCR bergantung pada fungsi pembobotan. Penelitian ini bertujuan untuk mengevaluasi kinerja RFCR. Kami mengusulkan beberapa fungsi pembobotan dalam evaluasi tersebut, yaitu Huber, Hampel, Ramsay, dan Tukey (Bisquare), dengan tidak menghilangkan atau memberikan bobot nol pada data observasi yang teridentifikasi sebagai outlier. Kontribusi ini penting untuk menentukan metode RFCR yang tepat tanpa menghilangkan data outlier. Hasil menunjukkan bahwa kinerja RFCR dengan fungsi pembobotan Huber lebih baik dibandingkan fungsi pembobotan lain berdasarkan goodness of fit, yang terdiri dari root mean square error of prediksi (RMSEP), korelasi antara data aktual dan model, dan mean kesalahan absolut (MAE).
Kata Kunci: analisis data fungsional; fungsi berbobot Huber; fungsi tertimbang Hampel; fungsi tertimbang Ramsay; fungsi berbobot Tukey (Bisquare).
2020MSC: 62J99, 62R10
Keywords
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DOI: 10.15408/inprime.v6i1.38928
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