Perbandingan Pembobot Welsch dan Tukey Bisquare pada Regresi Robust S-estimator
Abstract
Regresi robust merupakan sebuah metode yang dikembangkan untuk memiliki kinerja yang baik ketika data yang dianalisis menyimpang dari asumsi yang mendasari, misalnya terdapat pencilan yang dapat menyebabkan galat menjadi tidak berdistribusi normal. Salah satu metode estimasi pada regresi robust adalah S-estimator, metode ini memiliki fungsi pembobot antara lain pembobot Welsch dan Tukey Bisquare. Pada penelitian ini, kami membandingkan bobot-bobot pada metode S-estimator pada data berukuran: 30, 60, 100 dan 200 yang diberikan kontaminasi pencilan sebesar: 5%, 10%, 15%, 20%, 25% dan 30%. Berdasarkan hasil simulasi diperoleh bahwa kedua pembobot menghasilkan nilai MSE (Mean Square Error) dan bias yang serupa. Sehingga dapat disimpulkan bahwa kedua pembobot memberikan hasil yang sesuai dan sama baiknya pada regresi S-estimator.
Robust regression is a method developed to have good performance when the analyzed data deviates from the underlying assumptions, for example, there are outliers that can cause errors to be not normally distributed. One of the estimation methods in robust regression is the S-estimator, this method has weighting functions, including the Welsch and Tukey Bisquare weights. In this study, we compared the weights in the S-estimator method on data sizes: 30, 60, 100 and 200 which were given outlier contamination of: 5%, 10%, 15%, 20%, 25% and 30%. Based on the simulation results, it is found that the two weights produce similar MSE (Mean Square Error) and bias values. So it can be concluded that the two weights provide appropriate and equally good results in the S-estimator regression
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