Ridge Regression Based on Some Robust Estimators

Şamkar, Hatice; Alpu, Ozlem

doi:10.22237/jmasm/1288584960

Cited by 17 publications

(7 citation statements)

References 15 publications

(3 reference statements)

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“…The combination of LAD and ridge regression will produce the ridge least absolute deviation (RLAD) method. With the ability of LAD to overcome multicollinearity and ridge regression that is able to deal with outliers, the RLAD method will be able to surmount multicollinearity and outliers in the data simultaneously [12]. The parameter estimator of RLAD can be written as:…”

Section: Methodsmentioning

confidence: 99%

“…This method is a combination of the robust ridge regression method and the least absolute deviation method. The RLAD estimator that results will be stable and resistant to outliers [12]. However, there has been no comprehensive research using this method to seek the outcome of this method in overcoming various levels of outliers at various sample sizes.…”

Section: Introductionmentioning

confidence: 99%

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Ridge Least Absolute Deviation Performance in Addressing Multicollinearity and Different Levels of Outlier Simultaneously

Herawati¹,

Saidi²,

Azis³

2022

BAREKENG: J. Math. & App.

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If there is multicollinearity and outliers in the data, the inference about parameter estimation in the LS method will deviate due to the inefficiency of this method in estimating. To overcome these two problems simultaneously, it can be done using robust regression, one of which is ridge least absolute deviation method. This study aims to evaluate the performance of the ridge least absolute deviation method in surmounting multicollinearity in divers sample sizes and percentage of outliers using simulation data. The Monte Carlo study was designed in a multiple regression model with multicollinearity (ρ=0.99) between variables and and outliers 10%, 20%, 30% on response variables with different sample sizes (n = 25, 50,75,100,200; =0, and β=1 otherwise). The existence of multicollinearity in the data is done by calculating the correlation value between the independent variables and the VIF value. Outlier detection is done by using boxplot. Parameter estimation was carried out using the RLAD and LS methods. Furthermore, a comparison of the MSE values of the two methods is carried out to see which method is better in overcoming multicollinearity and outliers. The results showed that RLAD had a lower MSE than LS. This signifies that RLAD is more precise in estimating the regression coefficients for each sample size and various outlier levels studied.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ridge Least Absolute Deviation Performance in Addressing Multicollinearity and Different Levels of Outlier Simultaneously

Herawati¹,

Saidi²,

Azis³

2022

BAREKENG: J. Math. & App.

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“…Ketika kasus outlier dan multikolinieritas terjadi dalam dataset, akan lebih bermanfaat untuk meng-gabungkan metode yang dirancang untuk menangani masalah tersebut secara individual. Dengan demikian, estimator ridge yang robust akan tahan terhadap masalah multikolinieritas dan akan lebih sedikit terpengaruh oleh outlier dibandingkan dengan metode regresi ridge [11].…”

Section: Regresi Robust Ridgeunclassified

Analisis Regresi untuk Memprediksi Tahanan Kapal Cepat

Alvin¹,

Atok²,

Indiaryanto³

2020

JSSITS

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Kapal merupakan bagian penting dari kehidupan manusia, terutama dalam bidang transportasi laut. Industri perkapalan di Indonesia telah berkembang dengan pesat, ditandai dengan berdirinya galangan-galangan kapal di Indonesia. Tahap awal dalam proses pembuatan kapal adalah menentukan ukuran dan parameter bentuk kapal. Bersamaan dengan hal tersebut terdapat faktor penting yang berhubungan dengan performa kapal, yaitu tahanan kapal. Kesalahan perhitungan tahanan kapal dapat berdampak buruk terhadap performa kapal dan juga para stakeholder kapal. Salah satu metode statistika yang memungkinkan untuk memprediksi tahanan kapal berdasarkan pengujian tahanan model kapal, yaitu analisis regresi. Pemilihan metode regresi sangat diperlukan karena metode yang tepat akan menghasilkan prediksi yang tepat juga. Pemilihan metode regresi dipengaruhi oleh kondisi data penelitian, seperti terpenuhi atau tidaknya asumsi-asumsi klasik meliputi multikolinieritas, distribusi normal, autokorelasi, dan homoskedastisitas. Hasil pengujian asumsi menunjukan asumsi multikolinieritas dan distribusi normal tidak dapat terpenuhi yang mengarahkan pada penggunaan metode regresi robust ridge.

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“…As previously noted, the ridge estimator can be overly influenced by a few outliers among the dependent variable Y . Numerous estimators have been proposed and compared regarding how this issue might be addressed (e.g., Adegoke, Adewuyi, Ayinde, & Lukman, ; Arslan & Billor, ; Ertaş et al ., ; Kan et al ., ; Lukman et al ., ; Samkar & Alpu, ). A basic approach towards robust analogues of the ridge estimator is as follows.…”

Section: Review Of Extant Techniquesmentioning

confidence: 99%

Robust regression: Testing global hypotheses about the slopes when there is multicollinearity or heteroscedasticity

Wilcox

2018

Brit J Math & Statis

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A well-known concern regarding the usual linear regression model is multicollinearity. As the strength of the association among the independent variables increases, the squared standard error of regression estimators tends to increase, which can seriously impact power. This paper examines heteroscedastic methods for dealing with this issue when testing the hypothesis that all of the slope parameters are equal to zero via a robust ridge estimator that guards against outliers among the dependent variable. Included are results related to leverage points, meaning outliers among the independent variables. In various situations, the proposed method increases power substantially.

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Ridge Regression Based on Some Robust Estimators

Cited by 17 publications

References 15 publications

Ridge Least Absolute Deviation Performance in Addressing Multicollinearity and Different Levels of Outlier Simultaneously

Ridge Least Absolute Deviation Performance in Addressing Multicollinearity and Different Levels of Outlier Simultaneously

Analisis Regresi untuk Memprediksi Tahanan Kapal Cepat

Robust regression: Testing global hypotheses about the slopes when there is multicollinearity or heteroscedasticity

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