A new Liu-type estimator

Kurnaz, Fatma Sevinç; Akay, Kadri Ulaş

doi:10.1007/s00362-014-0594-6

Cited by 24 publications

(19 citation statements)

References 11 publications

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“…The acronym LTS refers to the FAST-LTS algorithm, which goes back to [16] in the robust regression setting. This strategy to find an optimal subset has been employed for several robust estimators, such as for linear and logistic regression with elastic net (enet) penalty [10]. The key feature of this algorithm are the C-steps (concentration steps), which works in the robust regression setting as follows.…”

Section: Definition Of the Estimatormentioning

confidence: 99%

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Robust and Sparse Multinomial Regression in High Dimensions

Kurnaz¹,

Filzmoser²

2022

Preprint

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A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty, which is a mixture of L 1 and L 2 penalties. From this point of view, the proposed estimator is an extension of the enet-LTS estimator [10] for linear and logistic regression to the multinomial regression setting. After introducing an algorithm for its computation, a simulation study is conducted to show the performance in comparison to the non-robust version of the multinomial regression estimator. Some real data examples underline the usefulness of this robust estimator.

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Section: Definition Of the Estimatormentioning

confidence: 99%

“…The goal of this paper is to introduce a robust counterpart to the elastic net estimator for multinomial regression. The main idea is to use a trimmed version of the penalized log-likelihood function, similar as done in [10] in the context of sparse binary logistic regression. The new estimator is introduced in detail in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Robust and Sparse Multinomial Regression in High Dimensions

Kurnaz¹,

Filzmoser²

2022

Preprint

Self Cite

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“…Furthermore, Liu [13] proved the supremacy of the Liu-type estimator over the ridge and Liu estimators. Details about Liu-type estimator, properties, and applications in regression models are shown in References Liu [14], Özkale and Kaciranlar [15], Li and Yang [16], Kurnaz and Akay [17], Sahriman and Koerniawan [18], and Algamal and Abonazel [19]. As a good alternative for the Liu-type estimator, Özkale and Kaciranlar [15] proposed the twoparameter estimator, and they proved that the two-parameter estimator utilizes the power of both the ridge estimator and the Liu estimator.…”

Section: Introductionmentioning

confidence: 99%

A New Two-Parameter Estimator for Beta Regression Model: Method, Simulation, and Application

Abonazel

Algamal

Awwad

et al. 2022

Front. Appl. Math. Stat.

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The beta regression is a widely known statistical model when the response (or the dependent) variable has the form of fractions or percentages. In most of the situations in beta regression, the explanatory variables are related to each other which is commonly known as the multicollinearity problem. It is well-known that the multicollinearity problem affects severely the variance of maximum likelihood (ML) estimates. In this article, we developed a new biased estimator (called a two-parameter estimator) for the beta regression model to handle this problem and decrease the variance of the estimation. The properties of the proposed estimator are derived. Furthermore, the performance of the proposed estimator is compared with the ML estimator and other common biased (ridge, Liu, and Liu-type) estimators depending on the mean squared error criterion by making a Monte Carlo simulation study and through two real data applications. The results of the simulation and applications indicated that the proposed estimator outperformed ML, ridge, Liu, and Liu-type estimators.

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“…Liu‐type estimator is a two parameters estimator that utilizes the power of both the ridge estimator and the Liu estimator. For more details about Liu‐type estimation, properties, and applications in linear regression model, see, for example, Liu, 12 Özkale and Kaciranlar, 13 Sakallıoğlu and Kaçıranlar, 14 Li and Yang, 15 Kurnaz and Akay, 16 and Sahriman and Koerniawan 17 . Extensions of Liu‐type estimation in GLMs includes: Huang, 18 Inan and Erdogan, 19 Huang and Yang, 20 Asar and Genç, 21 Asar, 22 Algamal, 23 Asar, 24 Asar and Genç, 25 Abonazel and Farghali, 26 Çetinkaya and Kaçıranlar, 27 Rady et al, 28,29 Akram et al, 30 Algamal, 31 Algamal, 32 Noeel and Algamal, 33 and Farghali et al 34…”

Section: Introductionmentioning

confidence: 99%

Developing a Liu‐type estimator in beta regression model

Algamal

Abonazel

2021

Concurrency and Computation

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The beta regression model is a commonly used when the response variable has the form of fractions or percentages. The maximum likelihood (ML) estimator is used to estimate the regression coefficients of this model. However, it is known that multicollinearity problem affects badly the variance of ML estimator. Therefore, this paper introduces the Liu‐type estimator for the beta regression model to handle the multicollinearity problem. The performance of the proposed (Liu‐type) estimator is compared to the ML estimator and other biased (ridge and Liu) estimators depending on the mean squared error (MSE) criterion by conducting a simulation study and through an empirical application. The results indicated that the proposed estimator outperformed the ML, ridge, and Liu estimators.

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A new Liu-type estimator

Cited by 24 publications

References 11 publications

Robust and Sparse Multinomial Regression in High Dimensions

Robust and Sparse Multinomial Regression in High Dimensions

A New Two-Parameter Estimator for Beta Regression Model: Method, Simulation, and Application

Developing a Liu‐type estimator in beta regression model

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