New Shrinkage Parameters for the Liu-type Logistic Estimators

Asar, Yasin; Genç, Aşır

doi:10.1080/03610918.2014.995815

Cited by 50 publications

(30 citation statements)

References 14 publications

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“…In practice, however, this assumption often not holds, which leads to the problem of multicollinearity. In the presence of multicollinearity, when estimating the regression coefficients for gamma regression model using the maximum likelihood (ML) method, the estimated coefficients usually become unstable with a high variance, and therefore low statistical significance . Numerous remedial methods have been proposed to overcome the problem of multicollinearity.…”

Section: Introductionmentioning

confidence: 99%

“…Ridge regression is a shrinkage method that shrinks all regression coefficients toward zero to reduce the large variance . This done by adding a positive amount to the diagonal of X T X .…”

Section: Introductionmentioning

confidence: 99%

“…In the presence of multicollinearity, when estimating the regression coefficients for gamma regression model using the maximum likelihood (ML) method, the estimated coefficients usually become unstable with a high variance, and therefore low statistical significance. 6,7 Numerous remedial methods have been proposed to overcome the problem of multicollinearity. The ridge regression method 8 has been consistently demonstrated to be attractive and alternative to the ML estimation method.…”

Section: Introductionmentioning

confidence: 99%

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Developing a ridge estimator for the gamma regression model

Algamal

2018

Journal of Chemometrics

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The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The gamma regression model is a very popular model in the application when the response variable is positively skewed. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the gamma regression coefficients. To address this problem, a gamma ridge regression model has been proposed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. Our Monte Carlo simulation results and the real data application suggest that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error.

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Section: Introductionmentioning

confidence: 99%

“…Ridge regression is a shrinkage method that shrinks all regression coefficients toward zero to reduce the large variance . This done by adding a positive amount to the diagonal of X T X .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Developing a ridge estimator for the gamma regression model

Algamal

2018

Journal of Chemometrics

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“…The data set is obtained from the official website of the Statistics Sweden (http://www.scb.se/) and it was also used in Asar and Genc [2] and a similar data set was used in Mansson et al [4]. There are 271 observations which are the municipalities of Sweden in the data set.…”

Section: Numerical Examplementioning

confidence: 99%

On almost unbiased ridge logistic estimator for the logistic regression model

Wu¹,

Asar²

2015

HJMS

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Schaefer et al. [15] proposed a ridge logistic estimator in logistic regression model. In this paper a new estimator based on the ridge logistic estimator is introduced in logistic regression model and we call it as almost unbiased ridge logistic estimator. The performance of the new estimator over the ridge logistic estimator and the maximum likelihood estimator in scalar mean squared error criterion is investigated. We also present a numerical example and a simulation study to illustrate the theoretical results.

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“…Different methods to select the parameters (k, d) used in LTE are proposed by [3]. In statistical research, there may be prior information regarding the variables considered in the statistical analysis.…”

Section: Introductionmentioning

confidence: 99%

Performance of a New Restricted Biased Estimator in Logistic Regression

Asar

2017

SDÜ Fen Bil Enst Der

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It is known that the variance of the maximum likelihood estimator (MLE) inflates when the explanatory variables are correlated. This situation is called the multicollinearity problem. As a result, the estimations of the model may not be trustful. Therefore, this paper introduces a new restricted estimator (RLTE) that may be applied to get rid of the multicollinearity when the parameters lie in some linear subspace in logistic regression. The mean squared errors (MSE) and the matrix mean squared errors (MMSE) of the estimators considered in this paper are given. A Monte Carlo experiment is designed to evaluate the performances of the proposed estimator, the restricted MLE (RMLE), MLE and Liu-type estimator (LTE). The criterion of performance is chosen to be MSE. Moreover, a real data example is presented. According to the results, proposed estimator has better performance than MLE, RMLE and LTE. Özet: Açıklayıcı degişkenler ilişkili oldugunda en çok olabilirlik tahmincisinin (MLE) varyansınınşiştigi bilinmektedir. Bu durum çoklu-baglantı problemi olarak adlandırılır. Sonuç olarak, modelin tahminleri güvenilir olmayabilir. Bu nedenle, bu makale, lojistik regresyon modelinde, düşük boyutlu veriler için (n > p), çoklu-baglantı problemini gidermek için parametrelerin bir alt uzayda oldugu durumda uygulanabilecek yeni kısıtlı bir tahminciyi ortaya koymaktadır. Bu makalede ele alınan tahmin edicilerin hata kareler ortalamaları (MSE) ve matris MSE'leri(MMSE) verilmiştir. Monte Carlo deneyi, öner-ilen tahmincinin (RLTE), kısıtlı en çok olabilirlik tahmincisinin (RMLE), MLE ve Liu tipi tahmincisinin (LTE) performanslarını degerlendirmek üzere tasarlanmıştır. Ayrıca gerçek veri üzerinde bir örnek gösterilmiştir. Performans degerlendirme kriteri olarak MSE seçilmiştir. Sonuçlara göre, yeni tahmincinin MLE, RMLE ve LTE'den daha iyi performansı vardır.

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New Shrinkage Parameters for the Liu-type Logistic Estimators

Cited by 50 publications

References 14 publications

Developing a ridge estimator for the gamma regression model

Developing a ridge estimator for the gamma regression model

On almost unbiased ridge logistic estimator for the logistic regression model

Performance of a New Restricted Biased Estimator in Logistic Regression

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