Beta ridge regression estimators: simulation and application

Concurrency and Computation

2021

Self Cite

The ordinary least-squares estimator is commonly used to estimate the parameters of a linear regression model but gives unreliable and unfavorable results when two problems occur together: multicollinearity and outliers. This article proposes two different robust estimators of the regression parameters to cope with these problems together. The proposed estimators are a robust version of the Özkale-Kaçiranlar and Yang-Chang estimators. Theoretical calculations, numerical simulations, and real-life data on manufacturing production are presented to demonstrate the superiority of the proposed robust estimators to existing estimators at dealing with multicollinearity and outliers at the same time.

“…The biasing parameter

k

in the ORR estimator and biasing parameter

d

in the Liu estimator were derived by Hoerl and Kennard 2 and Liu, 6 respectively. Different authors have proposed different estimators of

k

and

d

for different models 14–19 . We assumed that

{\overset{α}{true}}_{M}

is normally distributed with the mean

α

and covariance matrix

A^{2} B^{- 1} .

This assumption holds approximately in practice because

\sqrt{n} ({\overset{α}{true}}_{M}^{2} - α) \to N (0, A^{2} B^{- 1})

, where

A^{2} = v_{0}^{2} E [ρ^{2} (ε / v_{0})] / {([], E ρ^{'} ((), ε false/ v_{0}))}^{2}

with the scale estimate

v_{0}

.…”

Section: Statistical Methodologymentioning

confidence: 99%

“…Different authors have proposed different estimators of k and d for different models. [14][15][16][17][18][19] We assumed that αM is normally distributed with the mean 𝛼 and covariance matrix…”

Section: Determination Of the Biasing Parametersmentioning

confidence: 99%

Development of robust Özkale–Kaçiranlar and Yang–Chang estimators for regression models in the presence of multicollinearity and outliers

Awwad

Dawoud

Concurrency and Computation

2021

Self Cite

“…( 12) is an asymptotic variance, and the second term is a square bias. Abonazel and Taha [4] and Qasim et al [5] showed the derivation of the MSE properties of the RBR estimator.…”

Section: Ridge and Liu Estimatorsmentioning

confidence: 99%

“…Another comparative performance called relative efficiency (RE) can be utilized, it is calculated based on the MSE in Eq. ( 33) as follows [4,39]:…”

Section: Relative Efficiencymentioning

confidence: 99%

“…The concept of the ridge estimator is to add a small definite amount (k) to the diagonal entries of the covariance matrix to increase the conditioning of this matrix, reduce the mean squared error (MSE), and achieve consistent coefficients. For a review of the ridge estimator in both linear and GLMs, e.g., as shown in References Rady et al [3], Abonazel and Taha [4], Qasim et al [5], Alobaidi et al [6], and Sami et al [7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Front. Appl. Math. Stat.

Algamal

Awwad

et al. 2022

Self Cite

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.

Developing a Liu‐type estimator in beta regression model

Algamal

Concurrency and Computation

2021

Self Cite

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.