The ridge-type estimators have been intensively studied and modified for the linear regression model. In this article, we introduce a modified unbiased two-parameter estimator (MUTPE) as a new estimator to solve the m...
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The ridge-type estimators have been intensively studied and modified for the linear regression model. In this article, we introduce a modified unbiased two-parameter estimator (MUTPE) as a new estimator to solve the multicollinearity problem for the linear regression model. The MUTPE has been obtained as a linear combination of unbiased two-parameter estimator (UTPE). We give a simulation study to demonstrate the theoretical results. The results of the simulation have revealed that the proposed estimator has better effectiveness than both UTPE and ridge estimators under some circumstance. Finally, we analyzed a real-life data to justify the performance of the modified estimator MUTPE in the context of a linear regression model.
In this article, we consider the Stein-type approach to the estimation of the regression parameter in a multiple regression model under a multicollinearity situation. The Stein-type two-parameter estimator is proposed...
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In this article, we consider the Stein-type approach to the estimation of the regression parameter in a multiple regression model under a multicollinearity situation. The Stein-type two-parameter estimator is proposed when it is suspected that the regression parameter may be restricted to a subspace. The bias and the quadratic risk of the proposed estimator are derived and compared with the two-parameter estimator (TPE), the restricted TPE and the preliminary test TPE. The conditions of superiority of the proposed estimator are obtained. Finally, a real data example is provided to illustrate some of the theoretical results.
The identification of influential observations is an essential element in regression analysis as they posed a threat to the model building process. The existence of multicollinearity among the regressors complicates t...
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The identification of influential observations is an essential element in regression analysis as they posed a threat to the model building process. The existence of multicollinearity among the regressors complicates the presence of influential observations. Different influential diagnostics have been presented in literature so far using generalized linear models (GLM). In this paper, approximate deletion measures based on Sherman-Morrison Woodbury (SMW) theorem for the Poisson two-parameter regression model are proposed to detect influential observations in the presence of multicollinearity. Moreover, we conduct a Monte Carlo Simulation to evaluate the performance of the proposed measures. Finally, an example is presented to illustrate the proposed diagnostic measures. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
Ozkale and Kaciranlar (2007) proposed a two-parameter estimator (TPE) for the unknown parameter vector in linear regression when exact restrictions are assumed to hold. In this article, under the assumption that the e...
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Ozkale and Kaciranlar (2007) proposed a two-parameter estimator (TPE) for the unknown parameter vector in linear regression when exact restrictions are assumed to hold. In this article, under the assumption that the errors are not independent and identically distributed, we introduce a new estimator by combining the ideas underlying the mixed estimator (ME) and the two-parameter estimator when stochastic linear restrictions are assumed to hold. The new estimator is called the stochastic restricted two-parameter estimator (SRTPE) and necessary and sufficient conditions for the superiority of the SRTPE over the ME and TPE are derived by the mean squared error matrix (MSEM) criterion. Furthermore, selection of the biasing parameters is discussed and a numerical example is given to illustrate some of the theoretical results.
In this paper a generalized difference-based mixed two-parameter estimator in partially linear model is presented, when stochastic linear restrictions are assumed to hold. We also discussed the properties of the new e...
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In this paper a generalized difference-based mixed two-parameter estimator in partially linear model is presented, when stochastic linear restrictions are assumed to hold. We also discussed the properties of the new estimator and a method to select the biasing parameters is discussed. Finally a simulation study is given to show the performances of the estimators.
Sakallioglu and Kaciranlar (2008) proposed an estimator, two-parameter estimator, as an alternative to the ordinary least squares, the ordinary ridge and the Liu estimators in the presence of multicollinearity. In thi...
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Sakallioglu and Kaciranlar (2008) proposed an estimator, two-parameter estimator, as an alternative to the ordinary least squares, the ordinary ridge and the Liu estimators in the presence of multicollinearity. In this paper, we introduce a new class estimator by combining the ideas underlying the mixed estimator and the two-parameter estimator when stochastic linear restrictions are assumed to hold. The necessary and sufficient conditions for the superiority of the new estimator over the two-parameter estimator, modified mixed estimator and stochastic restricted two-parameter estimator Yang and Wu (2012) are derived by the matrix mean square error criterion. Furthermore, selections of the biasing parameters are discussed and two numerical examples and a Monte Carlo simulation are given to evaluate the performance of mentioned estimators in the theoretical results. (C) 2014 Elsevier Inc. All rights reserved.
In simultaneous equations model, two-stage least squares estimator is easy to apply and commonly preferred. When multicollinearity exists, two-stage least squares estimator has some drawbacks and it is no longer favor...
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In simultaneous equations model, two-stage least squares estimator is easy to apply and commonly preferred. When multicollinearity exists, two-stage least squares estimator has some drawbacks and it is no longer favorable. In this context, biased estimation methods are recommended. two-parameter estimator of A-zkale and Ka double dagger A +/- ranlar (Commun Stat Theory Methods 36(15):2707-2725, 2007) had been established to be superior to the ordinary least squares estimator under some conditions in linear regression model suffering from multicollinearity. In this paper, the idea of two-parameter estimation in linear regression model is carried out to the simultaneous equations model. For this model, two-stage two-parameter estimator is proposed to remedy the problem of multicollinearity. Estimation performance of this new estimator is evaluated by means of two real-life data analyses. In addition to the numerical example, an extensive Monte Carlo experiment is conducted.
In this article, we present a new general class of biased estimators which includes some popular estimators as special cases and discuss its properties for multiple linear regression models when regressors are correla...
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In this article, we present a new general class of biased estimators which includes some popular estimators as special cases and discuss its properties for multiple linear regression models when regressors are correlated. This proposal is based on some modification in the existing new two-parameter estimator. Performance of the proposed estimator is compared with many of the leading estimators, using the mean squared error matrix criterion, mitigating the adverse effects of multicollinearity. An extensive simulation study has been provided with a numerical example to illustrate the superiority of the proposed estimator.
This article is concerned with the parameter estimation in linear measurement error model when there is ill-conditioned data. To deal with the multicollinearity problem, a new two-parameter estimator is proposed. The ...
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This article is concerned with the parameter estimation in linear measurement error model when there is ill-conditioned data. To deal with the multicollinearity problem, a new two-parameter estimator is proposed. The asymptotic properties of the new estimator are considered using the mean squared error matrix. Finally, a Monte Carlo simulation is presented to show the performances of the estimators in terms of simulated mean squared error criteria. According to the results, the new estimator can be suggested as an alternative to the other existing estimators in the presence of ill-conditioned data.
This paper deals with parameter estimation in the linear regression model and an almost unbiased two-parameter estimator is introduced. The performance of this new estimator over the ordinary least-squares estimator a...
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This paper deals with parameter estimation in the linear regression model and an almost unbiased two-parameter estimator is introduced. The performance of this new estimator over the ordinary least-squares estimator and the two-parameter estimator [M.R. ozkale and S. Kaciranlar, The restricted and unrestricted two-parameter estimator, Comm. Statist. Theory Methods 36 (2007), pp. 27072725] in terms of scalar mean-squared error criterion is investigated and a simulation study is done.
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