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 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.
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.
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.
two-parameter (TP) estimators are more advantageous to their one-parameter competitors since they have two biasing parameters that serve different purposes in linear regression model. At least one of these biasing par...
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two-parameter (TP) estimators are more advantageous to their one-parameter competitors since they have two biasing parameters that serve different purposes in linear regression model. At least one of these biasing parameters intends to gain a remedial impact for multicollinearity. Within this respect, we define a new TP estimator to eliminate the disorder originated from multicollinearity. Also, we perform theoretical comparisons for new TP estimator according to mean square error criterion. By minimizing the mean square error, we derive optimal estimators for both of the biasing parameters of this new estimator. Moreover, we recommend a mathematical programming approach to determine two biasing parameters, simultaneously. In this approach, we minimize the mean square error and improve the length of the newly defined TP estimator. In application part, computations regarding the estimations of the biasing parameters and mean square errors, and the length of the estimated coefficients are examined.
In this article, a new two-type parameterestimator is introduced. This estimator is an extension of the two-parameter (TP) estimator presented by ozkale and Kaciranlar (2007), which includes the ordinary least square...
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In this article, a new two-type parameterestimator is introduced. This estimator is an extension of the two-parameter (TP) estimator presented by ozkale and Kaciranlar (2007), which includes the ordinary least squares (OLS), the generalized ridge, and the generalized Liu estimators, as special cases. Here, the performance of this new estimator over the OLS and TP estimators is, theoretically, evaluated in terms of quadratic bias and mean squared error matrix criteria, and the optimal biasing parameters are obtained to minimize the scalar mean squared error (MSE). Then a numerical example is given and a simulation study is done to illustrate the theoretical results of the article.
In this paper, a new two-type parameterestimator is proposed. This estimator is a generalization of the new twoparameter (NTP) estimator introduced by Yang and Chang, which includes the ordinary least squares (OLS),...
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In this paper, a new two-type parameterestimator is proposed. This estimator is a generalization of the new twoparameter (NTP) estimator introduced by Yang and Chang, which includes the ordinary least squares (OLS), the generalized ridge (GR) and the generalized Liu (GL) estimators, as special cases. Here, the performance of this new estimator is, theoretically, investigated over the OLS, the GR, the GL and the NTP estimators in terms of mean squared error matrix criterion. Furthermore, the estimation of the biasing parameters is obtained to minimize the scalar mean squared error. In addition, a complementary algorithm is proposed for the estimator presented by Yang and Chang. As well, a numerical example is given and a simulation study is done.
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.
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.
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