Combining Unbiased Ridge and Principal Component Regression Estimators

Batah, Feras Sh. M.; Özkale, M. Revan; Gore, Sonal

doi:10.1080/03610920802503396

Cited by 27 publications

(25 citation statements)

References 13 publications

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“…The data was then used by Course et al (1995) to compare SMSE performance of URR, ORR and OLS. Recently, Batah et al (2009) used the same data to illustrate the comparisons among OLS and various ridge type estimators. We now use this data to illustrate the performance of the MUR estimator to the OLS, ORR and URR estimators to compare the MMSE performance of these estimators.…”

Section: Resultsmentioning

confidence: 99%

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A Modification of the Ridge Type Regression Estimators

El-Salam¹

2011

American Journal of Applied Sciences

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Problem statement: Many regression estimators have been used to remedy multicollinearity problem. The ridge estimator has been the most popular one. However, the obtained estimate is biased. Approach: In this stuyd, we introduce an alternative shrinkage estimator, called modified unbiased ridge (MUR) estimator for coping with multicollinearity problem. This estimator is obtained from Unbiased Ridge Regression (URR) in the same way that Ordinary Ridge Regression (ORR) is obtained from Ordinary Least Squares (OLS). Properties of MUR estimator are derived. Results: The empirical study indicated that the MUR estimator is more efficient and more reliable than other estimators based on Matrix Mean Squared Error (MMSE).Conclusion: In order to solve the multicollinearity problem, the MUR estimator was recommended.

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Section: Resultsmentioning

confidence: 99%

“…This estimator is biased but reduces the variances of the regression coefficients. Subsequently, several other biased estimators of β have been proposed (Swindel, 1976;Sarkar, 1996;Batah and Gore, 2008;Batah et al, 2009;Arayesh and Hosseini, 2010;Asekunowo et al, 2010;Hirun and Sirisoponsilp, 2010;Rana et al, 2009). Swinded (1976) …”

Section: Introductionmentioning

confidence: 99%

A Modification of the Ridge Type Regression Estimators

El-Salam¹

2011

American Journal of Applied Sciences

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“…Its goal is to get the important information from the data, to represent it as a set of new orthogonal (independent) variables called principal components. Mathematically, PCA depends on the eigen decomposition of positive semi definite matrices and on the singular value decomposition SVD of rectangular matrices [7] and In case of multicollinearity problem, the researchers used another forms to estimate the parameters like principal component regression PCR [1]. Where this problem occurs when the predictors included in the linear model are highly correlated with each other.…”

Section: Principal Component Analysismentioning

confidence: 99%

A Review of Constrained Principal Component Analysis (CPCA) with Application on Bootstrap

Elmegaly¹

2019

IJTAM

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Linear model (LM) provide the advance in regression analysis, where it was considered an important statistical development of the last fifty years, following general linear model (GLM), principal component analysis (PCA) and constrained principal component analysis (CPCA) in the last thirty years. This paper introduce a series of papers prepared within the framework of an international workshop. Firstly, the LM and GLM has been discussed. Next, an overview of PCA has been presented. Then constrained principal component has been shown. Some of its special cases such as PCA, Canonical correlation analysis (CANO), Redundancy analysis (RA), Correspondence analysis (CA), Growth curve models (GCM), Extended growth curve models (ExGCM), Canonical discriminant analysis (CDA), Constrained correspondence analysis, non-symmetric correspondence analysis, Multiple Set CANO, Multiple Correspondence Analysis, Vector Preference Models, Seemingly unrelated regression (SUR), Weighted low rank approximations, Two-Way canonical decomposition with linear constraints, and Multilevel RA has been noted in this paper. Related methods and ordinary least squares (OLS) estimator as a special case form CPCA has been introduced. Finally, an example has been introduced to indicate the importance of CPCA and the different between PCA and CPCA. Where CPCA is a method for structural analysis of multivariate data that combine features of regression analysis and principal component analysis. In this method, the original data first decomposed into several components according to external information. The components then subjected to principal component analysis to explore structures within the components.

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“…Alternatively, Kaciranlar and Sakallioglu (2001) introduced the r − d class estimator which is the combination of the Liu estimator and the PCR estimator. Batah et al (2009) obtained the modified r − k class ridge regression (MCRR) estimator by modifying the URR estimator in the line of the PCR estimator. The properties of the above proposed estimators have been studied by Nomura and Ohkubo (1985), Sarkar (1996) and Ozkale and Kaciranlar (2007) among others.…”

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confidence: 99%

Combining two-parameter and principal component regression estimators

Chang

Yang

2011

Stat Papers

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This paper is concerned with the parameter estimation in linear regression model. To overcome the multicollinearity problem, a new class of estimator, namely principal component two-parameter (PCTP) estimator is proposed. The superiority of the new estimator over the principal component regression (PCR) estimator, the r − k class estimator, the r − d class estimator and the two-parameter estimator proposed by Yang and Chang (Commun Stat Theory Methods 39:923-934 2010) are discussed with respect to the mean squared error matrix (MSEM) criterion. Furthermore, we give a numerical example and a simulation study to illustrate some of the theoretical results.

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Combining Unbiased Ridge and Principal Component Regression Estimators

Cited by 27 publications

References 13 publications

A Modification of the Ridge Type Regression Estimators

A Modification of the Ridge Type Regression Estimators

A Review of Constrained Principal Component Analysis (CPCA) with Application on Bootstrap

Combining two-parameter and principal component regression estimators

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