Improvement of the Liu estimator in linear regression model

Hubert, Mia; Wijekoon, Pushpakanthie

doi:10.1007/s00362-006-0300-4

Cited by 73 publications

(34 citation statements)

References 4 publications

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“…The formal resemblence between (9) and the Liu estimator motivated Akdeniz and Kaçiranlar (1995), Hubert and Wijekoon (2006) and Yang and Xu (2009) to call it the difference based Liu type estimator of the semiparametric regression model.…”

Section: Ymentioning

confidence: 99%

Difference Based Ridge and Liu Type Estimators in Semiparametric Regression Models

2011

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We consider a difference based ridge regression estimator and a Liu type estimator of the regression parameters in the partial linear semiparametric regression model, y = Xβ + f + ε. Both estimators are analysed and compared in the sense of mean-squared error. We consider the case of independent errors with equal variance and give conditions under which the proposed estimators are superior to the unbiased difference based estimation technique. We extend the results to account for heteroscedasticity and autocovariance in the error terms. Finally, we illustrate the performance of these estimators with an application to the determinants of electricity consumption in Germany.

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Section: Ymentioning

confidence: 99%

Difference Based Ridge and Liu Type Estimators in Semiparametric Regression Models

2011

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“…In order to improve the OME, Hubert and Wijekoon [6] inserted the Liu estimator into the OME procedure and obtained a new type of stochastic restricted Liu estimators aŝ…”

Section: ) Wherementioning

confidence: 99%

“…Theil and Goldberger [12] and Theil [11] introduced the mixed estimator (OME) technique by bringing together the sample and the prior information (1.5) 6) where both random errors are uncorrelated E ( φ ) = 0. Since E ( ) = σ 2 I n , therefore, with (1.5), the variance-covariance matrix becomes…”

Section: Introductionmentioning

confidence: 99%

A new stochastic restricted biased estimator under heteroscedastic or correlated error

Alheety

2011

ESAIM: PS

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Abstract. In this paper, under the linear regression model with heteroscedastic and/or correlated errors when the stochastic linear restrictions on the parameter vector are assumed to be held, a generalization of the ordinary mixed estimator (GOME), ordinary ridge regression estimator (GORR) and Generalized least squares estimator (GLSE) is proposed. The performance of this new estimator against GOME, GORR, GLS and the stochastic restricted Liu estimator (SRLE) [Yang and Xu, Statist. Papers 50 (2007) 639-647] are examined in terms of matrix mean square error criterion. A numerical example is considered to illustrate the theoretical results.Mathematics Subject Classification. 62J05, 62J07.

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“…Some biased estimators are proposed to solve this problem such as the Ordinary Ridge Estimator (ORE) by Hoerl and Kennard [1], the Restricted Ridge Estimator (RRE) by Sarkar [2], the Liu Estimator (LE) by Liu [3], the Restricted Liu Estimator (RLE) by Kaçiranlar, et al [4] and the Stochastic Restricted Liu Estimator (SRLE) by Hubert and Wijekoon [5]. When different estimators are available the preliminary test estimation procedure is adopted to select a suitable estimator.…”

Section: Introductionmentioning

confidence: 99%

Improvement of the Preliminary Test Estimator When Stochastic Restrictions are Available in Linear Regression Model

Arumairajan¹,

Wijekoon²

2013

OJS

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Ridge type estimators are used to estimate regression parameters in a multiple linear regression model when multicolinearity exists among predictor variables. When different estimators are available, preliminary test estimation procedure is adopted to select a suitable estimator. In this paper, two ridge estimators, the Stochastic Restricted Liu Estimator and Liu Estimator are combined to define a new preliminary test estimator, namely the Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE). The stochastic properties of the proposed estimator are derived, and the performance of PTSRLE is compared with SRLE in the sense of mean square error matrix (MSEM) and scalar mean square error (SMSE) for the two cases in which the stochastic restrictions are correct and not correct. Moreover the SMSE of PTSRLE based on Wald (WA), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are derived, and the performance of PTSRLE is compared using WA, LR and LM tests as a function of the shrinkage parameter d with respect to the SMSE. Finally a numerical example is given to illustrate some of the theoretical findings.

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Improvement of the Liu estimator in linear regression model

Abstract: Ordinary least squares estimator, mixed estimator, Liu estimator, Stochastic Restricted Liu estimator, Mean Squared error matrix,

Cited by 73 publications

References 4 publications

Difference Based Ridge and Liu Type Estimators in Semiparametric Regression Models

Difference Based Ridge and Liu Type Estimators in Semiparametric Regression Models

A new stochastic restricted biased estimator under heteroscedastic or correlated error

Improvement of the Preliminary Test Estimator When Stochastic Restrictions are Available in Linear Regression Model

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