On the almost unbiased generalized liu estimator and unbiased estimation of the bias and mse

Akdeniz, Fikri; Kaçıranlar, Selahattin

doi:10.1080/03610929508831585

Cited by 135 publications

(58 citation statements)

References 8 publications

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“…Since we may consider the residual as an estimator of error, we can apply MSE criterion on the residuals. Akdeniz (2001) compared Liu estimator which is proposed by Liu (1993) and almost unbiased Liu estimator which is proposed by Akdeniz and Kaçıranlar (1995) to the OLS estimator in terms of MSE on their residuals.…”

Section: The Examination and Analysis Of Residualsmentioning

confidence: 99%

Comparisons of the Unbiased Ridge Estimation to the Other Estimations

Özkale

Kaçıranlar

2007

Communications in Statistics - Theory and Methods

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In the presence of multicollinearity, ordinary least squares (OLS) estimation is inadequate. Alternative estimation techniques were proposed. One of which is unbiased ridge regression (URR) estimator given by Crouse et al. (1995). In this article, we introduced the URR estimator in two different ways by following Farebrother (1984) and Troskie et al. (1994). We discuss its properties in some detail, comparing URR estimator to the OLS, the ordinary ridge regression (ORR), and the r − k class estimators in the sense of matrix mean square error (MMSE) and residuals. We also illustrate our findings with a numerical example based on the data generated by Hoerl and Kennard (1981) which is commonly used in literature to study the effect of multicollinearity.

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Section: The Examination and Analysis Of Residualsmentioning

confidence: 99%

Comparisons of the Unbiased Ridge Estimation to the Other Estimations

Özkale

Kaçıranlar

2007

Communications in Statistics - Theory and Methods

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“…(1993). This approach has been considered in many papers since, such as Akdeniz and Kaciranlar (1995), Kaciranlar (2003) and Alheety and Kibria (2009). The advantage of the Liu estimator, compared with the traditional ridge-regression method proposed by Hoerl and Kennard (1970a, b), is that the estimated coefficients are a linear function of the shrinkage parameter d [see Liu (1993)] instead of a non-linear function as in the case of ridge regression.…”

Section: Introductionmentioning

confidence: 97%

Developing Interaction Shrinkage Parameters for the Liu Estimator — with an Application to the Electricity Retail Market

2014

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In this article we examine multicollinearity in the standard OLS interactionterm model-a problem often disregarded by practitioners and in previous research. As a remedy we propose a number of new shrinkage parameters based on the Liu (Commun Stat 22:393-402, 1993) estimator. Using Monte Carlo simulations, we evaluate the robustness of all models for different data-generating processes under varying conditions such as altered sample sizes and error distributions. In the simulation study it is demonstrated that the Liu estimator, which is robust to multicollinearity, systematically outperforms the traditionally applied OLS approach. The simple reason is that interaction models by definition always induce substantial multicollinearity, which in turn distorts the inference of OLS. Conversely, the Liu estimator is robust against multicollinearity in interaction-term models. The advantages of our Liu-based method are also demonstrated in practice when examining the efficiency of the Swedish power retailing market. By the use of this unique data set we find strong evidence of positive asymmetric price transmission effects. Increases in Nord Pool electricity wholesale spot prices lead to immediate and full increases in the electricity retail prices, but

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“…It is useful in case of multicollinearity, see, e.g., Akdeniz and Kaçıranlar (1995), or Kaçıranlar et al (1999). One of the problems with the Liu estimator is determining the value of the biasing parameter d. Several methods have been motivated by Liu (1993) to find an estimate for the biasing parameter d in the Liu estimator (see Akdeniz and Erol, 2003).…”

Section: Introductionmentioning

confidence: 98%

The General Expressions for the Moments of the Stochastic Shrinkage Parameters of the Liu Type Estimator

Akdeniz

Styan

Werner

2006

Communications in Statistics - Theory and Methods

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One of the problems with the Liu estimator is the appropriate value for the unknown biasing parameter d. In this article we consider the optimum value for d and give upper bound for the expected value of the estimator of this biasing parameter. We also derive the general expressions for the moments of the stochastic shrinkage parameters of the Liu estimator and the generalized Liu estimator. Numerical calculations are carried out to illustrate the behavior of the mean and variance of the biasing parameter. Also, a numerical example is given to illustrate the effect of the biasing parameter d, on the mean square error of the Liu estimator.

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On the almost unbiased generalized liu estimator and unbiased estimation of the bias and mse

Cited by 135 publications

References 8 publications

Comparisons of the Unbiased Ridge Estimation to the Other Estimations

Comparisons of the Unbiased Ridge Estimation to the Other Estimations

Developing Interaction Shrinkage Parameters for the Liu Estimator — with an Application to the Electricity Retail Market

The General Expressions for the Moments of the Stochastic Shrinkage Parameters of the Liu Type Estimator

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