Unbiased ridge estimation with prior information and ridge trace

Crouse, Robert H.; Jin, Chun; Hanumara, R. Choudary

doi:10.1080/03610929508831620

Cited by 40 publications

(27 citation statements)

References 10 publications

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“…Hoerl and Kennard (1970 a, b) and, Marquardt (1970) have suggested problems associated with a ridge regression estimator. Until quite recently, there are being many researches for ridge regression (for example, See Crouse, Jin, and Hanumara(1995).). The ridge regression estimator for the parameters in the first order and second order polynomial models are calculated using the formula b(k) = (X'X + k~) -' XIy, --where k is a constant and usually 0 < k < 1.…”

Section: Introductionmentioning

confidence: 99%

Graphical methods for evaluating ridge regression estimator in mixture experiments

Jang¹,

Yoon²

1997

Communications in Statistics - Simulation and Computation

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When the component proportions in mixture experiments are restricted by lower and upper bounds, multicollinearity appears all too frequently. Thus, we can suggest the use of ridge regression as a mean for stabilizing the coefficient estimates in the fitted model. We propose graphical methods for evaluating the effect of ridge regression estimator with respect to the predicted response value and the prediction variance.

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Section: Introductionmentioning

confidence: 99%

Graphical methods for evaluating ridge regression estimator in mixture experiments

Jang¹,

Yoon²

1997

Communications in Statistics - Simulation and Computation

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“…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).…”

mentioning

confidence: 98%

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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“…In this section, we propose to construct MUR by using the operational ridge parameter proposed by Hoerl et al (1981) and Crouse et al (1995). First, since the harmonic mean of optimal ridge parameter values, (see (24)) depends on the unknown parameters L and σ 2 , we use their OLS estimates.…”

Section: Estimating the Ridge Parameter Kmentioning

confidence: 99%

“…As K increases indefinitely, the MRR estimator approaches b. Crouse et al (1995) defined the Unbiased Ridge Regression (URR) estimator as follows:…”

Section: Introductionmentioning

confidence: 99%

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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Unbiased ridge estimation with prior information and ridge trace

Cited by 40 publications

References 10 publications

Graphical methods for evaluating ridge regression estimator in mixture experiments

Graphical methods for evaluating ridge regression estimator in mixture experiments

Comparisons of the Unbiased Ridge Estimation to the Other Estimations

A Modification of the Ridge Type Regression Estimators

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