Evaluation of the Predictive Performance of the Liu Estimator

Özbey, Fela; Kaçıranlar, Selahattin

doi:10.1080/03610926.2012.756914

Cited by 7 publications

(17 citation statements)

References 7 publications

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“…9 They set ridge parameter k = 0.1, Liu parameter d = 0.9, 1 = 1.95, 2 = 0.05, and use r 12 = 0.95 to indicate the degree of collinearity. Let us recall the example given by Friedman and Montgomery 8 and Özbey and Kaçiranlar.…”

Section: Numerical Examplementioning

confidence: 99%

Retracted: Evaluation of the predictive performance of the principal component two‐parameter estimator

Chen

Huang

2018

Concurrency and Computation

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In this paper, detailed comparisons are given between those estimators that can be derived from the principal component two-parameter estimator such as the ordinary least squares estimator, the principal components regression estimator, the ridge regression estimator, the Liu estimator, the r − k estimator, and the r − d estimator by the prediction mean square error criterion. In addition, conditions for the superiority of the principal component two-parameter estimator over the others are obtained. Furthermore, a numerical example study is conducted to compare these estimators under the prediction mean squared error criterion. KEYWORDSLiu estimator, prediction mean squared error, ridge regression estimator, r − d estimator, r − k estimator, two-parameter estimator 1 Concurrency Computat Pract Exper. 2019;31:e4710.wileyonlinelibrary.com/journal/cpe( 1 +1) 2 ( 1 +k) 2 is always true, so, for any values of z 2 01 , z 2 02 , 2 2 , k, and d, we have J PCTP < J r − k .Theorem 6. For any value of z 2 01 , z 2 02 , 2 2 , k, d, and 1 , we have J PCTP < J r − d .

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Section: Numerical Examplementioning

confidence: 99%

Retracted: Evaluation of the predictive performance of the principal component two‐parameter estimator

Chen

Huang

2018

Concurrency and Computation

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“…If ρ = 0, then M = 0, V = I and γ becomes λ . Thus

f_{2} ((), α_{2}^{2}) = \frac{[\frac{1}{λ_{1}} - \frac{{(λ_{1} + d)}^{2}}{λ_{1} {((), λ_{1} + 1)}^{2}}]}{\frac{{((), λ_{2} + d)}^{2}}{λ_{2} {(λ_{2} + 1)}^{2}} + \frac{{(1 - d)}^{2} α_{2}^{2}}{{((), λ_{2} + 1)}^{2}} - \frac{1}{λ_{2}}}

(Özbey and Kaçıranlar's () results).…”

Section: Comparison Of Prediction Mean Squared Errors In Two‐dimensiomentioning

confidence: 92%

“…This independence assumption would seem to be appropriate for the classical case where V = I. Thus the LRP reduces to

{\overset{true^}{p}}_{1} = x'_{0} b_{k}

(Friedman and Montgomery, ) and the LLP reduces to

{\overset{true^}{p}}_{2} = x'_{0} b_{d}

(Özbey and Kaçıranlar, ).…”

Section: Properties and Comparison Of Predictorsmentioning

confidence: 99%

“…By using the two‐dimensional space, they had the opportunity to obtain the ratio

z_{02}^{2} true/ z_{01}^{2}

and use it as the reference point in their comparisons. Özbey and Kaçıranlar () also used the same method for the Liu estimator.…”

Section: Comparison Of Prediction Mean Squared Errors In Two‐dimensiomentioning

confidence: 99%

“…the ratio

z_{02}^{2} true/ z_{01}^{2}

). As in Friedman and Montgomery () and Özbey and Kaçıranlar ()

α_{1}^{2}

will be set to zero because non‐zero values of

α_{1}^{2}

increase only the intercept values for PMSE 1 and PMSE 2 but leave the curve for the PMSE unchanged. Theorem If

α_{2}^{2} > \frac{(2 γ_{2} + k)}{k γ_{2}}

, then PMSE 1 < PMSE for

α_{2}^{2} < \frac{{(γ_{2} + k)}^{2} ([], 2 ρ ((), a N_{1} + b N_{2}) - a ((), z_{01}^{2} + ρ^{2} Z_{1}^{2}) - ρ^{2} b Z_{2}^{2})}{ρ^{2} k^{2} ((), 4 N_{2} - ρ^{2} Z_{2}^{2})}

or for

α_{2}^{2} > \frac{{(γ_{2} + k)}^{2} ([], 2 ρ ((), a N_{1} + b N_{2}) - a ((), z_{01}^{2} + ρ^{2} Z_{1}^{2}) - ρ^{2} b Z_{2}^{2})}{ρ^{2} k^{2} ((), 4 N_{2} - ρ^{2} Z_{2}^{2})}

iff

\frac{z_{02}^{2}}{z_{01}^{2}} < f_{1} ((), α_{2}^{2})

. If

α_{2}^{2} < \frac{(2 γ_{2} + k)}{k γ}

…”

Section: Comparison Of Prediction Mean Squared Errors In Two‐dimensiomentioning

confidence: 99%

See 2 more Smart Citations

The Predictive Performance Evaluation of Biased Regression Predictors With Correlated Errors

Dawoud

Kaçıranlar

2015

Journal of Forecasting

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When the interdependence of disturbances is present in a regression model, the pattern of sample residuals contains information which is useful in the prediction of post-sample drawings and when multicollinearity among regressors is also present, it is useful to use biased regression estimators. This information is exploited in the biased predictors derived here. Also, the predictive performance of various biased predictors with correlated errors is discussed and all pair-wise comparisons are made among these predictors. The theoretical results are illustrated by a numerical example.

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The Prediction Performance of the Alternative Biased Estimators for the Distributed Lag Models

Dawoud

Kaçıranlar

2019

Iran J Sci Technol Trans Sci

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Evaluation of the Predictive Performance of the Liu Estimator

Cited by 7 publications

References 7 publications

Retracted: Evaluation of the predictive performance of the principal component two‐parameter estimator

Retracted: Evaluation of the predictive performance of the principal component two‐parameter estimator

The Predictive Performance Evaluation of Biased Regression Predictors With Correlated Errors

The Prediction Performance of the Alternative Biased Estimators for the Distributed Lag Models

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