Ridge regression methodology in partial linear models with correlated errors

Roozbeh, Mahdi; Arashi, Mohammad; Niroumand, Hossein Ali

doi:10.1080/00949650903362446

Cited by 25 publications

(3 citation statements)

References 23 publications

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“…Applying the differencing matrix to Model (3), permits direct estimation of the parametric effect. As a result of developments in Roozbeh et al (2011), it is known that the parameter vector β in (3) can be estimated with parametric efficiency. Since the data have been ordered so that the values of the nonparametric variable(s) are close, the application of the differencing matrix D in Model (3) removes the non-parametric effect in large samples (Yatchew 2000).…”

Section: Difference-based Estimatormentioning

confidence: 99%

Generalized difference-based weighted mixed almost unbiased ridge estimator in partially linear models

Akdeniz

Roozbeh

2017

Stat Papers

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In this paper, a generalized difference-based estimator is introduced for the vector parameter β in partially linear model when the errors are correlated. A generalized difference-based almost unbiased ridge estimator is defined for the vector parameter β. Under the linear stochastic constraint r = Rβ + e, a new generalized difference-based weighted mixed almost unbiased ridge estimator is proposed. The performance of this estimator over the generalized difference-based weighted mixed estimator, the generalized difference-based estimator, and the generalized differencebased almost unbiased ridge estimator in terms of the mean square error matrix criterion is investigated. Then, a method to select the biasing parameter k and nonstochastic weight ω is considered. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset. KeywordsDifference-based estimator • Generalized ridge estimator • Generalized difference-based weighted mixed almost unbiased ridge estimator • Partially linear model • Weighted mixed estimator

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Section: Difference-based Estimatormentioning

confidence: 99%

Generalized difference-based weighted mixed almost unbiased ridge estimator in partially linear models

Akdeniz

Roozbeh

2017

Stat Papers

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“…(Roozbeh et al, 2011) If β satisfies the linear restriction Rβ = r, then the bias, covariance matrix and risk functions of proposed estimator can be evaluated as follows:…”

Section: Computing the Risk Functionmentioning

confidence: 99%

New Ridge Regression Estimator in Semiparametric Regression Models

Roozbeh

Arashi

2015

Communications in Statistics - Simulation and Computation

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In the context of ridge regression, the estimation of shrinkage parameter plays an important role in analyzing data. Many efforts have been put to develop the computation of risk function in different full-parametric ridge regression approaches using eigenvalues and then bringing an efficient estimator of shrinkage parameter based on them. In this respect, the estimation of shrinkage parameter is neglected for semiparametric regression model. Not restricted, but the main focus of this approach is to develop necessary tools for computing the risk function of regression coefficient based on the eigenvalues of design matrix in semiparametric regression. For this purpose the differencing methodology is applied. We also propose a new estimator for shrinkage parameter which is of harmonic type mean of ridge estimators. It is shown that this estimator performs better than all the existing ones for the regression coefficient. For our proposal, a Monte Carlo simulation study and a real data set analysis related to housing attributes are conducted to illustrate the efficiency of shrinkage estimators based on the minimum risk and mean squared error criteria.

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“…And also, there are many methods in the literature for ridge regression [23][24][25][26][27][28][29]. And also, [30] proposed some new methods that take care of the skewed eigenvalues of the matrix of explanatory variables.…”

Section: Introductionmentioning

confidence: 99%