Optimal partial ridge estimation in restricted semiparametric regression models

Amini, Morteza; Roozbeh, Mahdi

doi:10.1016/j.jmva.2015.01.005

Cited by 67 publications

(24 citation statements)

References 20 publications

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“…Recently Roozbeh (2018) and Amini and Roozbeh (2015) have used the GCV criterion for selecting the optimal values of both ridge and bandwith parameters (k and λ) simultaneously, in the presence of multicollinearity for the semiparametric regression models. We can also apply the GCV method to select the optimal bandwidth λ and k simultaneously, which minimizes the following GCV function…”

Section: Estimating Smoothing Parameter λmentioning

confidence: 99%

Ridge stochastic restricted estimators in semiparametric linear measurement error models

Emami

2018

JIRSS

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In this article we consider the stochastic restricted ridge estimation in semiparametric linear models when the covariates are measured with additive errors. The development of penalized corrected likelihood method in such model is the basis for derivation of ridge estimates. The asymptotic normality of the resulting estimates is established. Also, necessary and sufficient conditions, for the superiority of the proposed estimator over its counterpart, for selecting the ridge parameter k are obtained. A Monte Carlo simulation study is also performed to illustrate the finite sample performance of the proposed procedures. Finally theoretical results are applied to Egyptian pottery industry data set.

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Section: Estimating Smoothing Parameter λmentioning

confidence: 99%

Ridge stochastic restricted estimators in semiparametric linear measurement error models

Emami

2018

JIRSS

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“…One of the mostly used regularization methods is the Tikhonov [21] regularization which was brought into statistical contexts by Hoerl and Kennard [12] as ridge regression. To mention a few recent researches, see e.g., [1,2,3,4,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Generalized Ridge Regression Estimator in High Dimensional Sparse Regression Models

Roozbeh

2018

Stat., optim. inf. comput.

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Modern statistical analysis often encounters linear models with the number of explanatory variables much larger than the sample size. Estimation in these high-dimensional problems needs some regularization methods to be employed due to rank deficiency of the design matrix. In this paper, the ridge estimators are considered and their restricted regression counterparts are proposed when the errors are dependent under a multicollinearity and high-dimensionality setting. The asymptotic distributions of the proposed estimators are exactly derived. Incorporating the information contained in the restricted estimator, a shrinkage type ridge estimator is also exhibited and its asymptotic risk is analyzed under some special cases. To evaluate the efficiency of the proposed estimators, a Monté-Carlo simulation along with a real example are considered.

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“…Several other methods for dealing with multicollinearity are the r-k class estimator which combines the techniques of ridge regression and principal component regression (PCR) while utilizing the ridge technique to reduce the mean square error of principal components estimators [10]; the biased estimator which combines the advantages of ridge and Stein estimators [23]; the r-d class estimator which includes OLS, PCR and Liu estimators, being superior to the OLSE, Liu estimator and PCR estimator in the scalar mean-squared error (mse) sense [21]; and a class of biased estimators based on the Cholesky and QR decompositions which make the data to be less distorted than the other biased methods [9,28,29]. As a brief review on applicability of these strategies, see [3,4,5,15] in which the ridge methodology has been used.…”

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confidence: 99%

“…As previously mentioned, it is difficult to give a satisfactory answer to the problem of selecting the ridge parameter. Because of good features of the generalized cross validation (GCV) and its simplicity (see [4]), here we use it for RLTSE to choose the optimum value of the ridge parameter (k opt ). The GCV criterion for RLTSE can be obtained by…”

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Two penalized mixed–integer nonlinear programming approaches to tackle multicollinearity and outliers effects in linear regression models

Roozbeh¹,

Babaie-Kafaki²,

Aminifard³

2021

JIMO

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In classical regression analysis, the ordinary least-squares estimation is the best strategy when the essential assumptions such as normality and independency to the error terms as well as ignorable multicollinearity in the covariates are met. However, if one of these assumptions is violated, then the results may be misleading. Especially, outliers violate the assumption of normally distributed residuals in the least-squares regression. In this situation, robust estimators are widely used because of their lack of sensitivity to outlying data points. Multicollinearity is another common problem in multiple regression models with inappropriate effects on the least-squares estimators. So, it is of great importance to use the estimation methods provided to tackle the mentioned problems. As known, robust regressions are among the popular methods for analyzing the data that are contaminated with outliers. In this guideline, here we suggest two mixed-integer nonlinear optimization models which their solutions can be considered as appropriate estimators when the outliers and multicollinearity simultaneously appear in the data set. Capable to be effectively solved by metaheuristic algorithms, the models are designed based on penalization schemes with the ability of down-weighting or ignoring unusual data and multicollinearity effects. We establish that our models are computationally advantageous in the perspective of the flop count. We also deal with a robust ridge methodology. Finally, three real data sets are analyzed to examine performance of the proposed methods.

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Optimal partial ridge estimation in restricted semiparametric regression models

Cited by 67 publications

References 20 publications

Ridge stochastic restricted estimators in semiparametric linear measurement error models

Ridge stochastic restricted estimators in semiparametric linear measurement error models

Generalized Ridge Regression Estimator in High Dimensional Sparse Regression Models

Two penalized mixed–integer nonlinear programming approaches to tackle multicollinearity and outliers effects in linear regression models

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