Mean squared error matrix comparisons between biased estimators — An overview of recent results

Trenkler, Götz; Toutenburg, Helge

doi:10.1007/bf02924687

Cited by 160 publications

(40 citation statements)

References 9 publications

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“…Furthermore, minimizing is equivalent to minimizing for any so that the choice of scaling is immaterial. Therefore, we assume that , leading to the following optimization problem: (25) The solution is referred to as the minimax matrix-MSE (MXMM) estimate and is denoted by . In Section IV we show that is admissible, and derive a size SDP formulation of (25).…”

Section: Estimation Strategymentioning

confidence: 99%

“…Therefore, we assume that , leading to the following optimization problem: (25) The solution is referred to as the minimax matrix-MSE (MXMM) estimate and is denoted by . In Section IV we show that is admissible, and derive a size SDP formulation of (25). This allows to compute the solution efficiently using standard software packages.…”

Section: Estimation Strategymentioning

confidence: 99%

“…A problem that has been treated previously in the statistical literature is that of local MSE superiority, where matrix domination holds for a specific value of , i.e., for some (see e.g., [24], [25] and references therein). Our interest is in domination over all feasible values of so that the condition for domination is independent of .…”

Section: Ls Matrix-dominating Estimatorsmentioning

confidence: 99%

“…Using Theorem 1 we can express (25) in terms of as (41) where is defined by (4) and for brevity we denoted…”

Section: Minimax Matrix-mse Estimatormentioning

confidence: 99%

“…The notion of local weighted-MSE superiority has been investigating previously in the statistical literature, where domination is required only for specific values of (see, e.g., [24], [25], and references therein). However, since is not known, the fact that one estimator may be better than another for some does not help us select between estimators.…”

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confidence: 99%

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Universal Weighted MSE Improvement of the Least-Squares Estimator

Eldar

2008

IEEE Trans. Signal Process.

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Abstract-Since the seminal work of Stein in the 1950s, there has been continuing research devoted to improving the total meansquared error (MSE) of the least-squares (LS) estimator in the linear regression model. However, a drawback of these methods is that although they improve the total MSE, they do so at the expense of increasing the MSE of some of the individual signal components. Here we consider a framework for developing linear estimators that outperform the LS strategy over bounded norm signals, under all weighted MSE measures. This guarantees, for example, that both the total MSE and the MSE of each of the elements will be smaller than that resulting from the LS approach. We begin by deriving an easily verifiable condition on a linear method that ensures LS domination for every weighted MSE. We then suggest a minimax estimator that minimizes the worst-case MSE over all weighting matrices and bounded norm signals subject to the universal weighted MSE domination constraint.

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Section: Estimation Strategymentioning

confidence: 99%

Section: Estimation Strategymentioning

confidence: 99%

Section: Ls Matrix-dominating Estimatorsmentioning

confidence: 99%

“…Using Theorem 1 we can express (25) in terms of as (41) where is defined by (4) and for brevity we denoted…”

Section: Minimax Matrix-mse Estimatormentioning

confidence: 99%

mentioning

confidence: 99%

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Universal Weighted MSE Improvement of the Least-Squares Estimator

Eldar

2008

IEEE Trans. Signal Process.

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Modified ridge‐type estimator to combat multicollinearity: Application to chemical data

Lukman

Ayinde

Binuomote

et al. 2019

Journal of Chemometrics

103

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The Linear regression model is one of the most widely used models in different fields of study. The most popularly used estimation technique is the ordinary least squares estimator. The technique becomes unstable and gives misleading result in the presence of multicollinearity. The ridge regression estimator has been widely accepted as an alternative method to combat the problem of multicollinearity. In this study, a modified ridge‐type estimator is suggested by modifying the ridge regression estimator. A Monte Carlo simulation study and real‐life application were conducted to compare the performance of this estimator and some other existing estimators. The results of both simulation study and real‐life application show that the proposed estimator outperforms other competing estimator.

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A new adjusted Liu estimator for the Poisson regression model

Amin

Akram

Kibria

2021

Concurrency and Computation

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The Poisson regression model (PRM) is usually applied in the situations when the dependent variable is in the form of count data. For estimating the unknown parameters of the PRM, maximum likelihood estimator (MLE) is commonly used. However, its performance is suspected when the regressors are multicollinear. The performance of MLE is not satisfactory in the presence of multicollinearity. To mitigate this problem, different biased estimators are discussed in the literature, that is, ridge and Liu. However, the drawback of using the traditional Liu estimator is that in most of the times, the shrinkage parameter d, attains a negative value which is the major disadvantage of traditional Liu estimator. So, to overcome this problem, we propose a new adjusted Poisson Liu estimator (APLE) for the PRM which is the robust solution to the problem of multicollinear explanatory variables. For assessment purpose, we perform a theoretical comparison with other competitive estimators. In addition, a Monte Carlo simulation study is conducted to show the superiority of the new estimator. At the end, two real life applications are also considered. From the findings of simulation study and two empirical applications, it is observed that the APLE is the most robust

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Mean squared error matrix comparisons between biased estimators — An overview of recent results

Cited by 160 publications

References 9 publications

Universal Weighted MSE Improvement of the Least-Squares Estimator

Universal Weighted MSE Improvement of the Least-Squares Estimator

Modified ridge‐type estimator to combat multicollinearity: Application to chemical data

A new adjusted Liu estimator for the Poisson regression model

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