Good ridge estimators based on prior information

Swindel, Benee F.

doi:10.1080/03610927608827423

Cited by 137 publications

(69 citation statements)

References 10 publications

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“…The distribution of GNSS data, after removal of a linear trend and low frequency signal, has a strong peak with relatively broad tails, a combination better suited to the logistic distribution. The low frequency signal is estimated using the Matlab function gridfit, which uses a modified ridge estimator [Swindel, 1976] to generate a smooth surface. Our observation of the underlying distribution of the white noise component is not an artifact of the presence of and our process of removing flicker and random walk noise sources, which we confirm with synthetic time series.…”

Section: 1002/2015jb012049mentioning

confidence: 99%

Crustal deformation in the New Madrid seismic zone and the role of postseismic processes

2015

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Global Navigation Satellite System data across the New Madrid seismic zone (NMSZ) in the central United States over the period from 2000 through 2014 are analyzed and modeled with several deformation mechanisms including the following: (1) creep on subsurface dislocations, (2) postseismic frictional afterslip and viscoelastic relaxation from the 1811–1812 and 1450 earthquakes in the NMSZ, and (3) regional strain. In agreement with previous studies, a dislocation creeping at about 4 mm/yr between 12 and 20 km depth along the downdip extension of the Reelfoot fault reproduces the observations well. We find that a dynamic model of postseismic frictional afterslip from the 1450 and February 1812 Reelfoot fault events can explain this creep. Kinematic and dynamic models involving the Cottonwood Grove fault provide minimal predictive power. This is likely due to the smaller size of the December 1811 event on the Cottonwood Grove fault and a distribution of stations better suited to constrain localized strain across the Reelfoot fault. Regional compressive strain across the NMSZ is found to be less than 3 × 10−9/yr. If much of the present‐day surface deformation results from afterslip, it is likely that many of the earthquakes we see today in the NMSZ are aftershocks from the 1811–1812 New Madrid earthquakes. Despite this conclusion, our results are consistent with observations and models of intraplate earthquake clustering. Given this and the recent paleoseismic history of the region, we suggest that seismic hazard is likely to remain significant.

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Section: 1002/2015jb012049mentioning

confidence: 99%

Crustal deformation in the New Madrid seismic zone and the role of postseismic processes

2015

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“…Sarkar (1992) proposed a new restricted estimator by combining the restricted least squares estimate with RE. Kaciranlar et al (1998) compared the estimator introduced by Sarkar (1992) and the modified ridge regression estimator based on prior information proposed by Swindel (1976). Grob (2003) studied another restricted ridge estimator by combing the estimator given by Swindel (1976) and the restricted least squares method.…”

Section: Introductionmentioning

confidence: 99%

“…Kaciranlar et al (1998) compared the estimator introduced by Sarkar (1992) and the modified ridge regression estimator based on prior information proposed by Swindel (1976). Grob (2003) studied another restricted ridge estimator by combing the estimator given by Swindel (1976) and the restricted least squares method. A new restricted ridge estimation method is proposed by minimizing the sum of squared residuals by Zhong and Yang (2007).…”

Section: Introductionmentioning

confidence: 99%

A new ridge estimator in linear measurement error model with stochastic linear restrictions

Ghapani

Babadi

2016

JIRSS

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Abstract. In this paper, a new ridge-type estimator is proposed and termed as the new mixed ridge estimator (NMRE) which is obtained by unifying the sample and prior information in linear measurement error model with additional stochastic linear restrictions. The new estimator is a generalization of the mixed estimator (ME) and ridge estimator (RE). The performances of this new estimator and mixed ridge estimator (MRE) with respect to the ME are examined under the criterion of mean squared error matrix. Finally, a numerical example and a Monte Carlo simulation are also presented to analyze.

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“…This estimator is biased but reduces the variances of the regression coefficients. Subsequently, several other biased estimators of β have been proposed (Swindel, 1976;Sarkar, 1996;Batah and Gore, 2008;Batah et al, 2009;Arayesh and Hosseini, 2010;Asekunowo et al, 2010;Hirun and Sirisoponsilp, 2010;Rana et al, 2009). Swinded (1976) …”

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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Good ridge estimators based on prior information

Cited by 137 publications

References 10 publications

Crustal deformation in the New Madrid seismic zone and the role of postseismic processes

Crustal deformation in the New Madrid seismic zone and the role of postseismic processes

A new ridge estimator in linear measurement error model with stochastic linear restrictions

A Modification of the Ridge Type Regression Estimators

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