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Keywords
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Mean Square Error
Multiple Regression
Parameter Estimation
Ridge Regression
Sum of Squares
Two Dimensions
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Ridge Regression: Biased Estimation for Nonorthogonal Problems
Ridge Regression: Biased Estimation for Nonorthogonal Problems,10.1080/00401706.1970.10488634,Technometrics,Arthur E. Hoerl,Robert W. Kennard
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Ridge Regression: Biased Estimation for Nonorthogonal Problems
(
Citations: 1330
)
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Arthur E. Hoerl
,
Robert W. Kennard
In
multiple regression
it is shown that parameter estimates based on minimum residual
sum of squares
have a high probability of being unsatisfactory, if not incorrect, if the prediction vectors are not orthogonal. Proposed is an estimation procedure based on adding small positive quantities to the diagonal of X′X. Introduced is the ridge trace, a method for showing in
two dimensions
the effects of nonorthogonality. It is then shown how to augment X′X to obtain biased estimates with smaller
mean square
error.
Journal:
Technometrics
, vol. 12, no. 1, pp. 5567, 1970
DOI:
10.1080/00401706.1970.10488634
Cumulative
Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
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dx.doi.org
)
Citation Context
(470)
...This first algorithm first updates using the gradient defined directly in (
5
) as,epoch takes less time than other algorithms we will introduce in the next several subsections thanks to the simple form of the gradient (
5
).,. As a result, the direction defined by gradient (
5
) is suboptimal...
Dong Yu
,
et al.
Efficient and Effective Algorithms for Training SingleHiddenLayer Ne...
...ridge regression (
Hoerl and Kennard, 1970
) and the LASSO), regression with a nonparametric mean function, (e.g...
Yoonkyung Lee
,
et al.
Regularization of CaseSpecific Parameters for Robustness and Efficien...
...The comparisons of finite sample performance between the proposed and several other methods, including stepwise selection, ridge regression
13
, group lasso and group smoothly clipped absolute deviation
33
are thoroughly done using simulated examples in Section 3...
Young Joo Yoon
,
et al.
Group variable selection in cardiopulmonary cerebral resuscitation dat...
...gif"/> proposed by Hoerl & Kennard (
1970
) minimizes where
x
_{ij}
is the
ith
observation of the
jth
component...
Alvaro NosedalSanchez
,
et al.
Reproducing Kernel Hilbert Spaces for Penalized Regression: A Tutorial
...gif"/> proposed by Hoerl and Kennard (
1970
) minimizes where
Alvaro NosedalSanchez
,
et al.
Reproducing Kernel Hilbert Spaces for Penalized Regression: A Tutorial
References
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An Operator Theoretic Formulation of a Class of Control Problems and a Steepest Descent Method of Solution
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, vol. 1, no. 2, 1963
The discarding of variables in multivariate analysis
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Biometrika
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Selection of Variables for Fitting Equations to Data
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Journal:
Technometrics
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Selection of the Best Subset in Regression Analysis
(
Citations: 37
)
R. R. Hocking
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R. N. Leslie
Journal:
Technometrics
, vol. 9, no. 4, pp. 531540, 1967
Estimation with Quadratic Loss
(
Citations: 594
)
W. James
,
Charles Stein
Published in 1961.
Sort by:
Citations
(1330)
Efficient and Effective Algorithms for Training SingleHiddenLayer Neural Networks
(
Citations: 2
)
Dong Yu
,
Li Deng
Published in 2012.
Regularization of CaseSpecific Parameters for Robustness and Efficiency
(
Citations: 1
)
Yoonkyung Lee
,
Steven N. MacEachern
,
Yoonsuh Jung
Journal:
Statistical Science  STAT SCI
, vol. 27, no. 2012, pp. 350372, 2012
Group variable selection in cardiopulmonary cerebral resuscitation data for veterinary patients
Young Joo Yoon
,
Erik Hofmeister
,
Sangwook Kang
Journal:
Journal of Applied Statistics  J APPL STAT
, vol. aheadofp, no. aheadofp, pp. 117, 2012
Reproducing Kernel Hilbert Spaces for Penalized Regression: A Tutorial
Alvaro NosedalSanchez
,
Curtis B. Storlie
,
Thomas C. M. Lee
,
Ronald Christensen
Journal:
American Statistician  AMER STATIST
, vol. justaccep, no. justaccep, 2012
Reproducing Kernel Hilbert Spaces for Penalized Regression: A Tutorial
Alvaro NosedalSanchez
,
Curtis B. Storlie
,
Thomas C. M. Lee
,
Ronald Christensen
Journal:
American Statistician  AMER STATIST
, vol. 66, no. 1, pp. 5060, 2012