Confidence intervals based on resampling methods using Ridge estimator in linear regression model

In multiple regression analysis, the use of ridge regression estimator over the conventional ordinary least squares estimator was suggested by Hoerl and Kennard in 1970 to beat the problem of multicollinearity that may exist among the independent variables. (7) Now, based on these estimates, we cons...

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Bibliographic Details
Published in:New trends in mathematical sciences 2018-11, Vol.4 (6), p.77-86
Main Authors: Khurana, Mansi, Chandra, Shalini, Chaubey, Yogendra P.
Format: Article
Language:English
Subjects:
Bias
Confidence intervals
Economic models
Estimates
Independent variables
Methods
Multiple regression analysis
Parameter estimation
Regression analysis
Regression coefficients
Regression models
Resampling
Simulation
Statistical analysis
Statistical methods
Studies
Theory
Variance
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Summary:In multiple regression analysis, the use of ridge regression estimator over the conventional ordinary least squares estimator was suggested by Hoerl and Kennard in 1970 to beat the problem of multicollinearity that may exist among the independent variables. (7) Now, based on these estimates, we construct the confidence intervals for the regression coefficient ß in following subsection. 2.1 Confidence Intervals for Regression Coefficients using RRE There are several methods for constructing bootstrap confidence intervals based on the estimate of variance given in (7) are described briefly below. 2.1.1Normal theory method The first method for constructing bootstrap confidence interval is based on the assumption that the sampling distribution of ßRRE is normal. [...]this method has not been not pursued in the numerical investigations carried out. 2.1.5Jackknife method Jackknife technique is generally used to reduce the bias of parameter estimates and to estimate the variance. According to Tables 1 and 2, all the bootstrap methods are generally conservative in terms coverage probabilities, however jackknife method seems to give coverage probabilities closer to the target.
ISSN:2147-5520
2147-5520
DOI:10.20852/ntmsci.2018.318