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CPS1141 Mahdi Roozbeh
The SPGRRE has the disadvantage that it has strange behavior for small
−1
values of £n. Also, the shrinkage factor (1 − £ ) becomes negative for £n <
d. Hence, we consider the positive-rule Stein-type partially generalized
restricted ridge estimator (PRSPGRRE) defined by
References
1. Akden¨ız, F. and Tabakan, G. (2009). Restricted ridge estimators of the
parameters in semiparametric regression model. Comm. Statist. Theo.
Meth., 38, 1852-1869.
2. Amini, M. and Roozbeh, M. (2015). Optimal partial ridge estimation in
restricted semiparametric regression models. J. Mult. Anal., 136, 26-40.
3. Arashi, M., (2012). Preliminary test and Stein estimators in simultaneous
linear equations. Linear Algebra and its Applications, 436(5), 1195-1211.
4. Arashi, M., Kibria, B.M.G., Norouzirad, M. and Nadarajah, S. (2014).
Improved Preliminary test and Stein-Rule Liu Estimators for the Ill-
Conditioned Elliptical Linear Regression Model. J. Mul. Anal.,124, 53-74.
5. Arashi, M. and Tabatabaey, S.M.M. (2009). Improved variance estimation
under sub-space restriction. J.Mul. Anal., 100, 1752-1760.
6. Buhlmann, ¨ P. and van de Geer, S. (2011). Statistics for High-
dimensional Data: Methods, Theory and Applications. Springer,
Heidelberg.
7. Fallahpour, S., Ahmed, S.E. and Doksum, K.A. (2012). L1 penalty and
shrinkage estimation in partially linear models with random coefficient
autoregressive errors. Appl. Stochastic Mod. Bus. Ind., 28,236-250.
8. Fan, J. and Lv, J. (2010). A selective overview of variable selection in high
dimensional feature space.Statist. Sinica, 20, 101-148.
9. Hoerl, A.E. and Kennard, R.W. (1970). Ridge regression: biased estimation
for non-orthogonal problems.Technometrics, 12, 55-67.
10. Roozbeh, M. (2015). Shrinkage ridge estimators in semiparametric
regression models. J. Mult. Anal., 136,56-74.
11. Roozbeh, M. and Arashi, M. (2013). Feasible ridge estimator in partially
linear models. J. Mult. Anal.,116, 35-44.
12. Shao, J. and Deng, X. (2012). Estimation in high-dimensional linear
models with deterministic design matrices. Ann. Statist., 40, 812-831.
13. Speckman, P. (1988). Kernel somoothing in partial linear models. J. Roy.
Statist. Soc., Ser B., 50, 413-4
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