Shrinkage Difference-Based Liu Estimators In Semiparametric Linear Models
AbstractIn this article, under a multicollinearity setting, we define difference-based Liu and non-Liu type shrinkage estimators along with their positive parts in the semiparametric linear model, when the errors are dependent and some nonstochastic linear restrictions are imposed. We derive the biases and exact risk expressions of these estimators and obtain the region of optimality of each estimator. Also, necessary and sufficient conditions, for the superiority of the difference-based Liu estimator over its counterpart, for choosing the Liu parameter d are established. Finally, we illustrate the performance of these estimators with a simulation study.
F. Akdeniz, E. Akdeniz Duran, M. Roozbeh, M. Arashi, Efficiency of the generalized difference-based Liu estimators in semiparametric regression models with correlated errors, Journal of Statistical Computation and Simulation, 85(1), 147-165, 2015.
M. Arashi, Preliminary test and Stein estimators in simultaneous linear equations, J Linear Algebra Appl. 436, 5: 1195-1211, 2012.
M. Arashi, B.M. Golam Kibria, M. Norouzirad, S. Nadarajah, Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model, J. Multivariate Anal. 124, 53-74, 2014.
M. Arashi, M. Roozbeh, Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data, Stat. Paper, 1-20, 2016.
N. Benda, Pre-test estimation and design in the linear model, Statist. Plann. Inference, 52: (2), 225-240, (1996).
L.D.Brown, L.Wang, T.T.Cai, A difference-based approach to the semiparametric partial linear model, Electron.J.Stat.5, 619-64, 2011.
D.G. Gibbons, A, Simulation study of some ridge estimators, J. Amer. Statist. Assoc. 76, 131139, 1981.
W. Hrdle, H. Liang, J. Gao,, Partially Linear Models, Physika Verlag, Heidelberg, 2000.
A.E. Hoerl, R.W. Kennard, Ridge regression: biased estimation in non-orthogonal problems, Technometrics, 12: (3), 55-67,1970.
G.G. Judge, M.E. Bock, The Statistical Implications of Pre-test and Stein-rule Estimators in Econometrics, North-Holland Publishing Company, Amsterdam, 1978.
K. Liu, A new class of biased estimate in linear regression, Comm.Statist.Theory Methods, 22:2, 393-402, 1993.
K. Liu, Using Liu-type estimator to combat collinearity, Comm. Statist. Theory Methods, 32: (5),1009-1020, 2003.
M. Norouzirad, M. Arashi, Preliminary test and Stein-type shrinkage ridge estimators in robust regression, Stat. Paper, 1-34, 2017.
G.C. McDonald, D.I. Galarneau, A Monte Carlo evaluation of some ridge-type estimators, J. Amer. Statist. Assoc. 70, 407-416, 1975.
M.Muller, Semiparametric Extensions to Generalized Linear Models, Habilitationsschrift,2000.
C.R, Rao, H.Toutenburg, Shalabh, C.Heumann, Linear Models:Least Squares and Alternatives, Springer, Berlin, 2008.
M. Roozbeh, Shrinkage ridge estimators in semiparametric regression models, J.Multivariate Anal.136, 56-74, 2015.
M. Roozbeh, M. Arashi, Feasible ridge estimator in partially linear models, Journal of Multivariate, 116, 35-44, 2013.
D. Ruppert, SJ. Sheather, MP. Wand, An effective bandwidth selector for local least squares regression, Journal of the American Statistical Association 90: 432, 1257-1270, 1995.
A.K.Md.E. Saleh, Theory of Preliminary Test and Stein-type Estimation with Applications, John Wiley, New York, 2006.
A.K.Md.E. Saleh, B.M.G. Kibria, Performances of some new preliminary test ridge regression estimators and their properties, Comm. Statist. Theory Methods, 22: (10), 2747-2764, 1993.
C. Stein, Inadmissibility of the usual estimator for the mean of a multivariate normal distribution, in: Proceedings of the Third Berkeley Symposium, vol. 1, pp. 197206, 1956.
P.A.V.B. Swamy, J.S. Mehta, A note on minimum average risk estimator for coefficients in linear models, Comm. Statist. Theory Methods, 6,1161-1186, 1977.
P.A.V.B. Swamy, J.S. Mehta, P.N. Rappoport, Two methods of evaluating Hoerl and Kennards ridge regression, Comm. Statist. Theory Methods, 6,1133-1155, 1978.
J.B. Wu, Y. Asr, A weighted stochastic restricted ridge estimator in partially linear model, Communications in Statistics-Theory and Methods, 46(18), 9274-9283, 2017.
A.Yatchew, Semiparametric Regression for the Applied Econometrican, Cambridge University Press,Cambridge, 2003.
B. Yuzbasi, S.E. Ahmed, D. Aydin, Ridge-type pretest and shrinkage estimations in partially linear models, Statistical papers. https://doi.org/10.1007/s00362-017-0967-8,2017.
B. Yuzbasi, Y. Asar, S.M. Sk, A. Demiralp, Improving estimations in quantile regression model with autoregressive errors, Thermal Science, https://doi.org/10.2298/TSCI170612275Y, 2018.
J. Li, W. Zhang, Z. Wu, Optimal zone for bandwidth selection in semiparametric models, J. Nonparametr.Stat. 23, 701-717, 2011.
Z. Zhong, Hu Yang, Ridge estimation to the restricted linear model, Comm. Statist. Theory Methods, 36:11, 2099-2115, (2007).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).