Feasible Stein-Type and Preliminary Test Estimations in the System Regression Model
Abstract
In a system of regression models, finding a feasible shrinkage is demanding since the covariance structure is unknown and cannot be ignored. On the other hand, specifying sub-space restrictions for adequate shrinkage is vital. This study proposes feasible shrinkage estimation strategies where the sub-space restriction is obtained from LASSO. Therefore, some feasible LASSO-based Stein-type estimators are introduced, and their asymptotic performance is studied. Extensive Monte Carlo simulation and a real-data experiment support the superior performance of the proposed estimators compared to the feasible generalized least-squared estimator.References
M. A. Alkhamisi, and G. Shukur, Developing ridge parameters for SUR model, Communications in Statistics–Theory and Methods, vol. 37, pp. 544–564, 2008.
T. Amemiya, Advanced Econometrics, Cambridge, Massachusetts: Harvard University Press, 1985.
M. Arashi, S. Khan, S. M. M. Tabatabaey, and H. Soleimani, Shrinkage estimation under multivariate elliptic models, Communications in Statistics – Theory and Methods, vol. 42, no. 11, pp. 2084–2103, 2013.
M. Arashi, B. G. Kibria, M. Norouzirad, and S. Nadarajah, Improved preliminary test and stein-rule liu estimators for the ill-conditioned elliptical linear regression model, Journal of Multivariate Analysis, vol. 126, pp. 53–74, 2014.
M. Arashi, and Roozbeh, M., Shrinkage estimation in system regression model. Computational Statistic, vol. 30, pp. 359–376, 2015.
M. Arashi and M. Roozbeh, Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data, Statistical Papers, vol. 60, pp. 667–686, 2019.
M. Arashi, M. Roozbeh, M., and H. A. Niroumand, A note on stein-type shrinkage estimator in partial linear models. Statistics, vol. 46, no. 5, pp. 673–685, 2012.
M. Arashi, and S. M. M. Tabatabaey, A note on classical stein-type estimators in elliptically contoured models. Journal of Statistical Planning and Inference, vol. 140, no. 5, pp. 1206–1213, 2010.
D. G. Fiebig, Seemingly unrelated regression. In H. Badi (Ed.) A Companion to Theoretical Econometrics, Baltagi, Oxford: Blackwell.
W. H. Green, Econometric Analysis (5th ed.). New Jersey: Pearson/Prentice Hall, 2003.
W. James, and C. Stein, Estimation with quadratic loss, in:. Proceedings of the Fourth Berkeley Symposium on
Mathematical Statistics and Probability, vol. 1, pp. 361 – 380, 1961.
G. G. Judge and M. E. Bock, The Statistical Implication of Pretest and Stein Rule Estimators in Econometrics,
Amsterdam: North-Holland, 1978.
M. Kashani, M. R. Rabie, M. Arashi, An integrated shrinkage strategy for improving efficiency in fuzzy regression
modeling, Soft Computing, vol. 25, pp. 8095-–8107, 2021.
J. Kleyn, M., Arashi, A., Bekker, and S. Millard, Preliminary testing of the cobb–douglas production function and related inferential issues, Communications in Statistics – Simulation and Computation, vol. 46, no. 1, pp. 469–488, 2017.
A. Mahmoudi, R. A., Belaghi, and S. Mandal, A comparison of preliminary test, stein-type and penalty estimators in
gamma regression model, Journal of Statistical Computation and Simulation, vol. 90, no. 17, pp. 3051–3079, 2022.
S. Mandal, R. Arabi Belaghi, A. Mahmoudi, and M. Aminnejad, Stein-type shrinkage estimators in gamma regression
model with application to prostate cancer data, Statistics in Medicine, vol. 38, no. 22, pp. 4310–4322, 2019.
A. Mehrabani, and A. Ullah, Improved average estimation in seemingly unrelated regression, Econimetrics, vol. 8, no. 2, pp. 15, 2020.
M. NooriAsl, H. Bevrani, and R. Arabi Belaghi, Penalized and ridge-type shrinkage estimators in Poisson regression model, Communications in Statistics – Simulation and Computation, vol. 5, no. 7, pp. 4039–4056, 2022.
M. Norouzirad, and M. Arashi, Preliminary test and stein-type shrinkage lasso-based estimators, SORT-Statistics and Operations Research Transactions, vol. 42, no. 1, pp. 45–58, 2018.
M. Norouzirad, and M. Arashi, Preliminary test and stein-type shrinkage ridge estimators in robust regression, Statistical Papers, vol. 60, pp. 1849–1882, 2019.
M. Norouzirad, M. Arashi, and S. E. Ahmed, Improved robust ridge M-estimation, Journal of Statistical Computation
and Simulation, vol. 87, no. 18, pp. 3469–3490.
M. Norouzirad, M. Arashi, and M. Roozbeh, Differenced-based double shrinking in partial linear models, Journal of
Computational Statistics and Modeling, vol. 1, no. 1, pp. 21–32, 2021.
M. Norouzirad, S. Hossain, and M. Arashi, Shrinkage and penalized estimators in weighted least absolute deviations
regression models, Journal of Statistical Computation and Simulation, vol. 88, no. 8, pp. 1557–1575, 2018.
M. Roozbeh, Shrinkage ridge estimators in semiparametric regression models, Journal of Multivariate Analysis, vol. 136, pp. 56–74, 2015.
A. Safariyan, M., Arashi, R. Arabi Belaghi, Improved estimators for stress-strength reliability using record ranked set
sampling scheme, Communications in Statistics – Simulation and Computation, vol. 48, no. 9, pp. 2708–2726, 2019.
A. Safariyan, M., Arashi, R. Arabi Belaghi, Improved point and interval estimation of the stress–strength reliability
based on ranked set sampling Statistics, vol. 53, no. 1, pp. 101–125.
A. K. M. E. Saleh, M. Arashi, B. M. G. Kibria, Theory of Ridge Regression Estimation with Applications, New Jersey: Wiley, 2019.
A. K. M. E. Saleh, M. Arashi, R. A. Saleh, and M. Norouzirad, Rank-Based Methods for Shrinkage and Selection: With Application to Machine Learning, John Wiley and Sons, 2022.
A. K. M. E. Saleh, M. Arashi, and S. M. M. Tabatabaey, Statistical Inference for Models with Multivariate t-Distributed
Errors, New Jersey: Wiley, 2014.
A. K. M. E. Saleh, Theory of preliminary test and stein-type estimation with applications, New York: John Wiley & Sons, 2006.
A. K. M. E. Saleh, R. Navrátil, and M. Norouzirad, Rank theory approach to ridge, lasso, preliminary test and stein-type estimators: A comparative study, Canadian Journal of Statistics, vol. 46, no. 4, pp. 690–704, 2018.
A. K. M. E. Saleh, and M. Norouzirad, On shrinkage estimation: Non-orthogonal case, Statistics, Optimization and
Information Computing, vol. 6, no.3, pp. 427–451, 2018.
S. L. Sclove, Improved estimators for coefficients in linear regression, Journal of American Statistical Association, vol. 63, pp. 596- 606, 1968.
D. Sengupta, and S. R. Jammalamadaka, Linear Models: An Integrated Approach, World Scientific Publishing Company, 2003.
Shalabh Regression analysis,. Lectures Notes for National Digital Library of India. http://www.ndl.gov.in/document/
YkxlRXFvZXJrTDBkVzVVZi9ESjl6L01uL3BEcDB2QzV1NHRUcGNLUXF0SVp6L3ZSUUVudUlNYitlZ1lRU3NKUQ, 2020
V. K. Srivastava, The efficiency of an improved method of estimating seemingly unrelated regression equations,
Journal of Econometrics, vol. 1, pp. 341–350, 1973.
V. K. Srivastava, and T. D. Dwivedi, Estimation of seemingly unrelated regression equations: A brief survey, Journal
of Econometrics, vol. 10, pp. 15–32, 1979.
V. K. Srivastava, and D. E. A. Giles, Seemingly Unrelated Regression Models: Estimation and Inference, Marcel
Dekker Inc.: New York, 1987.
V. K. Srivastava, and A. T. K. Wan, Seperate versus system methods of stein-rule estimation in seemingly unrelated
regression models, Communications in Statistics – Theory and Methods, vol. 31, no. 11, pp. 2077–2099, 2002.
R. Tibshirani, Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society (Series B), vol. 58, pp. 267–288, 1996.
B. Yuzbasi, and S. E. Ahmed, Ridge type shrinkage estimation of seemingly unrelated regressions and analytics of
economic and financial data from “fragile five” countries, Journal of Risk and Financial Management, vol. 13, pp. 131,
Z. Zandi, H. Bevrani, and R. Arabi Belaghi, Estimation of fixed parameters in negative binomial mixed model using
shrinkage estimators, Journal of Computational Statistics and Modeling, vol. 1, no. 2, pp. 99–124, 2021.
A. Zellner, An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias, Journal
of the American Statistical Association, vol. 57, no. 298, pp. 348 – 368, 1962.
A. Zellner, and W. Vandaele, Bayes-stein estimators for k-means, regression and simultaneous equation models, In
S. E. Fienberg, and A. Zellner (Eds.) Studies in Bayesian Econometrics and Statistics, (pp. 627–653). Amsterdam: North-Holland Publishing Company.
H. Zou, H., and T. Hastie, Regularization and variable selection via the elastic net, Journal of the Royal Statistical Society. Series B (Statistical Methodology), vol. 67, no. 2, pp. 301–320, 2005.
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