Preliminary test and Stein-type shrinkage LASSO-based estimators

• M. Norouzirad ^[1] ; M. Arashi ^[1]
  1. [1] Shahrood University of Technology, Shahrood, Iran
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 42, Nº. 1, 2018, págs. 45-58
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • Suppose the regression vector-parameter is subjected to lie in a subspace hypothesis in a linear regression model. In situations where the use of least absolute and shrinkage selection operator (LASSO) is desired, we propose a restricted LASSO estimator. To improve its performance, LASSO-type shrinkage estimators are also developed and their asymptotic performance is studied. For numerical analysis, we used relative efficiency and mean prediction error to compare the estimators which resulted in the shrinkage estimators to have better performance compared to the LASSO.

• Referencias bibliográficas
  • Ahmed, S.E. and Raheem, S.M.E. (2012). Shrinkage and absolute penalty estimation in linear regression models, Wires: Computational Statistics,...
  • Fallahpour, S., Ahmed, S.E. and Doksum, K.A. (2012). L1 penalty and shrinkage estimation in partially linear models with random coefficient...
  • Hossain, S. and Ahmed, S.E. (2014). Penalized and Shrinkage Estimation in the Cox Proportional Hazards Model. Communications in Statistics-Theory...
  • Hossain, S., Ahmed, S.E. and Doksum, K.A. (2015). Shrinkage, pretest, and penalty estimators in generalized linear models. Statistical Methodology,...
  • Hossain, S. and Ahmed, S.E. and Yi, Y. (2016). Shrinkage and pretest estimators for longitudinal data analysis under partially linear models....
  • Hossain, S. and Howlader, H. (2016). Shrinkage estimation in lognormal regression model for censored data. Journal of Applied Statistics,...
  • James, W. and Stein, C. (1961). Estimation with quadratic loss. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics...
  • Knight, K. and Fu, W. (2000). Asymptotics for lasso-type estimators. Annals of Statistics, 28, 1356–1378.
  • Roozbeh, M. (2015). Shrinkage ridge estimators in semiparametric regression models. Journal of Multivariate Analysis, 136, 56–74.
  • Roozbeh, M. (2016). Robust ridge estimator in restricted semiparametric regression models. Journal of Multivariate Analysis, 147, 127–144.
  • Saleh, A.K.M.E. (2006). Theory of preliminary test and stein-type estimation with applications, John Wiley & Sons, New York.
  • Sengupta, D. and Jammalamadaka, S.R. (2003). Linear models: An integrated approach, World Scientific Publishing Company.
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B., 58, 267–288.
  • Yuzbasi, B. and Ahmed, S.E. (2016). Shrinkage and penalized estimation in semi-parametric models with multicollinear data. Journal of Statistical...
  • Yuzbasi, B., Ahmed, S.E. and Gungor, M. (2017). Improved Penalty Strategies in Linear Regression Models. REVSTAT-Statistical Journal, Accepted.