LAD, LASSO and related strategies in regression models


YÜZBAŞI B., Ahmed S. E., Arashi M., Norouzirad M.

13th International Conference on Management Science and Engineering Management, ICMSEM 2019, St. Catharines, Canada, 5 - 08 August 2019, vol.1001, pp.429-444 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1001
  • Doi Number: 10.1007/978-3-030-21248-3_32
  • City: St. Catharines
  • Country: Canada
  • Page Numbers: pp.429-444
  • Keywords: LAD estimator, LAD-LASSO estimator, Outliers, Soft and hard thresh-holdings, SHRINKAGE, SELECTION, ESTIMATORS
  • Inonu University Affiliated: Yes

Abstract

© Springer Nature Switzerland AG 2020.In the context of linear regression models, it is well-known that the ordinary least squares estimator is very sensitive to outliers whereas the least absolute deviations (LAD) is an alternative method to estimate the known regression coefficients. Selecting significant variables is very important; however, by choosing these variables some information may be sacrificed. To prevent this, in our proposal, we can combine the full model estimates toward the candidate sub-model, resulting in improved estimators in risk sense. In this article, we consider shrinkage estimators in a sparse linear regression model and study their relative asymptotic properties. Advantages of the proposed estimators over the usual LAD estimator are demonstrated through a Monte Carlo simulation as well as a real data example.