Robust Linear Regression Using L1-Penalized MM-Estimation for High Dimensional Data

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Büyüklü A. H.

American Journal of Theoretical and Applied Statistics, cilt.4, sa.3, ss.78-84, 2015 (Diğer Kurumların Hakemli Dergileri)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 4 Konu: 3
  • Basım Tarihi: 2015
  • Doi Numarası: 10.11648/j.ajtas.20150403.12
  • Dergi Adı: American Journal of Theoretical and Applied Statistics
  • Sayfa Sayıları: ss.78-84


Large datasets, where the number of predictors p is larger than the sample sizes n, have become very popular in recent years. These datasets pose great challenges for building a linear good prediction model. In addition, when dataset contains a fraction of outliers and other contaminations, linear regression becomes a difficult problem. Therefore, we need methods that are sparse and robust at the same time. In this paper, we implemented the approach of MM estimation and proposed L1-Penalized MM-estimation (MM-Lasso). Our proposed estimator combining sparse LTS sparse estimator to penalized M-estimators to get sparse model estimation with high breakdown value and good prediction. We implemented MM-Lasso by using C programming language. Simulation study demonstrates the favorable prediction performance of MM-Lasso.