M-Estimation Functions Induced From Minimum L$_2$ Distance Estimation

  • Pak, Ro-Jin (Department of Statistics, Taejon University)
  • Published : 1998.12.01


The minimum distance estimation based on the L$_2$ distance between a model density and a density estimator is studied from M-estimation point of view. We will show that how a model density and a density estimator are incorporated in order to create an M-estimation function. This method enables us to create an M-estimating function reflecting the natures of both an assumed model density and a given set of data. Some new types of M-estimation functions for estimating a location and scale parameters are introduced.


  1. Annals of Statistics v.5 Minimum Hellinger distance estimates for parametric models Beran, R. J.
  2. Annals of Statistics v.16 The 'Automatic' robustness of minimum distance functionals Donoho, D. L.;Liu, R. C.
  3. Robust Statistics: The Approach Based on Influence Functions Hampel, F, R.;Ronchetti, E. M.;Rousseeuw, P. J.;Stahel, W. A.
  4. Robust Statistics Huber, P. J.
  5. Journal of the American Statistical Association v.75 Minimum distance and robust esti-mation Par, W. C.;Schucany. W. R.
  6. Density Estimation for Statistics and Data Analysis Silverman, B. W.