Modified Local Density Estimation for the Log-Linear Density

  • Published : 2000.04.01


We consider local likelihood method with a smoothed version of the model density in stead of an original model density. For simplicity a model is assumed as the log-linear density then we were able to show that the proposed local density estimator is less affected by changes among observations but its bias increases little bit more than that of the currently used local density estimator. Hence if we use the existing method and the proposed method in a proper way we would derive the local density estimator fitting the data in a better way.



  1. Annals of the Institute of Statistical Mathematics v.46 Minimum Dispartiy Estimation for Continuous Model: Efficiency, Distribution, and Robustness Basu, A.;Lindsay, B.G.
  2. Journal of the American Statistical Association v.74 Robust Locally Weighted Regression and Smoothing Scatterplots Cleveland, W.S.
  3. Statistical Sciences v.8 Local Regression: Automatic Kernel Carpentry (with discussion) Hastie, T.;Loader, C.
  4. Annals of Statistics v.24 Locally Parameter Nonparametric density estimation Hjort, N.L.;Jones, M.C.
  5. Annals of Statistics v.24 Local Likelihood Density Estimation Loader, C.R.
  6. Journal of the Royal Statistical Society B v.53 A reliable data-based bandwidth selection method for kernel density estimation Sheather, S.J.;Jones, M.C.
  7. Journal of the American Statistical Association v.84 The Kernel Estimate of A Regression Function In Likelihood-Based Models Staniswalis, J.
  8. Annals of Statistics v.5 Smoothing Bias In Density Dervative Estimation Stone, C.J.
  9. Modern Applied Statistics with S-Plus Venables, W.N.;Ripley, B.D.