Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Adaptive M-estimation in Regression Model

  • Published : 2003.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we introduce some adaptive M-estimators using selector statistics to estimate the slope of regression model under the symmetric and continuous underlying error distributions. This selector statistics is based on the residuals after the preliminary fit L$_1$ (least absolute estimator) and the idea of Hogg(1983) and Hogg et. al. (1988) who used averages of some order statistics to discriminate underlying symmetric distributions in the location model. If we use L$_1$ as a preliminary fit to get residuals, we find the asymptotic distribution of sample quantiles of residual are slightly different from that of sample quantiles in the location model. If we use the functions of sample quantiles of residuals as selector statistics, we find the suitable quantile points of residual based on maximizing the asymptotic distance index to discriminate distributions under consideration. In Monte Carlo study, this adaptive M-estimation method using selector statistics works pretty good in wide range of underlying error distributions.

Keywords

References

  1. Robust Estimation of Location: Survey and Advances Andrews,D.F.;Bickel,P.J.;Hampel,F.R.;Huber,P.J.;Roger,W.H.;Tukey,J.W.
  2. J. Amer. Stat. Assoc. 62 Some oberservations on robust estimation Hogg,R.V. https://doi.org/10.2307/2283768
  3. J. Amer. Stat. Assoc. v.70 A two-sample adaptive distribution-free test Hogg,R.V.;Fisher, D.M.;Randles,R.H. https://doi.org/10.2307/2285950
  4. Comm. Statist. v.11 On adaptive statistical inference Hogg,R.V. https://doi.org/10.1080/03610918208828404
  5. Probability and Statistics, Essay in Honor of Graybill, FA. An Argument for Adaptive Robust Estimation Hogg,R.V.;Bril,G.K.;S.M.Han;L.Yuh
  6. Robust Statistics, the Approach Based on Influence Functions Hampel,F.R.;Ronchetti,E.M.;Rousseeuw,P.M.;Stahel,W.A.
  7. 한국 통계학회 논문집 v.2 no.2 Adaptive M-estimation using Selector Statistics in Location Model Han,S.M. https://doi.org/10.5351/CKSS.2002.9.2.325
  8. Comm. Statist. v.A6 Robust Regression using Iteratively Reweighted Least Squares Holland,P.W.;Welsh,R.E.
  9. Ann. Math. Stat. v.35 Robust estimation of location parameter Huber,P.J. https://doi.org/10.1214/aoms/1177703732
  10. Robust statistics: A review. Ann. Math. Stat. v.43 Huber,P.J. https://doi.org/10.1214/aoms/1177692459
  11. Robust statistics Huber,P.J.
  12. Comm. Statist v.14 The performance of the linear and quadratic discriminant functions for three types of non-normal distributions Nakanish,H.;Sato,Y. https://doi.org/10.1080/03610928508828970
  13. J. Amer. Stat. Assoc. v.75 Trimmed Least Squares Estimation in the Linear Model Ruppert,D.;Carroll,R.J. https://doi.org/10.2307/2287169

Cited by

  1. Nonparametric Estimation using Regression Quantiles in a Regression Model vol.25, pp.5, 2012, https://doi.org/10.5351/KJAS.2012.25.5.793