Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지

Efficiency of Aggregate Data in Non-linear Regression

  • Huh, Jib (Department of Statistics, Seoul National University)
  • Published : 2001.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

This work concerns estimating a regression function, which is not linear, using aggregate data. In much of the empirical research, data are aggregated for various reasons before statistical analysis. In a traditional parametric approach, a linear estimation of the non-linear function with aggregate data can result in unstable estimators of the parameters. More serious consequence is the bias in the estimation of the non-linear function. The approach we employ is the kernel regression smoothing. We describe the conditions when the aggregate data can be used to estimate the regression function efficiently. Numerical examples will illustrate our findings.

Keywords

References

  1. Journal of the Royal Statistical Society, Series A v.149 Statistical modeling issues in school effectiveness studies Aitkin,M.;Longford,N.
  2. Biometrika v.84 Surprising effects of measurement error on an aggregate data estimator Carrol,R.J.
  3. Journal of the American Statistical Association v.74 Robust locally weighted regression and smoothing scatterplots Cleveland,W.
  4. Journal of the American Statistical Association v.87 Design-adaptive nonparametric regression Fan,J.
  5. Local polynomial modelling and its application Fan,J.;Gijbels,I.
  6. Journal of Computational Graphical Statistics v.3 Fast implementations of nonparametric curve estimators Fan,J.;Marron,J.S.
  7. Biometrika v.5 A note on design transformation and binning in nonparametric curve estimation Hall,P.;Park,B.U.;Turlach,B.A.
  8. Statistical Science v.6 Comment on Choosing a kernel regression estimator Hardle,W.;Grund,B.;C.K.Chu(ed.);J.S.Marron(ed.)
  9. Computational Statistics v.7 Smoothing by weighted averaging of rounded points Hardle,W.;Scott,D.W.
  10. Journal of the American Statistical Association v.82 Weighted local regression and kernel methods for nonparametric curve fitting Muller,H.G.
  11. Biometrika v.82 Aggregate data studies of disease risk factors Prentice,R.L.;Sheppard,L.
  12. The Annals of Statistics v.5 Consistent nonparametric regression Stone,C.J.
  13. Kernel smoothing Wand,M.P.;Jones,M.C.