Detecting Influential Observations on the Smoothing Parameter in Nonparametric Regression

  • Kim, Choong-Rak (Department of Statistics, Pusan National University, Pusan 609-735) ;
  • Jeon, Jong-Woo (Department of Statistics, Seoul National University, Seoul 151-742)
  • Published : 1995.12.01

Abstract

We present formula for detecting influential observations on the smoothing parameter in smoothing spline. Further, we express them as functions of basic building blocks such as residuals and leverage, and compare it with the local influence approach by Thomas (1991). An example based on a real data set is given.

Keywords

References

  1. Journal of the Royal Statistical Society, Ser. v.B. 48 Assessment of Local Influence (with Discussion) Cook,R.D.
  2. Numerische Mathematik v.31 Smoothing Noisy Data with Spline Functions: Estimating the Correct Degree of Smoothing by the Method of Generalized Cross-Validation Craven,P.;Wahba,G.
  3. Journal of the Royal Statistical Society, Ser. v.B. 47 Diagnostics for Smoothing Splines Eubank,R.L.
  4. Spline Smoothing and Nonparametric Regression Eubank,R.L.
  5. American Economic Review v.67 The Forward Exchange Rate, Expectations, and the Demand for Money: the German Hyperinflation Frenkel,J.A.
  6. Generalized Additive Models Hastie,T.;Tibshirani,R.
  7. Journal of the Royal Statistical Society, Ser. v.B. 47 Some Aspects of the Spline Smoothing Approach to Non-Parametric Regression Curve Fitting (with Discussion) Silverman,B.W.
  8. Journal of the American Statistical Association v.86 Influence Diagnostics for the Cross-Validated Smoothing Parameter in Spline Smoothing Thomas,W.
  9. Annals of Statistics v.13 A Comparison of GCV and GML for Choosing the Smoothing Parameter in the Generalized Spline Smoothing Problem Wahba,G.
  10. Spline Models in Statistics Wahba,G.
  11. Journal of the American Statistical Association v.78 Splines in Statistics Wegman,E.J.;Wright,I.W.