Computational Statistics

, Volume 16, Issue 1, pp 153–164 | Cite as

Symmetrizing and unitizing transformations for linear smoother weights

  • Oliver LintonEmail author

1 Introduction

Suppose that we have i.i.d. data \(\left\{ {{X_i},{Y_i}} \right\}_{i = 1}^n\)



I would like to thank John Hartigan for the reference to Arthur Cohen’s work. I would also like to thank an anonymous referee, Chris Jones and Berwin Turlach for helpful comments. This research was supported by the National Science Foundation and the North Atlantic Treaty Organization.


  1. Cohen, A. (1966). All admissible linear estimates of the mean vector. Annals of Mathematical Statistics 37, 458–463.MathSciNetCrossRefGoogle Scholar
  2. Deming, W.E. and F.F. Stephan (1940). On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Annals of Mathematical Statistics 11, 427–444.MathSciNetCrossRefGoogle Scholar
  3. Fienberg, S.E. (1970). An iterative procedure for estimation in contingency tables. Annals of Mathematical Statistics 41, 907–917.MathSciNetCrossRefGoogle Scholar
  4. Golub, G.H., and C.F. van Loan (1989): Matrix Computations. The Johns Hopkins University Press: Baltimore.zbMATHGoogle Scholar
  5. Härdle, W., and O.B. Linton (1994). Applied nonparametric methods. The Handbook of Econometrics, vol. IV, eds. D.F. McFadden and R.F. Engle III. North Holland.Google Scholar
  6. Hastie, T. and R. Tibshirani (1990). Generalized Additive Models. Chapman and Hall, London.zbMATHGoogle Scholar
  7. Linton, O.B. (1995). Second Order Approximation in the Partially Linear Regression Model. Econometrica 63, 1079–1112.MathSciNetCrossRefGoogle Scholar
  8. Robinson, P. M. (1987). Asymptotically Efficient Estimation in the Presence of Heteroscedasticity of Unknown form. Econometrica 56, 875–891.CrossRefGoogle Scholar
  9. Robinson, P. M. (1988). Root-N-Consistent Semiparametric Regression. Econometrica, 56, 931–954.MathSciNetCrossRefGoogle Scholar

Copyright information

© Physica-Verlag 2001

Authors and Affiliations

  1. 1.Department of EconomicsLondon School of EconomicsLondonUnited Kingdom

Personalised recommendations