Effects of curvature on leverage in nonlinear regression

  • Published : 2009.09.30

Abstract

The measures of leverage in linear regression has been extended to nonlinear regression models. We consider several curvature measures of nonlinearity in an estimation situation. The relationship between measures of leverage and statistical curvature are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a tangent plane leverage are discussed in connection with the effective residual curvature of the nonlinear model.

Keywords

References

  1. Bates, D. M. and Watts, D. G. (1980). Relative curvature measures of nonlinearity (with discussion). Journal of the Royal Statistical Society, Series B, 42, 1-25.
  2. Bates, D. M. and Watts, D. G. (1981). Parameter transformations for improved approximate confidence regions in nonlinear least squares. Annals of Statistics, 9, 1152-1167. https://doi.org/10.1214/aos/1176345633
  3. Bates, D. M. and Watts, D. G. (1988). Nonlinear regression analysis and its applications, John Wiley and Sons, New York.
  4. Beale, E. M. L. (1960). Confidence regions in nonlinear estimation (with discussion). Journal of the Royal Statistical Society, Series B, 22, 41-88.
  5. Belsley, D. A., Kuh, E. and Welsch, R. E. (1980). Regression diagnostics: Identifying in uential data and sources of collinearity, John Wiley and Sons, New York.
  6. Chatterjee, S. and Hadi, A. S. (1986). In uential observations, high leverage points and outliers in linear regression. Statistical Science, 1, 379-416. https://doi.org/10.1214/ss/1177013622
  7. Emerson, J. D., Hoaglin, D. C. and Kempthorne, P. J. (1984). Leverage in least squares additive-plus-multiplicative fits for two-way tables. Journal of the American Statistical Association, 79, 329-335. https://doi.org/10.2307/2288272
  8. Hamilton, D. C., Watts, D. G. and Bates, D. M. (1982). Accounting for intrinsic nonlinearity in nonlinear regression parameter inference regions. Annals of Statistics, 10, 386-393. https://doi.org/10.1214/aos/1176345780
  9. Kahng, M. (2007). Leverage measures in nonlinear regression. Journal of Korean Data & Information Science Society, 18, 229-235.
  10. Kahng, M. (2008). Leverage and outlier in nonlinear regression. Journal of Korean Data & Information Science Society, 19, 287-292.
  11. Ross, W. H. (1987). The geometry of case deletion and the assessments of influence in nonlinear regression. The Canadian Journal of Statistics, 15, 91-103. https://doi.org/10.2307/3315198
  12. St. Laurent, R. T. and Cook, R. D. (1992). Leverage and superleverage in nonlinar regression. Journal of the American Statistical Association, 87, 985-990. https://doi.org/10.2307/2290635
  13. St. Laurent, R. T. and Cook, R. D. (1993). Leverage, local in uence and curvature in nonlinar regression. Biometrika, 80, 99-106. https://doi.org/10.1093/biomet/80.1.99