Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Monotone Local Linear Quasi-Likelihood Response Curve Estimates

  • Published : 2006.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

In bioassay, the response curve is usually assumed monotone increasing, but its exact form is unknown, so it is very difficult to select the proper functional form for the parametric model. Therefore, we should probably use the nonparametric regression model rather than the parametric model unless we have at least the partial information about the true response curve. However, it is well known that the nonparametric regression estimate is not necessarily monotone. Therefore the monotonizing transformation technique is of course required. In this paper, we compare the finite sample properties of the monotone transformation methods which can be applied to the local linear quasi-likelihood response curve estimate.

Keywords

References

  1. Copas, J. (1983). Plotting p against x. Applied Statistics, Vol. 32, 25-31 https://doi.org/10.2307/2348040
  2. Dette, H., Neumeyer, N., and Pilz, K. (2003). A simple non-parametric estimator of a monotone regression function. Technical report, University of Bochum, Dept. Mathematics, Available from : http://www.ruhr-uni-bochum.de/mathematik3/preprint.htm
  3. Dette, H., Neumeyer, N., and Pilz, K. (2005). A note on nonparametric estimation of the effective dose in quantal bioassay. The Journal of the American Statistical Association, Vol. 100, 503-510 https://doi.org/10.1198/016214504000001493
  4. Dette, H. and Pilz, K. (2004). A comparative study of monotone nonparametric kernel estimates. Technical report, University of Bochum, Department of Mathematics, Available from: http://www.ruhr-uni-bochum.de/mathemat ik3/preprint.htm
  5. Fan, J. (1992). Design-adaptive nonparametric regression. The Journal of the American Statistical Association, Vol. 87, 998-1004 https://doi.org/10.2307/2290637
  6. Fan, J., Heckman, N., and Wand, M. (1995). Local polynomial kernel regression for generalized linear models and quasi -likelihood functions. The Journal of the American Statistical Association, Vol. 90, 141-150 https://doi.org/10.2307/2291137
  7. Friedman, J. and Tibshirani, R. (1984). The monotone smoothing of scatterplots. Technometrics, Vol. 26, 243-250 https://doi.org/10.2307/1267550
  8. Kappenman, R. (1987). Nonparametric estimation of dose-response curves with application to ED50 estimation. The Journal of Statistical Computation and Simulation, Vol. 28, 1-13
  9. Loader, C. (1999). Local Regression and Likelihood, Springer-Verlag, New York
  10. Mammen, E. (1991). Estimating a smooth monotone regression function. The Annals of Statistics, Vol. 19, 724-740 https://doi.org/10.1214/aos/1176348117
  11. Mukerjee, H. (1988). Monotone nonparametric regression. The Annals of Statistics, Vol. 16, 741-750 https://doi.org/10.1214/aos/1176350832
  12. Muller, H. and Schmitt, T. (1988). Kernel and probit estimates in quantal bioassay. The Journal of the American Statistical Association, Vol. 83, 750-759 https://doi.org/10.2307/2289301
  13. Park, D. (1999). Comparison of two response curve estimators. Journal of Statistical Computation and Simulation, Vol. 62, 259-269 https://doi.org/10.1080/00949659908811935
  14. Park, D. and Park, S. (2006). Parametric and nonparametric estimators of ED100a. Journal of Statistical Computation and Simulation, Vol. 76, 661-672 https://doi.org/10.1080/10629360500279706