[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5351/CKSS.2006.13.2.273

Monotone Local Linear Quasi-Likelihood Response Curve Estimates

Park, Dong-Ryeon (Department of Statistics, Hanshin University)

Publication Information

Communications for Statistical Applications and Methods / v.13, no.2, 2006 , pp. 273-283 More about this Journal

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

Local linear quasi-likelihood estimate; Monotone nonparametric estimate; Response curve;

Citations & Related Records

Reference

1	Park, D. (1999). Comparison of two response curve estimators. Journal of Statistical Computation and Simulation, Vol. 62, 259-269 DOI ScienceOn
2	Loader, C. (1999). Local Regression and Likelihood, Springer-Verlag, New York
3	Fan, J. (1992). Design-adaptive nonparametric regression. The Journal of the American Statistical Association, Vol. 87, 998-1004 DOI
4	Copas, J. (1983). Plotting p against x. Applied Statistics, Vol. 32, 25-31 DOI ScienceOn
5	Mukerjee, H. (1988). Monotone nonparametric regression. The Annals of Statistics, Vol. 16, 741-750 DOI
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 DOI
7	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
8	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 DOI ScienceOn
9	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
10	Friedman, J. and Tibshirani, R. (1984). The monotone smoothing of scatterplots. Technometrics, Vol. 26, 243-250 DOI
11	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
12	Mammen, E. (1991). Estimating a smooth monotone regression function. The Annals of Statistics, Vol. 19, 724-740 DOI
13	Muller, H. and Schmitt, T. (1988). Kernel and probit estimates in quantal bioassay. The Journal of the American Statistical Association, Vol. 83, 750-759 DOI
14	Park, D. and Park, S. (2006). Parametric and nonparametric estimators of ED100a. Journal of Statistical Computation and Simulation, Vol. 76, 661-672 DOI ScienceOn