A note on nonparametric estimation of the effective dose in quantal bioassay

Journal of the American Statistical Association

Volumn 100, Issue 470, 2005, Pages 503-510

  Dette, Holger ^a   Neumeyer, Natalie ^b   Pilz, Kay F ^b  

^a Department of Mathematics ^*  (Germany)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Binary response model; Effective dose level; Isotonic regression; Local linear regression; Nonparametric regression; Order restricted inference

Indexed keywords

EID: 20444445161     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214504000001493     Document Type: Article

References (19)

1. Agresti, A. (1990), Categorical Data Analysis, New York: Wiley.
2. Barlow, R. E., Bartholomew, D. J., Bremner, J. M., and Brunk, H. D. (1972), Statistical Inference Under Order Restrictions, London: Wiley.
3. Berkson, J. (1944), "Application of the Logistic Function to Bioassay," Journal of the American Statistical Association, 39, 357-365.
4. Bliss, C. I. (1934), The Method of Probits," Science, 79, 38-39.
5. Brunk, H. D. (1955), "Maximum Likelihood Estimates of Monotone Parameters," The Annals of Mathematical Statistics, 26, 607-616.
6. Dette, H., Neumeyer, N., and Pilz, K. F. (2003), "A Simple Non-Parametric Estimator of a Monotone Regression Function," technical report. University of Bochum, Dept. Mathematics, available at http://www.ruhr-uni-bochum.de/mathematik3/preprint.htm.
7. Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, London: Chapman & Hall.
8. Gasser, T., and Müller, H. G. (1979), Kernel Estimation of Regression Functions, Berlin: Springer-Verlag, pp. 23-68.
9. Gasser, T., Müller, H. G., and Mammitzsch, V. (1985), "Kernels for Nonparametric Curve Estimation,'' Journal of the Royal Statistical Society, Ser. B, 47, 238-252.
10. Lee, E. T. (1974), "A Computer Program for Linear Logistic Regression Analysis," Computer Methods and Programs in Biomedicine, 4, 80-92.
11. Mammen, E. (1991), "Estimating a Smooth Monotone Regression Function," The Annals of Statistics, 19, 724-740.
12. McCullagh, P., and Neider, J. A. (1983), Generalized Linear Models, London: Chapman & Hall.
13. Müller, H. G., and Schmitt, T. (1988), "Kernel and Probit Estimates in Quantal Bioassay," Journal of the American Statistical Association, 83, 750-759.
14. Rice, J. (1984), "Bandwidth Choice for Nonparametric Regression," The Annals of Statistics, 12, 1215-1230.
15. Sacks, J., and Ylvisaker, D. (1970), "Designs for Regression Problems for Correlated Errors," The Annals of Mathematical Statistics, 41, 2057-2074.
16. Schmoyer, R. L. (1984), "Sigmoidally Constrained Maximum Likelihood Estimation in Quantal Bioassay," Journal of the American Statistical Association, 79, 448-453.
17. Spearman, C. (1908), "The Method of Right and Wrong Cases (Constant Stimuli) Without Gauss's Formulae," British Journal of Psychology, 1, 227-242.
18. Thompson, W. R. (1947), "Use of Moving Averages and Interpolation to Estimate Median Effective Dose, I: Fundamental Formulas, Estimation of Error, and Relation to Other Methods," Bacteriological Reviews, 11, 116-145.
19. Wand, M. P., and Jones, M. G. (1995), Kernel Smoothing, London: Chapman & Hall.