Geodesic
Nonparametric estimation of effective doses at quantal response
Ufa mathematical journal, Tome 5 (2013) no. 2, pp. 94-108 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For the quantal response model we propose a new direct method for nonparametric estimation of the effective dose level $ED_{100\lambda}$ ($0 \lambda 1$). This method yields a simple and reliable monotone estimate of the effective dose level curve $\lambda\to ED_{100\lambda}$ and is appealing to users of conventional smoothing methods of kernel estimates. Moreover, it is computationally very efficient, because it does not require a numerical inversion of the estimate of the quantile dose response curve. We prove asymptotic normality of this new estimator and compare it with the DNP-estimator.
Keywords: binary response model, effective dose level, nonparametric estimate. 
@article{UFA_2013_5_2_a8,
     author = {M. S. Tikhov},
     title = {Nonparametric estimation of effective doses at quantal response},
     journal = {Ufa mathematical journal},
     pages = {94--108},
     year = {2013},
     volume = {5},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2013_5_2_a8/}
}
TY  - JOUR
AU  - M. S. Tikhov
TI  - Nonparametric estimation of effective doses at quantal response
JO  - Ufa mathematical journal
PY  - 2013
SP  - 94
EP  - 108
VL  - 5
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UFA_2013_5_2_a8/
LA  - en
ID  - UFA_2013_5_2_a8
ER  - 
%0 Journal Article
%A M. S. Tikhov
%T Nonparametric estimation of effective doses at quantal response
%J Ufa mathematical journal
%D 2013
%P 94-108
%V 5
%N 2
%U http://geodesic.mathdoc.fr/item/UFA_2013_5_2_a8/
%G en
%F UFA_2013_5_2_a8
M. S. Tikhov. Nonparametric estimation of effective doses at quantal response. Ufa mathematical journal, Tome 5 (2013) no. 2, pp. 94-108. http://geodesic.mathdoc.fr/item/UFA_2013_5_2_a8/

[1] Krishtopenko S. V., Tikhov M. S., Popova E. B., Doza-effekt, Meditsina, M., 2008, 288 pp.

[2] Kocheganov V. M., Tikhov M. S., “Otsenivanie effektivnykh doz v zavisimosti doza-effekt”, Obozrenie Prikladnoi i Promyshlennoi Matematiki, 18:1 (2011), 85–86

[3] H. Dette, N. Neumeyer, K. F. Pilz, “A note on nonparametric estimation of the effective dose in quantal bioassay”, Journal of the American Statistical Association, 100 (2005), 503–510 | DOI | MR | Zbl

[4] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Lan, M., 2008, 560 pp.

[5] H. Niederreiter, Random number generation and quasi-Monte Carlo methods, Society for Industrial and Applied Mathematics, Philadelphia, Pensilvania, 1992, 241 pp. | MR

[6] E. L. Lehmann, Theory of Point Estimation, John Wiley Sons, N.Y., 1983, 506 pp. | MR | Zbl

[7] Leman E., Teoriya tochechnogo otsenivaniya, Nauka, M., 1991, 448 pp. | MR

[8] Tikhov M. S., Krishtopenko D. S., Yaroschuk M. V., “Otsenivanie raspredelenii v zavisimosti doza-effekt pri fiksirovannom plane eksperimenta”, Statisticheskie metody otsenivaniya i proverki gipotez, Mezhvuz. sb. nauch. tr., Perm. un-t, Perm, 2006, 66–77

[9] Kramer G., Matematicheskie metody statistiki, Mir, M., 1976, 648 pp. | MR

[10] M. S. Tikhov, “Statistical Estimation on the Basis of Interval-Censored Data”, Journal Math. Sciences, 119:3 (1974), 321–335 | DOI | MR

[11] D. J. Finney, Probit Analysis, Cambridge University Press, N. Y., 1971, 333 pp. | MR | Zbl