An algorithm of adaptive determination of the bandwidth is considered for unbiased estimators of the efficiency function in the dose-effect relationship under a fixed experimental design in the case of direct measurements. Optimality of the proposed algorithm is proved.
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References
S.V. Krishtopenko, M. S. Tikhov, and E.B. Popova, Dose–Effect, Meditsina, Moscow (2008).
S.V. Krishtopenko and M. S. Tikhov, Toxicometry of Effective Doses, State University of Nizhny Novgorod Publishers, Nizhny Novgorod (1997).
S.V. Krishtopenko, M. S. Tikhov, and E.B. Popova, Paradoxical Toxicity, State Medical Academy of Nizhny Novgorod Publishers, Nizhny Novgorod (2001).
M. S. Tikhov, “Statistical estimation based on interval censored data,” in: Parametric and Semipara-metric Models with Applications to Reliability, Survival Analysis and Quality of Life, M. S. Nikulin, N. Balakrishnan, M. Mesbah, and N. Limnios (eds.), Birkhauser, Boston (2004), pp. 209–215.
M. S. Tikhov, D. S. Krishtopenko, and M.V. Yaroschuk, “Estimation of distributions under doseeffect dependence with fixed experiment plan,” J. Math. Sci., 220, 753–762 (2017).
M. S. Tikhov and D. S. Krishtopenko, “Asymptotic distributions for integrated square error at the fixed plan of experiment,” in: 9th International Vilnius Conference on Probability Theory and Math-ematical Statistics: Abstract of Communications, Vilnius (2006), p. 312.
M. S. Tikhov and D. S. Krishtopenko, “Asymptotic normality of the integrated square error at the random plan of experiment with dose measurement errors,” in: Proceedings of the 6th International Conference Reliability and Statistics in Transportation and Communication, Riga (2006). pp. 374–375.
M. S. Tikhov and D. S. Krishtopenko, “Asymptotic normality of the integrated square error of distribution function estimators in dependence dose-response from indirect observations,” in: XIIth International Conference on Applied Stochastic Models and Data Analysis (ASMDA), Chania, Crete (2007).
W. Hardle, P. Hall, and J. S. Marron, “How far are automatically chosen regression smoothing parameters from their optimum?” J. Amer. Statist. Assoc., 83, No. 401, 86–93 (1988).
J. Rice, “Bandwidth choice for nonparametric regression,” Ann. Statist., 12, No. 4, 1215–1230 (1984).
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Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 22, pp. 85–95, 2010
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Tikhov, M.S., Krishtopenko, D.S. Determination of the Smoothing Parameter of an Unbiased Estimator of the Efficiency Function in the Dose-Effect Relationships. J Math Sci 267, 36–42 (2022). https://doi.org/10.1007/s10958-022-06105-2
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DOI: https://doi.org/10.1007/s10958-022-06105-2