Asymptotics of the minimum sufficient number of observations for $d$-guaranteed discrimination of two-sided hypotheses
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 63-78
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We consider the problem of constructing guarantee procedures of statistical inference with fixed minimal observation number $n^*$ for discrimination of two hypotheses $H_0\colon\theta\in[\theta_1,\theta_2]$ and $H_1\colon\theta\notin[\theta_1,\theta_2]$ with a one-dimensional parameter $\theta$ under the so-called $d$-posterior approach. Here, constraints are placed on the conditional probabilities for the validity of one or another hypothesis under the condition that this hypothesis is rejected. We give an asymptotic formula for $n^*$ in a scheme with severe (tending to zero) constraints on these conditional probabilities of hypotheses. Earlier, Volodin and Novikov found a similar formula for discrimination of one-sided hypotheses. In the present paper, the proof of the asymptotic formula is carried out under weaker constraints on the probability model. The accuracy of our formula is illustrated numerically for some probability models.
Keywords:
Bayesian paradigm, $d$-posterior approach, discrimination of two hypotheses, minimal sample size, asymptotic analysis.
@article{TVP_2020_65_1_a3,
author = {R. F. Salimov and S. V. Simushkin},
title = {Asymptotics of the minimum sufficient number of observations for $d$-guaranteed discrimination of two-sided hypotheses},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {63--78},
publisher = {mathdoc},
volume = {65},
number = {1},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a3/}
}
TY - JOUR AU - R. F. Salimov AU - S. V. Simushkin TI - Asymptotics of the minimum sufficient number of observations for $d$-guaranteed discrimination of two-sided hypotheses JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2020 SP - 63 EP - 78 VL - 65 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a3/ LA - ru ID - TVP_2020_65_1_a3 ER -
%0 Journal Article %A R. F. Salimov %A S. V. Simushkin %T Asymptotics of the minimum sufficient number of observations for $d$-guaranteed discrimination of two-sided hypotheses %J Teoriâ veroâtnostej i ee primeneniâ %D 2020 %P 63-78 %V 65 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a3/ %G ru %F TVP_2020_65_1_a3
R. F. Salimov; S. V. Simushkin. Asymptotics of the minimum sufficient number of observations for $d$-guaranteed discrimination of two-sided hypotheses. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 63-78. http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a3/