Abstract:
By differential equation methods the author finds a complete asymptotic expansion for the probability of overshooting a high level of a conditional Wiener process given on an interval. These results are used to compute approximate values of percentage points for Kolmogorov–Smirnov statistics in the case of a composite hypothesis. A comparison between the results thus calculated and tabular values is carried out for a number of distributions.
Bibliography: 19 titles.
Citation:
Yu. N. Tyurin, “On the limit distribution of Kolmogorov–Smirnov statistics for a composite hypothesis”, Math. USSR-Izv., 25:3 (1985), 619–646
\Bibitem{Tyu84}
\by Yu.~N.~Tyurin
\paper On~the limit distribution of Kolmogorov--Smirnov statistics for a~composite hypothesis
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 3
\pages 619--646
\mathnet{http://mi.mathnet.ru/eng/im1520}
\crossref{https://doi.org/10.1070/IM1985v025n03ABEH001311}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=772118}
\zmath{https://zbmath.org/?q=an:0587.62040|0571.62009}
Linking options:
https://www.mathnet.ru/eng/im1520
https://doi.org/10.1070/IM1985v025n03ABEH001311
https://www.mathnet.ru/eng/im/v48/i6/p1314
This publication is cited in the following 5 articles:
A. B. Popov, “Neekstensivnaya statistika Tsallisa sistemy kontraktov organizatsii oboronno-promyshlennogo kompleksa”, Kompyuternye issledovaniya i modelirovanie, 14:5 (2022), 1163–1183
B. Yu. Lemeshko, S. B. Lemeshko, M. S. Nikulin, N. Saaidia, “Modeling statistic distributions for nonparametric goodness-of-fit criteria for testing complex hypotheses with respect to the inverse Gaussian law”, Autom. Remote Control, 71:7 (2010), 1358–1373
J. Appl. Industr. Math., 3:4 (2009), 462–475
M. B. Malyutov, Yu. N. Tyurin, “Some Research in Mathematical Statistics by the Department of Probability Theory of Moscow University”, Theory Probab Appl, 34:1 (1989), 193
A. A. Makarov, “The Asymptotic Behavior of the Limit Distribution of the Kolmogorov–Smirnov Statistic in the Case of a Composite Hypothesis for the Class of Projecting Estimates of an Unknown Parameter”, Theory Probab Appl, 32:2 (1987), 380
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