Abstract:
The asymptotic minimaxity of tests of the Kolmogorov and omega-square types is proved under natural nonparametric sets of alternatives. The tests are compared using a new asymptotic bound for the probabilities of moderate large deviations for the type I and type II errors. Our proof relies heavily on qualitatively new theorems about the probabilities of moderate large deviations of empirical measures.
Citation:
M. S. Ermakov, “Asymptotic minimaxity of tests of the Kolmogorov and omega-square types”, Teor. Veroyatnost. i Primenen., 40:1 (1995), 54–67; Theory Probab. Appl., 40:1 (1995), 41–51
\Bibitem{Erm95}
\by M.~S.~Ermakov
\paper Asymptotic minimaxity of tests of the Kolmogorov and omega-square types
\jour Teor. Veroyatnost. i Primenen.
\yr 1995
\vol 40
\issue 1
\pages 54--67
\mathnet{http://mi.mathnet.ru/tvp3290}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1346730}
\zmath{https://zbmath.org/?q=an:0898.62058}
\transl
\jour Theory Probab. Appl.
\yr 1995
\vol 40
\issue 1
\pages 41--51
\crossref{https://doi.org/10.1137/1140002}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1996UH07100002}
Linking options:
https://www.mathnet.ru/eng/tvp3290
https://www.mathnet.ru/eng/tvp/v40/i1/p54
This publication is cited in the following 8 articles:
Mikhail Ermakov, “Nonparametric signal detection with small type I and type II error probabilities”, Stat Inference Stoch Process, 14:1 (2011), 1
Juan Carlos Escanciano, Kyungchul Song, “Asymptotically Optimal Tests for Single-Index Restrictions With a Focus on Average Partial Effects”, SSRN Journal, 2007
M. S. Ermakov, “Importance sampling for simulation of large and moderate deviation probabilities of tests and estimators”, Theory Probab. Appl., 51:2 (2007), 279–290
M. S. Ermakov, “On large deviations of type II error probabilities of Kolmogorov and omega-squared tests”, J. Math. Sci. (N. Y.), 128:1 (2005), 2538–2555
M. S. Ermakov, “On asymptotically efficient statistical inference for moderate
deviation probabilities”, Theory Probab. Appl., 48:4 (2004), 622–641
Michael Ermakov, “On Asymptotic Minimaxity of Kernel-based Tests”, ESAIM: PS, 7 (2003), 279
M. S. Ermakov, “On the Lower Bound of the Exact Asymptotics for the Large-Deviation Probabilities of Statistical Estimates”, Problems Inform. Transmission, 35:3 (1999), 236–247
M. S. Ermakov, “Asymptotic minimaxity of chi-square tests”, Theory Probab. Appl., 42:4 (1998), 589–610
Citation in format AMSBIB
Contact us: