Asymptotically optimal sequential tests for nonhomogeneous processes

It is shown that under certain conditions the matrix sequential probability ratio test (SPRT) and the combinations of "rejecting" SPRTs minimize all moments of the stopping time distribution in the problem of sequential testing of several simple hypotheses for nonhomogeneous processes when probabilities of errors tend to zero. We consider the general case of observation process with discrete or continuous time parameter and asymmetric (relative to probabilities of errors) classes of tests.

[1]  Martingale identities and inequalities and their applications in nonlinear boundary-value problems for random processes , 1984 .

[2]  N. V. Verdenskaya,et al.  Asymptotically Optimal Sequential Testing of Multiple Hypotheses for Nonhomogeneous Gaussian Processes in Asymmetric Case , 1992 .

[3]  I. Pavlov.  Sequential Procedure of Testing Composite Hypotheses with Applications to the Kiefer–Weiss Problem , 1991 .

[4]  D. Burkholder.  Distribution Function Inequalities for Martingales , 1973 .

[5]  Volker Strassen,et al.  Almost sure behavior of sums of independent random variables and martingales , 1967 .

[6]  Walter T. Federer,et al.  Sequential Design of Experiments , 1967 .

[7]  Gerald S. Rogers,et al.  Mathematical Statistics: A Decision Theoretic Approach , 1967 .

[8]  Gary Lorden,et al.  Integrated Risk of Asymptotically Bayes Sequential Tests , 1967 .

[9]  E. Paulson,et al.  An Optimum Solution to the $k$-Sample Slippage Problem for the Normal Distribution , 1952 .

[10]  T. Lai.  Asymptotic Optimality of Invariant Sequential Probability Ratio Tests , 1981 .

[11]  Venugopal V. Veeravalli,et al.  A sequential procedure for multihypothesis testing , 1994, IEEE Trans. Inf. Theory.

[12]  Alexander Novikov,et al.  On Discontinuous Martingales , 1975 .

[13]  David R. Cox,et al.  Sequential tests for composite hypotheses , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[14]  J. Kiefer,et al.  Asymptotically Optimum Sequential Inference and Design , 1963 .

[15]  Tze Leung Lai,et al.  On $r$-Quick Convergence and a Conjecture of Strassen , 1976 .

[16]  G. Lorden.  Nearly-optimal sequential tests for finitely many parameter values , 1977 .

[17]  R. Khas'minskii,et al.  Sequential Testing for Several Signals in Gaussian White Noise , 1984 .

[18]  H. Chernoff.  Sequential Design of Experiments , 1959 .

[19]  V P Dragalin.  Asymptotic solution of a problem of detecting a signal from k channels , 1987 .