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Article information
2016 , Volume 21, ¹ 1, p.107-115
Podrezov R.V., Rajfeld M.A.
A nonparametric test sampling method providing independent distribution of the test statistics under the null-hypothesis
Signal detection problem is usually considered as a testing of statistical hypothesis. When minimal assumptions are made about the distributions, application of a nonparametric test may have considerable advantages in efficiency. Situation becomes more complex in case of non-stationary signal, e. g. signal differs from noise by variance at one time interval and by level at another interval. Thus, the joint hypothesis testing the scale and the shift is required. In practice, nonparametric signal detectors are often developed using a reference sample that represents only noise at some time interval. Two tests have dependent statistics distributions, if they use the same reference sample. In another case, usage of the different reference samples reduces efficiency of a test, because the efficiency is related to minimal sample sizes required to obtain given constraints of the error probabilities. For rank tests, a developed sampling and ranking method can be applied to make ranks in working samples to be independent, and consequently rank statistics distributions. Ranks of working samples are calculated on general sample that consists of current sample, previous samples and the reference sample. This sampling and recurrent ranking method modifies the statistics of the considered tests, so one needs to evaluate new statistics distributions. It is important to note, that this sampling method can be applied to other rank tests. A coarse approximation with normal distribution can be used for the joint test with independent statistics distributions. Results that are more interesting can be obtained using logical conjunction of decisions, because this operation allows to independently set the detection threshold for a given false alarm probability criteria.
[full text]
Keywords: nonparametric test, sampling method, digital signal processing
Author(s):
Podrezov Roman Vladimirovich
Position: Student
Office: Novosibirsk State Technical University
Address: 630073, Russia, Novosibirsk, 20, Karl Marx Av.
E-mail: podrezov-r.v@mail.ru
Rajfeld Michael Anatolevich
Dr. , Associate Professor
Position: Professor
Office: Novosibirsk State Technical University
Address: 630073, Russia, Novosibirsk, 20, Karl Marks Av.
Phone Office: (383)346-15-37
E-mail: rajfeld@mail.ru
SPIN-code: 3492-4519 References:
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[4] Bol'shev L.N., Smirnov N.V. Tablitsy matematicheskoy statistiki [Tables for mathematical statistics]. Moscow: Nauka. Glavnaya redaktsiya fiziko-matematicheskom literatury; 1983: 416. (In Russ.)
Bibliography link:
Podrezov R.V., Rajfeld M.A. A nonparametric test sampling method providing independent distribution of the test statistics under the null-hypothesis // Computational technologies. 2016. V. 21. ¹ 1. P. 107-115
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