Download e-book for kindle: Introduction to Nonparametric Detection with Applications by Gibson

By Gibson

This center IEEE Press vintage Reissue is the single ebook committed exclusively to nonparametric detection - the foremost to retaining stable functionality over a variety of stipulations. all through, the authors hire the Neyman-Pearson method, recognized because the perfect for detection in communications, radar, sonar, acoustics, and geophysics.

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2-2 1) and from Eq. 2-20), E { D ( x ) l H , } = Q, ( F ) = a for all F E H,. 2-22) The Student’s t test is therefore the UMP unbiased test of level a for testing the hypothesis H, versus the alternative K,. To evaluate the performance of the Student’s t test for a nonparametric problem, let the form of the underlying noise distribution be unknown so that the hypothesis and alternative become H,: p = 0, u2 finite, F ( x ) otherwise unknown K,: p > 0, u2 finite, F ( x ) otherwise unknown Since the detector defined by Eq.

Ug versus K , : F ( x j ) is Gaussian with p j = C > 0, u,? = ui where i = 1, 2, . . , n. The detector given by Eq. 2-6) which is sometimes called the linear detector. As before, the threshold T I may be determined under the NeymanPearson criterion by fixing the false alarm probability a. To determine T I , the density of the test statistic under the hypothesis H I must be obtained. 2-7) By setting a = a0,the threshold T I may be determined from Eq. 2-7), Making a change of variables with y = ( S / f i a.

A modification to the Neyman-Pearson lemma for determining a most powerful test when the hypothesis or alternative is composite was presented and discussed, thus introducing the concept of a least favorable distribution. The important concept of a UMP test was introduced and two examples were given to further clarify the subject. Since UMP tests cannot always be found, optimum unbiased and locally most powerful tests were defined and their applicability discussed. The two asymptotic properties of consistency and robustness were also defined.

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