Asymptotic robustness of Kelly's GLRT and Adaptive Matched Filter detector under model misspecification

A fundamental assumption underling any Hypothesis Testing (HT) problem is that the available data follow the parametric model assumed to derive the test statistic. Nevertheless, a perfect match between the true and the assumed data models cannot be achieved in many practical applications. In all these cases, it is advisable to use a robust decision test, i.e. a test whose statistic preserves (at least asymptotically) the same probability density function (pdf) for a suitable set of possible input data models under the null hypothesis. Building upon the seminal work of Kent (1982), in this paper we investigate the impact of the model mismatch in a recurring HT problem in radar signal processing applications: testing the mean of a set of Complex Elliptically Symmetric (CES) distributed random vectors under a possible misspecified, Gaussian data model. In particular, by using this general misspecified framework, a new look to two popular detectors, the Kelly's Generalized Likelihood Ration Test (GLRT) and the Adaptive Matched Filter (AMF), is provided and their robustness properties investigated.Comment: ISI World Statistics Congress 2017 (ISI2017), Marrakech, Morocco, 16-21 July 201

Singlet structure function g_1 at small x and small Q^2

Explicit expressions for the singlet g_1 at small x and small Q^2 are obtained with the total resummation of the leading logarithmic contributions. It is shown that g_1 practically does not depend on Q^2 in this kinematic region. In contrast, it would be interesting to investigate its dependence on the invariant energy 2pq because, being g_1 positive at small 2pq, it can turn negative at greater values of this variable. The position of the turning point is sensitive to the ratio between the initial quark and gluon densities, so its experimental detection would enable to estimate this ratioComment: Section 2 is totally changed, one more ref adde

Comment on the frozen QCD coupling

The frozen QCD coupling is a parameter often used as an effective fixed coupling. It is supposed to mimic both the running coupling effects and the lack of knowledge of alpha_s in the infrared region. Usually the value of the frozen coupling is fixed from the analysis of the experimental data. We present a novel way to define such coupling(s) independently of the experiments. We argue that there are different frozen couplings which are used in the double- (DL) and single- logarithmic (SL) Approximations. We introduce four kinds of the frozen couplings: the coupling used in DLA with a time-like argument (i.e. the coupling present in the non-singlet scattering amplitudes and DIS structure functions) which we find 0.24 approximately; the DLA coupling with a space-like argument (in e+e- -annihilation, in DY processes and in any scattering amplitude in the hard or backward kinematics) which is a factor two larger, namely 0.48. We also show that the frozen coupling in the SL evolution equations like BFKL has to be defined in a way less accurate compared to DLA, and our estimate for this coupling is 0.1. Our estimates for the singlet and non-singlet intercepts are also in a good agreement with the results available in the literature.Comment: 11 pages, 3 figure

Small -x behavior of the non-singlet and singlet structure functions g_1

Explicit expressions for the non-singlet and singlet structure functions g_1 at the small $x$-region are obtained. They include the total resummation of double-logarithmic contributions and accounting for the running QCD coupling effects. We predict that both the non-singlet and singlet g_1 asymptotically ~ x^{- \Delta}, with the singlet intercept = 0.86 and being more than twice larger than the non-singlet intercept = 0.4. The impact of the initial quark and gluon densities on the sign of g_1 at x << 1 is discussed.Comment: Talk given at Xth Workshop on high energy spin physics, Dubna, Russia, September,16-20, 2003. LateX 9pp, 4 fig