A Framework for Inference Using Goodness of Fit Tests Based on Ensemble of Phi-Divergences

Abstract

In this paper we study the inferential use of goodness of fit tests in a non-parametric setting. The utility of such tests will be demonstrated for the test case of spectrum sensing applications in cognitive radios. We provide the first comprehensive framework for decision fusion of an ensemble of goodness-of-fit testing procedures through an Ensemble Goodness-of-Fit test. Also, we introduce a generalized family of functionals and kernels called Φ-divergences which allow us to formulate goodness-of-fit tests that are parameterized by a single parameter. The performance of these tests is simulated under Gaussian and non-Gaussian noise in a MIMO setting. We show that under uncertainty in the noise statistics or non-Gaussianity in the noise, the performance of non-parametric tests in general, and phi-divergence based goodness-of-fit tests in particular, is significantly superior to that of the energy detector with reduced implementation complexity. In particular, the false alarm rates of our proposed tests is maintained at a fixed level over a wide variation in the channel noise distributions. Additionally, we describe a collaborative spatially separated version of the test for robust combining of tests in a distributed spectrum sensing setting and quantify the significant collaboration gains achieved.