An estimation method for the Neyman chi-square divergence with application to test of hypotheses

Abstract

We propose a new definition of the Neyman chi-square divergence between distributions. Based on convexity properties and duality, this version of the is well suited both for the classical applications of the for the analysis of contingency tables and for the statistical tests in parametric models, for which it is advocated to be robust against outliers.\ud We present two applications in testing. In the first one, we deal with goodness-of-fit tests for finite and infinite numbers of linear constraints; in the second one, we apply -methodology to parametric testing against contamination

Comparison Between Divergence Measures for Anomaly Detection of Mobile Agents in IP Networks

“…Existing methods for anomaly detection are based on different techniques, such as Haar-wavelet analysis [3], [4], Entropy based method [5] and Holt-Winters [6] seasonal forecasting method. Authors in [7] compare two different algorithms (CUSUM and adaptive threshold) for the detection of SYN flooding attack.…”

“…In [30], authors prove that χ2 divergence behaves better than all classical divergences (Hellinger distance, Kullback-Leibler, Likelihood, etc, [6].…”

Dual divergence estimators and tests: Robustness results

“…Let α be fixed and consider the dual φ-divergence estimators  θ n (α) defined in (7). The functional associated with an estimator  θ n (α) is…”

“…Some other robust tests based on dual φ-divergence estimators and saddlepoint approximations have been studied by Toma and Leoni-Aubin [28] in the case of small samples. We also mention that the use of the dual form of a divergence to derive robust tests was discussed in a different context by Broniatowski and Leorato [7] in the case of the Neyman χ 2 divergence.…”

Flooding attacks detection in traffic of backbone networks

“…In [30], authors prove that χ 2 divergence behaves better than all classical divergences (Hellinger distance, Kullback-Leibler, Likelihood, etc.). In our proposed approach, we use χ 2 divergence with dynamic threshold to increase the detection accuracy, and to reduce the false alarm ratio.…”