The use of fourth order cumulant tensors to detect outlier features modelled by a t-Student copula
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In this paper we use multivariate cumulant of order 4 to distinguish between data generated from a Gaussian copula and data generated from a t-Student copula. We introduce a family of algorithms that detects a subset of outlier features modelled by a t-Student sub-copula out of ordinary data modelled by a Gaussian sub-copula. As features we understand marginal variables of multivariate data. To test the proposed method, we introduce the data alternation algorithm of multivariate normal distributed data, where some marginals (features) subset is changed to such modelled by the t-Student sub-copula. During the data alternation the overall covariance matrix and the 3rd order multivariate cumulant are not significantly affected. Mention, that introduced in this paper outlier detection algorithms have variety applications, for example in multivariate financial data analysis. Here we can analyse series of prices of many assets as multivariate data, and use our algorithm to detect a subset of particularly risky assets.
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