A Non-Iterative Quantile Change Detection Method in Mixture Model with Heavy-Tailed Components

Estimating parameters of mixture model has wide applications Determining the number of components in a finite mixture model ranging from classification problems to estimating of complex distributions. is crucial in many application areas such as financial data [16, 31, 35], Most of the current literature on estimating the parameters biomedical studies [17, 36] and low-frequency accident occurrence of the mixture densities are based on iterative Expectation Maximization prediction [27, 32]. Existing literature have witnessed numerous (EM) type algorithms which require the use of either computational methods, and in particular Markov Chain Monte taking expectations over the latent label variables or generating Carlo methods [7, 14, 33] and EM algorithms [20-22] have been samples from the conditional distribution of such latent labels using used with a lot of success. However, either these methods are computationally the Bayes rule. Moreover, when the number of components is demanding and/or these methods are developed under unknown, the problem becomes computationally more demanding the assumption of data being generated from mixtures of densities due to well-known label switching issues [28]. In this paper, we from the exponential family, in part because the family of exponential propose a robust and quick approach based on change-point methods distribution has a sufficient statistic of constant dimension (i.e., to determine the number of mixture components that works the dimension of the sufficient statistic remains fixed for any sample for almost any location-scale families even when the components size) and so the updates of the data augmentation type algorithm are heavy tailed (e.g., Cauchy). We present several numerical illustrations involve their smaller dimensional sufficient statistics [11, 12, 24].