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In this paper, we provide some results related to the ∆ 2 -condition of Musielak-Orlicz functions and ϕ-families of probability distributions, which are modeled on Musielak-Orlicz spaces. We show that if two ϕ-families are modeled on Musielak-Orlicz spaces generated by Musielak-Orlicz functions satisfying the ∆ 2 -condition, then these ϕ-families are equal as sets. We also investigate the behavior of the normalizing function near the boundary of the set on which a ϕ-family is defined.

Abstract:In this paper, we propose a generalization of Rényi divergence, and then we investigate its induced geometry. This generalization is given in terms of a ϕ-function, the same function that is used in the definition of non-parametric ϕ-families. The properties of ϕ-functions proved to be crucial in the generalization of Rényi divergence. Assuming appropriate conditions, we verify that the generalized Rényi divergence reduces, in a limiting case, to the ϕ-divergence. In generalized statistical manifold, the ϕ-divergence induces a pair of dual connections D (−1) and D (1) . We show that the family of connections D

Abstract:In this paper, we investigate the mixture arc on generalized statistical manifolds. We ensure that the generalization of the mixture arc is well defined and we are able to provide a generalization of the open exponential arc and its properties. We consider the model of a ϕ-family of distributions to describe our general statistical model.

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We define a metric and a family of α-connections in statistical manifolds, based on ϕ-divergence, which emerges in the framework of ϕ-families of probability distributions. This metric and α-connections generalize the Fisher information metric and Amari's α-connections. We also investigate the parallel transport associated with the α-connection for α = 1. IntroductionIn the framework of ϕ-families of probability distributions [11], the authors introduced a divergence D ϕ (· ·) between probabilities distributions, called ϕ-divergence, that generalizes the Kullback-Leibler divergence. Based on D ϕ (· ·) we can define a new metric and connections in statistical manifolds. The definition of metrics or connections in statistical manifolds is a common subject in the literature [2,3,7]. In our approach, the metric and α-connections are intrinsically related to ϕ-families. Moreover, they can be recognized as a generalization of the Fisher information metric and Amari's α-connections [1,4].Statistical manifolds are equipped with the Fisher information metric, which is given in terms of the derivative of l(t; θ) = log p(t; θ). Another metric can be defined if the logarithm log(·) is replaced by the inverse of a ϕ-function ϕ(·) [11]. Instead of l(t; θ) = log p(t; θ), we can consider f (t; θ) = ϕ −1 (p(t; θ)). The manifold equipped with * This work was partially funded by CNPq (Proc. 309055/2014-8).

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In this paper we propose a pilot-based OFDM channel estimator based on the combination of low-pass filtering and delay-subspace projection. The proposed estimator, which we abbreviate ST-LP, is robust in the sense it does not require prior statistical knowledge of the channel. The only assumptions are the least-square (LS) estimates have limited spectrum and the channel follows the tapped delay line (TDL) model, which are commonly taken in practice. Since it is desirable slow delay variations operability acceptance, the delay-subspace is tracked by a subspace tracking (ST) algorithm. The ST-LP estimator can be implemented by two filtering structures, which provide a trade-off between accuracy and complexity. Simulation results confirm the superior performance of the ST-LP estimator when compared to methods already reported in the literature.