相关论文: Characterizing Logarithmic Bregman Functions

Divergence measures have a long association with statistical inference, machine learning and information theory. The density power divergence and related measures have produced many useful (and popular) statistical procedures, which provide…

Statistical inference based on divergence measures have a long history. Recently, Maji, Ghosh and Basu (2014) have introduced a general family of divergences called the logarithmic super divergence (LSD) family. This family acts as a…

M-estimators offer simple robust alternatives to the maximum likelihood estimator. Much of the robustness literature, however, has focused on the problems of location, location-scale and regression estimation rather than on estimation of…

Density-based minimum divergence procedures represent popular techniques in parametric statistical inference. They combine strong robustness properties with high (sometimes full) asymptotic efficiency. Among density-based minimum distance…

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed. The popular density power divergence (DPD) class of estimators is a sub-class of Bregman divergences. We propose and study a new…

Preserving the robustness of the procedure has, at the present time, become almost a default requirement for statistical data analysis. Since efficiency at the model and robustness under misspecification of the model are often in conflict,…

This paper introduces a new superfamily of divergences that is similar in spirit to the S-divergence family introduced by Ghosh et al. (2013). This new family serves as an umbrella that contains the logarithmic power divergence family…

Many real-life data sets can be analyzed using Linear Mixed Models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters…

Minimization of suitable statistical distances~(between the data and model densities) has proved to be a very useful technique in the field of robust inference. Apart from the class of $\phi$-divergences of \cite{a} and \cite{b}, the…

In this work we introduce a family of transformations, named \textit{divergence transformations}, interpolating between any pair of probability density functions sharing the same support. We prove the remarkable property that the whole…

Density-power-based divergences are known to provide robust inference procedures against outliers, and their extensions have been widely studied. A characteristic of successful divergences is that the estimation problem can be reduced to…

This paper derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a…

The log-logistic distribution is a versatile parametric family widely used across various applied fields, including survival analysis, reliability engineering, and econometrics. When estimating parameters of the log-logistic distribution,…

Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers. However, DPD involves an integral of the power of the parametric density models to be estimated; the…

Robust inferential methods based on divergences measures have shown an appealing trade-off between efficiency and robustness in many different statistical models. In this paper, minimum density power divergence estimators (MDPDEs) for the…

The Kullback-Leibler (KL) divergence plays a central role in probabilistic machine learning, where it commonly serves as the canonical loss function. Optimization in such settings is often performed over the probability simplex, where the…

In real life, we frequently come across data sets that involve some independent explanatory variable(s) generating a set of ordinal responses. These ordinal responses may correspond to an underlying continuous latent variable, which is…

Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning among others. An exponential family can either be normalized subtractively by its cumulant or free energy function…

Recently in [1, 2], Ali-Akbar Bromideh introduced the Kullback-Leibler Divergence (KLD) test statistic in discrim- inating between two models. It was found that the Ratio Minimized Kulback-Leibler Divergence (RMKLD) works better than the…

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to classical techniques based on maximum likelihood and related methods. Basu et al. (1998) introduced the density power divergence…