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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…

Statistics Theory · Mathematics 2022-09-07 Souvik Ray , Subrata Pal , Sumit Kumar Kar , Ayanendranath Basu

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…

Statistics Theory · Mathematics 2016-07-04 Avijit Maji , Abhik Ghosh , Ayanendranath Basu

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…

Methodology · Statistics 2017-06-20 Arun Kumar Kuchibhotla , Somabha Mukherjee , Ayanendranath Basu

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…

Methodology · Statistics 2020-12-23 Pushpinder Singh , Abhijit Mandal , Ayanendranath Basu

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…

Statistics Theory · Mathematics 2020-08-18 Soumik Purkayastha , Ayanendranath Basu

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,…

Statistics Theory · Mathematics 2019-10-29 Saptarshi Roy , Kaustav Chakraborty , Somnath Bhadra , Ayanendranath Basu

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…

Methodology · Statistics 2014-07-16 Avijit Maji , Abhik Ghosh , Ayanendranath Basu

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…

Methodology · Statistics 2024-02-06 Giovanni Saraceno , Abhik Ghosh , Ayanendranath Basu , Claudio Agostinelli

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…

Statistics Theory · Mathematics 2021-01-25 Sancharee Basak , Ayanendranath Basu

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…

Mathematical Physics · Physics 2025-12-15 Razvan Gabriel Iagar , David Puertas-Centeno , Elio V. Toranzo

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…

Information Theory · Computer Science 2025-02-03 Masahiro Kobayashi

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…

Methodology · Statistics 2018-06-27 E. Castilla , A. Ghosh , N. Martín , L. Pardo

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,…

Statistics Theory · Mathematics 2025-03-19 A. Felipe , M. Jaenada , P. Miranda , L. Pardo

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…

Methodology · Statistics 2024-02-09 Akifumi Okuno

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…

Statistics Theory · Mathematics 2023-12-06 A. Felipe , M. Jaenada , P. Miranda , L. Pardo

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…

Machine Learning · Computer Science 2025-07-31 Adwait Datar , Nihat Ay

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…

Methodology · Statistics 2024-01-08 Arijit Pyne , Subhrajyoty Roy , Abhik Ghosh , Ayanendranath Basu

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…

Information Theory · Computer Science 2024-02-27 Frank Nielsen

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…

Methodology · Statistics 2017-10-02 Papa Ngom , Jean de Dieu Nkurunziza , Carlos Simplice Ogouyandjou

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…

Statistics Theory · Mathematics 2025-02-17 Subhrajyoty Roy , Abir Sarkar , Abhik Ghosh , Ayanendranath Basu
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