Related papers: Codivergences and information matrices
We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic…
Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is…
Many datasets take the form of a bipartite graph where two types of nodes are connected by relationships, like the movies watched by a user or the tags associated with a file. The partitioning of the bipartite graph could be used to fasten…
The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for…
This paper proposes multivariate copula models for hierarchical data. They account for two types of correlation: one is between variables measured on the same unit and the other is a correlation between units in the same cluster. This model…
In this paper, we develop local expansions for the ratio of the centered matrix-variate $T$ density to the centered matrix-variate normal density with the same covariances. The approximations are used to derive upper bounds on several…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
We introduce quantum versions of the $\chi^2$-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes. An approach similar to the one presented in [1-3]…
Minimum divergence estimators provide a natural choice of estimators in a statistical inference problem. Different properties of various families of these divergence measures such as Hellinger distance, power divergence, density power…
Cross-correlation techniques provide a promising avenue for calibrating photometric redshifts and determining redshift distributions using spectroscopy which is systematically incomplete (e.g., current deep spectroscopic surveys fail to…
For testing independence it is very popular to use either the $\chi^{2}$-statistic or $G^{2}$-statistics (mutual information). Asymptotically both are $\chi^{2}$-distributed so an obvious question is which of the two statistics that has a…
Similarity measures play a fundamental role in memory-based nearest neighbors approaches. They recommend items to a user based on the similarity of either items or users in a neighborhood. In this paper we argue that, although it keeps a…
We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…
The Kullback-Leibler (KL) divergence is a foundational measure for comparing probability distributions. Yet in multivariate settings, its single value often obscures the underlying reasons for divergence, conflating mismatches in individual…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…