Related papers: Unbiased Estimating Equation on Inverse Divergence…
We discuss unbiased estimation equations in a class of objective function using a monotonically increasing function $f$ and Bregman divergence. The choice of the function $f$ gives desirable properties such as robustness against outliers.…
We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent…
A class of distortions termed functional Bregman divergences is defined, which includes squared error and relative entropy. A functional Bregman divergence acts on functions or distributions, and generalizes the standard Bregman divergence…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
We study unbiased estimation under Bregman losses and develop an extension of the classical theory of uniformly minimum variance unbiased estimators (UMVUEs). Exploiting bias--variance-type decompositions for Bregman divergences, we…
Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…
This work proposes the Bregman-Tweedie classification model and analyzes the domain structure of the extended exponential function, an extension of the classic generalized exponential function with additional scaling parameter, and related…
The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the "Bregman function"). Bregman functions and divergences have been extensively…
We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Calibration weighting is a fundamental technique in survey sampling and data integration for incorporating auxiliary information and improving efficiency of estimators. Classical calibration methods are typically formulated through distance…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true…
Bregman divergences are a class of distance-like comparison functions which play fundamental roles in optimization, statistics, and information theory. One important property of Bregman divergences is that they cause two useful formulations…
When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
In this work we consider the unbiased estimation of expectations w.r.t.~probability measures that have non-negative Lebesgue density, and which are known point-wise up-to a normalizing constant. We focus upon developing an unbiased method…
Inferences that arise from loss functions determined by the prior are considered and it is shown that these lead to limiting Bayes rules that are closely connected with likelihood. The procedures obtained via these loss functions are…