The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities
T. W. Anderson
- Vol. 6, Iss: 2, pp 170-176
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The article was published on 1955-02-01 and is currently open access. It has received 552 citations till now. The article focuses on the topics: Convex set & Subderivative.read more
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An MCMC Approach to Classical Estimation
Victor Chernozhukov,Han Hong +1 more
TL;DR: The Laplace type estimators (LTE) as discussed by the authors are derived from quasi-posterior distributions defined as transformations of general (non-likelihood-based) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods.
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Positive dependence in multivariate distributions
Alam Khursheed,K.M. Lai Saxena +1 more
TL;DR: In this paper, the authors give some new results on positive dependence between random variables which are jointly normally distributed with special reference to certain inequalities of the form P(X∊A,Y∊B) > P(x ∊ A, y ∊ B) where A and B are given sets and X and Y are random vectors.
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Asymptotic Properties for a Class of Partially Identified Models
TL;DR: In this paper, the authors show that the Hausdorff distance between the estimator and the population identification region, when properly normalized by square n, converges in distribution to the supremum of a Gaussian process whose covariance kernel depends on parameters of the population identificaiton region.
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Minimum chi-square, not maximum likelihood!
TL;DR: In this article, it was argued that statistics is a science, not mathematics or philosophy (inference), and as such requires that any claimed attributes of the MLE must be testable by a Monte Carlo experiment.
Posted Content
Learning Models with Uniform Performance via Distributionally Robust Optimization
John C. Duchi,Hongseok Namkoong +1 more
TL;DR: A distributionally robust stochastic optimization framework that learns a model providing good performance against perturbations to the data-generating distribution is developed, and a convex formulation for the problem is given, providing several convergence guarantees.
References
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Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
TL;DR: In this article, a general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations.
BookDOI
Theorie der Konvexen Körper
T. Bonnesen,W. Fenchel +1 more
TL;DR: In this article, Minkowski et al. den engen Zusammenhang dieser Begriffbildungen und Satze mit der Frage nach der bestimmung konvexer Flachen durch ihre GAusssche Krtim mung aufgedeckt und tiefliegende diesbeztigliche Satze bewiesen.
Journal ArticleDOI
The Cramer-Smirnov Test in the Parametric Case
TL;DR: In this paper, the authors extended the Cramer-Smirnov and von Mises test to the parametric case, a suggestion of Cramer [1], see also [2].