Related papers: A Note on Minimax Testing and Confidence Intervals…
Experimental designs that are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values.…
Missing data is pervasive in econometric applications, and rarely is it plausible that the data are missing (completely) at random. This paper proposes a methodology for studying the robustness of results drawn from incomplete datasets.…
Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical…
Mathematical Theory of Evidence (MTE), a foundation for reasoning under partial ignorance, is blamed to leave frequencies outside (or aside of) its framework. The seriousness of this accusation is obvious: no experiment may be run to…
Minimum divergence methods are popular tools in a variety of statistical applications. We consider tubular model adequacy tests, and demonstrate that the new divergences that are generated in the process are very useful in robust…
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…
Gini index is a widely used measure of economic inequality. This article develops a general theory for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width. Fixed sample size…
If moments of singular measures are passed as inputs to the entropy maximization procedure, the optimization algorithm might not terminate. The framework developed in our previous paper demonstrated how input moments of measures, on a broad…
Data from experiments and theoretical arguments are the two pillars sustaining the job of modelling physical systems through inference. In order to solve the inference problem, the data should satisfy certain conditions that depend also…
Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…
Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…
When the number of subjects, $n$, is large, paired comparisons are often sparse. Here, we study statistical inference in a class of paired comparison models parameterized by a set of merit parameters, under an Erd\"{o}s--R\'{e}nyi…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
The plausibility of the ``parallel trends assumption'' in Difference-in-Differences estimation is usually assessed by a test of the null hypothesis that the difference between the average outcomes of both groups is constant over time before…
What role should assumptions play in inference? We present a small theoretical case study of a simple, clean case, namely the nonparametric comparison of two continuous distributions using (essentially) information about quartiles, that is,…
We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of…
The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in…
This paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal…
The use of rapidity gaps is proposed as a measure of the spatial pattern of an event. When the event multiplicity is low, the gaps between neighboring particles carry far more information about an event than multiplicity spikes, which may…
Instead of testing for unanimous agreement, I propose learning how broad of a consensus favors one distribution over another (of earnings, productivity, asset returns, test scores, etc.). Specifically, given a sample from each of two…