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Empirical studies in various social sciences often involve categorical outcomes with inherent ordering, such as self-evaluations of subjective well-being and self-assessments in health domains. While ordered choice models, such as the…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
In risk theory, financial asset returns often follow heavy-tailed distributions. Investors and risk managers used to compare risk measures as the value at risk or tail value at risk in order over the whole confidence levels to avoid the…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order…
In this manuscript, we study stochastic comparisons of the second-order statistics from dependent or independent observations with modified proportional hazard rates models. First, we establish the usual stochastic order of the second-order…
Randomized experiments can provide unbiased estimates of sample average treatment effects. However, estimates of population treatment effects can be biased when the experimental sample and the target population differ. In this case, the…
In this paper new families of test statistics are introduced and studied for the problem of comparing two treatments in terms of the likelihood ratio order. The considered families are based on phi-divergence measures and arise as natural…
In this paper we extend the well-known L-Shaped method to solve two-stage stochastic programming problems with decision-dependent uncertainty. The method is based on a novel, unifying, formulation and on distribution-specific optimality and…
A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…
Let ${\bf X}$ and ${\bf X}$ be two $n$-dimensional elliptical random vectors, we establish an identity for $E[f({\bf Y})]-E[f({\bf X})]$, where $f: \Bbb{R}^n \rightarrow \Bbb{R}$ fulfilling some regularity conditions. Using this identity we…
This paper provides a theorem to compare the minimum total cost of two different Euclidean Random Assignment Problems with the same number of points, using the stochastic order of the costs of one of the pairs in these two problems. The…
An accurate multiclass classification strategy is crucial to interpreting antibody tests. However, traditional methods based on confidence intervals or receiver operating characteristics lack clear extensions to settings with more than two…
We propose and analyze a specific asymptotic stochastic order for random processes based on the measure of departure discussed in the literature. As applications, we stochastically compare mixtures of order statistics and record values…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…
We developed a novel direct algorithm to derive the mass-ratio distribution (MRD) of short-period binaries from an observed sample of single-lined spectroscopic binaries (SB1). The algorithm considers a class of parameterized MRDs and finds…
This work considers the allocation problem for multivariate stratified random sampling as a problem of integer non-linear stochastic multiobjective mathematical programming. With this goal in mind the asymptotic distribution of the vector…
For a bivariate random vector (X,Y), symmetry conditions are presented that yield stochastic orderings among |X|, |Y|, |max(X,Y)|, and | min(X, Y)|. Partial extensions of these results for multivariate random vectors (X1,...,Xn) are also…