Related papers: On multivariate quantiles under partial orders
Quantile regression permits describing how quantiles of a scalar response variable depend on a set of predictors. Because a unique definition of multivariate quantiles is lacking, extending quantile regression to multivariate responses is…
Preferences of individuals are distributions of elements generated by generalized functions. Models of economic decision-making derived from such distributions are consistent with results of physiological experiments, and explain any…
Quantile regression is used to study effects of covariates on a particular quantile of the data distribution. Here we are interested in the question whether a covariate has any effect on the entire data distribution, i.e., on any of the…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
Aggregation sets, which represent model uncertainty due to unknown dependence, are an important object in the study of robust risk aggregation. In this paper, we investigate ordering relations between two aggregation sets for which the sets…
The ability of an agent to do well in new environments is a critical aspect of intelligence. In machine learning, this ability is known as $\textit{strong}$ or $\textit{out-of-distribution}$ generalization. However, merely considering…
This work derives closed-form expressions computing the expectation of co-presence and of number of co-occurrences of nodes on paths sampled from a network according to general path weights (a bag of paths). The underlying idea is that two…
A new multivariate concept of quantile, based on a directional version of Koenker and Bassett's traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version,…
The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of…
Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the…
Stochastic dominance (SD) provides a quantile-based partial ordering of random variables and has broad applications. Its extension to multivariate settings, however, is challenging due to the lack of a canonical ordering in $\mathbb{R}^d$…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…
This article extends the widely-used synthetic controls estimator for evaluating causal effects of policy changes to quantile functions. The proposed method provides a geometrically faithful estimate of the entire counterfactual quantile…
Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…