Related papers: Cartesian Statistics on Spheres
We propose two classes of nonparametric point estimators of $\theta=P(X<Y)$ in the case where $(X,Y)$ are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of…
Empirical analyses of ordinal outcomes using repeated cross-sectional data rely on marginal distributions, leaving the joint distribution unobserved and the sources of distributional change unidentified. This paper develops a framework to…
For a multivariate normal distribution, the sparsity of the covariance and precision matrices encodes complete information about independence and conditional independence properties. For general distributions, the covariance and precision…
Random matrix theory has become a cornerstone in modern statistics and data science, providing fundamental tools for understanding high-dimensional covariance structures. Within this framework, the Wishart matrix plays a central role in…
The parameter space of nonnegative trigonometric sums (NNTS) models for circular data is the surface of a hypersphere; thus, constructing regression models for a circular-dependent variable using NNTS models can comprise fitting great…
A graphical tool for investigating unimodality of hyperspherical data is proposed. It is based on the notion of statistical data depth function for directional data which extends the univariate concept of rank. Firstly a local version of…
We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated…
Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…
This paper introduces two families of probability distributions for Bayesian analysis of hypertoroidal data. The first family consists of symmetric distributions derived from the projection of multivariate normal distributions under…
We compute a number of distance-dependent universal scaling functions characterizing the distance statistics of large maps of genus one. In particular, we obtain explicitly the probability distribution for the length of the shortest…
We investigate the influence of the nonextensive q-statistics and kinetic theory on galactic scales through the analysis of a devised sample of Spiral Rotation Curves. Largely supported by recent developments on the foundations of…
Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…
We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square…
We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when…
Comparing counterfactual distributions can provide more nuanced and valuable measures for causal effects, going beyond typical summary statistics such as averages. In this work, we consider characterizing causal effects via distributional…
Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained,…
This paper considers distributed statistical inference for general symmetric statistics %that encompasses the U-statistics and the M-estimators in the context of massive data where the data can be stored at multiple platforms in different…
The paper focuses on sequential experiments for categorical responses in which whether or not a further observation is made depends on the outcome of a previous experiment. Examples include subsequent medical interventions being performed…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Partial orderings and measures of information for continuous univariate random variables with special roles of Gaussian and uniform distributions are discussed. The information measures and measures of non-Gaussianity including third and…