Related papers: Breaking Bivariate Records
Observed associations in a database may be due in whole or part to variations in unrecorded (latent) variables. Identifying such variables and their causal relationships with one another is a principal goal in many scientific and practical…
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered…
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…
In this article, we consider the estimation of the marginal distributions for pairs of data are recorded, with unobserved order in each pair. New estimators are proposed and their asymptotic properties are established, by proving a…
This paper examines the asymptotic inference for AR(1) models with a possible structural break in the AR parameter $\beta $ near the unity at an unknown time $k_{0}$. Consider the model $y_{t}=\beta_{1}y_{t-1}I\{t\leq k_{0}\}+\beta…
Chain records is a new type of multidimensional record. We discuss how often the chain records are broken when the background sampling is from the unit cube with uniform distribution (or, more generally, from an arbitrary continuous product…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
Asymptotic normality of intermediate order statistics taken from univariate iid random variables is well-known. We generalize this result to random vectors in arbitrary dimension, where the order statistics are taken componentwise.
The persistent Betti numbers are used in topological data analysis to infer the scales at which topological features appear and disappear in the filtration of a topological space. Most commonly by means of the corresponding barcode or…
In this paper, we study a semiparametric family of bivariate copulas. The family is generated by an univariate function, determining the symmetry (radial symmetry, joint symmetry) and dependence property (quadrant dependence, total…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
We consider a rectangular grid induced by the south-west records from the planar Poisson point process in $R^2_+$. A random symmetry property of the matrix whose entries are the areas of tiles of the grid implies cute multivariate…
In this paper we study records obtained from partial comparisons within a sequence of independent and identically distributed (i.i.d.) random variables, indexed by positive integers, with a common density~\(f.\) Our main result is that if…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
In empirical studies, the data usually don't include all the variables of interest in an economic model. This paper shows the identification of unobserved variables in observations at the population level. When the observables are distinct…
We propose a new nonparametric procedure for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second- order) piecewise stationary process, which also identifies the components of…
The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of…
One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been…