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Measuring dependence between two events, or equivalently between two binary random variables, amounts to expressing the dependence structure inherent in a $2\times 2$ contingency table in a real number between $-1$ and $1$. Countless such…
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…
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of…
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…
For models evaluated at a random set of independent variables, the variance-based Shapley effects range between Sobol' indices, and the corresponding total indices admit derivative-based upper-bounds. Such relationships fail when the inputs…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
We investigate the relative information content of six measures of dependence between two random variables $X$ and $Y$ for large or extreme events for several models of interest for financial time series. The six measures of dependence are…
This paper studies the properties of linear regression on centrality measures when network data is sparse and observed with error. We make three contributions in this setting. First, we show that OLS estimators can become inconsistent under…
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this…
Given a response $Y$ and a vector $X = (X^1, \dots, X^d)$ of $d$ predictors, we investigate the problem of inferring direct causes of $Y$ among the vector $X$. Models for $Y$ that use all of its causal covariates as predictors enjoy the…
The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…
This paper suggests five measures of association between two random vectors X = (X_1, ..., X_p) and Y = (Y_1, ..., Y_q). They are copula based and therefore invariant with respect to the marginal distributions of the components X_i and Y_j.…
We consider time-inhomogeneous ODEs whose parameters are governed by an underlying ergodic Markov process. When this underlying process is accelerated by a factor $\varepsilon^{-1}$, an averaging phenomenon occurs and the solution of the…
We test recent claims that causal (driver/response) relationships can be deduced from interdependencies between simultaneously measured time series. We apply two recently proposed interdependence measures which should give similar results…
We introduce an extension to the standard reduction of oscillatory systems to a single phase variable. The standard reduction is often insufficient, particularly when the oscillations have variable amplitude and the magnitude of each…
Ordinary least squares (OLS) linear regression is one of the most basic statistical techniques for data analysis. In the main stream literature and the statistical education, the study of linear regression is typically restricted to the…
This paper addresses the open problem of conducting change-point analysis for interval-valued time series data using the maximum likelihood estimation (MLE) framework. Motivated by financial time series, we analyze data that includes daily…
A tacit assumption in classical linear regression problems is the full knowledge of the existing link between the covariates and responses. In Unlinked Linear Regression (ULR) this link is either partially or completely missing. While the…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
Double blind randomized controlled trials are traditionally seen as the gold standard for causal inferences as the difference-in-means estimator is an unbiased estimator of the average treatment effect in the experiment. The fact that this…