Related papers: Nonsense associations in Markov random fields with…
In this paper, we resolve a longstanding open statistical problem. The problem is to mathematically confirm Yule's 1926 empirical finding of "nonsense correlation" (\cite{Yule}). We do so by analytically determining the second moment of the…
In 1926, G. Udny Yule considered the following: given a sequence of pairs of random variables $\{X_k,Y_k \}$ ($k=1,2, \ldots, n$), and letting $X_i = S_i$ and $Y_ i= S'_i$ where $S_i$ and $S'_i$ are the partial sums of two independent…
In this paper, we study the distribution of the so-called "Yule's nonsense correlation statistic" on a time interval $[0,T]$ for a time horizon $T>0$ , when $T$ is large, for a pair $(X_{1},X_{2})$ of independent Ornstein-Uhlenbeck…
We study the continuous-time version of the empirical correlation coefficient between the paths of two possibly correlated Ornstein-Uhlenbeck processes, known as Yule's nonsense correlation for these paths. Using sharp tools from the…
We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioned on their feature vectors, but dependent, capturing settings where e.g. these observations are collected…
We consider so-called univariate unlinked (sometimes ``decoupled,'' or ``shuffled'') regression when the unknown regression curve is monotone. In standard monotone regression, one observes a pair $(X,Y)$ where a response $Y$ is linked to a…
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
Multicollinearity is relevant to many different fields where linear regression models are applied, and its existence may affect the analysis of ordinary least squares (OLS) estimators from both the numerical and statistical points of views.…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…
We show that scale-scale correlations are a generic feature of slow-roll inflation theories. These correlations result from the long-time tails characteristic of the time dependent correlations because the long wavelength density…
The slope coefficient in a rank-rank regression is a popular measure of intergenerational mobility. In this article, we first show that commonly used inference methods for this slope parameter are invalid. Second, when the underlying…
Causal inference necessarily relies upon untestable assumptions; hence, it is crucial to assess the robustness of obtained results to violations of identification assumptions. However, such sensitivity analysis is only occasionally…
A result from a standard linear model course is that the variance of the ordinary least squares (OLS) coefficient of a variable will never decrease when including additional covariates. The variance inflation factor (VIF) measures the…
The purpose of this paper is to provide an exact formula for the second moment of the empirical correlation of two independent Gaussian random walks as well as implicit formulas for higher moments. The proofs are based on a symbolically…
Least squares linear regression is one of the oldest and widely used data analysis tools. Although the theoretical analysis of the ordinary least squares (OLS) estimator is as old, several fundamental questions are yet to be answered.…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
In this paper, we consider the hypothesis testing of correlation between two $m$-uniform hypergraphs on $n$ unlabelled nodes. Under the null hypothesis, the hypergraphs are independent, while under the alternative hypothesis, the hyperdges…