Related papers: Asymptotic Inference for Rank Correlations
We consider semiparametric location-scatter models for which the $p$-variate observation is obtained as $X=\Lambda Z+\mu$, where $\mu$ is a $p$-vector, $\Lambda$ is a full-rank $p\times p$ matrix and the (unobserved) random $p$-vector $Z$…
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…
Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can…
Let $\{S_n=(X_n,W_n)\}_{n\ge0}$ be a random walk with $X_n\in \mathbb{R}$ and $W_n\in \mathbb{R}^m$. Let $\tau=\tau_a=\inf\{n:X_n>a\}$. The main results presented are two term asymptotic expansions for the joint distribution of $S_{\tau}$…
A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their…
This paper develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale. Perfect dependence is attainable for all marginal distributions. It furthermore proposes a set of dependence…
We study concentration in spectral norm of nonparametric estimates of correlation matrices. We work within the confine of a Gaussian copula model. Two nonparametric estimators of the correlation matrix, the sine transformations of the…
We consider change-point tests based on rank statistics to test for structural changes in long-range dependent observations. Under the hypothesis of stationary time series and under the assumption of a change with decreasing change-point…
We derive the asymptotic distribution of the spatial Cram'{e}r--von Mises statistic for testing bivariate independence in stationary random fields on $\mathbb{R}^2$ under polynomial $\beta$-mixing dependence, and document the Python…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
Real-life graphs usually have various kinds of events happening on them, e.g., product purchases in online social networks and intrusion alerts in computer networks. The occurrences of events on the same graph could be correlated,…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences…
Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition which goes beyond the self-evident 'dependence = non-independence'. This absence has allowed the term…
We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the…
Hoeffding proved that Kendall's and Spearman's nonparametric measures of correlation between two continuous random variables X and Y are each asymptotically normal with an asymptotic variance of the form sigma^2/n -- provided the…
This manuscript develops a general purpose inner-product norm for the Kendall \(\tau\) and Spearman's \(\rho\), which operates as an unbiased MLE even in the presence of ties. We derive and prove the strict sub-Gaussianity of the Kemeny…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
This paper proposes asymptotically distribution-free inference methods for comparing a broad range of welfare indices across dependent samples, including those employed in inequality, poverty, and risk analysis. Two distinct situations are…
Spatial association measures for univariate static spatial data are widely used. When the data is in the form of a collection of spatial vectors with the same temporal domain of interest, we construct a measure of similarity between the…