Related papers: A Simple Bootstrap for Chatterjee's Rank Correlati…
This paper develops bootstrap procedures for inference in linear regression models with two-way clustered data. We characterize the estimator's asymptotic behavior in five mutually exclusive and exhaustive regimes: three Gaussian and two…
Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…
Chatterjee's rank correlation \(\xi\) has emerged as a popular measure quantifying the strength of directed functional dependence between random variables $X$ and $Y$. If $X$ and $Y$ are continuous, $\xi$ equals Spearman's footrule~\(\psi\)…
In his seminal work, Chatterjee (2021) introduced a novel correlation measure which is distribution-free, asymptotically normal, and consistent against all alternatives. In this paper, we study the probabilistic relationships between…
We propose a simple modification to the wild bootstrap procedure and establish its asymptotic validity for linear regression models with many covariates and heteroskedastic errors. Monte Carlo simulations show that the modified wild…
Rank correlations have found many innovative applications in the last decade. In particular, suitable rank correlations have been used for consistent tests of independence between pairs of random variables. Using ranks is especially…
We present a test for independence of two strictly stationary time series based on a bootstrap procedure for the distance covariance. Our test detects any kind of dependence between the two time series within an arbitrary maximum lag $L$.…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
We propose a bootstrap procedure for data that may exhibit clustering in two or more dimensions. We use insights from the theory of generalized U-statistics to analyze the large-sample properties of statistics that are sample averages from…
The construction of minimum spanning trees (MSTs) from correlation matrices is an often used method to study relationships in the financial markets. However most of the work on this topic tends to use the Pearson correlation coefficient,…
We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively. We propose a method that covers both model averaging and model selection in the same framework.…
We consider the properties of the bootstrap as a tool for inference concerning the eigenvalues of a sample covariance matrix computed from an $n\times p$ data matrix $X$. We focus on the modern framework where $p/n$ is not close to 0 but…
In longitudinal and spatial studies, observations often demonstrate strong correlations that are stationary in time or distance lags, and the times or locations of these data being sampled may not be homogeneous. We propose a nonparametric…
The bootstrap is a versatile inference method that has proven powerful in many statistical problems. However, when applied to modern large-scale models, it could face substantial computation demand from repeated data resampling and model…
This paper highlights a tension between semiparametric efficiency and bootstrap consistency in the context of a canonical semiparametric estimation problem, namely the problem of estimating the average density. It is shown that although…
The recent seminal work of Chernozhukov, Chetverikov and Kato has shown that bootstrap approximation for the maximum of a sum of independent random vectors is justified even when the dimension is much larger than the sample size. In this…
The rank correlation \xi(X,Y), recently established by Sourav Chatterjee and already popular in the statistics literature, takes values in [0,1], where 0 characterizes independence of X and Y, and 1 characterizes perfect dependence of Y on…
The Nystrom method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by…
We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank…