Related papers: Heavy-tailed distribution for combining dependent …
We study the joint limit distribution of the $k$ largest eigenvalues of a $p\times p$ sample covariance matrix $XX^\T$ based on a large $p\times n$ matrix $X$. The rows of $X$ are given by independent copies of a linear process,…
We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…
Selective inference is a subfield of statistics that enables valid inference after selection of a data-dependent question. In this paper, we introduce selectively dominant p-values, a class of p-values that allow practitioners to easily…
The large-scale multiple testing inherent to high throughput biological data necessitates very high statistical stringency and thus true effects in data are difficult to detect unless they have high effect sizes. One solution to this…
This paper introduces the Trimmed Functional Empirical Process (TFEP) as a robust framework for statistical inference when dealing with heavy-tailed or skewed distributions, where classical moments such as the mean or variance may be…
This paper develops a new framework for alpha testing in high-dimensional factor pricing models with time-varying coefficients. To detect sparse alternatives, we propose a spatial-sign-based max-type test and derive its limiting null…
We study the probability tail properties of Inverse Probability Weighting (IPW) estimators of the Average Treatment Effect (ATE) when there is limited overlap between the covariate distributions of the treatment and control groups. Under…
We introduce the notion of symmetric covariation, which is a new measure of dependence between two components of a symmetric $\alpha$-stable random vector, where the stability parameter $\alpha$ measures the heavy-tailedness of its…
Permutation tests date back nearly a century to Fisher's randomized experiments, and remain an immensely popular statistical tool, used for testing hypotheses of independence between variables and other common inferential questions. Much of…
Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…
In the evaluation of treatment effects, it is of major policy interest to know if the treatment is beneficial for some and harmful for others, a phenomenon known as qualitative interaction. We formulate this question as a multiple testing…
We report some properties of heavy-tailed Sibuya-like distributions related to thinning, self-decomposability and branching processes. Extension of the thinning operation of on-negative integer-valued random variables to scaling by…
Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a…
Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order…
An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…
Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric,…
The topic of multiple hypotheses testing now has a potpourri of novel theories and ubiquitous applications in diverse scientific fields. However, the universal utility of this field often hinders the possibility of having a generalized…
Stable distributions are of fundamental importance in probability theory, yet their absolute continuity makes them unsuitable for modeling count data. A discrete analog of strict stability has been previously proposed by replacing scaling…
We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy…
We consider inference on the first principal direction of a $p$-variate elliptical distribution. We do so in challenging double asymptotic scenarios for which this direction eventually fails to be identifiable. In order to achieve…