arXiv subjects

Kerby Shedden

Publications and source records attributed to Kerby Shedden.

8 recordsLinked to original sources

arXiv2026

On the universal calibration of heavy-tailed combination tests

It is often of interest to test a global null hypothesis using multiple, possibly dependent $p$-values by combining their strengths while controlling the type-I error. Recently, several heavy-tailed combination tests, such as the harmonic mean test and the Cauchy combination test, have been proposed: they transform $p$-values into heavy-tailed random variables before combining them into a single test statistic. The resulting tests, which are calibrated under some form of independence assumption among the $p$-values, have been shown to be rather robust to dependence asymptotically as the $α$ level gets small. Yet, it has remained an open problem to understand this general phenomenon and characterize how such tests behave under dependence. Using the framework of multivariate regular variation from extreme value theory, we show that for a class of combination tests that are homogeneous, the asymptotic level of the test can be expressed using the angular measure under multivariate regular variation. This measure characterizes the dependence of the transformed heavy-tailed variables in their upper tails, or equivalently, the dependence of the $p$-values near zero. We use this result to study several tests. The harmonic mean test, which coincides with the Pareto linear combination test, is shown to be universally calibrated regardless of the tail dependence; further, this test is shown to be the only one that achieves universal calibration among all homogeneous heavy-tailed combination tests. In contrast, the Cauchy combination test is shown to be universally honest but often conservative; the Dunn-Šidák correction, also known as Tippett's method, while being honest, is calibrated if and only if the underlying $p$-values are independent near zero. These theoretical findings are corroborated with simulations and an application to independence testing with survey data.

math.ST↗

arXiv2025

Kronecker sum covariance models for spatio-temporal data

In this paper, we study the subgaussian matrix variate model, where we observe the matrix variate data $X$ which consists of a signal matrix $X_0$ and a noise matrix $W$. More specifically, we study a subgaussian model using the Kronecker sum covariance as in Rudelson and Zhou (2017). Let $Z_1, Z_2$ be independent copies of a subgaussian random matrix $Z =(Z_{ij})$, where $Z_{ij}, \forall i, j$ are independent mean 0, unit variance, subgaussian random variables with bounded $ψ_2$ norm. We use $X \sim \mathcal{M}_{n,m}(0, A \oplus B)$ to denote the subgaussian random matrix $X_{n \times m}$ which is generated using: $$ X = Z_1 A^{1/2} + B^{1/2} Z_2. $$ In this covariance model, the first component $A \otimes I_n$ describes the covariance of the signal $X_0 = Z_1 A^{1/2}$, which is an ${n \times m}$ random design matrix with independent subgaussian row vectors, and the other component $I_m \otimes B$ describes the covariance for the noise matrix $W =B^{1/2} Z_2$, which contains independent subgaussian column vectors $w^1, \ldots, w^m$, independent of $X_0$. This leads to a non-separable class of models for the observation $X$, which we denote by $X \sim \mathcal{M}_{n,m}(0, A \oplus B)$ throughout this paper. Our method on inverse covariance estimation corresponds to the proposal in Yuan (2010) and Loh and Wainwright (2012), only now dropping the i.i.d. or Gaussian assumptions. We present the statistical rates of convergence.

math.ST↗

arXiv2018

Tensor models for linguistics pitch curve data of native speakers of Afrikaans

We use tensor analysis techniques for high-dimensional data to gain insight into pitch curves, which play an important role in linguistics research. In particular, we propose that demeaned phonetics pitch curve data can be modeled as having a Kronecker product inverse covariance structure with sparse factors corresponding to words and time. Using data from a study of native Afrikaans speakers, we show that by targeting conditional independence through a graphical model, we reveal relationships associated with natural properties of words as studied by linguists. We find that words with long vowels cluster based on whether the vowel is pronounced at the front or back of the mouth, and words with short vowels have strong edges associated with the initial consonant.

stat.ME↗

arXiv2018

Joint mean and covariance estimation with unreplicated matrix-variate data

It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated high-dimensional data with unknown mean and dependence structures. Matrix-variate approaches that impose various forms of (inverse) covariance sparsity allow flexible dependence structures to be estimated, but cannot directly be applied when the mean and covariance matrices are estimated jointly. We present a practical method utilizing generalized least squares and penalized (inverse) covariance estimation to address this challenge. We establish consistency and obtain rates of convergence for estimating the mean parameters and covariance matrices. The advantages of our approaches are: (i) dependence graphs and covariance structures can be estimated in the presence of unknown mean structure, (ii) the mean structure becomes more efficiently estimated when accounting for the dependence structure among observations; and (iii) inferences about the mean parameters become correctly calibrated. We use simulation studies and analysis of genomic data from a twin study of ulcerative colitis to illustrate the statistical convergence and the performance of our methods in practical settings. Several lines of evidence show that the test statistics for differential gene expression produced by our methods are correctly calibrated and improve power over conventional methods.

stat.ML↗

arXiv2017

Non-separable covariance models for spatio-temporal data, with applications to neural encoding analysis

Neural encoding studies explore the relationships between measurements of neural activity and measurements of a behavior that is viewed as a response to that activity. The coupling between neural and behavioral measurements is typically imperfect and difficult to measure.To enhance our ability to understand neural encoding relationships, we propose that a behavioral measurement may be decomposable as a sum of two latent components, such that the direct neural influence and prediction is primarily localized to the component which encodes temporal dependence. For this purpose, we propose to use a non-separable Kronecker sum covariance model to characterize the behavioral data as the sum of terms with exclusively trial-wise, and exclusively temporal dependencies. We then utilize a corrected form of Lasso regression in combination with the nodewise regression approach for estimating the conditional independence relationships between and among variables for each component of the behavioral data, where normality is necessarily assumed. We provide the rate of convergence for estimating the precision matrices associated with the temporal as well as spatial components in the Kronecker sum model. We illustrate our methods and theory using simulated data, and data from a neural encoding study of hawkmoth flight; we demonstrate that the neural encoding signal for hawkmoth wing strokes is primarily localized to a latent component with temporal dependence, which is partially obscured by a second component with trial-wise dependencies.

stat.ME↗

arXiv2017

Optimal group testing designs for estimating prevalence with uncertain testing errors

We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that the most efficient design for simultaneously estimating the prevalence, sensitivity and specificity requires three different group sizes with equal frequencies. However, if estimating prevalence as accurately as possible is the only focus, the optimal strategy is to have three group sizes with unequal frequencies. On the basis of a chlamydia study in the U.S.A., we compare performances of competing designs and provide insights into how the unknown sensitivity and specificity of the test affect the performance of the prevalence estimator. We demonstrate that the locally D- and Ds-optimal designs proposed have high efficiencies even when the prespecified values of the parameters are moderately misspecified.

math.ST↗

arXiv2012

An imputation method for estimating the learning curve in classification problems

The learning curve expresses the error rate of a predictive modeling procedure as a function of the sample size of the training dataset. It typically is a decreasing, convex function with a positive limiting value. An estimate of the learning curve can be used to assess whether a modeling procedure should be expected to become substantially more accurate if additional training data become available. This article proposes a new procedure for estimating learning curves using imputation. We focus on classification, although the idea is applicable to other predictive modeling settings. Simulation studies indicate that the learning curve can be estimated with useful accuracy for a roughly four-fold increase in the size of the training set relative to the available data, and that the proposed imputation approach outperforms an alternative estimation approach based on parameterizing the learning curve. We illustrate the method with an application that predicts the risk of disease progression for people with chronic lymphocytic leukemia.

stat.AP↗

arXiv2007

Large-scale structure of time evolving citation networks

In this paper we examine a number of methods for probing and understanding the large-scale structure of networks that evolve over time. We focus in particular on citation networks, networks of references between documents such as papers, patents, or court cases. We describe three different methods of analysis, one based on an expectation-maximization algorithm, one based on modularity optimization, and one based on eigenvector centrality. Using the network of citations between opinions of the United States Supreme Court as an example, we demonstrate how each of these methods can reveal significant structural divisions in the network, and how, ultimately, the combination of all three can help us develop a coherent overall picture of the network's shape.

physics.soc-ph↗