Related papers: Multivariate Confidence Intervals
We show how clustering standard errors in one or more dimensions can be justified in M-estimation when there is sampling or assignment uncertainty. Since existing procedures for variance estimation are either conservative or invalid, we…
Robert Machol's surprising result, that from a single observation it is possible to have finite length confidence intervals for the parameters of location-scale models, is re-produced and extended. Two previously unpublished modifications…
Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are…
We develop a general framework for conducting inference on the mean of dependent random variables given constraints on their dependency graph. We establish the consistency of an oracle variance estimator of the mean when the dependency…
Models are consistently treated as approximations and all procedures are consistent with this. They do not treat the model as being true. In this context $p$-values are one measure of approximation, a small $p$-value indicating a poor…
Meta-analysis can be formulated as combining $p$-values across studies into a joint $p$-value function, from which point estimates and confidence intervals can be derived. We extend the meta-analytic estimation framework based on combined…
Reliability is probability of success in a success-failure experiment. Confidence in reliability estimate improves with increasing number of samples. Assurance sets confidence level same as reliability to create one number for easier…
Consider a linear regression model with n-dimensional response vector, p-dimensional regression parameter beta and independent normally distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified…
In recent years, addressing the challenges posed by massive datasets has led researchers to explore aggregated data, particularly leveraging interval-valued data, akin to traditional symbolic data analysis. While much recent research, with…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good…
Matching algorithms are commonly used to predict matches between items in a collection. For example, in 1:1 face verification, a matching algorithm predicts whether two face images depict the same person. Accurately assessing the…
This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
Defining a distance in a mixed setting requires the quantification of observed differences of variables of different types and of variables that are measured on different scales. There exist several proposals for mixed variable distances,…
Consider a two-by-two factorial experiment with more than 1 replicate. Suppose that we have uncertain prior information that the two-factor interaction is zero. We describe new simultaneous frequentist confidence intervals for the 4…
We study exact confidence intervals and two-sided hypothesis tests for univariate parameters of stochastically increasing discrete distributions, such as the binomial and Poisson distributions. It is shown that several popular methods for…
The problem of individualized prediction can be addressed using variants of conformal prediction, obtaining the intervals to which the actual values of the variables of interest belong. Here we present a method based on detecting the…
Modern statistics provides an ever-expanding toolkit for estimating unknown parameters. Consequently, applied statisticians frequently face a difficult decision: retain a parameter estimate from a familiar method or replace it with an…
Factor analysis (FA) and principal component analysis (PCA) are popular statistical methods for summarizing and explaining the variability in multivariate datasets. By default, FA and PCA assume the number of components or factors to be…