Related papers: High-Dimensional Invariant Tests of Multivariate N…
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
We consider high-dimensional generalized linear models when the covariates are contaminated by measurement error. Estimates from errors-in-variables regression models are well-known to be biased in traditional low-dimensional settings if…
Diagnostic accuracy studies assess sensitivity and specificity of a new index test in relation to an established comparator or the reference standard. The development and selection of the index test is usually assumed to be conducted prior…
There is an increasing interest in algorithms to learn invariant correlations across training environments. A big share of the current proposals find theoretical support in the causality literature but, how useful are they in practice? The…
For the mean vector test in high dimension, Ayyala et al.(2017,153:136-155) proposed new test statistics when the observational vectors are M dependent. Under certain conditions, the test statistics for one-same and two-sample cases were…
Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…
We develop a multiscale scanning method to find anomalies in a $d$-dimensional random field in the presence of nuisance parameters. This covers the common situation that either the baseline-level or additional parameters such as the…
In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…
We study the fundamental problem of estimating the mean of a $d$-dimensional distribution with covariance $\Sigma \preccurlyeq \sigma^2 I_d$ given $n$ samples. When $d = 1$, \cite{catoni} showed an estimator with error $(1+o(1)) \cdot…
In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source…
Over the last decade, an approach that has gained a lot of popularity to tackle nonparametric testing problems on general (i.e., non-Euclidean) domains is based on the notion of reproducing kernel Hilbert space (RKHS) embedding of…
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…
We propose a method to ease the challenges of exploring multi-dimensional parameter spaces in beyond-the-Standard Model theories. We evaluate the model likelihood for any choice of parameters by sampling the theory parameters intelligently…
Consider $d$ dependent change point tests, each based on a CUSUM-statistic. We provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both the sample size $n$ and $d$ tend to infinity. We achieve…
Recent technological advances in many domains including both genomics and brain imaging have led to an abundance of high-dimensional and correlated data being routinely collected. Classical multivariate approaches like Multivariate Analysis…
The purpose of this note is to point out that the theory of expander graphs leads to an interesting test whether $n$ real numbers $x_1, \dots, x_n$ could be $n$ independent samples of a random variable. To any distinct, real numbers $x_1,…
Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d.\ test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such…
Next-generation sequencing technologies now constitute a method of choice to measure gene expression. Data to analyze are read counts, commonly modeled using Negative Binomial distributions. A relevant issue associated with this…
Even though the Rao's score tests are classical tests, such as the likelihood ratio tests, their application has been avoided until now in a multivariate framework, in particular high-dimensional setting. We consider they could play an…