Related papers: High-dimensional MANOVA via Bootstrapping and its …
We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anisotropic smoothness properties of the target function from…
We consider the performance of the bootstrap in high-dimensions for the setting of linear regression, where $p<n$ but $p/n$ is not close to zero. We consider ordinary least-squares as well as robust regression methods and adopt a minimalist…
Recent advances in molecular simulations allow the evaluation of previously unattainable observables, such as rate constants for protein folding. However, these calculations are usually computationally expensive and even significant…
We propose a methodology for constructing confidence regions with partially identified models of general form. The region is obtained by inverting a test of internal consistency of the econometric structure. We develop a dilation bootstrap…
In this paper we address the problem of performing statistical inference for large scale data sets i.e., Big Data. The volume and dimensionality of the data may be so high that it cannot be processed or stored in a single computing node. We…
In high-dimensional time series, the component processes are often assembled into a matrix to display their interrelationship. We focus on detecting mean shifts with unknown change point locations in these matrix time series. Series that…
In statistics, forecast uncertainty is often quantified using a specified statistical model, though such approaches may be vulnerable to model misspecification, selection bias, and limited finite-sample validity. While bootstrapping can…
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…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
We consider testing for two-sample means of high dimensional populations by thresholding. Two tests are investigated, which are designed for better power performance when the two population mean vectors differ only in sparsely populated…
The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets…
Many modern estimators require bootstrapping to calculate confidence intervals because either no analytic standard error is available or the distribution of the parameter of interest is non-symmetric. It remains however unclear how to…
Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a…
In this paper we study the applicability of the bootstrap to do inference on Manski's maximum score estimator under the full generality of the model. We propose three new, model-based bootstrap procedures for this problem and show their…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
Estimating the mixing density of a latent mixture model is an important task in signal processing. Nonparametric maximum likelihood estimation is one popular approach to this problem. If the latent variable distribution is assumed to be…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…
This paper introduces new scan statistics for multivariate functional data indexed in space. The new methods are derivated from a MANOVA test statistic for functional data, an adaptation of the Hotelling T2-test statistic, and a…
Multivariate analysis-of-variance (MANOVA) is a well established tool to examine multivariate endpoints. While classical approaches depend on restrictive assumptions like normality and homogeneity, there is a recent trend to more general…
In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…