Related papers: Universal Bootstrap for Spectral Statistics: Beyon…

Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is…

Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…

Distribution forecast can quantify forecast uncertainty and provide various forecast scenarios with their corresponding estimated probabilities. Accurate distribution forecast is crucial for planning - for example when making production…

This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…

We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

The problem of comparing the entire second order structure of two functional processes is considered and a $L^2$-type statistic for testing equality of the corresponding spectral density operators is investigated. The test statistic…

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…

We propose a residual and wild bootstrap methodology for individual and simultaneous inference in high-dimensional linear models with possibly non-Gaussian and heteroscedastic errors. We establish asymptotic consistency for simultaneous…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

We propose a double bootstrap procedure for reducing coverage error in the confidence intervals of descriptive statistics for independent and identically distributed functional data. Through a series of Monte Carlo simulations, we compare…

We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…

Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…

We study simultaneous inference for multiple matrix-variate Gaussian graphical models in high-dimensional settings. Such models arise when spatiotemporal data are collected across multiple sample groups or experimental sessions, where each…

The bootstrap is a popular method of constructing confidence intervals due to its ease of use and broad applicability. Theoretical properties of bootstrap procedures have been established in a variety of settings. However, there is limited…

Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…

We consider the first serial correlation coefficient under an AR(1) model where errors are not assumed to be Gaussian. In this case it is necessary to consider bootstrap approximations for tests based on the statistic since the distribution…

We introduce the notion of Bartlett spectral measure for isometrically invariant random measures on proper metric commutative spaces. When the underlying Gelfand pair corresponds to a higher-rank, connected, simple matrix Lie group with…