Related papers: The bootstrap, covariance matrices and PCA in mode…

Recently, novel numerical computation on quantum mechanics by using a bootstrap method was proposed by Han, Hartnoll, and Kruthoff. We consider whether this method works in systems with a $\theta$-term, where the standard Monte-Carlo…

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…

Although much progress has been made in the theory and application of bootstrap approximations for max statistics in high dimensions, the literature has largely been restricted to cases involving light-tailed data. To address this issue, we…

We study the rate of convergence of the Mallows distance between the empirical distribution of a sample and the underlying population. The surprising feature of our results is that the convergence rate is slower in the discrete case than in…

We describe the volume dependence of matrix elements of local fields to all orders in inverse powers of the volume (i.e. only neglecting contributions that decay exponentially with volume). Using the scaling Lee-Yang model and the Ising…

For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…

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…

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…

We establish the asymptotic validity of the bootstrap-based IVX estimator proposed by Phillips and Magdalinos (2009) for the predictive regression model parameter based on a local-to-unity specification of the autoregressive coefficient…

Fitting sparse models to high-dimensional time series is an important area of statistical inference. In this paper we consider sparse vector autoregressive models and develop appropriate bootstrap methods to infer properties of such…

Kronecker product covariance structure provides an efficient way to modeling the inter-correlations of matrix-variate data. In this paper, we propose testing statistics for Kronecker product covariance matrix based on linear spectral…

Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…

In many life science experiments or medical studies, subjects are repeatedly observed and measurements are collected in factorial designs with multivariate data. The analysis of such multivariate data is typically based on multivariate…

This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…

We derive a risk lower bound in estimating the threshold parameter without knowing whether the threshold regression model is continuous or not. The bound goes to zero as the sample size $ n $ grows only at the cube root rate. Motivated by…

We derive the distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable $i=1,...,p$ is modelled as a linear process…

Monitoring machine learning models once they are deployed is challenging. It is even more challenging to decide when to retrain models in real-case scenarios when labeled data is beyond reach, and monitoring performance metrics becomes…

Astroparticle experiments such as IceCube or MAGIC require a deconvolution of their measured data with respect to the response function of the detector to provide the distributions of interest, e.g. energy spectra. In this paper,…

Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…

Assessing sampling uncertainty in extremum estimation can be challenging when the asymptotic variance is not analytically tractable. Bootstrap inference offers a feasible solution but can be computationally costly especially when the model…