Related papers: Bootstrap confidence sets for spectral projectors …
Approximately unbiased tests based on bootstrap probabilities are considered for the exponential family of distributions with unknown expectation parameter vector, where the null hypothesis is represented as an arbitrary-shaped region with…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample…
Traditional inference in cointegrating regressions requires tuning parameter choices to estimate a long-run variance parameter. Even in case these choices are "optimal", the tests are severely size distorted. We propose a novel…
In this paper we consider the construction of simultaneous confidence bands for the spectral density of a stationary time series using a Gaussian approximation for classical lag-window spectral density estimators evaluated at the set of all…
This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure…
We derive nonparametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a…
For an ergodic Brownian diffusion with invariant measure $\nu$, we consider a sequence of empirical distributions ($\nu$n) n$\ge$1 associated with an approximation scheme with decreasing time step ($\gamma$n) n$\ge$1 along an adapted…
We present a new fitting technique based on the parametric bootstrap method, which relies on the idea to produce artificial measurements using the estimated probability distribution of the experimental data. In order to investigate the main…
Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from…
Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a…
This paper establishes consistency of the weighted bootstrap for quadratic forms $\left( n^{-1/2} \sum_{i=1}^{n} Z_{i,n} \right)^{T}\left( n^{-1/2} \sum_{i=1}^{n} Z_{i,n} \right)$ where $(Z_{i,n})_{i=1}^{n}$ are mean zero, independent…
This paper studies the Gaussian and bootstrap approximations for the probabilities of a non-degenerate U-statistic belonging to the hyperrectangles in $\mathbb{R}^d$ when the dimension $d$ is large. A two-step Gaussian approximation…
The present contribution investigates multivariate bootstrap procedures for general stabilizing statistics, with specific application to topological data analysis. Existing limit theorems for topological statistics prove difficult to use in…
In this paper we propose a new test of heteroscedasticity for parametric regression models and partial linear regression models in high dimensional settings. When the dimension of covariates is large, existing tests of heteroscedasticity…
This article explores combinations of weighted bootstraps, like the Bayesian bootstrap, with the bootstrap $t$ method for setting approximate confidence intervals for the mean of a random variable in small samples. For this problem the…
Classical Krylov subspace projection methods for the solution of linear problem $Ax = b$ output an approximate solution $\widetilde{x}\simeq x$. Recently, it has been recognized that projection methods can be understood from a statistical…
An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold…
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…
We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors. We establish higher-order approximation bounds with error terms depending on a sample size and a…