Related papers: Can we trust the bootstrap in high-dimension?
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
There are some papers which describe the use of bootstrap techniques in point process statistics. The aim of the present paper is to show that the form in which bootstrap is used there is dubious. In case of variance estimation of pair…
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…
The bootstrap variance estimate is widely used in semiparametric inferences. However, its theoretical validity is a well known open problem. In this paper, we provide a {\em first} theoretical study on the bootstrap moment estimates in…
Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions,…
We consider the problem of finding confidence intervals for the risk of forecasting the future of a stationary, ergodic stochastic process, using a model estimated from the past of the process. We show that a bootstrap procedure provides…
The existing theory of penalized quantile regression for longitudinal data has focused primarily on point estimation. In this work, we investigate statistical inference. We propose a wild residual bootstrap procedure and show that it is…
Artificial neural networks (ANNs) are popular tools for accomplishing many machine learning tasks, including predicting continuous outcomes. However, the general lack of confidence measures provided with ANN predictions limit their…
Challenges with data in the big-data era include (i) the dimension $p$ is often larger than the sample size $n$ (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional…
This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
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…
Obtaining accurate estimates of machine learning model uncertainties on newly predicted data is essential for understanding the accuracy of the model and whether its predictions can be trusted. A common approach to such uncertainty…
Residual bootstrap is a classical method for statistical inference in regression settings. With massive data sets becoming increasingly common, there is a demand for computationally efficient alternatives to residual bootstrap. We propose a…
In recent years there has been significant progress in algorithms and methods for inducing Bayesian networks from data. However, in complex data analysis problems, we need to go beyond being satisfied with inducing networks with high…
In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…
Resampling methods are especially well-suited to inference with estimators that provide only "black-box'' access. Jackknife is a form of resampling, widely used for bias correction and variance estimation, that is well-understood under…
Cross validation (CV) and the bootstrap are ubiquitous model-agnostic tools for assessing the error or variability of machine learning and statistical estimators. However, these methods require repeatedly re-fitting the model with different…
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…
Out-of-bag error is commonly used as an estimate of generalisation error in ensemble-based learning models such as random forests. We present confidence intervals for this quantity using the delta-method-after-bootstrap and the…