Related papers: Higher-Order Coverage Errors of Batching Methods v…
This paper studies higher-order inference properties of nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for $t$ statistics and coverage error expansions for interval estimators that (i)…
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…
Besides the well-known effect of autocorrelations in time series of Monte Carlo simulation data resulting from the underlying Markov process, using the same data pool for computing various estimates entails additional cross correlations.…
This paper provides a finite sample bound for the error term in the Edgeworth expansion for a sum of independent, potentially discrete, nonlattice random vectors, using a uniform-in-$P$ version of the weaker Cram\'{e}r condition in Angst…
This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve approach, whereby the dynamics in the process used…
Mixture models are a popular tool in model-based clustering. Such a model is often fitted by a procedure that maximizes the likelihood, such as the EM algorithm. At convergence, the maximum likelihood parameter estimates are typically…
We develop generalized approach to obtaining Edgeworth expansions for $t$-statistics of an arbitrary order using computer algebra and combinatorial algorithms. To incorporate various versions of mean-based statistics, we introduce Adjusted…
Conformal inference, cross-validation+, and the jackknife+ are hold-out methods that can be combined with virtually any machine learning algorithm to construct prediction sets with guaranteed marginal coverage. In this paper, we develop…
Understanding the distributions of spectral estimators in low-rank random matrix models, also known as signal-plus-noise matrix models, is fundamentally important in various statistical learning problems, including network analysis, matrix…
We address the challenge of constructing valid confidence intervals and sets in problems of prediction across multiple environments. We investigate two types of coverage suitable for these problems, extending the jackknife and…
Machine learning models are increasingly used in practice. However, many machine learning methods are sensitive to test or operational data that is dissimilar to training data. Out-of-distribution (OOD) data is known to increase the…
Bias correction can often improve the finite sample performance of estimators. We show that the choice of bias correction method has no effect on the higher-order variance of semiparametrically efficient parametric estimators, so long as…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
Despite of the great efforts during the censuses, occurrence of some nonsampling errors such as coverage error is inevitable. Coverage error which can be classified into two types of under-count and overcount occurs when there is no unique…
We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks. We provide a tight…
This paper studies distribution-free inference in settings where the data set has a hierarchical structure -- for example, groups of observations, or repeated measurements. In such settings, standard notions of exchangeability may not hold.…
We consider batch size selection for a general class of multivariate batch means variance estimators, which are computationally viable for high-dimensional Markov chain Monte Carlo simulations. We derive the asymptotic mean squared error…
We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time…
Resampling techniques have become increasingly popular for estimation of uncertainty in data collected via surveys. Survey data are also frequently subject to missing data which are often imputed. This note addresses the issue of using…
Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the…