Related papers: Block bootstrap optimality for density estimation …
We consider bandwidth matrix selection for kernel density estimators (KDEs) of density level sets in $\mathbb{R}^d$, $d \ge 2$. We also consider estimation of highest density regions, which differs from estimating level sets in that one…
The goal of this paper is to study the bootstrap for the Grenander estimator. The first result is a proof of the inconsistency of the nonparametric bootstrap for the Grenander estimator at a given point. The second result is the development…
This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
The purpose of this note is to provide an approximation for the generalized bootstrapped empirical process achieving the rate in Kolmos et al. (1975). The proof is based on much the same arguments as in Horvath et al. (2000). As a…
Deciding what to sense is a crucial task, made harder by dependencies and by a nonadditive utility function. We develop approximation algorithms for selecting an optimal set of measurements, under a dependency structure modeled by a…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
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…
Multivariate kernel density estimations have received much spate of interest. In addition to conventional methods of (non-)classical associated-kernels for (un)bounded densities and bandwidth selections, the multiple extended-beta kernel…
In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…
Microbial ecology serves as a foundation for a wide range of scientific and biomedical studies. Rapidly-evolving high-throughput sequencing technology enables the comprehensive search for microbial biomarkers using longitudinal experiments.…
Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose…
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…
This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…
Bootstrap smoothed (bagged) estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. Efron, 2014, derived a widely applicable formula for a delta method approximation to the standard…
We propose a distributed bootstrap method for simultaneous inference on high-dimensional massive data that are stored and processed with many machines. The method produces an $\ell_\infty$-norm confidence region based on a…
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…
This paper deals with uncertainty quantification and out-of-distribution detection in deep learning using Bayesian and ensemble methods. It proposes a practical solution to the lack of prediction diversity observed recently for standard…
This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…
This paper presents approximate confidence intervals for each function of parameters in a Banach space based on a bootstrap algorithm. We apply kernel density approach to estimate the persistence landscape. In addition, we evaluate the…