Related papers: Smoothed and Iterated Bootstrap Confidence Regions…
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…
In this paper we consider the problem of minimizing a general quadratic function over the mixed integer points in an ellipsoid. This problem is strongly NP-hard, NP-hard to approximate within a constant factor, and optimal solutions can be…
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 investigate the performance of model based bootstrap methods for constructing point-wise confidence intervals around the survival function with interval censored data. We show that bootstrapping from the nonparametric maximum likelihood…
Eigenspaces of covariance matrices play an important role in statistical machine learning, arising in variety of modern algorithms. Quantitatively, it is convenient to describe the eigenspaces in terms of spectral projectors. This work…
We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our approach can be used to quantify uncertainty in realizations of stochastic processes…
A key tool to carry out inference on the unknown copula when modeling a continuous multivariate distribution is a nonparametric estimator known as the empirical copula. One popular way of approximating its sampling distribution consists of…
Conformal prediction is a statistical tool for producing prediction regions for machine learning models that are valid with high probability. A key component of conformal prediction algorithms is a \emph{non-conformity score function} that…
Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data…
This paper considers edge interval estimation between two regions of a Synthetic Aperture Radar (SAR) image which differ in texture. This is a difficult task because SAR images are contaminated with speckle noise. Different point estimation…
In order to test if an unknown matrix has a given rank (null hypothesis), we consider the family of statistics that are minimum squared distances between an estimator and the manifold of fixed-rank matrix. Under the null hypothesis, every…
In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…
Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…
Reconstruction of sets from a random sample of points intimately related to them is the goal of set estimation theory. Within this context, a particular problem is the one related with the reconstruction of density level sets and…
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 the validity of bootstrap methods for empirical likelihood (EL) inference under the density ratio model (DRM). In particular, we prove that the bootstrap maximum EL estimators share the same limiting distribution as their…
Randomized smoothing has been shown to provide good certified-robustness guarantees for high-dimensional classification problems. It uses the probabilities of predicting the top two most-likely classes around an input point under a…
Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance…
We advance the theory of parametric bootstrap in constructing highly efficient empirical best (EB) prediction intervals of small area means. The coverage error of such a prediction interval is of the order $O(m^{-3/2})$, where $m$ is the…
Nonparametric regression and regression-discontinuity designs suffer from smoothing bias that distorts conventional confidence intervals. Solutions based on robust bias correction (RBC) are now central to the economist's toolbox. In this…