Related papers: Saddlepoint approximations for likelihood ratio li…
Although much progress has been made in the theory and application of bootstrap approximations for max statistics in high dimensions, the literature has largely been restricted to cases involving light-tailed data. To address this issue, we…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
Policy evaluation is a crucial step in many reinforcement-learning procedures, which estimates a value function that predicts states' long-term value under a given policy. In this paper, we focus on policy evaluation with linear function…
The increasing volume of data streams poses significant computational challenges for detecting changepoints online. Likelihood-based methods are effective, but a naive sequential implementation becomes impractical online due to high…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
We give a general framework for approximations to combinatorial assemblies, especially suitable to the situation where the number $k$ of components is specified, in addition to the overall size $n$. This involves a Poisson process, which,…
Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…
The likelihood ratio is a crucial quantity for statistical inference in science that enables hypothesis testing, construction of confidence intervals, reweighting of distributions, and more. Many modern scientific applications, however,…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
Probabilistic generative models provide a powerful framework for representing data that avoids the expense of manual annotation typically needed by discriminative approaches. Model selection in this generative setting can be challenging,…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
In recent years, bootstrap methods have drawn attention for their ability to approximate the laws of "max statistics" in high-dimensional problems. A leading example of such a statistic is the coordinate-wise maximum of a sample average of…
We show a statistical version of Taylor's theorem and apply this result to non-parametric density estimation from truncated samples, which is a classical challenge in Statistics \cite{woodroofe1985estimating, stute1993almost}. The…
The Lugannani-Rice formula is a saddlepoint approximation method for estimating the tail probability distribution function, which was originally studied for the sum of independent identically distributed random variables. Because of its…
A variety of statistics based on sample spacings has been studied in the literature for testing goodness-of-fit to parametric distributions. To test the goodness-of-fit to a nonparametric class of univariate shape-constrained densities,…
Wilk's theorem, which offers universal chi-squared approximations for likelihood ratio tests, is widely used in many scientific hypothesis testing problems. For modern datasets with increasing dimension, researchers have found that the…
Various problems in Engineering and Statistics require the computation of the likelihood ratio function of two probability densities. In classical approaches the two densities are assumed known or to belong to some known parametric family.…
This paper presents a new approach to conditional inference, based on the simulation of samples conditioned by a statistics of the data. Also an explicit expression for the approximation of the conditional likelihood of long runs of the…