Related papers: Improving approximation error bounds via truncatio…
The analysis of a truncated sample can be hindered by censoring. Survival information may be lost to follow-up or the birthdate may be missing. The data can still be modeled as a truncated point process and it is close to a Poisson process,…
Poisson approximation using Stein's method has been extensively studied in the literature. The main focus has been on bounding the total variation distance. This paper is a first attempt on moderate deviations in Poisson approximation for…
The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed…
A finite-support constraint on the parameter space is used to derive a lower bound on the error of an estimator of the correlation coefficient in the bivariate exponential distribution. The bound is then exploited to examine optimality of…
In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of $n$ independent random variables under moment conditions. We use Stein's method to derive the approximation results in total variation…
Recently, we constructed a class of nonlocal Poisson model on manifold under Dirichlet boundary with global $\mathcal{O}(\delta^2)$ truncation error to its local counterpart, where $\delta$ denotes the nonlocal horizon parameter. In this…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression under L^\infty constraints on the linear combination. When the input distribution is known, there already exists…
We give lower bounds on the case of worst inhomogeneous approximation.
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn…
New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an…
We characterize the fundamental limits of high-dimensional mean testing under arbitrary truncation, where samples are drawn from the conditional distribution $P(\cdot \mid S)$ for an unknown truncation set $S$ that may hide up to an…
We present a process-level Poisson-approximation result for the degree-k vertices in a high-density weighted random connection model with preferential-attachment kernel in the unit volume. Our main focus lies on the impact of the left tails…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
We introduce a bottleneck method for learning data representations based on information deficiency, rather than the more traditional information sufficiency. A variational upper bound allows us to implement this method efficiently. The…
A number of authors have described randomized algorithms for solving the epsilon-approximate nearest neighbor problem. In this note I point out that the epsilon-approximate nearest neighbor property often fails to be a useful approximation…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
It is proved that the sum of n independent but non-identically distributed doubly truncated Normal distributions converges in distribution to a Normal distribution. It is also shown how the result can be applied in estimating a constrained…
In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed…