Related papers: Minimum sample size for detection of Gutenberg-Ric…
The Minimum Covariance Determinant (MCD) method is a highly robust estimator of multivariate location and scatter, for which a fast algorithm is available. Since estimating the covariance matrix is the cornerstone of many multivariate…
Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…
In this paper we compare the minimums of two independent and heterogeneous samples each following Kumaraswamy-G distribution with the same and the different parent distribution functions. The comparisons are carried out with respect to…
Gibbs sampling methods are standard tools to perform posterior inference for mixture models. These have been broadly classified into two categories: marginal and conditional methods. While conditional samplers are more widely applicable…
We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several…
Estimating Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor distances between these samples.…
In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as beta-exponential and generalized Gompertz…
The robust rank-order test (Fligner and Policello, 1981) was designed as an improvement of the non-parametric Wilcoxon-Mann-Whitney U-test to be more appropriate when the samples being compared have unequal variance. However, it tends to be…
We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…
We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…
We develop a theoretical framework for studying numerical estimation of lower previsions, generally applicable to two-level Monte Carlo methods, importance sampling methods, and a wide range of other sampling methods one might devise. We…
Monte Carlo methods are used to approximate the means, $\mu$, of random variables $Y$, whose distributions are not known explicitly. The key idea is that the average of a random sample, $Y_1, ..., Y_n$, tends to $\mu$ as $n$ tends to…
In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC)…
Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference. In each…
The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…
Using a microfluidics device filled with a colloidal suspension of microspheres, we test the laws of diffusion in the limit of small particle numbers. Our focus is not just on average properties such as the mean flux, but rather on the…
Maximum Mean Discrepancy (MMD) is a widely used concept in machine learning research which has gained popularity in recent years as a highly effective tool for comparing (finite-dimensional) distributions. Since it is designed as a…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more…
The commonly cited rule of thumb for regression analysis, which suggests that a sample size of $n \geq 30$ is sufficient to ensure valid inferences, is frequently referenced but rarely scrutinized. This research note evaluates the lower…