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Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
We present a novel method for image anomaly detection, where algorithms that use samples drawn from some distribution of "normal" data, aim to detect out-of-distribution (abnormal) samples. Our approach includes a combination of encoder and…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
New estimators for the mean and the covariance function for partially observed functional data are proposed using a detour via the fundamental theorem of calculus. The new estimators allow for a consistent estimation of the mean and…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…
Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
Existing domain adaptation methods aim to reduce the distributional difference between the source and target domains and respect their specific discriminative information, by establishing the Maximum Mean Discrepancy (MMD) and the…
Meta-analyses are regarded as the highest level in the hierarchy of evidence, yet standard models traditionally concentrated on estimating the mean effect size, often under restrictive assumptions about the underlying distribution, such as…
The aim of atypicality is to extract small, rare, unusual and interesting pieces out of big data. This complements statistics about typical data to give insight into data. In order to find such "interesting" parts of data, universal…
Functional data analysis has been a growing field of study in recent decades, and one fundamental task in functional data analysis is estimating the sample location. A notion called statistical depth has been extended from multivariate data…
Simulation studies are commonly used to evaluate the performance of newly developed meta-analysis methods. For methodology that is developed for an aggregated data meta-analysis, researchers often resort to simulation of the aggregated data…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
Compound Poisson distributions have been employed by many authors to fit experimental data, typically via the method of moments or maximum likelihood estimation. We propose a new technique and apply it to several sets of published data. It…