Related papers: A Robust Test for Elliptical Symmetry
Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are…
The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of…
We propose new goodness-of-fit tests for the Poisson distribution. The testing procedure entails fitting a weighted Poisson distribution, which has the Poisson as a special case, to observed data. Based on sample data, we calculate an…
This article deals with goodness-of-fit test for the Cauchy distribution. Some tests based on Kullback-Leibler information are proposed, and shown to be consistent. Monte Carlo evidence indicates that the tests have satisfactory…
We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional…
We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\tilde O(\sqrt{n}\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability…
Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. For group families, the procedure is to be implemented after preliminary…
Goodness-of-Fit tests, including Smooth ones, are introduced and applied to detect non-Gaussianity in Cosmic Microwave Background simulations. We study the power of three different tests: the Shapiro-Francia test (1972), the uncategorised…
We consider marked empirical processes indexed by a randomly projected functional covariate to construct goodness-of-fit tests for the functional linear model with scalar response. The test statistics are built from continuous functionals…
Gaussian Graphical Models (GGMs) are widely used to infer conditional dependence structures in high-dimensional data. However, standard precision matrix estimators are highly sensitive to data contamination, such as extreme outliers and…
In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source…
Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…
This study develops a framework for testing hypotheses on structural parameters in incomplete models. Such models make set-valued predictions and hence do not generally yield a unique likelihood function. The model structure, however,…
This paper provides parametric and rank-based optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and…
This paper derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a…
Reliable inference for spatial regression remains challenging because it requires the correct specification of the spatial dependence structure, the mean trend, and the error distribution. Existing parametric testing methods rely on…
State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which…
Nowadays, data analysis in the world of Big Data is connected typically to data mining, descriptive or exploratory statistics, e.~g.\ cluster analysis, classification or regression analysis. Aside these techniques there is a huge area of…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
Adaptivity is an important feature of data analysis---the choice of questions to ask about a dataset often depends on previous interactions with the same dataset. However, statistical validity is typically studied in a nonadaptive model,…