Related papers: A Robust Test for Elliptical Symmetry
Generalized linear models (GLMs) are used within a vast number of application domains. However, formal goodness of fit (GOF) tests for the overall fit of the model$-$so-called "global" tests$-$seem to be in wide use only for certain classes…
In this paper we consider Tyler's robust covariance M-estimator under group symmetry constraints. We assume that the covariance matrix is invariant to the conjugation action of a unitary matrix group, referred to as group symmetry. Examples…
Assessing model adequacy is a crucial step in regression analysis, ensuring the validity of statistical inferences. For Generalized Functional Linear Models (GFLMs), which are widely used for modeling relationships between scalar responses…
We propose a family of tests to assess the goodness-of-fit of a high-dimensional generalized linear model. Our framework is flexible and may be used to construct an omnibus test or directed against testing specific non-linearities and…
High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets…
This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…
This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the…
We consider the error distribution in functional linear models with scalar response and functional covariate. Different asymptotic expansions of the empirical distribution function and the empirical characteristic function based on…
In population genetics and other application fields, models with intractable likelihood are common. Approximate Bayesian Computation (ABC) or more generally Simulation-Based Inference (SBI) methods work by simulating instrumental data sets…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard…
Linear and Quadratic Discriminant Analysis are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not robust. To…
Consider a pair of cumulative distribution functions $F$ and $G$, where $F$ is unknown and $G$ is a known reference distribution. Given a sample from $F$, we propose tests to detect the convexity or the concavity of $G^{-1}\circ F$ versus…
Health data are often not symmetric to be adequately modeled through the usual normal distributions; most of them exhibit skewed patterns. They can indeed be modeled better through the larger family of skew-normal distributions covering…
Assessing goodness of fit to a given distribution plays an important role in computational statistics. The Probability integral transformation (PIT) can be used to convert the question of whether a given sample originates from a reference…
We propose a general and relatively simple method for the construction of goodness-of-fit tests on the sphere and the hypersphere. The method is based on the characterization of probability distributions via their characteristic function,…
Data depth provides a centre-outward ordering for multivariate data. Recently, some univariate GoF tests based on data depth have been studied by Li (2018). This paper discusses some univariate goodness of fit tests based on centre-outward…
While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy -- coming from robust statistics and optimization -- is thus…