Nonparametric goodness-of-fit testing for a continuous multivariate parametric model

Article Computer Science, Interdisciplinary Applications

A general Monte Carlo method for multivariate goodness-of-fit testing applied to elliptical families

Feifei Chen et al.

Summary: A general and relatively simple method for constructing multivariate goodness-of-fit tests is presented in this paper, with a focus on elliptical distributions. The method is based on characterizing probability distributions through their characteristic function. The consistency and other limit properties of the new test statistics are investigated. Additionally, a simulation study is conducted to compare the proposed tests with previous and more recent competitors.

COMPUTATIONAL STATISTICS & DATA ANALYSIS (2022)

Add to Collection

Article Statistics & Probability

Multivariate goodness-of-fit tests based on Wasserstein distance

Marc Hallin et al.

Summary: This study proposes goodness-of-fit tests based on empirical Wasserstein distance for simple and composite null hypotheses involving general multivariate distributions. The method is implemented for group families after preliminary data reduction through invariance, allowing for calculation of exact critical values and p-values at finite sample sizes. The proposed tests demonstrate practical feasibility and excellent performance for Wasserstein distance of order p = 1 and p = 2, and for dimensions up to d = 5, with simulations supporting the conjecture of asymptotic validity of the parametric bootstrap.

ELECTRONIC JOURNAL OF STATISTICS (2021)

Add to Collection

Article Statistics & Probability