arXiv subjects

M. Dolores Jiménez-Gamero

Publications and source records attributed to M. Dolores Jiménez-Gamero.

3 recordsLinked to original sources

arXiv2026

Testing the equality of parameters in fixed and increasing dimension

This paper proposes a general and unified framework for testing the equality of a broad class of parameters, defined as a smooth function of expectations of symmetric kernels, across multiple independent populations. We consider two test statistics, a Wald-type statistic and an ANOVA-type statistic. The asymptotic distribution of the first one is derived under a fixed-dimension regime, whereas the second one is studied under both fixed and increasing-dimension regimes, where the parameter dimension diverges with the sample size. Based on these limiting distributions, we construct test procedures enabling asymptotically exact inference without parametric assumptions. Additionally, an alternative null distribution estimator based on a weighted bootstrap approximation is studied, which is applicable to the ANOVA-type statistic under a fixed-dimension regime. The finite-sample performance and computational efficiency of the proposed procedures are evaluated through an extensive simulation study and a real dataset application.

stat.ME↗

arXiv2026

Logarithmic energy distances and Gini covariance for Hilbert-valued random elements

For $α\in(0,2)$, the generalized energy distance and the Gini covariance statistic are based on kernels of the form $(x,y)\mapsto \|x-y\|^α$, where $\|\cdot\|$ denotes the norm in a real separable Hilbert space. This paper investigates the boundary regime $α\downarrow 0$. After suitable normalization, the corresponding energy distance converges to a logarithmic energy distance involving the kernel $(x,y)\mapsto\log\|x-y\|$. We establish that the resulting logarithmic energy distance retains the fundamental characterization property of ordinary energy distances in separable Hilbert spaces and derive a representation in terms of Gaussian-kernel maximum mean discrepancies. Motivated by this representation, we introduce a logarithmic Gini covariance for the $k$-sample problem and investigate its structural and asymptotic properties. In particular, we derive a representation in terms of pairwise logarithmic energy distances, establish a characterization theorem for equality of distributions, develop asymptotic null and alternative theory for the corresponding empirical statistic, and discuss permutation-based implementation. The logarithmic framework reveals a new boundary phenomenon within the family of energy-type statistics and provides connections with kernel methods, functional data analysis, and high-dimensional inference.

stat.ME↗

arXiv2022

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

A general and relatively simple method for construction of multivariate goodness-of-fit tests is introduced. The proposed test is applied to elliptical distributions. The method is based on a characterization of probability distributions via their characteristic function. The consistency and other limit properties of the new test statistics are studied. Also in a simulation study the proposed tests are compared with earlier as well as more recent competitors.

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