arXiv subjects

Eduardo García-Portugués

Publications and source records attributed to Eduardo García-Portugués.

At least 19 recordsLinked to original sources

arXiv2026

Goodness-of-fit for distributions on metric spaces

We propose a general goodness-of-fit framework for distributions on separable metric spaces. Under suitable identifiability conditions, probability distributions are characterized by distance profiles, which motivates their use in goodness-of-fit testing, for simple and composite null hypotheses. For composite null hypotheses, parameter estimation is incorporated via a Bahadur-type expansion, and the asymptotic distribution of the empirical process for distance profiles is obtained under the null. We define test statistics based on this empirical process and derive their asymptotic null distributions. We further study the behavior of the proposed tests under fixed and local alternatives, establishing consistency results. Multiplier bootstrap procedures are developed, and their conditional asymptotic validity is established under both simple and composite null hypotheses. The methodology is illustrated with simulation studies and real-data applications for data on the sphere, hyperboloid, and simplex.

math.ST↗

arXiv2026

On new omnibus tests of uniformity on the hypersphere

Two new omnibus tests of uniformity for data on the hypersphere are proposed. The new test statistics exploit closed-form expressions for orthogonal polynomials, feature tuning parameters, and are related to a "smooth maximum" function and the Poisson kernel. We obtain exact moments of the test statistics under uniformity and rotationally symmetric alternatives, and give their null asymptotic distributions. We consider approximate oracle tuning parameters that maximize the power of the tests against known generic alternatives and provide tests that estimate oracle parameters through cross-validated procedures while maintaining the significance level. Numerical experiments explore the effectiveness of null asymptotic distributions and the accuracy of inexpensive approximations of exact null distributions. A simulation study compares the powers of the new tests with other tests of the Sobolev class, showing the benefits of the former. The proposed tests are applied to the study of the (seemingly uniform) nursing times of wild polar bears.

stat.ME↗

arXiv2026

A class of nonparametric homogeneity tests on the circle

We develop a unified framework for $c$-sample homogeneity testing on the circle. The proposed class of $c$-sample Sobolev tests generalizes the two-sample Sobolev tests based on uniform scores and encompasses the existing multisample tests as particular cases. We further embed this class into a broader aggregation framework, where the samplewise Sobolev components are combined through general merging functions, including average-type, maximum-type, and interpolating families. Within this class, we introduce the first Anderson-Darling-type homogeneity test for circular data, and we further propose two new tests designed to detect multimodal departures from homogeneity, constructed from softmax and Poisson kernels. We derive the asymptotic null distribution of the class, prove its consistency against a broad family of fixed alternatives, and obtain the asymptotic distribution under shift-type local alternatives. The tests are distribution-free and therefore do not require resampling. A comprehensive simulation study demonstrates the strong power of the Anderson-Darling-type test compared with Cramér-von Mises-type competitors across several scenarios, and the effectiveness of the softmax and Poisson tests under several alternatives. The testing toolbox is applied to analyze the nursing patterns of polar bears.

math.ST↗

arXiv2026

Soprano voices in opera seria: a corpus-based inquiry into eighteenth-century vocal types

Eighteenth-century Italian opera seria was dominated by soprano voices. Although masculine roles were typically performed by castrati and feminine roles by women, cross-casting was common, producing four soprano configurations in which performers of either sex could portray characters of either gender. We hypothesize that composers tailored their writing both to the singers premiering their arias and to the characters' gender. Using statistical models built on approximately 1,700 arias, we analyze relationships between vocal typology, characters' gender, and stylistic choices, comparing supervised learning methods and selecting ridge logistic regression as our primary model, whose performance is competitive with that of the best-performing alternative while allowing for interpretation and uncertainty quantification of its coefficients. Results reveal an asymmetry: character gender is consistently encoded in the writing, while the singer's sex is barely recoverable. Masculine-character arias feature large melodic leaps, intervallic variability, and wider ranges; feminine-character arias favor higher maximum pitches, minor intervals, and melodic stability. Female singers sang higher pitches than male sopranos, but this correlates more with character portrayal than with physiology.

stat.AP↗

arXiv2026

High-dimensional Sobolev tests on hyperspheres

We derive the limit null distribution of the class of Sobolev tests of uniformity on the hypersphere as the dimension and the sample size diverge to infinity at arbitrary rates. The limiting non-null behavior of these tests is also explored: (i) a general consistency result for Sobolev tests in high dimensions is shown and (ii) the asymptotic power of the tests under sequences of integrated von Mises-Fisher local alternatives is obtained. The asymptotic results are applied to test for high-dimensional rotational symmetry and spherical symmetry. Numerical experiments illustrate the derived behavior of the uniformity and spherical symmetry tests under the null and under local and fixed alternatives. A real data application tests the high-dimensional normality of the cosmic microwave background.

math.ST↗

arXiv2026

On the spherical cardioid distribution and its goodness-of-fit

In this paper, we study the spherical cardioid distribution, a higher-dimensional and arbitrary-order generalization of the circular cardioid distribution. This distribution is rotationally symmetric and generates unimodal, multimodal, axial, and girdle-like densities. We identify various properties of the spherical cardioid that make it highly tractable: simple density evaluation, closedness under convolution, explicit expressions for vectorized moments, and efficient simulation. The moments of the spherical cardioid of order $k$ up to order $k-1$ coincide with those of the uniform distribution on the sphere, highlighting its closeness to the latter. We derive estimators by the method of moments and maximum likelihood, their asymptotic distributions, and their asymptotic relative efficiencies. We give the machinery for bootstrap goodness-of-fit tests based on the projected empirical cumulative distribution function approach, including the projected distribution and closed-form expressions for test statistics. An application to modeling the orbits of long-period comets shows the usefulness of the spherical cardioid distribution in real data analyses.

stat.ME↗

arXiv2026

On Stein's test of uniformity on the hypersphere

We propose a new test of uniformity on the hypersphere based on a Stein characterization associated with the Laplace-Beltrami operator. We identify a sufficient class of test functions for this characterization, linked to the moment generating function. Exploiting the operator's eigenfunctions to obtain a harmonic decomposition in terms of Gegenbauer polynomials, we show that the proposed procedure belongs to the class of Sobolev tests. We derive closed-form series representations for the asymptotic distribution of the test statistic under the null hypothesis and under fixed alternatives. To enhance power against a range of alternatives, we introduce a tuning parameter into the characterization and study its impact on rejection probabilities. We discuss data-driven strategies for selecting this parameter to maximize rejection rates for a given alternative and compare the resulting performance with that of related parametric tests. Additional numerical experiments compare the proposed test with competing Sobolev-class procedures, highlighting settings in which it offers clear advantages.

math.ST↗

arXiv2026

Out-of-bag prediction balls for random forests in metric spaces

Statistical methods for metric spaces provide a general and versatile framework for analyzing complex data types. We introduce a novel approach for constructing confidence regions around new predictions from any bagged regression algorithm with metric-space-valued responses. This includes the recent extensions of random forests for metric responses: Fréchet random forests (Capitaine et al., 2024), random forest weighted local constant Fréchet regression (Qiu et al., 2024), and metric random forests (Bulté and Sørensen, 2024). Our prediction regions leverage out-of-bag observations generated during a single forest training, employing the entire data set for both prediction and uncertainty quantification. We establish asymptotic guarantees of out-of-bag prediction balls for four coverage types under certain regularity conditions. Moreover, we demonstrate the superior stability and smaller radius of out-of-bag balls compared to split-conformal methods through extensive numerical experiments where the response lies on the Euclidean space, sphere, hyperboloid, and space of positive definite matrices. A real data application illustrates the potential of the confidence regions for quantifying the uncertainty in the study of solar dynamics and the use of data-driven non-isotropic distances on the sphere.

stat.ME↗

arXiv2026

Blessing of dimensionality in cross-validated bandwidth selection on the sphere

We study the asymptotic behavior of least-squares cross-validation bandwidth selection in kernel density estimation on the $d$-dimensional hypersphere, $d\geq 1$. We show that the exact rate of convergence with respect to the optimal bandwidth minimizing the mean integrated squared error, shown to exist under mild non-uniformity conditions, is $n^{-d/(2d+8)}$, thus approaching the $n^{-1/2}$ parametric rate as $d$ grows. This ``blessing of dimensionality'' in bandwidth selection offers theoretical support for utilizing the conceptually simpler cross-validation selector over plug-in techniques for larger dimensions $d$. We compare this result for bandwidth estimation on the $d$-dimensional Euclidean space through explicit expressions for the asymptotic variance functionals. Numerical experiments corroborate the speed of this convergence in an array of scenarios and dimensions, precisely illustrating the tipping dimension where cross-validation outperforms plug-in approaches.

math.ST↗

arXiv2025

Density estimation for compositional data using nonparametric mixtures

Compositional data, representing proportions constrained to the simplex, arise in diverse fields such as geosciences, ecology, genomics, and microbiome research. Existing nonparametric density estimation methods often rely on transformations, which may induce substantial bias near the simplex boundary. We propose a nonparametric mixture-based framework for density estimation on compositions. Nonparametric Dirichlet mixtures are employed to naturally accommodate boundary values, thereby avoiding the transformation or zero-replacement, while also identifying components supported on the boundary, providing reliable estimates for data with zero or near-zero values. Bandwidth selection and initialization schemes are addressed. For comparison, nonparametric Gaussian mixtures, coupled with log-ratio transformations, are also considered. Extensive simulations show that the proposed estimators outperform existing approaches. Three real data applications, including GDP data analysis, handwritten digit recognition, and skin detection, demonstrate the usefulness of nonparametric Dirichlet mixtures in practice.

stat.ME↗

arXiv2024

Kernel density estimation with polyspherical data and its applications

A kernel density estimator for data on the polysphere $\mathbb{S}^{d_1}\times\cdots\times\mathbb{S}^{d_r}$, with $r,d_1,\ldots,d_r\geq 1$, is presented in this paper. We derive the main asymptotic properties of the estimator, including mean square error, normality, and optimal bandwidths. We address the kernel theory of the estimator beyond the von Mises-Fisher kernel, introducing new kernels that are more efficient and investigating normalizing constants, moments, and sampling methods thereof. Plug-in and cross-validated bandwidth selectors are also obtained. As a spin-off of the kernel density estimator, we propose a nonparametric $k$-sample test based on the Jensen-Shannon divergence. Numerical experiments illuminate the asymptotic theory of the kernel density estimator and demonstrate the superior performance of the $k$-sample test with respect to parametric alternatives in certain scenarios. Our smoothing methodology is applied to the analysis of the morphology of a sample of hippocampi of infants embedded on the high-dimensional polysphere $(\mathbb{S}^2)^{168}$ via skeletal representations ($s$-reps).

stat.ME↗

arXiv2024

A family of toroidal diffusions with exact likelihood inference

We provide a class of diffusion processes for continuous time-varying multivariate angular data with explicit transition probability densities, enabling exact likelihood inference. The presented diffusions are time-reversible and can be constructed for any pre-specified stationary distribution on the torus, including highly-multimodal mixtures. We give results on asymptotic likelihood theory allowing one-sample inference and tests of linear hypotheses for $k$ groups of diffusions, including homogeneity. We show that exact and direct diffusion bridge simulation is possible too. A class of circular jump processes with similar properties is also proposed. Several numerical experiments illustrate the methodology for the circular and two-dimensional torus cases. The new family of diffusions is applied (i) to test several homogeneity hypotheses on the movement of ants and (ii) to simulate bridges between the three-dimensional backbones of two related proteins.

stat.ME↗

arXiv2024

A stereographic test of spherical uniformity

We introduce a test of uniformity for (hyper)spherical data motivated by the stereographic projection. The closed-form expression of the test statistic and its null asymptotic distribution are derived using Gegenbauer polynomials. The power against rotationally symmetric local alternatives is provided, and simulations illustrate the non-null asymptotic results. The stereographic test outperforms other tests in a testing scenario with antipodal dependence between observations.

math.ST↗

arXiv2024

Optimal stopping of Gauss-Markov bridges

We solve the non-discounted, finite-horizon optimal stopping problem of a Gauss-Markov bridge by using a time-space transformation approach. The associated optimal stopping boundary is proved to be Lipschitz continuous on any closed interval that excludes the horizon, and it is characterized by the unique solution of an integral equation. A Picard iteration algorithm is discussed and implemented to exemplify the numerical computation and geometry of the optimal stopping boundary for some illustrative cases.

math.PR↗

arXiv2024

Optimal stopping of an Ornstein-Uhlenbeck bridge

We make a rigorous analysis of the existence and characterization of the free boundary related to the optimal stopping problem that maximizes the mean of an Ornstein--Uhlenbeck bridge. The result includes the Brownian bridge problem as a limit case. The methodology hereby presented relies on a time-space transformation that casts the original problem into a more tractable one with an infinite horizon and a Brownian motion underneath. We comment on two different numerical algorithms to compute the free-boundary equation and discuss illustrative cases that shed light on the boundary's shape. In particular, the free boundary generally does not share the monotonicity of the Brownian bridge case.

math.PR↗

arXiv2024

Optimal exercise of American options under time-dependent Ornstein-Uhlenbeck processes

We study the barrier that gives the optimal time to exercise an American option written on a time-dependent Ornstein--Uhlenbeck process, a diffusion often adopted by practitioners to model commodity prices and interest rates. By framing the optimal exercise of the American option as a problem of optimal stopping and relying on probabilistic arguments, we provide a non-linear Volterra-type integral equation characterizing the exercise boundary, develop a novel comparison argument to derive upper and lower bounds for such a boundary, and prove its Lipschitz continuity in any closed interval that excludes the expiration date and, thus, its differentiability almost everywhere. We implement a Picard iteration algorithm to solve the Volterra integral equation and show illustrative examples that shed light on the boundary's dependence on the process's drift and volatility.

math.PR↗

arXiv2024

On a class of Sobolev tests for symmetry of directions, their detection thresholds, and asymptotic powers

We consider a class of symmetry hypothesis testing problems including testing isotropy on $\mathbb{R}^d$ and testing rotational symmetry on the hypersphere $\mathcal{S}^{d-1}$. For this class, we study the null and non-null behaviors of Sobolev tests, with emphasis on their consistency rates. Our main results show that: (i) Sobolev tests exhibit a detection threshold (see Bhattacharya, 2019, 2020) that does not only depend on the coefficients defining these tests; and (ii) tests with non-zero coefficients at odd (respectively, even) ranks only are blind to alternatives with angular functions whose $k$th-order derivatives at zero vanish for any $k$ odd (even). Our non-standard asymptotic results are illustrated with Monte Carlo exercises. A case study in astronomy applies the testing toolbox to evaluate the symmetry of orbits of long- and short-period comets.

math.ST↗

arXiv2024

Testing for linearity in scalar-on-function regression with responses missing at random

A goodness-of-fit test for the Functional Linear Model with Scalar Response (FLMSR) with responses Missing at Random (MAR) is proposed in this paper. The test statistic relies on a marked empirical process indexed by the projected functional covariate and its distribution under the null hypothesis is calibrated using a wild bootstrap procedure. The computation and performance of the test rely on having an accurate estimator of the functional slope of the FLMSR when the sample has MAR responses. Three estimation methods based on the Functional Principal Components (FPCs) of the covariate are considered. First, the simplified method estimates the functional slope by simply discarding observations with missing responses. Second, the imputed method estimates the functional slope by imputing the missing responses using the simplified estimator. Third, the inverse probability weighted method incorporates the missing response generation mechanism when imputing. Furthermore, both cross-validation and LASSO regression are used to select the FPCs used by each estimator. Several Monte Carlo experiments are conducted to analyze the behavior of the testing procedure in combination with the functional slope estimators. Results indicate that estimators performing missing-response imputation achieve the highest power. The testing procedure is applied to check for linear dependence between the average number of sunny days per year and the mean curve of daily temperatures at weather stations in Spain.

stat.ME↗