arXiv subjects

Daniel Gaigall

Publications and source records attributed to Daniel Gaigall.

5 recordsLinked to original sources

arXiv2026

A unified approach for testing in Hilbert spaces on incomplete data

We consider statistical testing on the basis of incomplete observations with values in a separable Hilbert space, where the dimension is possibly large or even infinite. The general Hilbert space setting allows various data types as they arise in modern applications, in particular high dimensional and functional data. Possible Hilbert space testing problems are goodness-of-fit, symmetry, homogeneity and independence. We present an approach for modeling incomplete data that covers several problems in practice, e.g., ultra high dimensional random vectors with missing entries or partially observed stochastic processes. We identify a specific structure (independent and identically distributed) in the incomplete data that enables the analysis of statistical procedures with the help of suitable mathematical results (e.g., laws of large numbers and central limit theorems). Additionally, a general and novel concept for testing different hypotheses in this situation is suggested and sketched for the example of testing goodness-of-fit for normality.

math.ST↗

arXiv2026

A BHEP test for multivariate normality on incomplete data

A BHEP test for the null hypotesis of multivariate normality on the basis of incomplete data is introduced. Estimators for the underlying unknown parameters in this situation are suggested. The test uses characteristic functions and circumvents the problem of singular covariance matrix estimates. As the sample size tends to infinity, an almost sure limit of the test statistic is obtained under the null hypothesis and under alternatives. The convergence in distribution under the null hypothesis is also proved. Critical values can be obtained using a bootstrap procedure. Simulation studies investigate size and power of the test and confirm the adequacy of the approach. A real data example demonstrates the application of the test.

math.ST↗

arXiv2025

Jointly Exchangeable Collective Risk Models: Interaction, Structure, and Limit Theorems

We introduce a framework for systemic risk modeling in insurance portfolios using jointly exchangeable arrays, extending classical collective risk models to account for interactions. Joint exchangeability is a more general probabilistic symmetric than de Finetti's exchangeability, characterized by the Aldous-Hoover-Kallenberg representation. We establish central limit theorems that asymptotically capture total portfolio losses, providing a theoretical foundation for approximations in large portfolios and over long time horizons. These approximations are validated through simulation-based numerical experiments. Additionally, we analyze the impact of dependence on portfolio loss distributions, with a particular focus on tail behavior.

q-fin.RM↗

arXiv2020

Testing marginal homogeneity in Hilbert spaces with applications to stock market returns

The paper considers a paired data framework and discuss the question of marginal homogeneity of bivariate high dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cramer-von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived, that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns on the basis of functional data. The approach is demonstrated on the basis of historical data for different stock market indices.

stat.ME↗

arXiv2016

Testing hypotheses about mixture distributions using not identically distributed data

Testing hypotheses of goodness-of-fit about mixture distributions on the basis of independent but not necessarily identically distributed random vectors is considered. The hypotheses are given by a specific distribution or by a family of distributions. Moreover, testing hypotheses formulated by Hadamard differentiable functionals is discussed in this situation, in particular the hypothesis of central symmetry, homogeneity and independence. Kolmogorov-Smirnov or Cramér-von-Mises type statistics are suggested as well as methods to determine critical values. The focus of the investigation is on asymptotic properties of the test statistics. Further, outcomes of simulations for finite sample sizes are given. Applications to models with not identically distributed errors are presented. The results imply that the tests are of asymptotically exact size and consistent.

math.ST↗