arXiv subjects

Aleksey Min

Publications and source records attributed to Aleksey Min.

3 recordsLinked to original sources

arXiv2023

Distribution free MMD tests for model selection with estimated parameters

There exist some testing procedures based on the maximum mean discrepancy (MMD) to address the challenge of model specification. However, they ignore the presence of estimated parameters in the case of composite null hypotheses. In this paper, we first illustrate the effect of parameter estimation in model specification tests based on the MMD. Second, we propose simple model specification and model selection tests in the case of models with estimated parameters. All our tests are asymptotically standard normal under the null, even when the true underlying distribution belongs to the competing parametric families. A simulation study and a real data analysis illustrate the performance of our tests in terms of power and level.

stat.ME↗

arXiv2022

Stationary vine copula models for multivariate time series

Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the maximal class of graph structures that guarantee stationarity under a natural and verifiable condition called translation invariance. We propose computationally efficient methods for estimation, simulation, prediction, and uncertainty quantification and show their validity by asymptotic results and simulations. The theoretical results allow for misspecified models and, even when specialized to the iid case, go beyond what is available in the literature. Their proofs are based on new results for general semiparametric method-of-moment estimators, which shall be of independent interest. The new model class is illustrated by an application to forecasting returns of a portfolio of 20 stocks, where they show excellent forecast performance. The paper is accompanied by an open source software implementation.

stat.ME↗

arXiv2020

Testing for equality between conditional copulas given discretized conditioning events

Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some covariates belong to general borelian conditioning subsets. Several test statistics based on the equality of conditional Kendall's tau are introduced, and we derive their asymptotic distributions under the null. When such conditioning events are not fixed ex ante, we propose a data-driven procedure to recursively build such relevant subsets. It is based on decision trees that maximize the differences between the conditional Kendall's taus corresponding to the leaves of the trees. The performances of such tests are illustrated in a simulation experiment. Moreover, a study of the conditional dependence between financial stock returns is managed, given some clustering of their past values. The last application deals with the conditional dependence between coverage amounts in an insurance dataset.

stat.ME↗