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Search Results (3)

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Keywords = empirical checkerboard copula

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17 pages, 3203 KiB  
Article
Nonparametric Estimation of Conditional Copula Using Smoothed Checkerboard Bernstein Sieves
by Lu Lu and Sujit Ghosh
Mathematics 2024, 12(8), 1135; https://doi.org/10.3390/math12081135 - 10 Apr 2024
Cited by 1 | Viewed by 1424
Abstract
Conditional copulas are useful tools for modeling the dependence between multiple response variables that may vary with a given set of predictor variables. Conditional dependence measures such as conditional Kendall’s tau and Spearman’s rho that can be expressed as functionals of the conditional [...] Read more.
Conditional copulas are useful tools for modeling the dependence between multiple response variables that may vary with a given set of predictor variables. Conditional dependence measures such as conditional Kendall’s tau and Spearman’s rho that can be expressed as functionals of the conditional copula are often used to evaluate the strength of dependence conditioning on the covariates. In general, semiparametric estimation methods of conditional copulas rely on an assumed parametric copula family where the copula parameter is assumed to be a function of the covariates. The functional relationship can be estimated nonparametrically using different techniques, but it is required to choose an appropriate copula model from various candidate families. In this paper, by employing the empirical checkerboard Bernstein copula (ECBC) estimator, we propose a fully nonparametric approach for estimating conditional copulas, which does not require any selection of parametric copula models. Closed-form estimates of the conditional dependence measures are derived directly from the proposed ECBC-based conditional copula estimator. We provide the large-sample consistency of the proposed estimator as well as the estimates of conditional dependence measures. The finite-sample performance of the proposed estimator and comparison with semiparametric methods are investigated through simulation studies. An application to real case studies is also provided. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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22 pages, 696 KiB  
Article
Nonparametric Estimation of Multivariate Copula Using Empirical Bayes Methods
by Lu Lu and Sujit Ghosh
Mathematics 2023, 11(20), 4383; https://doi.org/10.3390/math11204383 - 21 Oct 2023
Cited by 4 | Viewed by 2588
Abstract
In the fields of finance, insurance, system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are easy to estimate but can be highly biased [...] Read more.
In the fields of finance, insurance, system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are easy to estimate but can be highly biased when such assumptions are false, while the empirical copulas are nonsmooth and often not genuine copulas, making the inference about dependence challenging in practice. As a compromise, the empirical Bernstein copula provides a smooth estimator, but the estimation of tuning parameters remains elusive. The proposed empirical checkerboard copula within a hierarchical empirical Bayes model alleviates the aforementioned issues and provides a smooth estimator based on multivariate Bernstein polynomials that itself is shown to be a genuine copula. Additionally, the proposed copula estimator is shown to provide a more accurate estimate of several multivariate dependence measures. Both theoretical asymptotic properties and finite-sample performances of the proposed estimator based on simulated data are presented and compared with some nonparametric estimators. An application to portfolio risk management is included based on stock prices data. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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23 pages, 1322 KiB  
Article
Modelling and Simulation of Seasonal Rainfall Using the Principle of Maximum Entropy
by Jonathan Borwein, Phil Howlett and Julia Piantadosi
Entropy 2014, 16(2), 747-769; https://doi.org/10.3390/e16020747 - 10 Feb 2014
Cited by 15 | Viewed by 8725
Abstract
We use the principle of maximum entropy to propose a parsimonious model for the generation of simulated rainfall during the wettest three-month season at a typical location on the east coast of Australia. The model uses a checkerboard copula of maximum entropy to [...] Read more.
We use the principle of maximum entropy to propose a parsimonious model for the generation of simulated rainfall during the wettest three-month season at a typical location on the east coast of Australia. The model uses a checkerboard copula of maximum entropy to model the joint probability distribution for total seasonal rainfall and a set of two-parameter gamma distributions to model each of the marginal monthly rainfall totals. The model allows us to match the grade correlation coefficients for the checkerboard copula to the observed Spearman rank correlation coefficients for the monthly rainfalls and, hence, provides a model that correctly describes the mean and variance for each of the monthly totals and also for the overall seasonal total. Thus, we avoid the need for a posteriori adjustment of simulated monthly totals in order to correctly simulate the observed seasonal statistics. Detailed results are presented for the modelling and simulation of seasonal rainfall in the town of Kempsey on the mid-north coast of New South Wales. Empirical evidence from extensive simulations is used to validate this application of the model. A similar analysis for Sydney is also described. Full article
(This article belongs to the Special Issue Maximum Entropy and Its Application)
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