Nonparametric universal copula modeling

Abstract

To handle the ubiquitous problem of “dependence learning,” copulas are quickly becoming a pervasive tool across a wide range of data‐driven disciplines encompassing neuroscience, finance, econometrics, genomics, social science, machine learning, healthcare, and many more. At the same time, despite their practical value, the empirical methods of “learning copula from data” have been unsystematic with full of case‐specific recipes. Taking inspiration from modern LP‐nonparametrics, this paper presents a modest contribution to the need for a more unified and structured approach of copula modeling that is simultaneously valid for arbitrary combinations of continuous and discrete variables.

Exhaustive goodness-of-fit via smoothed inference and graphics

“…To overcome this problem, they introduce data-driven smooth tests where the size of the orthonormal basis to be considered is selected using Schwartz's BIC criterion. A similar approach has been proposed by Mukhopadhyay (2017); Mukhopadhyay and Parzen (2020) in the context of LP modeling and, given an initial set of m Max coefficients, it con-sists in arranging them in decreasing magnitude i.e., LP…”

Informative Goodness-of-Fit for Multivariate Distributions

“…which models directly the true dependence among the components of X. A useful nonparametric estimator of c X F X (x) has been proposed in recent literature by Mukhopadhyay and Parzen (2020). Interestingly, the latter can be framed as a special case of the approach presented in this manuscript.…”

“…Interestingly, the latter can be framed as a special case of the approach presented in this manuscript. Specifically, in Mukhopadhyay and Parzen (2020), the copula density is estimated by setting G d ≡ F X d , for all d = 1, . .…”

“…Remark 5.1. The deviance statistics D ld in (42) is the equivalent of the LPINFOR dependence measure proposed by Mukhopadhyay and Parzen (2020). The latter offers the rather unique advantage of quantify dependence (beyond linearity) among random variables, regardless of their discrete or continuous nature.…”

Grid-Uniform Copulas and Rectangle Exchanges: Bayesian Model and Inference for a Rich Class of Copula Functions

“…In the context of continuous data, classical semiparametric approaches have been discussed by Genest et al (1995), while classical nonparametric approaches can be traced back to Deheuvels (1979), and can be found in Mukhopadhyay and Parzen (2020). The classical methods commonly rely on the use on partial-or pseudo-likelihood and do not allow for a proper quantification of the uncertainties associated to the lack of knowledge of the marginal distributions.…”