On non-linear dependence of multivariate subordinated Lévy processes

Nardo, E. Di; Marena, Marina; Semeraro, Patrizia

doi:10.1016/j.spl.2020.108870

Cited by 3 publications

(2 citation statements)

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“…These estimators have minimum variance when compared to all other unbiased estimators and are built by free-distribution methods without using sample moments. Due to the properties of joint cumulants, multivariate k-statistics are employed to check multivariate gaussianity (Ferreira, Magueijo, and Silk 1997) or to quantify high-order interactions among data (Geng, Liang, and Wang 2011), for applications in topology inference (Smith et al 2022), in neuronal science (Staude, Rotter, and Grün 2010) and in mathematical finance (E. Di Nardo, Marena, and Semeraro 2020). Polykays are unbiased estimators of cumulant products (Robson 1957) and are particularly useful in estimating covariances between k-statistics (McCullagh 1987).…”

Section: Introductionmentioning

confidence: 99%

“…Among its various applications, we recall the cumulant polynomial sequences and their connection with special families of stochastic processes (E. Di Nardo 2016a). Indeed, cumulant polynomials allow us to compute moments and cumulants of multivariate Lévy processes (E. Di Nardo and Oliva 2011), subordinated multivariate Lévy processes (E. Di Nardo, Marena, and Semeraro 2020) and multivariate compound Poisson processes (E. Di Nardo 2016b). Further examples can be found in Reiner (1976), Shrivastava (2002), Withers and Nadarajah (2010) or Privault (2021).…”

Section: Introductionmentioning

confidence: 99%

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kStatistics: Unbiased Estimates of Joint Cumulant Products from the Multivariate Faà Di Bruno's Formula

Nardo

Guarino

2022

The R Journal

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kStatistics is a package in R that serves as a unified framework for estimating univariate and multivariate cumulants as well as products of univariate and multivariate cumulants of a random sample, using unbiased estimators with minimum variance. The main computational machinery of kStatistics is an algorithm for computing multi-index partitions. The same algorithm underlies the general-purpose multivariate Faà di Bruno's formula, which therefore has been included in the last release of the package. This formula gives the coefficients of formal power series compositions as well as the partial derivatives of multivariable function compositions. One of the most significant applications of this formula is the possibility to generate many well-known polynomial families as special cases. So, in the package, there are special functions for generating very popular polynomial families, such as the Bell polynomials. However, further families can be obtained, for suitable choices of the formal power series involved in the composition or when suitable symbolic strategies are employed. In both cases, we give examples on how to modify the R codes of the package to accomplish this task. Future developments are addressed at the end of the paper

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