SSRN Author: Giovanni PuccettiGiovanni Puccetti SSRN Content
https://www.ssrn.com/author=2190556
https://www.ssrn.com/rss/en-usSat, 11 Jun 2022 01:08:08 GMTeditor@ssrn.com (Editor)Sat, 11 Jun 2022 01:08:08 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Measuring Linear Correlation Between Random VectorsWe introduce a new scalar coefficient to measure linear correlation between random vectors which preserves all the relevant properties of Pearson’s correlation in arbitrarily large dimensions. The new measure and its bounds are derived from a mass transportation approach in which the expected inner product of two random vectors is taken as a measure of their covariance and then standardized by the maximal attainable value given their marginal covariance matrices. The new correlation is maximized when the average squared Euclidean distance between the random vectors is minimal and attains value one when, additionally, it is possible to establish an affine relationship between the vectors. In several simulative studies we show the limiting distribution of the empirical estimator of the newly defined index and of the corresponding rank correlation.<br>A comparative study based on financial data shows that our proposed correlation, though derived from a novel approach, behaves similarly ...
https://www.ssrn.com/abstract=3116066
https://www.ssrn.com/2149577.htmlFri, 10 Jun 2022 12:50:29 GMTREVISION: Measuring Linear Correlation Between Random VectorsWe introduce a new scalar coefficient to measure linear correlation between random vectors which preserves all the relevant properties of Pearson’s correlation in arbitrarily large dimensions. The new measure and its bounds are derived from a mass transportation approach in which the expected inner product of two random vectors is taken as a measure of their covariance and then standardized by the maximal attainable value given their marginal covariance matrices. The new correlation is maximized when the average squared Euclidean distance between the random vectors is minimal and attains value one when, additionally, it is possible to establish an affine relationship between the vectors. In several simulative studies we show the limiting distribution of the empirical estimator of the newly defined index and of the corresponding rank correlation.<br>A comparative study based on financial data shows that our proposed correlation, though derived from a novel approach, behaves similarly ...
https://www.ssrn.com/abstract=3116066
https://www.ssrn.com/2147591.htmlMon, 06 Jun 2022 14:15:56 GMTREVISION: General Construction and Classes of Explicit L
<sup>1</sup>-Optimal CouplingsThe main scope of this paper is to give some explicit classes of examples of L<sup>1</sup>-optimal couplings. Optimal transportation w.r.t. the Kantorovich metric ℓ1 (resp. the Wasserstein metric W1) between two absolutely continuous measures is known since the basic papers of Kantorovich and Rubinstein (1957) and Sudakov (1979) to occur on rays induced by a decomposition of the basic space (and more generally to higher dimensional decompositions in the case of general measures) induced by the corresponding dual potentials. Several papers have given this kind of structural result and established existence and uniqueness of solutions in varying generality. Since the dual problems pose typically too strong challenges to be solved in explicit form, these structural results have so far been applied for the solution of few particular instances.<br><br>First, we give a self-contained review of some basic optimal coupling results and we propose and investigate in particular some basic ...
https://www.ssrn.com/abstract=3855631
https://www.ssrn.com/2103130.htmlTue, 08 Feb 2022 19:05:04 GMTREVISION: Measuring Linear Correlation Between Random VectorsWe introduce a new scalar coefficient to measure linear correlation between random vectors which preserves all the relevant properties of Pearson’s correlation in arbitrarily large dimensions. The new measure and its bounds are derived from a mass transportation approach in which the expected inner product of two random vectors is taken as a measure of their covariance and then standardized by the maximal attainable value given their marginal covariance matrices. The new correlation is maximized when the average squared Euclidean distance between the random vectors is minimal and attains value one when, additionally, it is possible to establish an affine relationship between the vectors. In several simulative studies we show the limiting distribution of the empirical estimator of the newly defined index and of the corresponding rank correlation.<br>A comparative study based on financial data shows that our proposed correlation, though derived from a novel approach, behaves similarly ...
https://www.ssrn.com/abstract=3116066
https://www.ssrn.com/2100083.htmlMon, 31 Jan 2022 21:32:35 GMT