Automatic differentiation and maximal correlation of order statistics from discrete parents
| Autor: | B. Salamanca-Miño, Fernando López-Blázquez |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Correlation coefficient Multivariate random variable Automatic differentiation 05 social sciences Order statistic Bivariate analysis 01 natural sciences Measure (mathematics) 010104 statistics & probability Computational Mathematics Maximal correlation Gradient based algorithm 0502 economics and business Applied mathematics 0101 mathematics Statistics Probability and Uncertainty 050205 econometrics Mathematics |
| Zdroj: | Computational Statistics. 36:2889-2915 |
| ISSN: | 1613-9658 0943-4062 |
| DOI: | 10.1007/s00180-021-01103-5 |
| Popis: | The maximal correlation is an attractive measure of dependence between the components of a random vector, however it presents the difficulty that its calculation is not easy. Here, we consider the case of bivariate vectors which components are order statistics from discrete distributions supported on $$N\ge 2$$ points. Except for the case $$N=2$$ , the maximal correlation does not have a closed form, so we propose the use of a gradient based optimization method. The gradient vector of the objective function, the correlation coefficient of pairs of order statistics, can be extraordinarily complicated and for that reason an automatic differentiation algorithm is proposed. |
| Databáze: | OpenAIRE |
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