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Dependence Measuring from Conditional Variances

100%

Kamnitui N., Santiwipanont T., Sumetkijakan S.

Dependence Modeling

2015

tom 3

nr 1

A conditional variance is an indicator of the level of independence between two random variables. We exploit this intuitive relationship and define a measure v which is almost a measure of mutual complete dependence. Unsurprisingly, the measure attains its minimum value for many pairs of non-independent ran- dom variables. Adjusting the measure so as to make it invariant under all Borel measurable injective trans- formations, we obtain a copula-based measure of dependence v* satisfying A. Rényi’s postulates. Finally, we observe that every nontrivial convex combination of v and v* is a measure of mutual complete dependence.

Equivalent or absolutely continuous probability measures with given marginals

76%

Berti P., Pratelli L., Rigo P., Spizzichino F.

Dependence Modeling

2015

tom 3

nr 1

Let (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.

Ograniczanie wyników

2 Dependence Modeling

1 Berti P.

1 Kamnitui N.

1 Pratelli L.

1 Rigo P.

1 Santiwipanont T.

1 Spizzichino F.

1 Sumetkijakan S.

2 2015

Wyniki wyszukiwania

Dependence Measuring from Conditional Variances

Equivalent or absolutely continuous probability measures with given marginals