On the Strong Law of Large Numbers for Linear Combinations of Concomitants

Gribkova N.V.

doi:10.1134/S1063454120030061

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On the Strong Law of Large Numbers for Linear Combinations of Concomitants

. Vestnik St. Petersburg University, Mathematics . 2020. Vol. 53. P. 282–286.

Gribkova N.V.

The article proves a theorem on the strong law of large numbers for linear functions of concomitants (induced order statistics) for sequences of independent identically distributed two-dimensional random vectors. The result complements previous work by Yang (1981), Gribkova and Zitikis (2017, 2019). The proof is based on the conditional independence property of concomitants Bhattacharya (1974), the strong law of large numbers for functions of order statistics by van Zwet (1980) is used, classical inequalities apply, including Rosenthal’s (1970).

Language: English

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Keywords: concomitants induced order statistics linear combinations strong law of large numbers.

Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants

N. V. Gribkova, Su J., Zitikis R., Insurance: Mathematics and Economics 2022 Vol. 107 P. 199–222

We derive consistency, asymptotic normality, and standard error estimation for the tail conditional allocation, also known as the marginal expected shortfall, under minimal conditions and thus geared toward widest applicability. These advances have become possible due to a newly developed technique that hinges on compound sums of concomitants. An insurance inspired numerical study has been designed to illustrate the ...

Added: October 18, 2022