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Asymptotic normality of quadratic forms with random vectors of

Asymptotic normality of quadratic forms with random vectors of 2025

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The paper discusses sufficient conditions for the asymptotic normality of quadratic forms derived from averages of random vectors as their dimensions increase. It improves upon existing literature by addressing gaps in previous proofs and providing new results applicable to empirical likelihood methods, particularly when the number of constraints grows with sample size. The authors demonstrate how these results can be utilized in statistical testing, such as assessing the equality of marginal distributions in bivariate random vectors.

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