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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
This extended Hermite polynomial is associated with a matrix which is the difference between two covariance matrices, in other words, with any symmetric matrix.
📌 3 Key Takeaways
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Objective & Hypothesis:We give formulas for the conditional and unconditional expectations of products of multivariate Hermite and modified Hermite polynomials, each with a multivariate normal argument.
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Key Findings & Data:A unified approach is given that covers both of these polynomials, each associated with a covariance matrix.
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Conclusion & Impact:This extended Hermite polynomial is associated with a matrix which is the difference between two covariance matrices, in other words, with any symmetric matrix.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Conditional expectation · Multivariate Hermite polynomial · Multivariate normal
Abstract
We give formulas for the conditional and unconditional expectations of products of multivariate Hermite and modified Hermite polynomials, each with a multivariate normal argument. A unified approach is given that covers both of these polynomials, each associated with a covariance matrix. This extended Hermite polynomial is associated with a matrix which is the difference between two covariance matrices, in other words, with any symmetric matrix.
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Cite This Article
NADARAJAH, S., WİTHER, C. R. S. (2022). Some conditional and unconditional expectation identities for the multivariate normal with non-zero mean. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 4, 679–687. https://ajindex.com/articles/530362