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Limit theorems for polylinear forms

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  • Rotar', V. I.

Abstract

The limit theorems for polylinear forms are obtained. Conditions are found under which the distribution of the polylinear form of many random variables is essentially the same as if all the distributions of arguments were normal.

Suggested Citation

  • Rotar', V. I., 1979. "Limit theorems for polylinear forms," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 511-530, December.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:4:p:511-530
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    Cited by:

    1. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    2. Peng, Hanxiang & Schick, Anton, 2018. "Asymptotic normality of quadratic forms with random vectors of increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 22-39.
    3. Youri Davydov & Vladimir Rotar, 2009. "On Asymptotic Proximity of Distributions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 82-98, March.
    4. Nourdin, Ivan & Poly, Guillaume, 2015. "An invariance principle under the total variation distance," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2190-2205.
    5. Shuyang Bai & Murad S. Taqqu, 2016. "The Universality of Homogeneous Polynomial Forms and Critical Limits," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1710-1727, December.
    6. Yuta Koike, 2023. "High-Dimensional Central Limit Theorems for Homogeneous Sums," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-45, March.
    7. Bartels, Knut, 1998. "A model specification test," SFB 373 Discussion Papers 1998,109, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Ivan Nourdin & Giovanni Peccati & Guillaume Poly & Rosaria Simone, 2016. "Classical and Free Fourth Moment Theorems: Universality and Thresholds," Journal of Theoretical Probability, Springer, vol. 29(2), pages 653-680, June.

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