Limit theorems for polylinear forms

DOI10.1016/0047-259X(79)90055-1zbMath0426.62013OpenAlexW2131433282MaRDI QIDQ1136172

Vladimir I. Rotar'

Publication date: 1979

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0047-259x(79)90055-1

zbMATH Keywords

limit theoremsinvariance classpolylinear forms

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic distribution theory in statistics (62E20) Exact distribution theory in statistics (62E15)

Related Items (23)

Classical and free fourth moment theorems: universality and thresholds ⋮ Gaussian limits for subcritical chaos ⋮ A generalization of the Lindeberg principle ⋮ A quantitative Arrow theorem ⋮ High-dimensional central limit theorems for homogeneous sums ⋮ Asymptotic normality of quadratic forms with random vectors of increasing dimension ⋮ The critical 2d stochastic heat flow ⋮ Identification-robust nonparametric inference in a linear IV model ⋮ Noise correlation bounds for uniform low degree functions ⋮ Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos ⋮ A central limit theorem for generalized multilinear forms ⋮ The universality of homogeneous polynomial forms and critical limits ⋮ Sharp kernel clustering algorithms and their associated Grothendieck inequalities ⋮ Noise stability of functions with low influences: invariance and optimality ⋮ Diffusions interacting through a random matrix: universality via stochastic Taylor expansion ⋮ On asymptotic proximity of distributions ⋮ Approximate Kernel Clustering ⋮ On Khot’s unique games conjecture ⋮ Approximation to stable law by the Lindeberg principle ⋮ Expansions for von Mises functionals ⋮ The multivariate functional de Jong CLT ⋮ An invariance principle under the total variation distance ⋮ Weak invariance principles for weighted \(U\)-statistics

Cites Work

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• Some Remarks on Summing Independent Variables in the Non-Classical Case
• Limit Theorems for Multilinear Forms and Quasipolynomial Functions
• Series Representations of Distributions of Quadratic Forms in Normal Variables. I. Central Case
• On the distribution of a quadratic form
• Distribution Theory of a Positive Definite Quadratic Form with Matrix Argument
• A Generalization of the Lindeberg-Feller Theorem

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