Functional limit theorems for random quadratic forms

DOI10.1016/0304-4149(91)90062-HzbMath0726.60030MaRDI QIDQ804076

Thomas Mikosch

Publication date: 1991

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

functional central limit theoremindependent random variablesSkorokhod embeddingstrong invariance principlerandom quadratic formscompact law of the iterated logarithmsymmetric double array

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items (20)

A LIMIT THEOREM FOR QUADRATIC FORMS AND ITS APPLICATIONS ⋮ Functional limit theorems for random multilinear forms ⋮ Convergence of quadratic forms with nonvanishing diagonal ⋮ On Moran's \(I\) coefficient under heterogeneity ⋮ Approximations and limit theory for quadratic forms of linear processes ⋮ Quadratic forms of the empirical processes for the two-sample problem for functional data ⋮ The integrated periodogram for long-memory processes with finite or infinite variance ⋮ A note on quadratic forms of stationary functional time series under mild conditions ⋮ Asymptotic normality of quadratic forms of martingale differences ⋮ A simple framework for nonparametric specification testing ⋮ General Gaussian estimation ⋮ ASYMPTOTICS OF SPECTRAL DENSITY ESTIMATES ⋮ Generalized score test of homogeneity for mixed effects models ⋮ The asymptotic behavior of quadratic forms in \(\varphi\)-mixing random variables ⋮ The rate of convergence in the functional central limit theorem for random quadratic forms with some applications to the law of the iterated logarithm ⋮ Gaussian limit fields for the integrated periodogram ⋮ The multivariate functional de Jong CLT ⋮ Weak invariance principles for weighted \(U\)-statistics ⋮ Some higher-order theory for a consistent non-parametric model specification test ⋮ Functional central limit theorem for random multilinear forms

Cites Work

• Convergence of quadratic forms in p-stable random variables and \(\theta _ p\)-radonifying operators
• Random multilinear forms
• A central limit theorem for generalized quadratic forms
• Double stochastic integrals, random quadratic forms and random series in Orlicz spaces
• On the asymptotic distribution of quadratic forms in uniform order statistics
• Bounded laws of the iterated logarithm for quadratic forms in Gaussian random variables
• A nonuniform bound on the rate of convergence in the martingale central limit theorem
• Stability of random variables and iterated logarithm laws for martingales and quadratic forms
• The almost sure stability of quadratic forms
• The rate of convergence in the functional central limit theorem for random quadratic forms with some applications to the law of the iterated logarithm
• Convergence results for sequences of quadratic forms
• On the convergence of bilinear and quadratic forms in independent random variables
• Some Limit Theorems for Polynomials of Second Degree
• On the Distribution of a Quadratic Form in Many Random Variables
• Limit Theorems for Multilinear Forms and Quasipolynomial Functions
• On the Rate of Convergence in the Limit Theorem for Quadratic Forms
• An invariance principle for the law of the iterated logarithm
• Convergence of Quadratic Forms in Independent Random Variables
• Almost Sure Convergence of Quadratic Forms in Independent Random Variable
• Martingale Central Limit Theorems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Functional limit theorems for random quadratic forms