Functional central limit theorems for self-normalized least squares processes in regression with possibly infinite variance data
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References listed on IDEAS
- Maller, R. A., 1993. "Quadratic Negligibility and the Asymptotic Normality of Operator Normed Sums," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 191-219, February.
- Vu, H. T. V. & Maller, R. A. & Klass, M. J., 1996. "On the Studentisation of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 142-155, April.
- Rackauskas, Alfredas & Suquet, Charles, 2001. "Invariance principles for adaptive self-normalized partial sums processes," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 63-81, September.
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- Martsynyuk, Yuliya V., 2012. "Invariance principles for a multivariate Student process in the generalized domain of attraction of the multivariate normal law," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2270-2277.
More about this item
KeywordsSimple linear regression; Domain of attraction of the normal law; Infinite variance; Slowly varying function at infinity; Studentized/self-normalized least squares estimator/process; Cholesky square root of a matrix; Symmetric positive definite square root of a matrix; Standard/bivariate Wiener process; Functional central limit theorem; Sup–norm approximation in probability; Direct product of two measurable spaces; Uniform Euclidean norm approximation in probability; Asymptotic confidence interval; Signal-to-noise ratio; Generalized domain of attraction of the d-variate normal law;
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