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On the Normality of the Sum of Two Normal Operators

✍ Scribed by Mohammed Hichem Mortad

Book ID
107508774
Publisher
SP Birkhäuser Verlag Basel
Year
2010
Tongue
English
Weight
149 KB
Volume
6
Category
Article
ISSN
1661-8254

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Quadratic Negligibility and the Asymptot
Quadratic Negligibility and the Asymptotic Normality of Operator Normed Sums
✍ R.A. Maller 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 711 KB

The condition \(\max _{1 \leqslant i \leqslant n} X_{i}^{\top} V_{n}{ }^{1} X_{i} \xrightarrow{p} 0\), where \(X_{i}\) are vectors in \(R^{d}\) and \(V_{n}=\sum_{i=1}^{n} X_{i} X_{i}^{\mathrm{\top}}\), is important in the asymptotics of various linear and nonlinear regression models. We call it "qua