Geodesic
Comparison theorems for distribution functions of quadratic forms of Gaussian vectors
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 2, pp. 404-412 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $Q_1$ and $Q_2$ be nonnegatively definite quadratic forms of centered Gaussian random variables (r.v.'s) satisfying normalization condition $\mathbf{E}Q_1={\mathbf E}Q_2=1$. If the vector of eigenvalues of $Q_1$ majorizes that of $Q_2$, then the distribution function of $Q_1$ is less than the distribution function of $Q_2$ when their arguments exceed 2. Some statistical applications are given.
Keywords: comparison theorem, quadratic form of r.v.'s, quadratic statistics. 
@article{TVP_1995_40_2_a11,
     author = {N. K. Bakirov},
     title = {Comparison theorems for distribution functions of quadratic forms of {Gaussian} vectors},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {404--412},
     year = {1995},
     volume = {40},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_2_a11/}
}
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N. K. Bakirov. Comparison theorems for distribution functions of quadratic forms of Gaussian vectors. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 2, pp. 404-412. http://geodesic.mathdoc.fr/item/TVP_1995_40_2_a11/