The expectation of products of quadratic forms in normal variables: The practice Statistica Neerlandica

By J. R. Magnus. 1979

Citations in the corpus

• Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, neutral): “The expectations follow directly from the results of Magnus [1979] and Kendall and Stuart [1977].”
• Finite sample properties of maximum likelihood estimator in spatial models (2007, result): “Utilizing the results of Magnus (1978, 1979) , among others, and noting that both M 1 and M2 are symmetric, we have the following results on yij ¼ E½ðe0M 1yÞ i �ð e0M 2eÞ j � :”
• From moments of sum to moments of product (2008, unknown): “…Q s 1 ,...,s p as a sum of various products of the traces of s = s 1 + . . . + s p matrices related to A i ’s and Σ (see Kumar [11], Magnus [12,13], Don [4], Tracy and Jindasa [21], Jindasa and Tracy [9], Tracy and Sultan [22] for the development of this type of formulae, see also Mathai and…”
• The Second-Order Bias and Mean Squared Error of Estimators in Time Series Models (2007, background): “For any symmetric matrix Ni, Magnus (1978, 1979), among others, derived the following results on the expectations of products of quadratic forms in a normal vector y ∼ N (0, I) , E (y0N1y) = trN1, E (y0N1y · y0N2y) = (trN1) (trN2) + 2tr (N1N2) , E (y0N1y · y0N2y · y0N3y) = (trN1) (trN2) (trN3) +…”
• Testing Slope Homogeneity in Large Panels (2005, unknown): “See Lemma 4 in Pesaran (2006). Lemma 3 Suppose that D is a p×p stochastic matrix; non-singular with probability one, such that D = Op(1), E(D) = O(1), and D−E(D) = Op(T−1/2).”