On the expectation of the product of four matrix-valued Gaussian random variables
نویسنده
چکیده
The formula for the expectation of the product of four scalar real Gaussian random variables is generalized to matrix-valued (real or complex) Gaussian random variables. As an application of the extended formula, we present a simple derivation of the covariance matrix of instrumental variable (IV) estimates of parameters in multivariate linear regression models. (*) Faculty of Electrical Engineering, Eindhoven University of Technology (EUT), P.o. Box 513, NL-5600 ME Eindhoven, the Netherlands. (**) Facultatea de Automatica,Institutul politehnic Bucuresti, Splaiul Independentei 313, R-77206 Bucharest, Romania. Mailing address: P.H.M. Janssen, Eindhoven University of Technology, Faculty of Electrical Engineering, Measurement and Control Group, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands
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