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Consider the partitioned linear regression model $$ {\user1{\mathcal{A}}} = {\left( {y,X_{1} \beta _{1} + X_{2} \beta _{2} ,\sigma ^{2} V} \right)} $$ and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2V, where σ2 is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X1 :...
Consider the partitioned linear regression model [MATHEMATICAL FORMULA] and its four reduced linear models, where y is an n 1 observable random vector with E(y) = X and dispersion matrix Var(y) = 2V, where 2 is an unknown positive scalar, V is an n n known symmetric nonnegative definite matrix, X = (X1 : X2) is an n(p+q) known design matrix with rank(X) = r (p+q), and = ( 1: 2 ) with 1 and 2 being...
Abstract. Razzaghi (1987) examined the difference of covariance matrices of competing estimators in misspecified restricted linear models. Further, Gross, Trenkler and Liski (1998) extended Razzaghis result by asserting his sufficient condition for nonnegative definiteness of the covariance matrix difference to be also necessary. In this paper, when the covariance matrix of the disturbance vector...
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