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Competitive Stats
Q161Section III (Statistics)161 of 190

Solving the normal equations for an exactly-identified three-parameter, three-observation model

y1,y2,y3y_1,y_2,y_3 are three uncorrelated random variables with common variance σ2\sigma^2 and E(y1)=θ1+θ3E(y_1)=\theta_1+\theta_3, E(y2)=θ2+θ3E(y_2)=\theta_2+\theta_3, E(y3)=θ1−θ3E(y_3)=\theta_1-\theta_3. Hence:

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