Category Springer Texts in Business and Economics

Joint Confidence Intervals and Test of Hypotheses

We have learned how to test any single hypothesis involving any linear combination of the в’s. But what if we are interested in testing two or three or more hypotheses involving linear combinations of the в’s. For example, testing that в2 = в4 = 0, i. e., that variables X2 and X4 are not significant in the model. This can be written as c’2в = c’4в = 0 where cj is a row vector of zeros with a one in the j-th position. In order to test these two hypotheses simultaneously, we rearrange these restrictions on the ^s in matrix form Rв = 0 where R’ = [c2,c4]. In a similar fashion, we can rearrange g restrictions on the ^s into this matrix R which will now be of dimension (g x k)...

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