the Wald, Likelihood Ratio (LR) the Lagrange Multiplier (LM) test statistics Are monotonic function of F statistics

Asked Sep 19 '22 at 21:37

Active Sep 20 '22 at 01:45

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Consider a classic linear regression model.

I want to show that the Wald, Likelihood Ratio (LR) the Lagrange Multiplier (LM) test statistics for the null hypothesis $H_0: R\beta =r$ for a constant vector $r$ are all monotonic functions of the standard F statistic.

Please suggest a book or document which show this theoretical proof.

Update: I found the article which exactly proves the statement in this question.

edited Sep 20 '22 at 01:45

asked Sep 19 '22 at 21:37

1190

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Does this answer your question? Likelihood ratio, Wald, and Score are equivalent? – Dave Sep 19 '22 at 22:03
Exactly no. I want to theoretically prove that these tests follows F distribution (with mathematical proving ways) @Dave – 1190 Sep 19 '22 at 22:09
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I thought that answer addressed the inequality. It’s in a follow-up. – Dave Sep 19 '22 at 23:00
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@Dave I found its proof. https://www.sciencedirect.com/science/article/abs/pii/0165176581900264?via%3Dihub Thank you. – 1190 Sep 20 '22 at 01:46
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You might consider typing up an answer to close out this question. Self-answers are not particularly common, but they are not frowned-upon. (I have done it a couple of times.) That also gives you a chance to evaluate your knowledge: if the post gets downvotes or other negative feedback, it could signal a gap in need of filling. – Dave Sep 20 '22 at 01:53

the Wald, Likelihood Ratio (LR) the Lagrange Multiplier (LM) test statistics Are monotonic function of F statistics

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