4.4 Likelihood Ratio and Wald Tests

Recall that there is no UMP test for two-tail test. So, there is a pressing question: how do we justify the two-tail test? On what basis did we come up with that? Was it out of convenience?

This subsection is devoted to justify the two-tail test.

Read (Hogg, McKean, and Craig 2019, sec. 6.3) and (Wasserman 2004, sec. 10.1).

Hogg, Robert V., Joseph W. McKean, and Allen T. Craig. 2019. Introduction to Mathematical Statistics. 8th ed. Boston: Pearson.

Keener, Robert W. 2010. Theoretical Statistics: Topics for a Core Course. New York: Springer.

Lehmann, Erich L., and Joseph P. Romano. 2005. Testing Statistical Hypotheses. 3rd ed. New York: Springer.

Wasserman, Larry. 2004. All of Statistics: A Concise Course in Statistical Inference. New York: Springer.

References

Hogg, Robert V., Joseph W. McKean, and Allen T. Craig. 2019. Introduction to Mathematical Statistics. 8th ed. Boston: Pearson.

Wasserman, Larry. 2004. All of Statistics: A Concise Course in Statistical Inference. New York: Springer.