It seems like there is a discrepancy between these two authors on what a LRT is.

Casella and Berger state on pg. 375. That the LRT statistic is:


While Wasserman in "All of Statistics" states the likelihood ratio statistic is:

$\lambda = 2\log\left(\frac{L(\hat{\theta})}{L(\hat{\theta}_0)}\right)$

Are these the same? If so is one more common than the other?

  • $\begingroup$ Does L in Casella and Berger refer to the likelihood or the log-likelihood? Same question for Wasserman. $\endgroup$ May 3 '16 at 18:37
  • $\begingroup$ Both refer to the likelihood. $\endgroup$
    – Alex
    May 5 '16 at 15:28

There does not seem to be any reasonable response to this question, therefore I offer a late explanation.

Casella's is more standard, however, Wasserman's gives you the asymptotic null distribution. That is, if we denote the Casella's statistic by $T_C$ and Wasserman's by $T_W$, then of course $T_W=-2\log(T_C)$ and under some regularity conditions you can show that under the null, $T_W\to \chi^2_k$ weakly where $k$ is the difference in dimensions of the null and full parameter space.

So Wasserman gives you the ready statistic whose asymptotic distribution is well known.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.