# Why not always use CI's from LRT since they don't require symmetry?

I'm confused on why anyone would appeal to asymptotic normality of mle,

$$\hat{\theta} - \theta_0 \rightarrow^D N(0,I^{-1}(\theta))$$

When we can simply invert the likelihood ratio test

$$L(\hat{\theta}) - L(\theta_0) \rightarrow^D \chi^2_1$$

to obtain a $$(1-\alpha)$$ CI. Is there a situation where this is not a good idea?

• There are other options too, such as inverting a score test.
– Ben
Jun 21 at 19:53
• Agreed, but why not always use something (LRT, score etc) that converge to chi square to exploit asymmetric CIs? Jun 22 at 0:27