In my elementary statistics course, I learnt how to construct 95% confidence interval such as population mean, $\mu$, based on asymptotic normality for "large" sample sizes. Apart from resampling methods (such as bootstrap), there is another approach based on "profile likelihood". Could someone elucidate this approach?
Under what situations, the constructed 95% CI based on asymptotic normality and profile likelihood are comparable? I could not find any references on this topic, any suggested references, please? Why isn't it more widely used?