# coverage of confidence interval

I need to check the coverage of a confidence interval, but I don't know which one of the following approaches I should use.

Approach 1:

1. Estimate the regression parameter $\theta$
2. Use the sandwich estimator to estimate the variance $\hat{\sigma}$
3. Create the confidence interval (assuming asymptotic normality)

Repeat it N times and get the proportion of times that the true $\theta$ falls inside the confidence interval.

Approach 2:

1. Estimate the regression parameter $\theta$ for N simulations
2. Take the standard error of $\hat{\theta}$, which returns a single number
3. Create N confidence intervals (assuming asymptotic normality) based on the estimates of $\theta$ and the standard error of $\hat{\theta}$
4. Get the proportion of times that the true $\theta$ falls inside the confidence interval

In summary, the first one we check if the true $\theta$ falls inside the confidence interval at each simulation (hence, we use the sandwich estimator for the variance). In the second one, we check only after the N simulations have been done, so that the standard error of the estimates is used to create the interval.\

They will create different confidence interval with different coverage. Which one should I use? I have seem people using both.

• As a side note, I see that both the sandwich and empirical variance estimates will be asymptotically equivalent, but they differ in finite samples. So I don't know which one to use. Thanks for the help. – bnh May 13 '15 at 14:12