I have an experiment with $N$ signal trials and $M$ no signal trials and I have measure the number of hits $nHit$ and the number of false alarms $nFA$. From this I can compute the probability of a hit $p(Hit)$, the probability of a false alarm $p(FA)$, and the index of sensitivity $d^\prime$. Specifically, I define $d^\prime=z(p(Hit))-z(p(FA))$ where $z(.)$ is the inverse of the normal distribution cumulative density function.
I can also find the confidence intervals of $p(Hit)$ and $p(FA)$ with the inverse of the binomial distribution cumulative density function. Is there a similar way of calculating the confidence interval of $d^\prime$ that doesn't involve resampling the data (e.g., bootstrapping).