I have a set of $N$ samples $\{x_{i}\},\,{i=1,\cdots,N}$ sampled from a circular random variable $X$ (wrap around at $\pm\pi$) that is NOT von-Mises distributed but is unimodal. I can calculate summary statistics, such as the circular mean and so on but I haven't found a good reference to describe the uncertainty of these statistics. For example, in a non-circular dataset I would calculate the standard error of the mean (SEM), However, from what I've been reading, calculating the SEM for circular data is a little complicated unless the distribution is von-Mises (see this question here.
My questions are
- How can I calculate the SEM for circular data when the underlying distribution is unimodal but not von-Mises
- Are there general methods (a bootstrap of jacknife of some such similar technique) used to calculate undertainties for summary statistics in circular datasets.