The TraMiner Package includes an option to include sampling weights in the analysis. However, I haven't found any discussion in the package documentation (or associated user manual) of how standard errors are calculated in the presence of sampling weights - such as the calculation of the standard error of the mean for the number of times that a state appears in each sequence.
I assume that some version of the Horvitz-Thompson variance estimator is used, assuming non-uniform first-order inclusion probabilities in a non-stratified, non-clustered probabilistic sample. However, I would like to know what assumptions are made about second-order inclusion probabilities - in practice, are finite population corrections introduced (e.g. treating the finite population size as the sum of the weights) or not?
Apologies if this is documented somewhere that I haven't found. If TraMiner's SE calculations rely on some other package's facilities I would be happy to be directed to those so that I can consult their documentation. Thank you in advance for any assistance with this.