# Hosmer-Lemeshow test with weighted data

I am trying to perform Hosmer-Lemeshow test on weighted data (i.e. each observation in a data set has its weight). Unfortunately, I cannot find any literature on how to perform such test. Do you know any method of dealing with this problem?

To give you a background, I try to assess the predictive power of a model on a out-of-sample data. However, these observations have different weight. I tried bootstrapping but I was wondering if there is any purely statistical method for this problem - you know confidence intervals, tests and so on :).

For information on Hosmer-Lemeshow test, its critique and better alternatives, see corresponding links in my answer. As it has been mentioned in this answer by Prof. Frank Harrell, the alternative methods are implemented in R package rms (http://biostat.mc.vanderbilt.edu/wiki/Main/Rrms). The corresponding paper, describing the above-mentioned methods, can be found here.