Hello! I also had a problem to get stats_json working. The solution is to create the file and make it accessible by the PageSpeed module. In Josefs case I would do the following:
mkdir -p /var/www/mydomain/htdocs/ngx_pagespeed_statistics/
touch /var/www/mydomain/htdocs/ngx_pagespeed_statistics/stats_json
This will create all necessary directories and files for the ngx_pagespeed_statistics to work. The problem is that PageSpeed is still in Beta which means that they have still forgotten to add some things. If there is something else missing try to create the paths and files and make them accessible by PageSpeed and it will work out for the most part.
To get a basic and nice starting config I used this tutorial: https://easyengine.io/tutorials/nginx/using-pagespeed/
Hope this helps.
