Incremental stats on heavy partitioned table

My client has huge table with partitioned table. They do not have control for any DML changes..  For example, they may update few hundred of records or some times they may delete millions of records per day. They see performance issues when they take stats and also re-indexing the indexes taking lot of time. Looks like the current stats update process is not for the changed records only. We would like to review the best practices for such huge partitioned table with daily / weekly re-indexing.