inaccurate statistics in multitenant database We are using Azure SQL and have "multi tenant" database. All tables have tenantid + entityid pk. Some tenants have a lot of data and some tenants quite small. 
Also auto update statistics is enabled.

Sometimes (quite often recently) after auto update of statistics  we get inaccurate statistics (depending on sample) and according to it tenant has 1 row (but actually 10-100k).
This leads to bad execution plans and performance problem for the whole db.

Maybe somebody has ideas how to fix it.
My suggestion with Azure SQL Database, perform index maintenance during off-hours using Ola Hallengren's scripts and after that update all columns statistics with full scan. Do not rely on automatic features on medium size databases (> 100 GB).

Here you will find steps to create elastic jobs to update indexes and statistics using Ola Hallengren's scripts.

Another way to perform maintenance of indexes and statistics can be found here using Azure Automation and PowerShell.