How to maintain Index and Statistics on AWS RDS?
I am running SQL Server RDS maintenance jobs (DBCC CHECKDB, index reorgs/rebuilds, statistics updates) without a problem.  The only limitation I had to work around was that I could not run sp_updatestats, so instead had to generate an 'UPDATE STATISTICS' script for each table like this:

DECLARE @sql NVARCHAR(max) = '';
SELECT @sql = @sql+
'UPDATE STATISTICS ' + '[' + table_name + ']' + ' WITH FULLSCAN;
PRINT ''UPDATING STATISTICS ON ' + table_name +'...'';
' 
FROM information_schema.tables
where TABLE_TYPE = 'BASE TABLE';

EXEC sp_executesql @statement=@sql;