are overlapping multi column statistics redundant?
They're not redundant, no.

Each statistics object includes a histogram of the values stored in the first listed column. For the remaining columns, only density information is kept at each level (no histogram).

For example, the proposed statistic on (ClassID, SegmentID, GroupID, Tier1, LanguageID, Active) would create:


A histogram for ClassID values
A density number for:


ClassID, SegmentID
ClassID, SegmentID, GroupID
ClassID, SegmentID, GroupID, Tier1
ClassID, SegmentID, GroupID, Tier1, LanguageID
ClassID, SegmentID, GroupID, Tier1, LanguageID, Active



These densities can be useful when there is correlation between columns, but only for equality predicates (and you will need SQL Server 2016 to get this benefit when using the 'new' cardinality estimator. The original cardinality estimator used this density information by default).

You can see the histogram and density information using DBCC SHOW_STATISTICS.

Note the order of columns is important. This statistic could provide average density information for equality predicates on (ClassID, SegmentID, and GroupID) but not (ClassID, GroupID).

Statistics are quite lightweight as far as storage is concerned, but you need to be aware of the potential cost of maintaining them, especially on large tables where a high sampling rate is necessary to achieve acceptable quality.

If DTA recommends a statistic, that is a good indication that the statistic would be useful for one or more queries in your workload. I don't recall if DTA reports on the queries that contributed to a recommendation, but if not, for the example above, you would be looking for queries with equality predicates on all the columns listed. Compare the quality of the plan and cardinality estimates with and without the new statistic if you really want to dive into the detail.

The missing index would create an associated statistic on (IconTypeID, Active), with a histogram on IconTypeID, and average density information for the combination (IconTypeID, Active).

See the following for more information:


Statistics
Statistics Used by the Query Optimizer in Microsoft SQL Server 2005