Keeping fresh statistics on join indexes is as critical for join indexes ass for base tables for optimizing the query plans generated by the Optimizer.
This is particularly true for a single-table join index whose definition includes a complex expression in its select list and whose statistics are to be used to make more accurate single-table cardinality estimates when a query that specifies a matching expression in its predicate is run against the table on which the join index is defined.
The Optimizer can also use expression mapping for an expression in a query predicate within a nonmatching predicate. The Optimizer maps to the join index column that is defined using the matched expression.See Using Join Index Statistics to Estimate Single-Table Expression Cardinalities .
You cannot collect statistics on the PARTITION column of a PPI join index.