To list the objects that are stale:

declare 
mylist dbms_stats.ObjectTab; 

begin 
   -- GET list of missing stats 
   dbms_output.put_line( 'BEFORE' ); 
   dbms_stats.gather_schema_stats(ownname=>'DBAADMIN',options=>'LIST STALE',cascade=>true,objlist=>mylist); 

   FOR i IN 1..mylist.count 
   LOOP 
      dbms_output.put_line( mylist(i).ownname||'.'||mylist(i).objname||' '||mylist(i).objtype ); 
   END LOOP; 
   
   -- GATHER STATS 
   dbms_stats.gather_schema_stats(ownname=>'DBAADMIN',options=>'GATHER STALE',cascade=>true ); 
   
   -- CHECK LIST AGAIN 
   dbms_output.put_line( 'AFTER' ); 
   dbms_stats.gather_schema_stats(ownname=>'DBAADMIN',options=>'LIST STALE',cascade=>true,objlist=>mylist); 
   
   FOR i IN 1..mylist.count 
   LOOP 
      dbms_output.put_line( mylist(i).ownname||'.'||mylist(i).objname||' '||mylist(i).objtype ); 
   END LOOP; 
end; 
/