my %rehash;
for my $SUBNAME (sort keys %HoH){
  for my $testname (sort keys %{ $HoH{$SUBNAME}  })  {
    for my $value_name (sort keys %{  $HoH{$SUBNAME}{$testname} } ){
     my $val =  $HoH{$SUBNAME}{$testname}{$value_name};
     if (exists  $rehash{$testname}{$value_name}
         and      $rehash{$testname}{$value_name}[1] > $val){
       # Do not update - greater value exists
     }else{
       $rehash{$testname}{$value_name} = [$SUBNAME,  $val];
     }
    } 
  }
}


for my $testname (sort keys %rehash){
   print "For $testname:\n";
   for my $value_name(sort keys %{ $rehash{$testname} }){
     print "   $rehash{$testname}{$value_name}[0] has $value_name\=$rehash{$testname}{$value_name}[1]\n";
  }
}