Do you mean 'integrity' as in like for rootkits, viruses, and that sort of thing?
Far as I know, you could build & use 'RKhunter' or 'chkrootkit' without root installation privileges, but hopefully (probably
) someone will correct me quickly if I am mistaken. You would need to alter their default configuration and/or search paths, but I think that can be done.
As for viruses, I won't attempt to suggest anything, because I don't use anything.
If it is something totally NOT along these lines that you are seeking, please clarify.
Sasha
PS - if this IS the stuff you seek, then you might suggest these tools to your server admin, for root installation, though I would like to think that any respectable server admin/host has tools of this sort in place already... Then again, who knows :/