[kitd]

IBM use "on-premise" all the time. Like it or loathe it, it's become the accepted neologism for "self-hosted".

[ghaff]

My personal preference is to use "on-prem" because:

1.) There are arguments but no definitive justification for choosing between on-premise and on-premises.

2.) A lot of what gets lumped under on-prem is not actually on your premises anyway. It's in a colo or a managed hosting provider, etc.