I am a standard user of a Mac Mini. There are certain applications I would like to download from the web, but they require the Apple installer, which then requires the admin password. Is there any way I could circumvent this?
The whole purpose of the OS requesting authorisation is to prevent software being installed without permission. If there were a method of bypassing the request, that would be considered a 'security flaw' and Apple would (hopefully) fix it quickly.
If you are not the actual owner of the Mac, then you need to ask the owner for permission to install the software.
As long as you have an account with admin privileges you can just fill in the name and password of the admin account even if you are logged in with your standard account. You can not circumvent the question for admin password for security reasons as benwiggy said.