Self employed People - hard to verify

You need to check if they have physical address of their business. You may pay a visit to verify existing of the business. Further more, you need to verify document income such as

1) tax return

2) bank statement if any

3) business invoices

4) etc

It's hard to verify this kind of income. 

$4k+ is a lot of rent money on monthly basis. You'd better to find people employed by well known companies.