I'm not sure it's possible to entirely remove one's own voice from the work, though perhaps that should be a goal when writing in third or first person.
I suspect there is a remainder of one's own self in the text always--a portion that we don't often see or notice, just as the unconscious tends to impact our real lives below radar. I think of myself and other people as multidimensional with many more undeveloped than developed dimensions, given we only have one life apiece. So my POV characters are to some extent previously undeveloped dimensions of myself. (A scary concept I daresay for mystery/suspense authors.)
PS: I almost never use the word "daresay" but I've got a new first person POV character in an historical Gothic thriller I'm writing, and he does. The walls are permeable, people, I'm telling you!
I'm not sure it's possible to entirely remove one's own voice from the work
I can't think of any reason you'd want to, unless you're writing user manuals for microwave ovens, or something. Whatever voice you invent is ultimately your voice--I think that's what Chekhov was talking about. Characters are inventions: the degree to which they seem multifaceted and independent of us is entirely our doing. All of my characters resemble me in the sense that they're the products of my imagination. Someone else would have imagined different characters. Ishmael is Melville--but so is Queequeg, and so is Ahab. Not to compare myself to Melville, but you get the point.
Right. Just people. And our characters resemble is in that they can't do, think or say anything we're incapable of imagining. So they bear our mark for everyone to see, for better or worse. There are Parker characters, and there are Loomis characters, and they're more like us than not, even if we like to pretend otherwise. Which we do.
The idea is to get into the character's head and converse the way that character would converse. Easy to do in first-person singular (at least, for me). Third-person is harder. Overviewing all characters almost forces the writer to make commentary, or stamp their 'writer's voice' into the pages. Yet is that necessarily bad?
This is why I started with first-person PI fiction: it could be in my voice and I'd get away with it until I learned how to do it better.
Now I hear other voices in my head when I write--no, not those voices, my characters'--and it's much easier. I also usually make one draft of each long piece solely for the characters' voices, one character at a time. For example, one time through just for Joe. I get myself into his frame of mind, and do all his dialog and/or narratives. Then I do something else (cleanse my palate) and do another character until they're all done.