I was taught the same as 237SJ, if you don't have the name of the person, then it's your Faithfully, and if you address the letter to a named person, then it's your Sincerely................things have changed though, less formal these days!...I usually just add my signature!.........
This is not a letter. It is a statement. It is not addressed to an individual. So no "Yours sincerely" or "Yours faithfully" is required. Just a signature.
I think, that if XXX Company has written to you to provide a character (or other) reference for a person; you could write either Dear Sir, and end with Yours faithfully, or Dear Mr. F, I have known etc. and end it Yours sincerely, but if it was an open reference, to be given to ten (for example) future employers, it would be an "open letter" like I described, to enclose with each of their applications for employment, and just your name would suffice.
I have noticed a distinct slackening of formal address nowadays. I have received letters ending Warmest regards from people I don't know from Adam (whoever he was). I even joined the masses and now end my letters with Best regards, Good wishes or other such blatant lies.
My original post assumed that the questioner particularly wanted to append "Yours >something<" at the end of the letter. (In which case, I'm sticking with "Yours faithfully").
However, as others have stated, simply signing the document alone would suffice. (The last time I wrote "To whom it may concern" was for a court reference for someone. I simply signed it at the bottom, omitting any formal ending).