Well there are at least three Arthur Schmidts in the DB:

Arthur Schmidt born 1912, died 1965 - also known as Arthur P. Schmidt.
http://www.imdb.com/name/nm0772834/
http://en.wikipedia.org/wiki/Arthur_P._Schmidt

Arthur Schmidt born 1937 - also known as Arthur R. Schmidt (but not in CLT).
http://www.imdb.com/name/nm0772831/
http://en.wikipedia.org/wiki/Arthur_Schmidt_(film_editor)

Arthur Schmidt born 1895, died 1987 - credited in one profile (The Battle of Russia)
http://www.imdb.com/name/nm0772833/
http://en.wikipedia.org/wiki/Arthur_Schmidt_(soldier)
http://www.lexikon-der-wehrmacht.de/Personenregister/S/SchmidtArthur.htm

So there's no doubt in the need for a BY for at least the second and third. But what's the common name for the first?
According to CLT there are these profiles crediting him:

Arthur Schmidt:
Ace in the Hole
Anne of Green Gables
The Blue Dahlia
Monsieur Beaucaire
Red Garters
Sorrowful Jones
We're No Angels

Arthur P. Schmidt
Bonanza
Cinderfella
The Disorderly Orderly
The Errand Boy
The Family Jewels
Finishing School
Li'l Abner
The Old Man and the Sea
The Patsy
Sayonara
The Spirit of St. Louis
The Vagabond King

Both (I found those in CLT as Arthur Schmidt and as Arthur P. Schmidt):
Bulldog Drummond: Secret Police
Bulldog Drummond: Revenge
The Nutty Professor
Sabrina
Some Like it Hot
Sunset Blvd.
When Worlds Collide

And these profiles, I cannot link to any of the mentioned:
Kenneth Anger: Magick Lantern Cycle (credited as Arthur P. Schmidt, but not mentioned on IMDB or wikipedia)
George A. Romero's Night of the Living Dead
Pirates of the Caribbean: A Dead Man's Chest (I guess this is wrong, because it's just credited ones on 7-890552-045993 Brazil)

Pirates is wrong as it's the editor Arthur Schmidt on that. I know as I only had titles with the editor in my colection. I also own 2 dvd versions of Night of the Living Dead and neither has this name. If that is really George Romero's or even Savini's remake (also own), it is wrong. I've audited both titles myself.

Beginning creditd for Sabrina show "Arthur Schmidt"
Some like it Hot shows "Arthur P. Schmidt" as you have noted already

When Worlds Collide - Edited by . . . ARTHUR SCHMIDT (opening credits)

Quoting StaNDarD:

Quote:
Still looking for:
The Old Man and the Sea

Cinderfella - Arthur P. Schmidt - Edited by

The Family Jewels - Arthur P. Schmidt - Associate Producer and Editorial Supervisor

The Nutty Professor (1963) - Arthur P. Schmidt - Associate Producer

Sorrowful Jones - Arthur Schmidt - Editorial Supervisor