"收藏家收集的对象" can be translated into English as "the objects collected by collectors" or more concisely as "collector's collections" (though this latter phrase slightly shifts the focus to the entirety of the collections rather than individual objects).
For a more literal and precise translation that emphasizes the individual items being collected, "the items/objects that collectors collect" or simply "collector's items" (when referring to the specific things of value or interest that collectors seek) would also be appropriate, depending on the context.
Among these, "the objects collected by collectors" most directly corresponds to the Chinese original in terms of structure and meaning.