For example, in the sentence A quick brown fox jumped over the lazy dog, determined noun phrases are a quick brown fox and the lazy dog, while quick brown fox and lazy dog are bare noun phrases.
A bare noun phrase lacks a determiner slot whereas a determined noun phrase has a determiner slot. However, the determiner slot in a determined noun phrase may be an empty slot (null element). The test therefore is not whether a noun phrase has a determiner but whether a determiner can be added. A pronoun can act as the head of a determined noun phrase but not as the head of a bare noun phrase.