Caller ID says "Delivery Dept" but no one was on the line.

same here - picked up, no one on line

From this number 314-627-5553 are calling me every day and nobody talk when I answer the phone.
It's not right that they are calling me every day for nothing.

Got a call from this number yesterday.  Line was silent for a second then the person on the other end picked up.  Said the New York Times has a Maryland edition and asked if I was still living at my address (which she gave me), I said I wasn't interested in receiving a newspaper and she just hung up.

This may be a call center to keep nagging people to re-subscribe to newspapers, or to pay a subscription fee to keep a newspaper subscription coming to you. They computer call you, then wait to detect a voice on the line, then are supposed to switch you to a person. However, the vast majority of the time, nothing happens and the line hangs up.

Caller: DEPT DELIVERY