I am producing a research statement to be sent to a statistics department and I was trying to avoid the term Machine learning in favour of the more friendly one of Statistical learning. Probably I could not avoid such use.
The classic The Elements of Statistical Learning handbook by Hastie et al discusses neural networks among other algorithms, so it needs to be a “statistical learning” algorithm.
Depending whom you’d ask, neural networks are either statistics, statistical learning, pattern recognition, machine learning, deep learning, or artificial intelligence. There’s no single, agreed category used by everybody to describe them.
That's a political question, not a statistical one :-)
Historically, statistics and machine learning were two distinct communities, with little interaction. ANNs were developed by the machine learning community. Today, the lines might be somewhat blurred, with some statisticians counting ANNs to statistics, while some machine learners count logistic regression and even linear regression to machine learning. Needless to say, some members of the opposite camp beg to differ.
So, there is no simple answer to your question. Calling ANNs statistical method might be seen as justified by some and objected to by others.