The most common occurrence of this type of word sequence is, in my experience, in newspaper headlines. There is an obvious reason for this.
But first, the way this statement would be made in mid paragraph might be slightly different: at least in punctuation.
What is meant, of course, is:-
Studies indicate that violence often begins at home.
It is, in other words, a kind of indirect or reported speech. That is how it would be phrased in a book or article about violence. In a headline, however, you might want concentrate the reader’s’ attention on the striking claim that violence often starts at home. So you put that first.
In any such headline I have seen, however, there is no full stop: just one long statement.
Violence Often Begins In The Home Studies Indicate
Perhaps there might be a comma after “home”, but not necessarily. The grammar ressembles the direct speech:
“Violence often begins in the home”, studies indicate.
It is as if someone had said this.
“Charity begins at home”, said Charlie. Or it could be. “.... home”, she said.
What is really going on is more about rhetoric than about grammar. The device makes many a rapid reader, skimming the headlines, to take on board only the first part:-
Violence often begins at home.
The qualification, that this is a proposition suggested by studies, can be ignored. The more common rhetorical abuse of this approach is more familiar in more startling claims:
JUSTICE MINISTER IN LOVE NEST WITH DRUG BOSS, SOURCES CLAIM
The headline makes no false claim by may leave a false impression.
The use of “indicates” is also odd. What is meant by “studies”?
- all studies?
- many studies?
- some studies?
The avoidance of precision may encourage the reader of a newspaper, speeding along on the 7:20 from Esher to Waterloo to assume the case is stronger than it really is. But this is not an ‘error’ of grammar or punctuation. It is a lack of semantic precision, which makes it possible to misunderstand the strength of the assertion. That may be intended or unintended: probably unintended, because the verb ‘indicate’ is more ‘cautious’ than you would expect of someone slipping in a sneaky exaggeration.
So your ‘sentence’ is either itself a headline or represents the misuse of a convention for headlines in the body of an article