The most common and most likely answer to this crossword clue is the 10 letter word GENERALISE
I've seen this crossword clue in Financial Times
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More clues leading to the result GENERALISE
Buddy explains!

The straight part
We know that "Make sweeping statement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make sweeping statement = generalise.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does GENERALISE mean?
GENERALISE verb- To speak in generalities, or in vague terms.
- To infer or induce from specific cases to more general cases or principles.
- To derive or deduce (a general concept or principle) from particular facts.