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This is more of a semantic question. I'm working on translating a work from French to English related to statistics. In French, there is only 1 word as far as I can tell to describe both bias and variance, and that is 'précision'.

In English, there is 'accuracy' for essentially bias, and 'precision' when talking about variance.

Here, the author is talking about two estimators, one of which has always lower MSE than the other, and uses the word 'précis' in French. For English, would this be more 'accurate' or 'precise' when talking about MSE?

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Note that French indeed has two words: biais and variance.

For your actual question, recall that MSE is composed of both bias and variance, via the bias-variance tradeoff and related decomposition. So if all we know is that one estimator has lower MSE than another one, we don't know whether this is due to lower bias or lower variance (i.e., higher precision).

I personally would not quibble overmuch and simply use "more accurate". Or "lower MSE" when precision is required (yes, pun intended).

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