5

How do I call a forecast (more precisely, a forecasting rule) that is both accurate and precise?
Is there a word that expresses both properties combined?

I do not mean the forecasting rule is perfect, i.e. it does not have to produce forecasts that always perfectly coincide with their respective targets, but its accuracy is good (low bias) and its precision too (low variance).

Richard Hardy
  • 54,375
  • 10
  • 95
  • 219

3 Answers3

2

When I first studied statistics, it was actually an econometrics module and from what I remember (it was a while ago) a great deal of emphasis was placed on estimators that were BLUE. Best Linear Unbiased Predictor, arising from the Gauss-Markov Theorem in the context of linear regression models.

So if you are dealing with a linear model, maybe BLUE can apply to you ? If not, then BUE.

I suppose that, to be BLUE or BUE, although they would be unbiased, they are not necessarily precise, because Best just means lowest variance - so there could be several very imprecise estimators, but one of them will be best. To get over this hurdle, there could need to be some (presumably subjective) choice as to the hurdle for what level of precision is desired.

With that in mind, perhaps it is useful for your case ?

Edit: There doesn't seem to be a word which simultaneously means both (unless we can create one into existence in this thread perhaps !) so to avoid the problem of comparison by using Best, another alternative is simply Precise and Unbiased.

Robert Long
  • 53,316
  • 10
  • 84
  • 148
  • Thank you for your answer. The **B**est thing is a little too much. I need an absolute term (like good or bad), not a comparative one (like better, worse, best, worst). (I know grammatically the latter is called superlative, but substantively I think I can call that comparative since it compares one or more against the rest.) – Richard Hardy Jun 22 '18 at 13:53
  • @RichardHardy By definition, a precise estimator has a low variance, and an estimator with lower variance is called "more precise". Therefore, I wonder if you can just use: "**Precise &Unbiased**" – Robert Long Jun 22 '18 at 16:25
  • Truly unbiased forecasts are difficult to get. Unbiased would mean of ideal accuracy, and that is a tough requirement. – Richard Hardy Jun 22 '18 at 16:31
  • @RichardHardy I agree. More often than not, we rely on asymptotic unbiased-ness. Still, the terminology persists ! To be pedantic then: **Precise and Asymptotically Unbiased**? **PAU**, there you go :D – Robert Long Jun 22 '18 at 17:37
  • This comes from an idealized world. What if one cannot guarantee the forecast is asymptotically unbiased? Reasonably precise and accurate, yes, but (asymptotically) unbiased? Who knows. – Richard Hardy Jun 22 '18 at 18:08
  • @RichardHardy again, I don't disagree. We can make assumptions and test them, but at the end of the day, who knows, as you say !? – Robert Long Jun 22 '18 at 18:19
0

How about "correct"?

Correct = free from error. Therefore free from bias-error, i.e accurate, and free from variance-error, i.e. precise.

AlainD
  • 513
  • 2
  • 8
  • I think *correct* is not a good idea. First, it reminds me of *perfect*, suggesting that the outcome is forecasted perfectly (the forecast equal the outcome). Second, it suggests that the forecast-generating rule is not systematically faulty, while neither *accurate* nor *precise* implies that, unless we mean *perfectly accurate* and *perfectly precise*. – Richard Hardy Jun 21 '18 at 15:30
  • What about simply "useful"? – kjetil b halvorsen Jun 22 '18 at 10:39
  • Then why not *accurate and precise*? I do not think you can escape explaining what you mean with a few words... – AlainD Jun 22 '18 at 13:13
  • @AlainD, hmm, that is an option indeed. Would not sound elegant, but at least that would be informative. – Richard Hardy Jun 22 '18 at 13:51
  • 1
    @Richard. You are right, not elegant, but you have to admit it'll be both accurate and precise. – AlainD Jun 22 '18 at 18:07
0

My guess would be 'consistent forecast'. As you said:

How do I call a forecast (more precisely, a forecasting rule) that is both accurate and precise?

Quoting Wikipedia on consistency: Use of the terms consistency and consistent in statistics is restricted to cases where essentially the same procedure can be applied to any number of data items. I am taking procedure and rule to be synonymous in this case.

And some more: A consistent estimator is one for which, when the estimate is considered as a random variable indexed by the number n of items in the data set, as n increases the estimates converge to the value that the estimator is designed to estimate.

So if the estimate converges to the value the forecasting rule is designed to estimate then it can be called accurate and given the same information the forecasting rule must give precise forecasts.

naive
  • 899
  • 1
  • 9
  • 14
  • 1
    This is rather specific (an accurate and precise forecast need not be consistent) and tangential to the part "precise" (a consistent forecasting rule can be imprecise in any finite sample). – Richard Hardy Jun 22 '18 at 19:03
  • By imprecise do you mean high standard deviation? I didn't get the first part of your comment I.e. an accurate and precise forecast need not be consistent. – naive Jun 22 '18 at 19:11
  • By imprecise, yes. Consistent means it converges to a perfect forecast; mine need not converge. It can stay about as good as it is for any sample size. – Richard Hardy Jun 22 '18 at 19:24
  • That means your forecast's goodness has to be independent of sample size. What if the sample size is 1? – naive Jun 22 '18 at 19:27
  • Vis-à-vis a sample size of lets say 1000? – naive Jun 22 '18 at 19:31
  • I think this is getting off-topic. Consistent is not the same as accurate and precise. It is neither a superset nor a subset. I doubt discussing this further can be relevant. – Richard Hardy Jun 22 '18 at 19:34
  • I have been a fan of your answers on CV. Just wanted to learn something new. Thanks! – naive Jun 22 '18 at 19:39
  • Hey, thanks for the kind words! I did not mean to sound rude, I simply thought this was getting off topic, that's all. Thanks for your answer. – Richard Hardy Jun 22 '18 at 19:41