4
$\begingroup$

We often see the terminology "confidence ellipse". This is not correct: in dimension 2, an ellipse is a curve, and the confidence region is the interior of this curve, not the curve. Similarly, in dimension 3, an ellipsoid is a surface, not a volume. And I don't know any name for the interior of an ellipsoid (though this is a ball for an appropriate metric).

What is the correct name, in arbitrary dimension ?

  • an ellipsoidal confidence region ?
  • an elliptic confidence region ?
  • an elliptical confidence region ?
  • another name ?

In French, my mother tongue, I would hesitate between "ellipsoïdal" and "elliptique". I don't know what is the French for "elliptical".

$\endgroup$
1
  • 2
    $\begingroup$ There are 400 thousand google hits for "area of an ellipse" which is strictly speaking a meaningless phrase if ellipse is defined as a curve (area of a curve is always zero). Personally, I am happy to tolerate this slight sloppiness. $\endgroup$
    – amoeba
    Aug 7, 2017 at 10:01

1 Answer 1

2
$\begingroup$

In common English use we regularly find people using "circle" to refer to the circular disc, not just its boundary, usually without confusion of what was intended. I agree that "ellipsoid" refers to the boundary while that is simply the bounds for the confidence region but I would have little hesitation in saying an ellipsoidal confidence region in spite of it being a bit of a fudging of the terminology.

If you wanted to be strict you could say something like a confidence region consisting of the interior of an ellipsoid but that seems slightly awkward; the less precise term would be unlikely to be misunderstood in most cases.

In some situations I might say something like "ellipsoidal ball"; while not all that common, it has sometimes been used -- see for example its use on page 652 here (near the middle of the page) -- and would likely be understood.

I'm unaware of a widely accepted single-word term for the interior; while one probably exists, enough people may be unfamiliar with it that it might not be the ideal choice anyway.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.