Talk:Confidence region

I will likely add more to this article in the next few weeks. --Coppertwig 22:17, 8 September 2007 (UTC)[reply]

Non-ellipsoidal regions

"Usually represented as an ellipsoid, although any shape can appear" - how do other shapes appear? The ellipsoid is a consequence of using least-squared error, I believe... is this meant to imply that other shapes would exist with other norms (like say mean absolute divergence)? --User:jmalicki

I've weakened it a bit to "other shapes can occur" as "any shape can occur" is a very strong claim and was unreferenced. (e.g. I've never seen concave shapes in practice, though perhaps they aren't impossible.) Shapes other than ellipses are certainly possible though as confidence regions apply to any multiparameter statistical estimation procedure, not just least-squares. For example, they can be defined by a contour of the likelihood function, which certainly aren't always elliptical. Also you may have used a Data transformation before fitting a model by least-squares and wish to back-transform before plotting the confidence region, which in general will change the shape of the confidence region. Qwfp (talk) 20:34, 25 June 2010 (UTC)[reply]