When it comes to confidence intervals on parameter estimates and prediction intervals on the predictions of a statistical model - do larger "widths" of these intervals "necessarily" imply sub-optimality of the statistical model itself?
From a very naïve perspective, one could say that confidence/prediction intervals with smaller widths are better, seeing as the smaller sizes could be indicative of "lesser risk" and "higher certainty" attributable to the model - but on the other hand, "smaller widths" might be the result of "model arrogance": the model could be very confident about the confidence/prediction intervals, but nonetheless be outright wrong about these intervals (e.g. the true value might not even be straddled within the intervals).
Regarding confidence/prediction intervals with larger widths - these are generally viewed as undesirable, seeing as large widths are indicative of models that are inherently more certain, even if the true value is straddled within the intervals (e.g. suppose the true value is 51, but the interval is between - 10,000 and 5,400).
My Question: Is the above statement true? Are "larger" confidence/prediction intervals (another point, there is no real threshold to compare "widths", i.e. what ranges are truly big?) necessarily indicative of poor models, whereas smaller confidence/prediction intervals may or may not be associated with poor models?
Is this a reasonable statement?
Thanks!
