accurate vs unbiased statistic
In the 6 desirable qualities of a complement of credibility, what's the difference between an accurate statistic and an unbiased statistics. Isn't an unbiased estimator also accurate? This is what Werner says
I don't understand the "close" portion, it seems like the sentences are saying the same thing... an unbiased statistic may vary randomly but should average out to zero right? so wouldn't it also be close?
Comments
Yes, the error in the unbiased estimator may average out to 0 over many years but you could have a situation where the true value of the parameter is 50 but over many observations, you see predictions anywhere from 20 to 80 (distributed randomly)
For an accurate estimator, if the true value of the parameter is 50, your predictions over many observations would always be close to 50, say between 50 and 52. The prediction error using an accurate estimator might not average out to 0, but the prediction would always be "close", where the definition of "close" depends on the context.