Announcement
Technical note:
Best means best in terms of something called quadratic loss (or
squared-error loss). The name says what it is. Suppose there is a true
value you wish to estimate and you are required to pay a penalty
depending on how far off you are. In particular, suppose the penalty is
(estimated value - true value)2 , that
is, the square of the difference between your estimated value and the
true value. You do this repeatedly and are free to use whatever estimate
you choose. For many of these problems, statistical theory shows that
you'll lose the least amount of money if your estimate is the sample
mean. For example, suppose you have to estimate a population mean. You
might estimate it by using the first observation alone, or the mean of
the largest and smallest observations, or by the median. However,
statistical theory says if you use anything other than the sample mean,
you'll pay more in the long run.