An example where minimizing the squared error gives terrible estimates

• Suppose we have a network of 500 computers and they all have slightly imperfect clocks. • After doing statistics 101 we decide to improve the clocks by averaging all the times to get a least squares estimate – Then we broadcast the average to all of the clocks. • Problem: The probability of being wrong by ten hours is more than one hundredth of the probability of being wrong by one hour. In fact, its about the same!

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