Point Estimation from a Decision-Theoretic Viewpoint
True story: I was out for lunch with two friends recently. I didn’t care what restaurant we went to, but my friends John and Marsha had strong preferences, one for Indian food and the other for Chinese. When it became clear that neither one was going to yield to the other in a reasonable amount of time, I proposed to settle the argument by picking a random digit between 1 and 9 (using the random number generator on the fancy-dan cell phone I always carry on my belt) and having each of them try to guess its value. Whoever was closest to my number would get to choose the restaurant. John made the gentlemanly but ill-advised gesture of letting Marsha guess first. Marsha immediately guessed “5“ and guaranteed herself an advantage, since no matter what John guessed, there were at least five out of nine numbers that she would be closer to than John. When John unexpectedly won the game, he made the gentlemanly but ill-advised gesture of choosing Marsha’s restaurant. It was John’s misfortune to end the day with a nontrivial case of food poisoning. Fortunately, Marsha and I managed to dodge that bullet.
KeywordsPoint Estimation Decision Rule Loss Function Decision Problem Action Space
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