Can someone explain what are point estimators good for? Hypothesis tests and interval estimations give a fuzzy answer in terms of something sort of like a probability of the value being in some interval. In applied statistics why would you look at a single number or point estimator rather than these intervals?
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Decision theory provides powerful motivation for point estimators. If I'm a hot dog vendor then I might be interested in an estimate of how many hot dogs people will buy so that I know how many to stock. I can't stock a fuzzy number of hot dogs; I need to pick one number and go with it. So the idea is to introduce a loss function and try to make a decision that makes the expected loss small. If the loss is some sort of measure of distance between our decision (the number of hot dogs we decide to stock) and a parameter (the actual number of hot dogs people want to buy) then in this setup the problem is essentially one of point estimation.