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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.

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Is there a book that gives an indepth discussion of point estimation vs hypothesis testing and interval estimation? – user782220 Feb 25 '12 at 6:13
See Berger's Statistical Decision Theory. – Stuck_pls_help Feb 25 '12 at 15:32
I didn't mention this, but obviously hypothesis testing and interval estimation can be framed as decision problems, so decision theory serves to unify some of these ideas. – guy Feb 25 '12 at 15:35
Normally wouldn't you have both a point estimation and an interval of confidence around it? When would you have just a point estimation and not an interval of confidence? – user782220 Mar 1 '12 at 1:26
If you are making a decision, and your decision is a point estimate, then you wouldn't have a confidence interval, although you could construct one if you want. All that matters from a decision theory standpoint is the point estimator and properties associated with (e.g. its expected loss, efficiency relative to other estimators, and so forth). – guy Mar 1 '12 at 3:51

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