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CTK Exchange
Ralphbne
Member since Nov-9-07
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Mar-17-10, 05:02 PM (EST) |
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"Probability/Stats question"
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Suppose that I sample from some unknown continuous distribution. I know that the draws are iid, but the distribution itself is unknown. However, I know that the true distribution is one of two, either f(x|H) and f(x|L) with common support. I form the likelihood ratio, L(x1,...,xN)=/Is it true that if I can sample an unlimited number of times that I will learn the true distribution for certain? That is, does L(x1,...,xN) converge to zero or infinity in probability (or almost surely)? For Bernoulli trials, the proof is not hard (Based on LLN), but I am wondering whether this result holds more generally... Any comments, or even a reference to a textbook are appreciated. |
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alexb
Charter Member
2483 posts |
Mar-17-10, 08:02 PM (EST) |
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1. "RE: Probability/Stats question"
In response to message #0
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What you ask about is in the pervue of the "hypotethis testing" theory. The ratio is known as the "likelihood ratio" and there is also the "likelihood ratio test". Any decent statistics test covers this material. I have two: 1. R. B. Ash, Basic Probability Theory, Dover, 2008
2. R. Lupton, Statistics in Theory and Practice, PUP, 1993 Ash's can be gotten for pennies and is very readable. |
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