Comments on: Is joint parameter estimation always strictly better than individual parameter estimation?
http://ask.metafilter.com/208671/Is-joint-parameter-estimation-always-strictly-better-than-individual-parameter-estimation/
Comments on Ask MetaFilter post Is joint parameter estimation always strictly better than individual parameter estimation?Mon, 20 Feb 2012 14:09:03 -0800Mon, 20 Feb 2012 15:42:07 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: Is joint parameter estimation always strictly better than individual parameter estimation?
http://ask.metafilter.com/208671/Is-joint-parameter-estimation-always-strictly-better-than-individual-parameter-estimation
Is it true that it is always better to estimate parameters jointly, even when they are completely unrelated? <br /><br /> I vaguely recall reading about a result in statistics which stated something along the lines of "the joint estimation of two parameters always performs better (i.e. smaller variance) than the separate estimation of each parameter, even if the parameters are completely unrelated".<br>
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Is this statement, or some modification of it, true? If so, is there an intuitive explanation? Can anyone point me to a reference?post:ask.metafilter.com,2012:site.208671Mon, 20 Feb 2012 14:09:03 -0800TheyCallItPeacestatisticsestimationmathematicsexplanationresolvedBy: cupcake1337
http://ask.metafilter.com/208671/Is-joint-parameter-estimation-always-strictly-better-than-individual-parameter-estimation#3009657
your statement doesn't make a whole lot of sense on it's own. you could construct examples where it's true and where it's not true. it all depends on the question you're asking. what variances are you comparing?<br>
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maybe you're thinking about regression? if you keep adding variables to the regression equation the R-squared can't go down, and depending on the data it can go up. so, by adding a bunch of arbitrary variable you can explain more variation in the response variable, but the result isn't very useful.comment:ask.metafilter.com,2012:site.208671-3009657Mon, 20 Feb 2012 15:42:07 -0800cupcake1337By: TheyCallItPeace
http://ask.metafilter.com/208671/Is-joint-parameter-estimation-always-strictly-better-than-individual-parameter-estimation#3009818
I am not sure what to change to make the statement make sense, as it is just a vague recollection. My interpretation of performance of the estimate would lead me say that the variances that would be compared would be the variances of each variable separately using each estimation procesure/approach.<br>
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If the performance of linear regression does not change by adding variables, then it does not sound like the foggy result I have in mind.comment:ask.metafilter.com,2012:site.208671-3009818Mon, 20 Feb 2012 18:03:25 -0800TheyCallItPeaceBy: TheyCallItPeace
http://ask.metafilter.com/208671/Is-joint-parameter-estimation-always-strictly-better-than-individual-parameter-estimation#3009826
Found it! I was thinking of <a href="http://en.wikipedia.org/wiki/Stein%27s_example">Stein's example</a>, although it does not appear to lead to a real improvement in the estimate of any given variable.comment:ask.metafilter.com,2012:site.208671-3009826Mon, 20 Feb 2012 18:08:57 -0800TheyCallItPeace