Information in additional observations from a non-parametric experiment
 
 
Description:  Given some statistical experiment E we may, at least in principle, make multiple, independent, repetitions of it. Say that one statistician repeats the experiment n times, while another repeats it n+1 times. How much better off will the latter be? They certainly should not do be any worse off, as they may choose to throw out and ignore the extra observation they have received. One way of quantifying how much the second statistician should celebrate is by considering how much better they would do in case they were allowed to choose a statistical problem (say some estimation task or testing problem) on which to compete. This corresponds to finding the Le Cam deficiency between two experiments, the n-fold and the (n+1)-fold powers of E. For ``finite dimensional'' experiments this quantity is known to typically decay at a rate of 1/n, while for many very large experiments it is easy to see that it does not decay at all. We show that for certain non-parametric experiments it decays at a rate of 1/\sqrt{n}. Moreover, for at least one such experiment the underlying distribution is, in an appropriate sense, impossible to estimate, even though this quantity tends to 0.
Date:  2019-12-18
Start Time:   14:30
Speaker:  Tilo Wiklund (Univ. of Uppsala, Sweden)
Institution:  Univ. of Uppsala, Sweden
Place:  Sala 5.5
Research Groups: -Probability and Statistics
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