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- W4385946119 abstract "Given $n$ independent and identically distributed observations and measuring the value of obtaining an additional observation in terms of Le Cam's notion of deficiency between experiments, we show for certain types of non-parametric experiments that the value of an additional observation decreases at a rate of $1/sqrt{n}$. This is distinct from the known typical decrease at a rate of $1/n$ for parametric experiments and the non-decreasing value in the case of very large experiments. In particular, the rate of $1/sqrt{n}$ holds for the experiment given by observing samples from a density about which we know only that it is bounded from below by some fixed constant. Thus there exists an experiment where the value of additional observations tends to zero but for which no estimator that is consistent (in total variation distance) exists." @default.
- W4385946119 created "2023-08-18" @default.
- W4385946119 creator A5076236838 @default.
- W4385946119 date "2020-07-19" @default.
- W4385946119 modified "2023-09-23" @default.
- W4385946119 title "Information in additional observations of a non-parametric experiment that is not estimable" @default.
- W4385946119 doi "https://doi.org/10.48550/arxiv.2007.09691" @default.
- W4385946119 hasPublicationYear "2020" @default.
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