Information in additional observations of a non-parametric experiment that is not estimable
Year: 2025
Type: article
Abstract: Using Le Cam’s notion of deficiency between experiments, one can measure the value of obtaining an additional observation, when one has already been given n n independent and identically distributed observations. We show that for certain types of non-parametric experiments, the value of an additional observation decreases at a rate of 1 / n 1/\sqrt {n} . This is distinct from the typical rate of 1 / n 1/n in the case of parametric experiments, and from the non-decreasing value in the case of very large experiments. In particular, the rate of 1 / n 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 positive constant. For such densities, there exists no estimator that is consistent in total variation distance. We have therefore an example of an experiment which is, in this sense, not estimable, but for which the value of additional observations tends to zero.
DOI: 10.1090/tpms/1232
Author: Tilo Wiklund
Institution: Uppsala University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3042450192