2023-02-09T12:13:27Z
https://soar-ir.repo.nii.ac.jp/oai
oai:soar-ir.repo.nii.ac.jp:00020887
2022-12-14T04:38:58Z
310:311
Estimation of a continuous distribution on the real line by discretization methods
Sheena, Yo
f-divergence
Alpha-divergence
Asymptotic risk
Asymptotic expansion
Multinomial distribution
First Online: 24 September 2018
For an unknown continuous distribution on the real line, we consider the approximate estimation by discretization. There are two methods for discretization. The first method is to divide the real line into several intervals before taking samples (fixed interval method). The second method is to divide the real line using the estimated percentiles after taking samples (moving interval method). In either method, we arrive at the estimation problem of a multinomial distribution. We use (symmetrized) f-divergence to measure the discrepancy between the true distribution and the estimated distribution. Our main result is the asymptotic expansion of the risk (i.e., expected divergence) up to the second-order term in the sample size. We prove theoretically that the moving interval method is asymptotically superior to the fixed interval method. We also observe how the presupposed intervals (fixed interval method) or percentiles (moving interval method) affect the asymptotic risk.
Article
METRIKA. 82(3):339-360 (2019)
journal article
SPRINGER HEIDELBERG
2019-04
application/pdf
METRIKA
3
82
339
360
0026-1335
AA00284719
https://soar-ir.repo.nii.ac.jp/record/20887/files/discretized_contin_ver4.pdf
eng
10.1007/s00184-018-0683-y
https://doi.org/10.1007/s00184-018-0683-y
The final publication is available at link.springer.com