| Issue |
ESAIM: PS
Volume 26, 2022
|
|
|---|---|---|
| Page(s) | 473 - 494 | |
| DOI | https://doi.org/10.1051/ps/2022010 | |
| Published online | 08 December 2022 | |
On the intermediate asymptotic efficiency of goodness-of-fit tests in multinomial distributions
V.I. Romanovskiy Institute of Mathematics, Academy of Sciences of Uzbekistan University str., 9, Tashkent 100174, Uzbekistan
* Corresponding author: shmirakhmedov@yahoo.com
Received:
20
May
2022
Accepted:
1
September
2022
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime, where the number of cells grows with the sample size. Most attention is focused on the class of power divergence statistics. The aim of this article is to study the intermediate asymptotic relative efficiency of two tests, where the powers of the tests are asymptotically non-degenerate and the sequences of alternatives converge to the hypothesis, but not too fast. The intermediate asymptotic relative efficiency of the χ2 test wrt an arbitrary symmetric test is considered in details.
Mathematics Subject Classification: 62G10 / 62G20
Key words: Asymptotic efficiency / χ2 statistic / log-likelihood ratio statistic / goodness-of-fit tests / multinomial distribution / power divergence statistics
© The authors. Published by EDP Sciences, SMAI 2022
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