On the statistical analysis of grouped data: when Pearson $χ^2$ and other divisible statistics are not goodness-of-fit tests
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910005101330432 |
|---|---|
| author | Algeri, Sara Khmaladze, Estate V. |
| author_facet | Algeri, Sara Khmaladze, Estate V. |
| contents | Thousands of experiments are analyzed and papers are published each year involving the statistical analysis of grouped data. While this area of statistics is often perceived -- somewhat naively -- as saturated, several misconceptions still affect everyday practice, and new frontiers have so far remained unexplored. Researchers must be aware of the limitations affecting their analyses and what are the new possibilities in their hands.
Motivated by this need, the article introduces a unifying approach to the analysis of grouped data, which allows us to study the class of divisible statistics -- that includes Pearson's $χ^2$, the likelihood ratio as special cases -- with a fresh perspective. The contributions collected in this manuscript span from modeling and estimation to distribution-free goodness-of-fit tests.
Perhaps the most surprising result presented here is that, in a sparse regime, all tests proposed in the literature are dominated by members of the class of weighted linear statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09195 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the statistical analysis of grouped data: when Pearson $χ^2$ and other divisible statistics are not goodness-of-fit tests Algeri, Sara Khmaladze, Estate V. Methodology Statistics Theory Data Analysis, Statistics and Probability Computation Thousands of experiments are analyzed and papers are published each year involving the statistical analysis of grouped data. While this area of statistics is often perceived -- somewhat naively -- as saturated, several misconceptions still affect everyday practice, and new frontiers have so far remained unexplored. Researchers must be aware of the limitations affecting their analyses and what are the new possibilities in their hands. Motivated by this need, the article introduces a unifying approach to the analysis of grouped data, which allows us to study the class of divisible statistics -- that includes Pearson's $χ^2$, the likelihood ratio as special cases -- with a fresh perspective. The contributions collected in this manuscript span from modeling and estimation to distribution-free goodness-of-fit tests. Perhaps the most surprising result presented here is that, in a sparse regime, all tests proposed in the literature are dominated by members of the class of weighted linear statistics. |
| title | On the statistical analysis of grouped data: when Pearson $χ^2$ and other divisible statistics are not goodness-of-fit tests |
| topic | Methodology Statistics Theory Data Analysis, Statistics and Probability Computation |
| url | https://arxiv.org/abs/2406.09195 |