A family of asymptotically independent statistics in polynomial scheme containing the Pearson statistic
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Maxim P. Savelov
Abstract
We consider a polynomial scheme with N outcomes. The Pearson statistic is the classical one for testing the hypothesis that the probabilities of outcomes are given by the numbers p1, …, pN. We suggest a couple of N − 2 statistics which along with the Pearson statistics constitute a set of N − 1 asymptotically jointly independent random variables, and find their limit distributions. The Pearson statistics is the square of the length of asymptotically normal random vector. The suggested statistics are coordinates of this vector in some auxiliary spherical coordinate system.
Note: Originally published in Diskretnaya Matematika (2020) 32,№3, 76–84 (in Russian).
References
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Articles in the same Issue
- Frontmatter
- Single diagnostic tests for inversion faults of gates in circuits over arbitrary bases
- Generalized de Bruijn graphs
- A family of asymptotically independent statistics in polynomial scheme containing the Pearson statistic
- Linear recurrent relations, power series distributions, and generalized allocation scheme
- Variance of the number of cycles of random A-permutation
- Multi-dimensional Kronecker sequences with a small number of gap lengths
Articles in the same Issue
- Frontmatter
- Single diagnostic tests for inversion faults of gates in circuits over arbitrary bases
- Generalized de Bruijn graphs
- A family of asymptotically independent statistics in polynomial scheme containing the Pearson statistic
- Linear recurrent relations, power series distributions, and generalized allocation scheme
- Variance of the number of cycles of random A-permutation
- Multi-dimensional Kronecker sequences with a small number of gap lengths
