### Abstract

Non-parametric and parametric explicit decompositions of the classical Pearson, Pearson-Fisher, Hsuan-Robson-Mirvaliev and other tests on a sum of asymptotically independent chi-squared random variables with one degree of freedom in case of non-equiprobable cells are discussed. The parametric decompositions can be used for constructing more powerful tests, and can be considered as alternative proofs of limit theorems for some chi-squared type goodness-of-fit statistics.

Original language | English |
---|---|

Title of host publication | Recent Advances in Stochastic Modeling and Data Analysis |

Publisher | World Scientific Publishing Co. |

Pages | 243-250 |

Number of pages | 8 |

ISBN (Electronic) | 9789812709691 |

ISBN (Print) | 9812709681, 9789812709684 |

DOIs | |

Publication status | Published - Jan 1 2007 |

### Fingerprint

### Keywords

- Chi-squared tests
- Decomposition of chi-squared tests
- Modified chisquared tests
- Power of goodness-of-fit tests

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

_{1}

^{2}: Distributed in the limit components of some chi-squared tests. In

*Recent Advances in Stochastic Modeling and Data Analysis*(pp. 243-250). World Scientific Publishing Co.. https://doi.org/10.1142/9789812709691_0030

**Independent x _{1} ^{2} : Distributed in the limit components of some chi-squared tests.** / Voinov, Vassilly; Nikulin, Mikhail; Pya, Natalie.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

_{1}

^{2}: Distributed in the limit components of some chi-squared tests. in

*Recent Advances in Stochastic Modeling and Data Analysis.*World Scientific Publishing Co., pp. 243-250. https://doi.org/10.1142/9789812709691_0030

_{1}

^{2}: Distributed in the limit components of some chi-squared tests. In Recent Advances in Stochastic Modeling and Data Analysis. World Scientific Publishing Co. 2007. p. 243-250 https://doi.org/10.1142/9789812709691_0030

}

TY - CHAP

T1 - Independent x1 2

T2 - Distributed in the limit components of some chi-squared tests

AU - Voinov, Vassilly

AU - Nikulin, Mikhail

AU - Pya, Natalie

PY - 2007/1/1

Y1 - 2007/1/1

N2 - Non-parametric and parametric explicit decompositions of the classical Pearson, Pearson-Fisher, Hsuan-Robson-Mirvaliev and other tests on a sum of asymptotically independent chi-squared random variables with one degree of freedom in case of non-equiprobable cells are discussed. The parametric decompositions can be used for constructing more powerful tests, and can be considered as alternative proofs of limit theorems for some chi-squared type goodness-of-fit statistics.

AB - Non-parametric and parametric explicit decompositions of the classical Pearson, Pearson-Fisher, Hsuan-Robson-Mirvaliev and other tests on a sum of asymptotically independent chi-squared random variables with one degree of freedom in case of non-equiprobable cells are discussed. The parametric decompositions can be used for constructing more powerful tests, and can be considered as alternative proofs of limit theorems for some chi-squared type goodness-of-fit statistics.

KW - Chi-squared tests

KW - Decomposition of chi-squared tests

KW - Modified chisquared tests

KW - Power of goodness-of-fit tests

UR - http://www.scopus.com/inward/record.url?scp=84967663260&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84967663260&partnerID=8YFLogxK

U2 - 10.1142/9789812709691_0030

DO - 10.1142/9789812709691_0030

M3 - Chapter

SN - 9812709681

SN - 9789812709684

SP - 243

EP - 250

BT - Recent Advances in Stochastic Modeling and Data Analysis

PB - World Scientific Publishing Co.

ER -