On the optimal number of classes in the Pearson goodness-of-fit tests

Morales, Domingo, Pardo, Leandro, and Vajda, Igor. "On the optimal number of classes in the Pearson goodness-of-fit tests." Kybernetika 41.6 (2005): [677]-698. <http://eudml.org/doc/33781>.

@article{Morales2005,
abstract = {An asymptotic local power of Pearson chi-squared tests is considered, based on convex mixtures of the null densities with fixed alternative densities when the mixtures tend to the null densities for sample sizes $n\rightarrow \infty .$ This local power is used to compare the tests with fixed partitions $\mathcal \{P\}$ of the observation space of small partition sizes $|\mathcal \{P\}|$ with the tests whose partitions $\mathcal \{P\}=\mathcal \{P\}_\{n\}$ depend on $n$ and the partition sizes $|\mathcal \{P\}_\{n\}|$ tend to infinity for $n\rightarrow \infty $. New conditions are presented under which it is asymptotically optimal to let $|\mathcal \{P\}|$ tend to infinity with $n$ or to keep it fixed, respectively. Similar conditions are presented under which the tests with fixed $|\mathcal \{P\}|$ and those with increasing $|\mathcal \{P\}_\{n\}|$ are asymptotically equivalent.},
author = {Morales, Domingo, Pardo, Leandro, Vajda, Igor},
journal = {Kybernetika},
keywords = {Pearson goodness-of-fit test; Pearson-type goodness-of-fit tests; asymptotic local test power; asymptotic equivalence of tests; optimal number of classes; asymptotic local test power; asymptotic equivalence of tests},
language = {eng},
number = {6},
pages = {[677]-698},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the optimal number of classes in the Pearson goodness-of-fit tests},
url = {http://eudml.org/doc/33781},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Morales, Domingo
AU - Pardo, Leandro
AU - Vajda, Igor
TI - On the optimal number of classes in the Pearson goodness-of-fit tests
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 6
SP - [677]
EP - 698
AB - An asymptotic local power of Pearson chi-squared tests is considered, based on convex mixtures of the null densities with fixed alternative densities when the mixtures tend to the null densities for sample sizes $n\rightarrow \infty .$ This local power is used to compare the tests with fixed partitions $\mathcal {P}$ of the observation space of small partition sizes $|\mathcal {P}|$ with the tests whose partitions $\mathcal {P}=\mathcal {P}_{n}$ depend on $n$ and the partition sizes $|\mathcal {P}_{n}|$ tend to infinity for $n\rightarrow \infty $. New conditions are presented under which it is asymptotically optimal to let $|\mathcal {P}|$ tend to infinity with $n$ or to keep it fixed, respectively. Similar conditions are presented under which the tests with fixed $|\mathcal {P}|$ and those with increasing $|\mathcal {P}_{n}|$ are asymptotically equivalent.
LA - eng
KW - Pearson goodness-of-fit test; Pearson-type goodness-of-fit tests; asymptotic local test power; asymptotic equivalence of tests; optimal number of classes; asymptotic local test power; asymptotic equivalence of tests
UR - http://eudml.org/doc/33781
ER -