# Asymptotically valid and exact permutation tests

## Abstract/Contents

- Abstract
- Given independent samples from P and Q, two-sample permutation tests allow one to construct exact level tests when the null hypothesis is P = Q. On the other hand, when comparing or testing particular parameters [theta] of P and Q, such as their means or quantiles, the classical permutation tests need not be level [alpha], or even approximately level [alpha] in large samples. Under very weak assumptions, this dissertation provides general test procedures whereby the asymptotic validity of the permutation test holds even when the assumption of identical distribution is unknown, while retaining the exact rejection probability [alpha] in finite samples when the underlying distributions are identical. A quite general theory is possible based on a coupling construction, as well as a key contiguity argument for the multinomial and multivariate hypergeometric distributions. The mathematical and statistical foundations for understanding permutation tests are laid out. Based on these technical arguments, the ideas are broadly applicable and generalizations have been made to the k-sample problem of comparing general parameters, the two-sample U-statistics, and d-dimensional multivariate cases and multiple testing. In the U-statistics case, we consider the Wilcoxon statistic or some rank statistics where the parameter of interest is a function of the joint distribution [theta](P, Q) and not just a simple difference [theta](P) - [theta](Q). In multivariate case, we apply the modified Hotelling's T^2-statistic as well as tests based on the maximum of studentized absolute differences. In the latter case, we must employ a bootstrap prepivoting operation, which leads to a bootstrapping after permuting algorithm. Then, we apply these tests as a basis for testing multiple hypotheses simultaneously by invoking the closure method to control the Familywise Error Rate. Monte Carlo simulation studies illustrate how the classical permutation tests and the proposed new permutation tests perform under various scenarios of underlying distributions with small, moderate, and large samples. Lastly, we also present some economic empirical applications where the permutation tests are utilized for testing some parameters of the underlying distributions.

## Description

Type of resource | text |
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Form | electronic; electronic resource; remote |

Extent | 1 online resource. |

Publication date | 2013 |

Issuance | monographic |

Language | English |

## Creators/Contributors

Associated with | Chung, Eun Yi | |
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Associated with | Stanford University, Department of Economics. | |

Primary advisor | Romano, Joseph P, 1960- | |

Thesis advisor | Romano, Joseph P, 1960- | |

Thesis advisor | Hong, Han | |

Thesis advisor | Wolak, Frank A | |

Advisor | Hong, Han | |

Advisor | Wolak, Frank A |

## Subjects

Genre | Theses |
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## Bibliographic information

Statement of responsibility | Eun Yi Chung. |
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Note | Submitted to the Department of Economics. |

Thesis | Thesis (Ph.D.)--Stanford University, 2013. |

Location | electronic resource |

## Access conditions

- Copyright
- © 2013 by Eun Yi Chung

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