## Abstract

Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube [0, 1]^{d} (d ≥ 2). These statistics are derived from number-theoretic or quasi-Monte Carlo methods for measuring the discrepancy of points in [0, 1]^{d}. Under the null hypothesis that the samples are independent and identically distributed with a uniform distribution in [0, 1]^{d}, we obtain some asymptotic properties of the new statistics. By Monte Carlo simulation, it is found that the finite-sample distributions of the new statistics are well approximated by the standard normal distribution, N(0, 1), or the chi-squared distribution, χ^{2}(2). A power study is performed, and possible applications of the new statistics to testing general multivariate goodness-of-fit problems are discussed.

Original language | English |
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Pages (from-to) | 337-355 |

Number of pages | 19 |

Journal | Mathematics of Computation |

Volume | 70 |

Issue number | 233 |

Early online date | 17 Feb 2000 |

DOIs | |

Publication status | Published - Jan 2001 |

Externally published | Yes |

## Scopus Subject Areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

## User-Defined Keywords

- Discrepancy
- Goodness-of-fit
- Quasi-Monte Carlo methods
- Testing uniformity