### Abstract

A major weakness of the classical Monte Carlo test is that it is biased when the null hypothesis is composite. This problem persists even when the number of simulations tends to infinity. A standard remedy is to perform a double bootstrap test involving two stages of Monte Carlo simulation: under suitable conditions, this test is asymptotically exact for any fixed significance level. However, the two-stage test is shown to perform poorly in some common applications: for a given number of simulations, the test with the smallest achievable significance level can be strongly biased. A ‘balanced’ version of the two-stage test is proposed, which is exact, for all achievable significance levels, when the null hypothesis is simple, and which performs well for composite null hypotheses.

Original language | English |
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Pages (from-to) | 75-87 |

Number of pages | 13 |

Journal | Computational Statistics and Data Analysis |

Volume | 114 |

DOIs | |

Publication status | Published - 1 Oct 2017 |

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### Cite this

*Computational Statistics and Data Analysis*,

*114*, 75-87. https://doi.org/10.1016/j.csda.2017.04.003

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*Computational Statistics and Data Analysis*, vol. 114, pp. 75-87. https://doi.org/10.1016/j.csda.2017.04.003

**On two-stage Monte Carlo tests of composite hypotheses.** / Baddeley, Adrian; Hardegen, Andrew; Lawrence, Thomas; Milne, Robin K.; Nair, Gopalan; Rakshit, Suman.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On two-stage Monte Carlo tests of composite hypotheses

AU - Baddeley, Adrian

AU - Hardegen, Andrew

AU - Lawrence, Thomas

AU - Milne, Robin K.

AU - Nair, Gopalan

AU - Rakshit, Suman

PY - 2017/10/1

Y1 - 2017/10/1

N2 - A major weakness of the classical Monte Carlo test is that it is biased when the null hypothesis is composite. This problem persists even when the number of simulations tends to infinity. A standard remedy is to perform a double bootstrap test involving two stages of Monte Carlo simulation: under suitable conditions, this test is asymptotically exact for any fixed significance level. However, the two-stage test is shown to perform poorly in some common applications: for a given number of simulations, the test with the smallest achievable significance level can be strongly biased. A ‘balanced’ version of the two-stage test is proposed, which is exact, for all achievable significance levels, when the null hypothesis is simple, and which performs well for composite null hypotheses.

AB - A major weakness of the classical Monte Carlo test is that it is biased when the null hypothesis is composite. This problem persists even when the number of simulations tends to infinity. A standard remedy is to perform a double bootstrap test involving two stages of Monte Carlo simulation: under suitable conditions, this test is asymptotically exact for any fixed significance level. However, the two-stage test is shown to perform poorly in some common applications: for a given number of simulations, the test with the smallest achievable significance level can be strongly biased. A ‘balanced’ version of the two-stage test is proposed, which is exact, for all achievable significance levels, when the null hypothesis is simple, and which performs well for composite null hypotheses.

KW - Conservative test

KW - Dao–Genton test

KW - Double bootstrap

KW - Nested bootstrap

KW - p-value

UR - http://www.scopus.com/inward/record.url?scp=85018748177&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2017.04.003

DO - 10.1016/j.csda.2017.04.003

M3 - Article

VL - 114

SP - 75

EP - 87

JO - Computational Statistics & Data Analysis

JF - Computational Statistics & Data Analysis

SN - 0167-9473

ER -