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A note on simultaneous Monte Carlo tests

By Ute Hahn
CSGB Research Reports
No. 06, May 2015

In this short note, Monte Carlo tests of goodness of fit for data of the form $X(t), t\in I$ are considered, that reject the null hypothesis if $X(t)$ leaves an acceptance region bounded by an upper and lower curve for some $t$ in $I$. A construction of the acceptance region is proposed that complies to a given target level of rejection, and yields exact $p$-values. The construction is based on pointwise quantiles, estimated from simulated realizations of $X(t)$ under the null hypothesis.

Keywords: Cdf transform, functional data, multiple testing, multivariate data, simulation based tests.

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