Hypothesis Tests and Simulation Envelopes 409
test) is comp utationally expensive to perform, and a nother test (e. g., the score test) is much easier
to perform. Different tests also depend on different underly ing assumptio ns.
• I have plotted pointwise envelopes of the L-function, and also perfo rmed a DCLF test using the
L-function. The empirical L-function stays entirely inside the pointwise envelopes (although it
lies very close to the upper envelope) while the DCLF test gives me a very significant result of
p = 0 .007. Aren’t these results contradictory?
No. The DCLF test statistic accumulates evidence against the null hypothesis from each distan c e
r in the specified range. Essentially the DCLF test statistic is something like the a rea