Table 5.

Estimates of test size, P, and FPR using modified procedures 15 and 16, with $T^{*}=\mathrm{10,000}$, for different values of $n_t$ and for $m_t=1$

			Uniform contamination (Eq. 12)				Dirac-type contamination (Eq. 13)
		${\tau }_t=0$	${\tau }_t=0.5$		${\tau }_t=0.8$		${\tau }_t=0.5$		${\tau }_t=0.8$
No. of transactions	Test	$\widehat{\alpha }$	P	FPR	P	FPR	P	FPR	P	FPR
$n_t=100$	$V_{\left\{1\right\}}^{\left(t\right)}$	0.071	0.414	0.716	0.928	0.600	1	0.579	1	0.572
	Test 15	0.010	0.000	1	0.000	1	0.850	0.167	1	0.180
	Test 16	0.011	0.350	0.329	0.864	0.179	0.990	0.161	1	0.144
$n_t=200$	$V_{\left\{1\right\}}^{\left(t\right)}$	0.094	0.812	0.683	1	0.630	1	0.648	1	0.634
	Test 15	0.010	0.000	1	0.000	1	0.878	0.157	1	0.187
	Test 16	0.012	0.678	0.213	0.934	0.182	0.998	0.153	0.992	0.175
$n_t=500$	$V_{\left\{1\right\}}^{\left(t\right)}$	0.132	1	0.719	1	0.714	1	0.708	1	0.717
	Test 15	0.010	0.004	0.983	0.000	1	0.776	0.173	1	0.154
	Test 16	0.010	0.894	0.189	0.938	0.149	0.996	0.171	1	0.143

The estimated test sizes for $V_{\left\{1\right\}}^{\left(t\right)}$ are also given as a reference. The nominal test size is $\alpha =0.01$. The number of independent idealized traders in each market configuration is $T^{†}=\mathrm{85,500}$ for procedure 15 and $T^{†}=\mathrm{10,000}$ for procedure 16, P and FPR. $\varsigma =0.05$ when computing P and FPR