Fig. 3.

False positives. This figure shows the number of FPs obtained with different sample size $n$. The number of FPs are shown in Panels (a) and (b) under $H_0$: no partial correlation (i.e. the percentages of true correlations $\delta$ is zero). Inference is carried out from simulated data for $p$ = 100 and $n$ ranging from 10 to 150 in steps of size 10. The black horizontal line represents the expected number of FPs under$\mathrm{ }{H}_0$, tested at $\alpha$ = 0.05 and$\mathrm{ }0.01$ respectively (i.e. 247.5 for $\alpha$ = 0.05 and 49.5 for $\alpha$=0.01). Panels (c) and (d) show the number of FPs for different proportions $p/n$ when the percentages of non-zero correlations is $\delta$ = 0.01. Here $p$ = 50, 100, 150, 200 and $n$ = 20. Three approaches are compared: ENF (dot with dashed line), Shrunk MLE (square with dotted line), and MC with 15 iterations (triangle with continuous line). Symbols (and bars) represent the average (±2 SE) over 25 repeated simulations. The upper horizontal axis shows the average shrinkage intensity $\stackrel{}{\mathrm{\lambda }}$ rounded to two digits