Fig. 3
The P factor defined in (30) for different M and [μ]i, when the post-change mean vector has entries all equal to [μ]i. Assume N=100. The white regions correspond to P≥1, and dark regions correspond to P<1 and the darker, the smaller P is (note that the smallest P in this graph is above 0.75). We also plot the Mmin (defined later in (35)) required in these cases such that the EDD of the sketching procedure is no more than δ larger than the corresponding procedure without sketching (fixing ARL = 5000), for δ=1 and δ=0.5. The Mmin are obtained by Monte Carlo simulation. The Mmin versus [μ]i correspond to the blue and the red curves, respectively. Above these two curves, the EDD with sketching is almost the same as before (without sketching), i.e., the regime where sketching has little loss. The left-bottom corner corresponds to the region where sketching has more loss. This also shows that indeed P<1 is an indicator of significant performance loss using sketching