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. Author manuscript; available in PMC: 2010 Nov 12.
Published in final edited form as: Ann Stat. 2010 Nov 1;38(5):2723–2750. doi: 10.1214/10-AOS802

Table 2.

Mean integrated squared bias (Bias2), mean integrated variance (VAR), mean integrated squared error (MISE) over 1000 simulations for different variance estimators η̂2(x) and σ^O2(x). Seven different correlation schemes are simulated: ρ = −0.4, ρ = −0.2, ρ = 0, ρ = 0.2, ρ = 0.4, ρ = 0.6, and ρ = 0.8. All quantities are multiplied by 1000.

ρ = −0.4 −0.2 0 0.2 0.4 0.6 0.8
Bias2 η̂2(x) 5.93 1.48 0.00 1.48 5.91 13.31 23.67
σ^A2(x)
0.00 0.00 0.00 0.00 0.00 0.00 0.00
σ^O2(x)
0.00 0.00 0.00 0.00 0.00 0.00 0.01

VAR η̂2(x) 0.44 0.33 0.24 0.16 0.10 0.05 0.02
σ^A2(x)
0.27 0.25 0.24 0.22 0.20 0.19 0.20
σ^O2(x)
0.27 0.25 0.24 0.22 0.20 0.18 0.23

MISE η̂2(x) 6.37 1.81 0.24 1.64 6.01 13.37 23.69
σ^A2(x)
0.27 0.25 0.24 0.22 0.21 0.19 0.20
σ^O2(x)
0.27 0.25 0.24 0.22 0.20 0.18 0.24