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. Author manuscript; available in PMC: 2023 Jun 1.
Published in final edited form as: Stat Biosci. 2022 May 25;14(3):582–610. doi: 10.1007/s12561-022-09346-6

Table 6.

Coverage probabilities of the circular block bootstrap change point 95% confidence intervals for the case with the same mean function across units and a change solely in the mean functions.Note, Δi=Δ∈{−0.7,−0.5,−0.2,0.2,0.5,0.7} for all i, in this scenario.

Coverage Probabilities for Change Point Confidence Intervals
   n = 60 n = 120
Δ Parameter Truth Units: 1 3 5 10 Units: 1 3 5 10
−0.7 τ 31 if n = 60
61 if n = 120		 0.577 0.761 0.845 0.921 0.666 0.848 0.918 0.953
β 0 2 0.161 0 0 0 0.001 0 0 0
β 1 −0.2 0.998 0.997 0.999 0.997 0.997 0.995 0.997 0.999
δ 0 0.993 0.999 0.997 1 0.992 0.985 0.988 0.976
Δ −0.7 0.996 1 0.999 1 0.997 1 0.999 1
ρ 0.1 0.959 0.965 0.967 0.957 0.979 0.99 0.986 0.978
−0.5 τ 31 if n = 60
61 if n = 120		 0.499 0.609 0.702 0.833 0.554 0.756 0.828 0.913
β 0 2 0.159 0 0 0 0.001 0 0 0
β 1 −0.2 0.992 0.998 0.998 1 0.992 0.997 0.998 0.999
δ 0 0.995 0.999 0.999 1 0.993 0.99 0.992 0.995
Δ −0.5 0.999 0.999 1 1 0.998 1 0.997 1
ρ 0.1 0.936 0.949 0.918 0.847 0.961 0.968 0.961 0.925
−0.2 τ 31 if n = 60
61 if n = 120		 0.408 0.454 0.533 0.561 0.41 0.478 0.569 0.669
β 0 2 0.146 0.001 0 0 0.001 0 0 0
β 1 −0.2 0.999 0.999 0.998 1 0.991 0.998 1 1
δ 0 0.994 0.994 0.998 0.998 0.983 0.991 0.996 0.992
Δ −0.2 0.996 0.998 0.999 0.999 0.992 0.998 0.998 1
ρ 0.1 0.903 0.869 0.848 0.695 0.912 0.907 0.854 0.719
0.2 τ 31 if n = 60
61 if n = 120		 0.432 0.465 0.53 0.584 0.442 0.521 0.584 0.672
β 0 2 0.177 0.001 0 0 0 0 0 0
β 1 −0.2 0.99 0.992 0.992 0.993 0.994 0.994 0.991 0.99
δ 0 0.991 0.995 0.994 0.997 0.981 0.993 0.993 0.998
Δ 0.2 0.987 0.994 0.996 0.999 0.993 0.997 0.998 1
ρ 0.1 0.877 0.83 0.786 0.645 0.894 0.86 0.803 0.653
0.5 τ 31 if n = 60
61 if n = 120		 0.511 0.662 0.761 0.883 0.61 0.786 0.824 0.928
β 0 2 0.267 0.001 0 0 0.006 0 0 0
β 1 −0.2 0.982 0.981 0.987 0.981 0.98 0.973 0.966 0.971
δ 0 0.987 0.993 0.994 0.99 0.979 0.976 0.985 0.959
Δ 0.5 0.986 0.991 0.989 0.994 0.989 0.991 0.988 0.988
ρ 0.1 0.916 0.883 0.845 0.714 0.928 0.904 0.858 0.742
0.7 τ 31 if n = 60
61 if n = 120		 0.634 0.778 0.864 0.957 0.694 0.855 0.911 0.958
β 0 2 0.315 0.019 0 0 0.032 0 0 0
β 1 −0.2 0.985 0.974 0.968 0.973 0.971 0.962 0.966 0.96
δ 0 0.99 0.991 0.991 0.98 0.973 0.971 0.958 0.849
Δ 0.7 0.99 0.986 0.978 0.982 0.977 0.971 0.983 0.975
ρ 0.1 0.922 0.915 0.9 0.794 0.942 0.946 0.928 0.878