Table 1.
n | BD | censoring rate is 15% | censoring rate is 50% | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Bias | RB | SD | SE | CP(%) | Bias | RB | SD | SE | CP(%) | ||
Half Kernel | |||||||||||
100 | n−0.7 | 0.051 | 0.034 | 0.420 | 0.502 | 91 | 0.169 | 0.113 | 0.543 | 0.740 | 90 |
n−0.6 | 0.019 | 0.013 | 0.346 | 0.384 | 91 | 0.084 | 0.056 | 0.451 | 0.584 | 91 | |
auto | 0.042 | 0.028 | 0.434 | 0.385 | 93 | 0.047 | 0.031 | 0.595 | 0.500 | 90 | |
400 | n−0.7 | 0.040 | 0.026 | 0.299 | 0.321 | 93 | 0.046 | 0.031 | 0.365 | 0.423 | 92 |
n−0.6 | −0.009 | −0.006 | 0.222 | 0.242 | 93 | 0.008 | 0.006 | 0.277 | 0.301 | 93 | |
auto | 0.028 | 0.019 | 0.298 | 0.263 | 93 | 0.035 | 0.023 | 0.378 | 0.332 | 95 | |
900 | n−0.7 | 0.008 | 0.005 | 0.247 | 0.253 | 95 | 0.033 | 0.022 | 0.305 | 0.327 | 93 |
n−0.6 | 0.006 | 0.004 | 0.181 | 0.188 | 94 | 0.007 | 0.005 | 0.220 | 0.236 | 94 | |
auto | 0.014 | 0.010 | 0.244 | 0.216 | 94 | 0.020 | 0.013 | 0.306 | 0.260 | 93 | |
Last Value | |||||||||||
100 | −0.157 | −0.104 | 0.232 | 0.220 | 85 | −0.086 | −0.057 | 0.339 | 0.309 | 90 | |
400 | −0.180 | −0.120 | 0.115 | 0.106 | 59 | −0.130 | −0.087 | 0.146 | 0.146 | 83 | |
900 | −0.178 | −0.119 | 0.073 | 0.070 | 30 | −0.137 | −0.091 | 0.098 | 0.095 | 69 | |
Full Kernel | |||||||||||
100 | n−0.7 | 0.005 | 0.003 | 0.294 | 0.316 | 93 | 0.025 | 0.017 | 0.354 | 0.383 | 93 |
n−0.6 | −0.053 | −0.035 | 0.242 | 0.247 | 93 | 0.011 | 0.007 | 0.298 | 0.305 | 94 | |
auto | 0.039 | 0.026 | 0.311 | 0.278 | 93 | 0.018 | 0.012 | 0.359 | 0.335 | 91 | |
400 | n−0.7 | −0.003 | −0.002 | 0.204 | 0.209 | 94 | 0.015 | 0.010 | 0.247 | 0.247 | 95 |
n−0.6 | −0.020 | −0.014 | 0.159 | 0.160 | 95 | −0.013 | −0.008 | 0.192 | 0.192 | 94 | |
auto | −0.022 | −0.015 | 0.185 | 0.186 | 94 | 0.013 | 0.009 | 0.235 | 0.222 | 94 | |
900 | n−0.7 | 0.001 | 0.001 | 0.172 | 0.179 | 94 | 0.004 | 0.003 | 0.209 | 0.213 | 94 |
n−0.6 | −0.018 | −0.012 | 0.126 | 0.135 | 95 | −0.003 | −0.002 | 0.223 | 0.231 | 94 | |
auto | −0.004 | −0.003 | 0.146 | 0.151 | 96 | −0.005 | −0.004 | 0.206 | 0.185 | 94 | |
Nearest Value | |||||||||||
100 | −0.196 | −0.130 | 0.159 | 0.155 | 73 | −0.190 | −0.126 | 0.204 | 0.188 | 76 | |
400 | −0.220 | −0.145 | 0.081 | 0.073 | 20 | −0.219 | −0.146 | 0.100 | 0.088 | 3 | |
900 | −0.218 | −0.146 | 0.056 | 0.048 | 2 | −0.220 | −0.146 | 0.065 | 0.058 | 7 |
Note: “BD” represents different bandwidths, “Bias” is the empirical bias, “RB” is the “Bias” divided by the true β0, “SD” is the sample standard deviation, “SE” is the average of the standard error estimates and “CP” represents the coverage probability of the 95% confidence interval for β̂n.