Proposed method | CL method | Ignoring truncation | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
n | Par | True | Bias | SSE | SEE | CP | Bias | SSE | SEE | CP | Bias | SSE | SEE | CP | ||
\(A^{*}\) follows the uniform distribution | ||||||||||||||||
100 | \(\beta _1\) | 1 | 0.041 | 0.246 | 0.254 | 96.6 | 0.061 | 0.290 | 0.278 | 92.7 | 0.192 | 0.273 | 0.311 | 94.1 | ||
\(\beta _2\) | 1 | 0.045 | 0.403 | 0.408 | 95.6 | 0.055 | 0.492 | 0.467 | 93.7 | 0.180 | 0.474 | 0.445 | 90.8 | |||
\(\Lambda (0.4)\) | 0.16 | 0.009 | 0.094 | 0.087 | 95.6 | 0.002 | 0.092 | – | – | -0.084 | 0.043 | – | – | |||
\(\Lambda (0.8)\) | 0.64 | -0.037 | 0.165 | 0.161 | 93.9 | -0.048 | 0.164 | – | – | -0.245 | 0.103 | – | – | |||
\(\Lambda (1.2)\) | 1.44 | -0.038 | 0.240 | 0.248 | 93.5 | -0.067 | 0.240 | – | – | -0.445 | 0.209 | – | – | |||
300 | \(\beta _1\) | 1 | 0.008 | 0.134 | 0.129 | 93.5 | 0.013 | 0.156 | 0.151 | 93.1 | 0.120 | 0.148 | 0.306 | 95.9 | ||
\(\beta _2\) | 1 | 0.012 | 0.212 | 0.212 | 94.6 | 0.025 | 0.248 | 0.253 | 95.2 | 0.146 | 0.244 | 0.305 | 92.4 | |||
\(\Lambda (0.4)\) | 0.16 | 0.020 | 0.067 | 0.064 | 94.2 | 0.020 | 0.067 | – | – | -0.081 | 0.026 | – | – | |||
\(\Lambda (0.8)\) | 0.64 | 0.020 | 0.104 | 0.105 | 95.3 | 0.020 | 0.107 | – | – | -0.240 | 0.061 | – | – | |||
\(\Lambda (1.2)\) | 1.44 | -0.028 | 0.179 | 0.189 | 96.5 | -0.024 | 0.182 | – | – | -0.436 | 0.116 | – | – | |||
500 | \(\beta _1\) | 1 | 0.014 | 0.101 | 0.099 | 95.4 | 0.018 | 0.115 | 0.117 | 96.0 | 0.154 | 0.101 | 0.197 | 79.6 | ||
\(\beta _2\) | 1 | 0.014 | 0.161 | 0.163 | 94.6 | 0.020 | 0.191 | 0.193 | 95.0 | 0.146 | 0.193 | 0.219 | 85.7 | |||
\(\Lambda (0.4)\) | 0.16 | 0.012 | 0.048 | 0.048 | 96.7 | 0.012 | 0.048 | – | – | -0.081 | 0.018 | – | – | |||
\(\Lambda (0.8)\) | 0.64 | 0.010 | 0.076 | 0.075 | 95.0 | 0.009 | 0.077 | – | – | -0.244 | 0.044 | – | – | |||
\(\Lambda (1.2)\) | 1.44 | -0.012 | 0.133 | 0.131 | 94.6 | -0.012 | 0.135 | – | – | -0.443 | 0.094 | – | – | |||
\(A^{*}\) follows the exponential distribution | ||||||||||||||||
100 | \(\beta _1\) | 1 | 0.045 | 0.242 | 0.251 | 94.9 | 0.062 | 0.272 | 0.266 | 93.1 | 0.146 | 0.266 | 0.294 | 95.3 | ||
\(\beta _2\) | 1 | 0.047 | 0.396 | 0.405 | 95.3 | 0.071 | 0.451 | 0.453 | 95.3 | 0.149 | 0.435 | 0.435 | 90.5 | |||
\(\Lambda (0.4)\) | 0.16 | 0.009 | 0.083 | 0.080 | 95.5 | 0.009 | 0.085 | – | – | -0.068 | 0.046 | – | – | |||
\(\Lambda (0.8)\) | 0.64 | -0.036 | 0.159 | 0.160 | 93.7 | -0.038 | 0.159 | – | – | -0.178 | 0.114 | – | – | |||
\(\Lambda (1.2)\) | 1.44 | -0.042 | 0.234 | 0.240 | 92.7 | -0.042 | 0.235 | – | – | -0.280 | 0.251 | – | – | |||
300 | \(\beta _1\) | 1 | 0.011 | 0.131 | 0.133 | 95.9 | 0.016 | 0.147 | 0.148 | 94.9 | 0.084 | 0.137 | 0.250 | 97.4 | ||
\(\beta _2\) | 1 | -0.001 | 0.210 | 0.217 | 95.9 | 0.007 | 0.228 | 0.246 | 96.7 | 0.082 | 0.229 | 0.294 | 95.6 | |||
\(\Lambda (0.4)\) | 0.16 | 0.017 | 0.053 | 0.053 | 96.5 | 0.017 | 0.054 | – | – | -0.065 | 0.025 | – | – | |||
\(\Lambda (0.8)\) | 0.64 | 0.014 | 0.097 | 0.093 | 93.8 | 0.013 | 0.100 | – | – | -0.173 | 0.066 | – | – | |||
\(\Lambda (1.2)\) | 1.44 | -0.016 | 0.184 | 0.182 | 94.5 | -0.015 | 0.184 | – | – | -0.300 | 0.140 | – | – | |||
500 | \(\beta _1\) | 1 | 0.012 | 0.100 | 0.101 | 95.2 | 0.016 | 0.115 | 0.113 | 94.4 | 0.069 | 0.116 | 0.263 | 92.3 | ||
\(\beta _2\) | 1 | 0.010 | 0.165 | 0.167 | 94.7 | 0.008 | 0.187 | 0.188 | 94.7 | 0.097 | 0.173 | 0.247 | 92.3 | |||
\(\Lambda (0.4)\) | 0.16 | 0.014 | 0.044 | 0.045 | 95.3 | 0.015 | 0.044 | – | – | -0.067 | 0.020 | – | – | |||
\(\Lambda (0.8)\) | 0.64 | 0.013 | 0.075 | 0.073 | 94.6 | 0.013 | 0.077 | – | – | -0.174 | 0.061 | – | – | |||
\(\Lambda (1.2)\) | 1.44 | -0.003 | 0.136 | 0.138 | 97.5 | -0.003 | 0.138 | – | – | -0.292 | 0.118 | – | – |