Table 12 Coefficients and MSEs of estimators in the number of equations and citation data.
Estimates | Parameters | \(\beta _0\) | \(\beta _1\) | \(\beta _2\) | \(\beta _3\) | \(\beta _4\) | \(\beta _5\) | \(\beta _6\) | MSE |
|---|---|---|---|---|---|---|---|---|---|
PIGMLE | – | 0.0683 | 0.027 | 0.1014 | 0.1054 | − 0.0265 | − 5e−04 | − 0.0422 | 0.0237 |
PIGRRE | \(\hat{k}_1\) | 0.0424 | 0.0215 | 0.101 | 0.1055 | − 0.0198 | 0.0051 | − 0.0365 | 0.0114 |
\(\hat{k}_2\) | 0.0303 | 0.0179 | 0.1003 | 0.1055 | − 0.0155 | 0.0089 | − 0.0327 | 0.0078 | |
\(\hat{k}_3\) | 0.0451 | 0.0222 | 0.1011 | 0.1055 | − 0.0206 | 0.0044 | − 0.0372 | 0.0124 | |
\(\hat{k}_4\) | 0.0173 | 0.0128 | 0.0981 | 0.1056 | − 0.0096 | 0.0144 | − 0.0273 | 0.0058 | |
\(\hat{k}_5\) | 0.006 | 0.006 | 0.0171 | 0.0646 | − 0.0036 | 0.0209 | − 0.0102 | 0.0158 | |
PIGGRE | \(\hat{K}_1\) | 0.0012 | 0.0038 | 0.1155 | 0.0932 | − 0.0012 | 0.0238 | − 0.0167 | 0.0056 |
\(\hat{K}_2\) | 0.0012 | 0.0037 | 0.1156 | 0.0931 | − 0.0011 | 0.0239 | − 0.0167 | 0.0056 | |
\(\hat{K}_3\) | 0.0012 | 0.0037 | 0.1157 | 0.093 | − 0.001 | 0.024 | − 0.0166 | 0.0055 | |
\(\hat{K}_4\) | 0.0005 | 0.002 | 0.1306 | 0.0566 | − 0.0039 | 0.0294 | − 0.0114 | 0.0068 | |
\(\hat{K}_5\) | 0.0069 | 0.0168 | 0.1014 | 0.1048 | − 0.0135 | 0.01 | − 0.0313 | 0.0066 |
