The exact risks of some pre-test and stein-type regression estimators umder balanced loss

Risk and Pitman closeness properties of feasible generalized double k-class estimators in linear regression models with non-spherical disturbances under balanced loss function

“…Taking the criterion as risk, i.e., the expected value of balanced loss function, interesting findings arising from comparison of estimators are reported by, e.g., Giles et al [6], Ohtani [12,13], Dey et al [4], Ohtani et al [14], Wan [23] and Zellner [26], Toutenburg and Shalabh [21] to site a few. Such a performance criterion on being based on quadratic losses may fail to reveal the intrinsic properties of estimator as pointed out by Rao [16], and it is recommended to use a criterion that measures appropriately the clustering of estimates around true parameter value.…”

“…Accordingly, he has proposed the balanced loss function which has gained considerable popularity during the recent past; see, e.g., Giles et al [6], Ohtani [12], Ohtani et al [14], Wan [23] and Zellner [26] for various applications.…”

The Exact Risk of a Weighted Average Estimator of the Ols and Stein-Rule Estimators in Regression Under Balanced Loss

“…The first term allows for "goodness of fit" and the second term "precision of estimation." Giles et al (1996) showed that if the value of a is a = (1 -u;)(fe -2)/(i/ -I-2) for A; > 3, then the risk function of the SR estimator is minimized under balanced loss, and the SR estimator dominates the OLS estimator. However, they also showed that if the usual value of o (i.e., a = (fc -2)/{u -1-2)) is used, then the SR and PSR estimators no longer dominate the OLS estimator.…”

“…put o* = a(l -u)) and use(4.6) inGUes et al (1996), then the risk function of the OLS-SR estimator is written as Jtmo)) = R(b) + <TV(f + 2)b -(gj where x? denotes the noncentral chi-square distribution with u degrees of fi-eedom and noncentrality parameter X = ß'Sß/a^.…”

All admissible linear estimators of a regression coefficient under a balanced loss function

“…It has received considerable attention in the literature under different setups. For more details, the readers are referred to Rodrigues and Zellner [17], Giles et al [5], Ohtani et al [14], Ohtani [12,13], Gruber [6], Jozani et al [10] and Arashi [1]. Moreover, we know that the balanced loss function is more sensitive than the quadratic loss function, which means that if an estimator is admissible under the balanced loss function, it is also admissible under the quadratic loss function.…”