Simultaneous Estimation of Skewness Parameters

The improved simultaneous estimation of the skewness parameters is considered under the uncertain prior information (UPI) that component skewness parameters may be equal. It is advantageous to combine the data to estimate the common skewness parameter. However, the combined estimator becomes biased and inconsistent when the quality of the parameters may not hold. In this situation, estimators based on pretest and shrinkage estimation are proposed. Asymptotic properties of the suggested estimators are established and compared. A simulation study is conducted to appraise the performance of the estimators numerically, as well. Further, a real data example is presented to demonstrate the usefulness of the suggested estimation strategies. The relative dominance picture of the proposed estimators is presented.