Genton Marc G, Kim Mijeong, Ma Yanyuan
Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA.
Stat. 2012 Aug 24;1(1):1-11. doi: 10.1002/sta4.2.
We study a class of semiparametric skewed distributions arising when the sample selection process produces non-randomly sampled observations. Based on semiparametric theory and taking into account the symmetric nature of the population distribution, we propose both consistent estimators, i.e. robust to model mis-specification, and efficient estimators, i.e. reaching the minimum possible estimation variance, of the location of the symmetric population. We demonstrate the theoretical properties of our estimators through asymptotic analysis and assess their finite sample performance through simulations. We also implement our methodology on a real data example of ambulatory expenditures to illustrate the applicability of the estimators in practice.
我们研究了一类半参数偏态分布，这类分布产生于样本选择过程产生非随机抽样观测值的情况。基于半参数理论并考虑到总体分布的对称性质，我们提出了对称总体位置的一致估计量（即对模型误设具有稳健性）和有效估计量（即达到最小可能估计方差）。我们通过渐近分析证明了估计量的理论性质，并通过模拟评估了它们的有限样本性能。我们还将我们的方法应用于门诊支出的实际数据示例，以说明估计量在实践中的适用性。
