In this paper, we consider the two-sample location shift model, a classic semiparametric model introduced by Stein (1956). This model is known for its adaptive nature, enabling nonparametric estimation with full parametric efficiency. Existing nonparametric estimators of the location shift often depend on external tuning parameters, which restricts their practical applicability (Van der Vaart and Wellner, 2021). We demonstrate that introducing an additional assumption of log-concavity on the underlying density can alleviate the need for tuning parameters. We propose a one step estimator for location shift estimation, utilizing log-concave density estimation techniques to facilitate tuning-free estimation of the efficient influence function. While we employ a truncated version of the one step estimator for theoretical adaptivity, our simulations indicate that the one step estimators perform best with zero truncation, eliminating the need for tuning during practical implementation.

翻译：本文考虑两样本位置偏移模型，该模型由Stein（1956）提出的经典半参数模型，以其能够实现完全参数化效率的非参数估计的自适应特性而著称。现有位置偏移的非参数估计量通常依赖于外部调优参数，这限制了其实际应用性（Van der Vaart and Wellner, 2021）。我们证明，在潜在密度上增加对数凹性假设可消除调优参数的需求。我们提出一种基于对数凹密度估计技术的位置偏移一步估计量，通过有效影响函数的免调优估计促进理论自适应。虽然我们采用截断版本的一步估计量来保证理论自适应性，但模拟结果表明，零截断的一步估计量在实际实现中表现最优，彻底避免了调优过程。