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引用次数: 0
摘要
本文考虑Stein(1956)提出的经典半参数模型——双样本位置移位模型。该模型以其自适应特性而闻名,使非参数估计具有充分的参数效率。现有的位置移位的非参数估计器通常依赖于外部调谐参数,这限制了它们的实际适用性(Van der Vaart和Wellner, 2021)。我们证明了在底层密度上引入一个额外的对数凹性假设可以减轻对参数调优的需要。我们提出了一个用于位置移位估计的一步估计器,利用对数凹密度估计技术来促进有效影响函数的无调谐估计。虽然我们采用截断版本的一步估计器进行理论自适应,但我们的模拟表明,一步估计器在零截断时表现最佳,从而消除了在实际实现期间调整的需要。
Revisiting the two-sample location shift model with a log-concavity assumption
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.