论文标题
加权$ψ$估计器的存在和独特性
Existence and uniqueness of weighted generalized $ψ$-estimators
论文作者
论文摘要
我们介绍了广义和加权$ψ$估计器的概念，作为某些适当功能的符号更改的独特点，我们为它们的存在提供了必要的条件。我们还得出了一组足够的条件，在该条件下，所谓的$ψ$ - 期望功能具有唯一的标志更改点。我们从统计估计理论中介绍了几个示例，其中我们的结果非常适用。例如，我们考虑了经验分位数，经验期望，一些在健壮统计中很重要的$ψ$估计器以及最大似然理论的一些示例。此外，我们介绍了bajraktarević-type（尤其是Quasi-arithmetic-type）$ψ$估计器。我们的结果专门针对$ψ$估计器，其第二个变量连续函数$ψ$为（通常）$ψ$估计器（也称为z估计器）提供了新的结果。
We introduce the notions of generalized and weighted generalized $ψ$-estimators as unique points of sign change of some appropriate functions, and we give necessary as well as sufficient conditions for their existence. We also derive a set of sufficient conditions under which the so-called $ψ$-expectation function has a unique point of sign change. We present several examples from statistical estimation theory, where our results are well-applicable. For example, we consider the cases of empirical quantiles, empirical expectiles, some $ψ$-estimators that are important in robust statistics, and some examples from maximum likelihood theory as well. Further, we introduce Bajraktarević-type (in particular, quasi-arithmetic-type) $ψ$-estimators. Our results specialized to $ψ$-estimators with a function $ψ$ being continuous in its second variable provide new results for (usual) $ψ$-estimators (also called Z-estimators).
