The aim of this Lecture Note is to introduce the Signal Processing (SP) community to a powerful yet still under-utilised tool: the semiparametric statistics. In short, the semiparametric framework allows us to estimate or perform hypothesis testing on a finite-dimensional parameter in the presence of an infinite-dimensional nuisance parameter (i.e. a function), such as the density of the noise. Clearly, this framework is general enough to include almost every SP application. Remarkably, as the title suggests drawing on George R. R. Martin's famous book series, the greatest advantage of semiparametric statistics over parametric and non-parametric ones lies in the fact that it is able to reconcile two seemingly dichotomous concepts: statistical efficiency and robustness. Here, robustness is understood in the sense of distribution-freeness, that is the estimation performance must be robust with respect to the lack of knowledge of the functional form of the generating data distribution. To explain exactly what this means, in this Lecture Note we will focus our attention on the famous and fundamental symmetric location problem. The symmetric location problem is a fundamental problem that can be found (in various forms) in countless areas of SP: source localization, time synchronization, array signal processing, and distributed sensor networks, just to name a few. Furthermore, it is important to note that the methodology we will develop for this specific problem can be extended to much more general semiparametric estimation problems, such as the estimation of the location vector and covariance matrix in elliptical data.

翻译：本讲义旨在向信号处理领域介绍一种强大但尚未充分利用的工具：半参数统计。简言之，半参数框架允许我们在存在无限维冗余参数（即函数，如噪声密度）的情况下估计有限维参数或进行假设检验。显然，该框架足够通用，几乎涵盖所有信号处理应用。值得注意的是，正如标题借鉴乔治·R·R·马丁著名系列丛书所暗示的，半参数统计相较于参数与非参数统计的最大优势在于其能调和两个看似对立的概念：统计效率与鲁棒性。这里的鲁棒性指分布自由性质，即估计性能必须对生成数据分布函数形式未知具有鲁棒性。为阐明这一内涵，本讲义将聚焦于经典且基础的对称位置问题。这类问题以不同形式广泛存在于信号处理领域：源定位、时间同步、阵列信号处理及分布式传感器网络等。此外需强调，针对该特定问题开发的方法论可推广至更一般的半参数估计问题，如椭圆分布数据中的位置向量与协方差矩阵估计。