摘要
In this chapter, we give a very brief but up-to-date review of parametric, nonparametric, and locally parametric techniques that forms the background for the main topics of the book. Among topics discussed, there are distributional aspects such as Gaussian and elliptic distributions. Next, parametric regression models, linear, and nonlinear are covered. A compressed version of time series models, including ARMA, GARCH, and nonlinear models, is included. The last part of the chapter deals with nonparametric methods in density estimation, regression estimation, bandwidth choice, and the curse of dimensionality. Additive models, quantile regression, and semiparametric models are also mentioned. Finally, locally parametric models are introduced as leading up to local Gaussian approximations, which are the main topic of the book.
摘要译文
在本章中，我们对参数，非参数和本地参数技术进行了非常简短但最新的评论，该技术构成了本书的主要主题的背景。在讨论的主题中，有分布方面，例如高斯和椭圆分布。接下来，涵盖了参数回归模型，线性和非线性。包括ARMA，GARCH和非线性模型在内的时间序列模型的压缩版。本章的最后一部分涉及密度估计，回归估计，带宽选择和维度诅咒的非参数方法。还提到了加性模型，分位数回归和半参数模型。最后，将本地参数模型引入了本地高斯近似值，这是本书的主要主题。
DagTjøstheim;HåkonOtneim;BårdStøve. Parametric, nonparametric, locally parametric. Statistical Modeling Using Local Gaussian Approximation[M].US: ELSEVIER, 2022: 7-47