Gaussianization Machines for Non-Gaussian Function Estimation Models
Gaussianization Machines for Non-Gaussian Function Estimation Models
复制标题
非高斯函数估计模型的高斯化机
作者：
T. Cai
广泛的非参数函数估计模型，
在文献中被单独研究过。其中，
非参数高斯回归可以说是最为人所知和理解的。
受渐近等价理论的启发，Brown，Cai和Zhou
(Ann.中央集权主义者36（2008）2055-2084; Ann. Statist. 38（2010）2005-2046）和
Brown等人（Probab. Theory Related Fields 146（2010）401-433）开发
一个统一的方法把一个集合的非高斯函数估计
模型转换为标准高斯回归和任何良好的高斯非参数
然后可以使用回归方法。
这些高斯化机器有两个关键组成部分，分箱和
转型当与BlockJS结合使用时，
对于高斯回归，该过程在计算上是有效的
有坚实的理论保障。Brown，Cai给出的技术分析
和Zhou（Ann. Statistist. 36（2008）2055-2084; Ann. Statist.第38（2010）号来文，2005年
2046）和Brown等人（Probab.理论相关领域146（2010）401-433）
表明估计器自适应地达到最优收敛速度
在一个大的Besov空间集和一个非高斯的集合上，
函数估计模型，包括稳健非参数回归，密度
估计和指数族中的非参数回归的
估计器也是空间自适应的。
高斯化机器显著地扩展了灵活性，
最初为传统方法开发的理论和方法的范围
非参数高斯回归本文旨在提供一个
对Brown，Cai开发的高斯化机的简要说明
和Zhou（Ann. Statistist. 36（2008）2055-2084; Ann. Statist.第38（2010）号来文，2005年
2046）、Brown等人（Probab. Theory Related Fields 146（2010）401-433）。
A wide range of nonparametric function estimation models have
been studied individually in the literature. Among them the homoscedastic
nonparametric Gaussian regression is arguably the best known and understood.
Inspired by the asymptotic equivalence theory, Brown, Cai and Zhou
(Ann. Statist. 36 (2008) 2055–2084; Ann. Statist. 38 (2010) 2005–2046) and
Brown et al. (Probab. Theory Related Fields 146 (2010) 401–433) developed
a unified approach to turn a collection of non-Gaussian function estimation
models into a standard Gaussian regression and any good Gaussian nonparametric
regression method can then be used.
These Gaussianization Machines have two key components, binning and
transformation. When combined with BlockJS, a wavelet thresholding procedure
for Gaussian regression, the procedures are computationally efficient
with strong theoretical guarantees. Technical analysis given in Brown, Cai
and Zhou (Ann. Statist. 36 (2008) 2055–2084; Ann. Statist. 38 (2010) 2005–
2046) and Brown et al. (Probab. Theory Related Fields 146 (2010) 401–433)
shows that the estimators attain the optimal rate of convergence adaptively
over a large set of Besov spaces and across a collection of non-Gaussian
function estimation models, including robust nonparametric regression, density
estimation, and nonparametric regression in exponential families. The
estimators are also spatially adaptive.
The Gaussianization Machines significantly extend the flexibility and
scope of the theories and methodologies originally developed for the conventional
nonparametric Gaussian regression. This article aims to provide a
concise account of the Gaussianization Machines developed in Brown, Cai
and Zhou (Ann. Statist. 36 (2008) 2055–2084; Ann. Statist. 38 (2010) 2005–
2046), Brown et al. (Probab. Theory Related Fields 146 (2010) 401–433).