A Note on Bayesian Nonparametric Inference for Spherically Symmetric Distribution

Characterising variation of nonparametric random probability measures using the Kullback-Leibler divergence

This work studies the variation in Kullback-Leibler divergence between random draws from some popular nonparametric processes and their baseline measure. In particular we focus on the Dirichlet process, the Pólya tree and the frequentist and Bayesian bootstrap. The results shed light on the support of these nonparametric processes. Of particular note are results for finite Pólya trees that are used to model continuous random probability measures. Our results provide guidance for specifying the parameterisation of the Pólya tree process that allows for greater understanding while highlighting l…

关于非参数估计边际回归的偏相关系数分布的注记

A note on the distribution of the partial correlation coefficient with nonparametrically estimated marginal regressions

本文提出一种基于样本偏相关系数并采用非参数边际回归的置换检验，证明其在大样本和小样本下均表现良好，用于条件独立性的非参数检验。

Some comments about James Watson's and Chris Holmes' "Approximate Models and Robust Decisions": Nonparametric Bayesian clay for robust decision bricks

This note discusses Watson and Holmes (2016) and their pro- posals towards more robust Bayesian decisions. While we acknowledge and commend the authors for setting new and all-encompassing prin- ciples of Bayesian robustness, and we appreciate the strong anchoring of those within a decision-theoretic referential, we remain uncertain as to which extent such principles can be applied outside binary de- cisions. We also wonder at the ultimate relevance of Kullback-Leibler neighbourhoods to characterise robustness and favour extensions along non-parametric axes.

On ill-posedness of nonparametric instrumental variable regression with convexity constraints

This note shows that adding monotonicity or convexity constraints on the regression function does not restore well-posedness in nonparametric instrumental variable regression. The minimum distance problem without regularisation is still locally ill-posed.

Rates of convergence for nonparametric deconvolution

This Note presents original rates of convergence for the deconvolution problem. We assume that both the estimated density and noise density are supersmooth and we compute the risk for two kinds of estimators.

Adaptive confidence bands in the nonparametric fixed design regression model

In this note, we consider the problem of existence of adaptive confidence bands in the fixed design regression model, adapting ideas in Hoffmann and Nickl (2011) to the present case. In the course of the proof, we show that sup-norm adaptive estimators exist as well in regression.

Baysian inference via classes of normalized random measures

One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures in order to provide a comprehensive Bayesian analysis of random probabilities which are obtained by an appropriate normalization. Specifically we achieve explicit and tractable forms of the posterior and the marginal distributions, including an explicit and easily used description of generalizations of the important Blackwell-MacQueen Pólya urn distribution. Such simplifications are achieved by th…

Identification and well-posedness in a class of nonparametric problems

This is a companion note to Zinde-Walsh (2010), arXiv:1009.4217v1[MATH.ST], to clarify and extend results on identification in a number of problems that lead to a system of convolution equations. Examples include identification of the distribution of mismeasured variables, of a nonparametric regression function under Berkson type measurement error, some nonparametric panel data models, etc. The reason that identification in different problems can be considered in one approach is that they lead to the same system of convolution equations; moreover the solution can be given under more general as…

A note on the best invariant estimation of continuous probability distributions under mean square loss

We consider the nonparametric estimation problem of continuous probability distribution functions. For the integrated mean square error we provide the statistic corresponding to the best invariant estimator proposed by Aggarwal (1955) and Ferguson (1967). The table of critical values is computed and a numerical power comparison of the statistic with the traditional Cramér-von Mises statistic is done for several representative distributions.

嵌套复合随机测度

Nested Compound Random Measures

针对现有嵌套非参数过程模型计算效率低、数学难处理的问题，本文基于复合随机测度提出兼具易处理性与高效性的嵌套过程，推导其理论性质与首个Ferguson & Klass算法，实验验证其性能优于同类贝叶斯模型。

关于断点回归设计中双稳健估计量的注记

A Note on Doubly Robust Estimator in Regression Discontinuity Designs

本文提出了用于断点回归设计的双稳健估计量（DR-RD），通过结合两个条件期望结果估计量，在至少一个估计量一致时即可保证处理效应估计的一致性，从而增强了估计的稳健性。

关于通过逆推得分检验得到的局部平均处理效应置信集性质的注记

A note on the properties of the confidence set for the local average treatment effect obtained by inverting the score test

该研究刻画了非参/半参工具变量模型中局部平均处理效应得分置信集的六种形式，证明其与双重稳健Wald区间的渐近一致性及弱工具下的优良性，还给出了可在DoubleML包中实现的计算算法。

度量空间中基于度量分布函数的非参数统计推断

Nonparametric Statistical Inference via Metric Distribution Function in Metric Spaces

本文在度量空间中引入度量分布函数，证明对应定理与 Glivenko-Cantelli 定理，并据此提出非欧几里得随机对象的同质性检验和相互独立性检验方法。