LAD Regression and Nonparametric Methods for Detecting Outliers and Leverage Points

Cross-validation in nonparametric regression with outliers

A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers in the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist. (1984) 26 163--184]. However, under these circumstances standard cross-validation is no longer a satisfactory bandwidth selector because it is unduly influenced by extreme prediction errors caused by the existence of these outliers. A more robust method proposed here is a cross-validation method that d…

Nonparametric Estimation in the Model of Moving Average

The subject of robust estimation in time series is widely discussed in literature. One of the approaches is to use GM-estimation. This method incorporates a broad class of nonparametric estimators which under suitable conditions includes estimators robust to outliers in data. For the linear models the sensitivity of GM-estimators to outliers have been studied in the work by Martin and Yohai [5], and influence functionals for this estimator were derived. In this paper we follow this direction and examine the asymptotical properties of the class of M-estimators, which is narrower than the class …

Robust Estimation and Wavelet Thresholding in Partial Linear Models

This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We present a wavelet thresholding based estimation procedure to estimate the components of the partial linear model by establishing a connection between an $l_1$-penalty based wavelet estimator of the nonparametric component and Huber's M-estimation of a standard linear model with outliers. Some general results on the large sample properties of the estimates of b…

二维正弦模型最小绝对偏差估计量的一致性与渐近正态性研究

On Consistency and Asymptotic Normality of Least Absolute Deviation Estimators for 2-dimensional Sinusoidal Model

针对二维正弦模型参数估计问题，提出鲁棒最小绝对偏差估计量，证明其强一致性与渐近正态性，通过仿真和纹理数据分析验证其在异常值、重尾噪声场景下的优势与实用性。

基于共形p值的异常值检测

Testing for Outliers with Conformal p-values

本文从多重检验视角研究非参数异常值检测的p值构建，提出基于共形推断的方案及新p值计算方法，利用集中不等式建立有限样本保证，还给出假阳性率一致置信界，经实验验证有效。

左截断与右删失下的函数相对误差回归

Functional relative error regression under left truncation and right censoring

本文针对函数解释变量和左截断右删失标量变量，构建了基于均方相对误差的非参数回归函数估计量，证明了其逐点与一致收敛性，并通过数值研究验证了其稳健性。