Related papers: High-Breakdown Robust Multivariate Methods
Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…
We discuss recent work for causal inference and predictive robustness in a unifying way. The key idea relies on a notion of probabilistic invariance or stability: it opens up new insights for formulating causality as a certain risk…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model…
In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…
Functional quadratic regression models postulate a polynomial relationship between a scalar response rather than a linear one. As in functional linear regression, vertical and specially high-leverage outliers may affect the classical…
Bai (2010) and Bai et al. (2012) proposed robust mixture regression method based on the M regression estimation. However, the M-estimators are robust against the outliers in response variables, but they are not robust against the outliers…
Missing data is frequently encountered in many areas of statistics. Propensity score weighting is a popular method for handling missing data. The propensity score method employs a response propensity model, but correct specification of the…
Gaussian process regression (GPR) model is well-known to be susceptible to outliers. Robust process regression models based on t-process or other heavy-tailed processes have been developed to address the problem. However, due to the nature…
Causal discovery aims to learn causal relationships between variables from targeted data, making it a fundamental task in machine learning. However, causal discovery algorithms often rely on unverifiable causal assumptions, which are…
One of the significant challenges in monitoring the quality of products today is the high dimensionality of quality characteristics. In this paper, we address Phase I analysis of high-dimensional processes with individual observations when…
Segmented regression is a standard statistical procedure used to estimate the effect of a policy intervention on time series outcomes. This statistical method assumes the normality of the outcome variable, a large sample size, no…
Unsupervised learning methods are well established in the area of anomaly detection and achieve state of the art performances on outlier datasets. Outliers play a significant role, since they bear the potential to distort the predictions of…
The classical tests in the instrumental variable model can behave arbitrarily if the data is contaminated. For instance, one outlying observation can be enough to change the outcome of a test. We develop a framework to construct testing…
Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…
Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be…
Gradient boosting algorithms construct a regression predictor using a linear combination of ``base learners''. Boosting also offers an approach to obtaining robust non-parametric regression estimators that are scalable to applications with…
The problem of linear predictions has been extensively studied for the past century under pretty generalized frameworks. Recent advances in the robust statistics literature allow us to analyze robust versions of classical linear models…
High-dimensional data poses unique challenges in outlier detection process. Most of the existing algorithms fail to properly address the issues stemming from a large number of features. In particular, outlier detection algorithms perform…
We consider the problem of robustly fitting a model to data that includes outliers by formulating a percentile optimization problem. This problem is non-smooth and non-convex, hence hard to solve. We derive properties that the minimizers of…
Robust test statistics for the two-way MANOVA based on the minimum covariance determinant (MCD) estimator are proposed as alternatives to the classical Wilks' Lambda test statistics which are well known to be very sensitive to outliers as…