Related papers: M-Estimation Method Based Asymmetric Objective Fun…
M-type smoothing splines are a broad class of spline estimators that include the popular least-squares smoothing spline but also spline estimators that are less susceptible to outlying observations and model-misspecification. However,…
We mainly study the M-estimation method for the high-dimensional linear regression model, and discuss the properties of M-estimator when the penalty term is the local linear approximation. In fact, M-estimation method is a framework, which…
We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to…
Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing…
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…
The joint estimation of means and scatter matrices is often a core problem in multivariate analysis. In order to overcome robustness issues, such as outliers from Gaussian assumption, M-estimators are now preferred to the traditional sample…
Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical…
Huber loss, its asymmetric variants and their associated functionals (here named Huber functionals) are studied in the context of point forecasting and forecast evaluation. The Huber functional of a distribution is the set of minimizers of…
We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted…
We introduce an optimization model for maximum likelihood-type estimation (M-estimation) that generalizes a large class of existing statistical models, including Huber's concomitant M-estimator, Owen's Huber/Berhu concomitant estimator, the…
This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…
M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…
We provide a unified approach to MM-estimation with auxiliary scale for balanced linear models with structured covariance matrices. This approach leads to estimators that are highly robust against outliers and highly efficient for normal…
This paper develops asymptotic normality results for individual coordinates of robust M-estimators with convex penalty in high-dimensions, where the dimension $p$ is at most of the same order as the sample size $n$, i.e, $p/n\le\gamma$ for…
We develop an asymptotic theory of adversarial estimators ('A-estimators'). They generalize maximum-likelihood-type estimators ('M-estimators') as their average objective is maximized by some parameters and minimized by others. This class…
We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms.…
To address model uncertainty under flexible loss functions in prediction problems, we propose a model averaging method that accommodates various loss functions, including asymmetric linear and quadratic loss functions, as well as many other…
M-quantile regression is a general form of quantile-like regression which usually utilises the Huber influence function and corresponding tuning constant. Estimation requires a nuisance scale parameter to ensure the M-quantile estimates are…
We propose a novel sampling-based federated learning framework for statistical inference on M-estimators with non-smooth objective functions, which frequently arise in modern statistical applications such as quantile regression and AUC…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…