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Model averaging is an alternative to model selection for dealing with model uncertainty, which is widely used and very valuable. However, most of the existing model averaging methods are proposed based on the least squares loss function,…
Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…
Spatio-temporal disease mapping models are commonly used to estimate the relative risk of a disease over time and across areas. For each area and time point, the disease count is modelled with a Poisson distribution whose mean is the…
The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…
This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…
We investigate a problem estimating coefficients of linear regression under sparsity assumption when covariates and noises are sampled from heavy tailed distributions. Additionally, we consider the situation where not only covariates and…
The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…
Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…
Outlier detection is a fundamental task in data mining and has many applications including detecting errors in databases. While there has been extensive prior work on methods for outlier detection, modern datasets often have sizes that are…
Functional linear regression is a widely used approach to model functional responses with respect to functional inputs. However, classical functional linear regression models can be severely affected by outliers. We therefore introduce a…
Model mis-specification (e.g. the presence of outliers) is commonly encountered in astronomical analyses, often requiring the use of ad hoc algorithms which are sensitive to arbitrary thresholds (e.g. sigma-clipping). For any given dataset,…
Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…
This paper examines the problem of locating outlier columns in a large, otherwise low-rank matrix, in settings where {}{the data} are noisy, or where the overall matrix has missing elements. We propose a randomized two-step inference…
Reliable outlier detection in high-dimensional data is crucial in modern science, yet it remains a challenging task. Traditional methods often break down in these settings due to their reliance on asymptotic behaviors with respect to sample…
This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing $L_1$-regularized estimation methods, including the…
Outliers are the points which are different from or inconsistent with the rest of the data. They can be novel, new, abnormal, unusual or noisy information. Outliers are sometimes more interesting than the majority of the data. The main…
The parameters of the log-logistic distribution are generally estimated based on classical methods such as maximum likelihood estimation, whereas these methods usually result in severe biased estimates when the data contain outliers. In…
We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
In the study of heavy tail data, several models have been introduced. If the interest is in the tail of the distribution, block maxima or excess over thresholds are the typical approaches, wasting relevant information in the bulk of the…