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This article introduces trimmed estimators for the mean and covariance function of general functional data. The estimators are based on a new measure of outlyingness or data depth that is well defined on any metric space, although this…

Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…

We propose a new method to visualize and detect shape outliers in samples of curves. In functional data analysis we observe curves defined over a given real interval and shape outliers are those curves that exhibit a different shape from…

Despite tremendous progress in outlier detection research in recent years, the majority of existing methods are designed only to detect unconditional outliers that correspond to unusual data patterns expressed in the joint space of all data…

Outlier detection is a major topic in robust statistics due to the high practical significance of anomalous observations. Many existing methods are, however, either parametric or cease to perform well when the data is far from linearly…

Machine learning and data analysis have been used in many robotics fields, especially for modelling. Data are usually the result of sensor measurements and, as such, they might be subjected to noise and outliers. The presence of outliers…

This paper proposes robust estimators of the variogram, a statistical tool that is commonly used in geostatistics to capture the spatial dependence structure of data. The new estimators are based on the highly robust minimum covariance…

Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…

Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in…

Real data often contain anomalous cases, also known as outliers. These may spoil the resulting analysis but they may also contain valuable information. In either case, the ability to detect such anomalies is essential. A useful tool for…

We propose a novel procedure for outlier detection in functional data, in a semi-supervised framework. As the data is functional, we consider the coefficients obtained after projecting the observations onto orthonormal bases (wavelet, PCA).…

The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we generalize classical depth to directional outlyingness for functional data. We investigate theoretical…

Outlying observations are frequently encountered across a wide spectrum of scientific domains, posing notable challenges to the generalizability of statistical models and the reproducibility of downstream analysis. They are identified…

An outlier is an observation or a data point that is far from rest of the data points in a given dataset or we can be said that an outlier is away from the center of mass of observations. Presence of outliers can skew statistical measures…

This paper considers the problem of outlier detection in functional data analysis focusing particularly on the more difficult case of shape outliers. We present an inductive conformal anomaly detection method based on elastic functional…

Advances in sensor technology have enabled the collection of large-scale datasets. Such datasets can be extremely noisy and often contain a significant amount of outliers that result from sensor malfunction or human operation faults. In…

Surface, image and video data can be considered as functional data with a bivariate domain. To detect outlying surfaces or images, a new method is proposed based on the mean and the variability of the degree of outlyingness at each grid…

A core data-centric learning challenge is the identification of training samples that are detrimental to model performance. Influence functions serve as a prominent tool for this task and offer a robust framework for assessing training data…

Robustness to outliers is often a desirable property of statistical estimators. Indeed many well known estimators offer very good optimal performance in theory but are unusable in applied contexts because of their sensitivity to outliers.…

This note investigates the problem of detecting outliers in longitudinal data. It compares well-known methods used in official statistics with proposals from the fields of data mining and machine learning that are based on the distance…