Related papers: Outliers and related problems
We are trying to give a mathematically correct definition of outliers. Our approach is based on the distance between two last order statistics and appears to be connected to the law of large numbers. Key words: outliers, law of large…
A possibility to give strong mathematical definitions of outliers and heavy tailed distributions or their modification is discussed. Some alternatives for the notion of tail index are proposed. Key words: outliers, heavy tails, tail index.
The aim of the paper is to show that the presence of one possible type of outliers is not connected to that of heavy tails of the distribution. In contrary, typical situation for outliers appearance is the case of compact supported…
There are a number of mathematical formalisms of the term "outlier" in statistics, though there is no consensus on what the right notion ought to be. Accordingly, we try to give a consistent and robust definition for a specific type of…
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…
In statistics and machine learning, the traditional meaning of the terms `outlier' and `anomaly' is a case in the dataset that behaves differently from the bulk of the data. This raises suspicion that it may belong to a different…
Bayesian statistics emphasizes the importance of prior distributions, yet finding an appropriate one is practically challenging. When multiple sample results are taken regarding the frequency of the same event, these samples may be…
In this paper we provide a definition of pattern of outliers in contingency tables within a model-based framework. In particular, we make use of log-linear models and exact goodness-of-fit tests to specify the notions of outlier and pattern…
Outlier hypothesis testing is studied in a universal setting. Multiple sequences of observations are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are distributed…
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…
An outlier is a datapoint that is set apart from a sample population. The outlier theorem in algorithmic information theory states that given a computable sampling method, outliers must appear. We present a simple proof to the outlier…
Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and…
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…
The development of effective knowledge discovery techniques has become in the recent few years a very active research area due to the important impact it has in several relevant application areas. One interesting task thereof is that of…
Outlier detection is a core task in data mining with a plethora of algorithms that have enjoyed wide scale usage. Existing algorithms are primarily focused on detection, that is the identification of outliers in a given dataset. In this…
It is well-known that real data often contain outliers. The term outlier typically refers to a case, that is, a row of the $n \times d$ data matrix. In recent times a different type has come into focus, the cellwise outliers. These are…
Dynamic factor models have a wide range of applications in econometrics and applied economics. The basic motivation resides in their capability of reducing a large set of time series to only few indicators (factors). If the number of time…
Using methods of statistical mechanics, we analyse the effect of outliers on the supervised learning of a classification problem. The learning strategy aims at selecting informative examples and discarding outliers. We compare two…
Universal outlier hypothesis testing is studied in a sequential setting. Multiple observation sequences are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are…
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…