02.2 - Missing Data Treatment - DATS

Recall the meaning of Outlier and how to find them in our data

Outlier

outlier

According to [[Douglas Hawkins]]

An outlier is an observation which deviates so much from the other observations as to arouse suspicions that it was generated by a different mechanism.

Types of outliers

Mild outlier

mild outlier

$x_{0}$ is a Mild [[#Outlier]] if:
$x_{0} \notin [Q 1 - 1.5 I Q R; Q 3 + 1.5 I Q R]$

Severe outlier

Outlier detection

Univariate and multivariate outlier detection

When a data sample is given, we can often assumed it to be generated by one basic generating mechanism (ex. a probability distribution like the logistic one). Often times, the same data can be generated by 2 or more mechanisms. This could cause one set of data to have observations in 2 completely different classes of similar objects. When looking at the data through one generating mechanism, the other class would appear as a big group of outliers.

Univariate outlier detection

Outliers in boxplots

The boxplot is a graphical display for Exploratory Data Analysis, where the outliers appear tagged. In the boxplot we are able to show both #Types of outliers.

Outlier 2024-11-14 10.37.32.excalidraw.png

Multivariate outlier detection

Outliers can be detected by computing the distance between the central point of data, by means of an iterative algorithm:
$D_{M}^{2} (i, G) = (x_{i} - G)^{'} V^{- 1} (x_{i} - G)$

Once we find outliers, there are several options we might consider:

Eliminate them - but loose information of the eliminated observations
Weight the individuals inversely to the outlying degree, to diminish their importance
Make robust estimation of the parameteers of the generating mechanism without oultiers
Declare univariate outliers as #Missing values and treat them as missing data