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Related Concept Videos

What Are Outliers?01:12

What Are Outliers?

Outliers are observed data points that are far from the least squares line. They have unusual values and need to be examined carefully. Though an outlier may result from erroneous data, at other times, it may hold valuable information about the population under study and should be included in the data. Hence, it is crucial to examine what causes a data point to be an outlier.
The z score is used to find outliers or unusual values. It should be noted that any values beyond -2 and +2 are...
Outliers and Influential Points01:08

Outliers and Influential Points

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the vertical...
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
State Space to Transfer Function01:21

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Detection of Gross Error: The Q Test01:00

Detection of Gross Error: The Q Test

When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...

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Related Experiment Videos

Outlier detection in state-space models using mean-shift penalisation.

Rajan Shankar1, Ines Wilms2, Jakob Raymaekers3

  • 1School of Mathematics and Statistics, The University of Sydney, Sydney, 2006 Australia.

Statistics and Computing
|July 15, 2026
PubMed
Summary

Robust estimation method ROAMS effectively handles outliers in time series data. This approach improves state-space model parameter estimation for cleaner, more reliable data analysis.

Keywords:
FilteringMissing observationsObject-trackingOutlier detectionSparsityTime series

Related Experiment Videos

Area of Science:

  • Statistics
  • Time Series Analysis
  • Machine Learning

Background:

  • State-space models (SSMs) are powerful for time series but sensitive to outliers due to Gaussian error assumptions.
  • Outliers can significantly distort parameter estimates in traditional SSMs, leading to unreliable analyses.

Purpose of the Study:

  • To introduce ROBUST ESTIMATION METHOD (ROAMS), a novel method for robustly estimating state-space models in the presence of additive outliers.
  • To enable automatic outlier detection and simultaneous parameter estimation within the SSM framework.

Main Methods:

  • ROAMS incorporates shift parameters in the observation equation to isolate outlier effects.
  • A penalty term is added to the loss function for automatic outlier detection and model fitting.
  • The method was validated on simulated and real-world animal tracking datasets.

Main Results:

  • ROAMS demonstrated superior robustness, yielding more reliable parameter estimates compared to classical and benchmark methods.
  • The method successfully identified and mitigated the influence of outliers in time series data.
  • ROAMS provides diagnostic tools like BIC curves for parameter selection and outlier visualization.

Conclusions:

  • ROAMS offers a robust and practical solution for time series analysis contaminated with outliers.
  • This method enhances the reliability of state-space models for diverse research and practitioner applications.
  • ROAMS facilitates accurate modeling even with significant data anomalies.