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Related Concept Videos

Outliers and Influential Points01:08

Outliers and Influential Points

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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...
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Estimating Population Mean with Unknown Standard Deviation01:22

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
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Coefficient of Correlation01:12

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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
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Detection of Gross Error: The Q Test01:00

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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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Quantifying and Rejecting Outliers: The Grubbs Test01:02

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Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This...
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Updated: Sep 8, 2025

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A robust estimation method for the linear regression model parameters with correlated error terms and outliers.

Sajjad Piradl1, Ali Shadrokh1, Masoud Yarmohammadi1

  • 1Department of Statistics, Payame Noor University, Tehran, Iran.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary

This study introduces a new method for linear regression with correlated errors, using non-parametric kernel density estimation. The proposed minimum Matusita distance estimators show lower bias and mean squared errors, improving robustness and efficiency.

Keywords:
Robust estimation methodcorrelated error termsminimum Matusita distance estimation methodnon-parametric kernel density estimation methodoutliers

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Area of Science:

  • Statistics
  • Econometrics
  • Data Science

Background:

  • Linear regression models often assume independent error terms, which is frequently not met in practice.
  • Correlated error terms can compromise the robustness of standard linear regression analysis.
  • Existing methods like M-estimators and Cochrane-Orcutt adjusted least squares have limitations regarding robustness and efficiency.

Purpose of the Study:

  • To develop a novel estimation method for linear regression models with correlated error terms, specifically addressing the presence of outliers.
  • To introduce minimum Matusita distance estimators enhanced by non-parametric kernel density estimation.
  • To evaluate the performance of the proposed method against existing techniques.

Main Methods:

  • Utilizing non-parametric kernel density estimation to derive minimum Matusita distance estimators.
  • Applying the proposed method to linear regression models with correlated error terms and outliers.
  • Conducting simulation studies and analyzing real-world data.

Main Results:

  • The proposed minimum Matusita distance estimation method demonstrated superior performance compared to M-estimators and Cochrane-Orcutt adjusted least squares.
  • The new method effectively handles correlated error terms and outliers in linear regression.
  • Lower biases and mean squared errors were observed for the proposed estimation technique.

Conclusions:

  • The non-parametric kernel density estimation-based minimum Matusita distance approach offers a robust and efficient solution for linear regression with correlated errors.
  • This method provides improved parameter estimation in the presence of data complexities like outliers and error term dependence.
  • The findings suggest a valuable advancement for statistical modeling in various applied fields.