### Abstract

Outliers are common in many sources of data used for estimation of variation; for example, they are a constant problem in data used to determine the precision of analytical methods. Ordinary analysis of unaltered data is often undesirable because the value of an estimate of variation can be essentially determined by only a few points. This paper shows that outlier rejection followed by an ordinary analysis of the remaining data is not acceptable method either - when any data are actually rejected, the variance of the remaining points is badly biased down, even when the distribution from which the data are generated is outlier-prone. By comparison, the robust method of Rocke (1983) performs well. Maximum likelihood for mixtures of normals is promising, but requires further development before its use is practical in small samples.

Original language | English (US) |
---|---|

Pages (from-to) | 9-20 |

Number of pages | 12 |

Journal | Computational Statistics and Data Analysis |

Volume | 13 |

Issue number | 1 |

State | Published - Jan 1992 |

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### Keywords

- Components of variance
- Maximum likelihood estimation
- Mixture of normals

### ASJC Scopus subject areas

- Statistics and Probability
- Numerical Analysis
- Computational Mathematics
- Electrical and Electronic Engineering
- Statistics, Probability and Uncertainty
- Computational Theory and Mathematics

### Cite this

**Estimation of variation after outlier rejection.** / Rocke, David M.

Research output: Contribution to journal › Article

*Computational Statistics and Data Analysis*, vol. 13, no. 1, pp. 9-20.

}

TY - JOUR

T1 - Estimation of variation after outlier rejection

AU - Rocke, David M

PY - 1992/1

Y1 - 1992/1

N2 - Outliers are common in many sources of data used for estimation of variation; for example, they are a constant problem in data used to determine the precision of analytical methods. Ordinary analysis of unaltered data is often undesirable because the value of an estimate of variation can be essentially determined by only a few points. This paper shows that outlier rejection followed by an ordinary analysis of the remaining data is not acceptable method either - when any data are actually rejected, the variance of the remaining points is badly biased down, even when the distribution from which the data are generated is outlier-prone. By comparison, the robust method of Rocke (1983) performs well. Maximum likelihood for mixtures of normals is promising, but requires further development before its use is practical in small samples.

AB - Outliers are common in many sources of data used for estimation of variation; for example, they are a constant problem in data used to determine the precision of analytical methods. Ordinary analysis of unaltered data is often undesirable because the value of an estimate of variation can be essentially determined by only a few points. This paper shows that outlier rejection followed by an ordinary analysis of the remaining data is not acceptable method either - when any data are actually rejected, the variance of the remaining points is badly biased down, even when the distribution from which the data are generated is outlier-prone. By comparison, the robust method of Rocke (1983) performs well. Maximum likelihood for mixtures of normals is promising, but requires further development before its use is practical in small samples.

KW - Components of variance

KW - Maximum likelihood estimation

KW - Mixture of normals

UR - http://www.scopus.com/inward/record.url?scp=38249014752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249014752&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:38249014752

VL - 13

SP - 9

EP - 20

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 1

ER -