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Simple graphs and bounds for the elements of the hat matrix. (English) Zbl 0939.62064

Summary: In regression analysis, the matrix \({\mathbf H}={\mathbf X}({\mathbf X}^T{\mathbf X})^{-1}{\mathbf X}^T\) is known as the ‘hat’ or ‘projection’ matrix, among other names. It has been studied by many authors from different perspectives. The main area of study has been the type of measure best adapted to detect leverage points in linear regression. For computational reasons, these measures were originally based on the diagonal elements of the hat matrix. We propose a very simple procedure for identifying leverage groups. The procedure is based on upper and lower bounds for the diagonal and the off-diagonal elements of \({\mathbf H}\). These upper and lower bounds can easily be shown on an index plot of the elements of \({\mathbf H}\).

MSC:

62J05 Linear regression; mixed models
62A09 Graphical methods in statistics
65C60 Computational problems in statistics (MSC2010)
15A99 Basic linear algebra

Keywords:

leverage groups
Full Text: DOI

References:

[1] BEROD A. C., S 2 pp 1– (1997)
[2] BIRKES D., Alternative Methods of Regression (1993) · Zbl 0850.62528
[3] COOK R. D., Residuals and Influence in Regression (1982) · Zbl 0564.62054
[4] DOI: 10.1006/jmva.1997.1666 · Zbl 0877.62067 · doi:10.1006/jmva.1997.1666
[5] DOI: 10.2307/1269490 · doi:10.2307/1269490
[6] DOI: 10.1080/02664769000000004 · doi:10.1080/02664769000000004
[7] DOI: 10.2307/2683469 · Zbl 0375.62070 · doi:10.2307/2683469
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