Deletion diagnostics in fitting a given regression model to a new observation

- Journal title : Communications for Statistical Applications and Methods
- Volume 23, Issue 3, 2016, pp.231-239
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CSAM.2016.23.3.231

Title & Authors

Deletion diagnostics in fitting a given regression model to a new observation

Kim, Myung Geun;

Kim, Myung Geun;

Abstract

A graphical diagnostic method based on multiple case deletions in a regression context is introduced by using the sampling distribution of the difference between two least squares estimators with and without multiple cases. Principal components analysis plays a key role in deriving this diagnostic method. Multiple case deletions of test statistic are also considered when a new observation is fitted to a given regression model. The result is useful for detecting influential observations in econometric data analysis, for example in checking whether the consumption pattern at a later time is the same as the one found before or not, as well as for investigating the influence of cases in the usual regression model. An illustrative example is given.

Keywords

case deletions;covariance matrix;influence;principal components analysis;test statistic;

Language

English

Cited by

References

1.

Chatterjee S and Hadi AS (1988). Sensitivity Analysis in Linear Regression, JohnWiley & Sons, New York.

2.

Chow GC (1960). Tests of equality between sets of coefficients in two linear regressions, Econometrica, 28, 591-605.

3.

Cook RD (1977). Detection of influential observation in linear regression, Technometrics, 19, 15-18.

4.

Cook RD and Weisberg S (1982). Residuals and Influence in Regression, Chapman and Hall, New York.

5.

Ghilagaber G (2004). Another look at Chow's test for the equality of two heteroscedastic regression models, Quality and Quantity, 38, 81-93.

6.

Kim MG (2015). Influence measure based on probabilistic behavior of regression estimators, Computational Statistics, 30, 97-105.

7.

Neter J, Kutner MH, Nachtsheim CJ, and Wasserman W (1996). Applied Linear Regression Models (3rd ed), McGraw-Hill Higher Education/Irwin, New York.

8.

Seber GAF (1977). Linear Regression Analysis, John Wiley & Sons, New York.