Some inferential questions in regard to analysing two-way Layouts and associated linear model theory and practice

Brenton R. Clarke; Antony G. Monaco

Discussiones Mathematicae Probability and Statistics (2004)

  • Volume: 24, Issue: 2, page 183-195
  • ISSN: 1509-9423

Abstract

top
In analysing a well known data set from the literature which can be thought of as a two-way layout it transpires that a robust adaptive regression approach for identifying outliers fails to be sensitive enough to detect the possible interchange of two observations. On the other hand if one takes the classical approach of diagnostic checking one may also stop too early and be satisfied with a model that falls short of a more detailed analysis that takes account of heteroscedasticity in the data. An exact F-test for heteroscedasticity in the two way layout is compared with various more general tests proposed by Shukla. In conclusion it is noted that when modelling the particular form of heteroscedasticity countenanced here, the estimated column effects are unchanged from those estimated from the model assuming homogeneous error variance structure. It is only the estimated variances of these column effects that changes.

How to cite

top

Brenton R. Clarke, and Antony G. Monaco. "Some inferential questions in regard to analysing two-way Layouts and associated linear model theory and practice." Discussiones Mathematicae Probability and Statistics 24.2 (2004): 183-195. <http://eudml.org/doc/287669>.

@article{BrentonR2004,
abstract = {In analysing a well known data set from the literature which can be thought of as a two-way layout it transpires that a robust adaptive regression approach for identifying outliers fails to be sensitive enough to detect the possible interchange of two observations. On the other hand if one takes the classical approach of diagnostic checking one may also stop too early and be satisfied with a model that falls short of a more detailed analysis that takes account of heteroscedasticity in the data. An exact F-test for heteroscedasticity in the two way layout is compared with various more general tests proposed by Shukla. In conclusion it is noted that when modelling the particular form of heteroscedasticity countenanced here, the estimated column effects are unchanged from those estimated from the model assuming homogeneous error variance structure. It is only the estimated variances of these column effects that changes.},
author = {Brenton R. Clarke, Antony G. Monaco},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {outlier; two-way layout; adaptive estimation; heteroscedaticity; outliers},
language = {eng},
number = {2},
pages = {183-195},
title = {Some inferential questions in regard to analysing two-way Layouts and associated linear model theory and practice},
url = {http://eudml.org/doc/287669},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Brenton R. Clarke
AU - Antony G. Monaco
TI - Some inferential questions in regard to analysing two-way Layouts and associated linear model theory and practice
JO - Discussiones Mathematicae Probability and Statistics
PY - 2004
VL - 24
IS - 2
SP - 183
EP - 195
AB - In analysing a well known data set from the literature which can be thought of as a two-way layout it transpires that a robust adaptive regression approach for identifying outliers fails to be sensitive enough to detect the possible interchange of two observations. On the other hand if one takes the classical approach of diagnostic checking one may also stop too early and be satisfied with a model that falls short of a more detailed analysis that takes account of heteroscedasticity in the data. An exact F-test for heteroscedasticity in the two way layout is compared with various more general tests proposed by Shukla. In conclusion it is noted that when modelling the particular form of heteroscedasticity countenanced here, the estimated column effects are unchanged from those estimated from the model assuming homogeneous error variance structure. It is only the estimated variances of these column effects that changes.
LA - eng
KW - outlier; two-way layout; adaptive estimation; heteroscedaticity; outliers
UR - http://eudml.org/doc/287669
ER -

References

top
  1. [1] B.R. Clarke, An adaptive method of estimation and outlier detection in regression applicable for small to moderate sample sizes, Discussiones Mathematicae Probability and Statistics 20 (2000), 25-50. Zbl0971.62034
  2. [2] B.R. Clarke, A representation of orthogonal components in analysis of variance, International Mathematical Journal 1 (2002), 133-147. Zbl0978.62054
  3. [3] B.R. Clarke and E.J. Godolphin, Uncorrelated residuals and an exact test for two variance components in experimental design, Communications in Statistics, Part A - Theory and Methods 21 (1992), 2501-2526. Zbl0776.62060
  4. [4] C. Daniel, Applications of Statistics to Industrial Experimentation, Wiley, New York 1976. Zbl0345.62058
  5. [5] R.A. Fisher, Design of Experiments, 5th ed., Oliver and Boyd, Edinburgh 1949. 
  6. [6] P.J. Huber, Robust Statistical Procedures, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia 1996. Zbl0859.62003
  7. [7] S. Puntanen and G.P.H. Styan, The equality of the ordinary least squares estimator and the best linear unbiased estimator, (with discussion) The American Statistician 43 (1989), 153-164. 
  8. [8] T.S. Russell and R.A. Bradley, One-way variances in a two-way classification, Biometrika 45 (1958), 111-129. Zbl0086.34602
  9. [9] H. Scheffé, The Analysis of Variance, Wiley, New York 1959. 
  10. [10] G.K. Shukla, An invariant test for the homogeneity of variances in a two-way classification, Biometrics 28 (1972), 1063-1072. 
  11. [11] G.K. Shukla, Testing the homogeneity of variances in a two-way classification, Biometrika 69 (1982), 411-416. Zbl0494.62068

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.