JOURNAL BROWSE
Search
Advanced SearchSearch Tips
An Orthogonal Representation of Estimable Functions
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
An Orthogonal Representation of Estimable Functions
Yi, Seong-Baek;
  PDF(new window)
 Abstract
Students taking linear model courses have difficulty in determining which parametric functions are estimable when the design matrix of a linear model is rank deficient. In this note a special form of estimable functions is presented with a linear combination of some orthogonal estimable functions. Here, the orthogonality means the least squares estimators of the estimable functions are uncorrelated and have the same variance. The number of the orthogonal estimable functions composing the special form is equal to the rank of the design matrix. The orthogonal estimable functions can be easily obtained through the singular value decomposition of the design matrix.
 Keywords
Estimable functions;linear model;singular value decomposition;
 Language
English
 Cited by
 References
1.
Elswick, R. K. Jr., Gennings, C., Chinchilli, V. M. and Dawson, K. S. (1991). A simple approach for finding estimable functions in linear models, The American Statistician, 45, 51-53 crossref(new window)

2.
Eubank, R. L. and Webster, J. T. (1985). The singular-value decomposition as a tool for solving estimability problems, The American Statistician, 39, 64-66 crossref(new window)

3.
Hill, R. O. (1996). Elementary Linear Algebra with Applications (3rd ed.), Harcourt Brace College Publishers, San Diego

4.
Mandel, J. (1982). Use of the singular value decomposition in regression analysis, The American Statistician, 36, 15-24 crossref(new window)

5.
Mulcahy, C. and Rossi, J. (1998). A fresh approach to the singular value decomposition, The College Mathematics Journal, 29, 199-207 crossref(new window)

6.
Nelder, J. A. (1985). An alternative interpretation of the singular-value decomposition in regression, The American Statistician, 39, 63-64 crossref(new window)

7.
SAS Institute Inc. (1990). SAS/IML Software: Usage and Reference (Version 6, First Edition), SAS Institute Inc., Cary, NC

8.
Scheffe, H. (1959). The Analysis of Variance, Wiley-Interscience, New York

9.
Wolfram, S. (1999). The Mathematica Book, (4th ed.), Cambrigde University Press