Browse > Article
http://dx.doi.org/10.7465/jkdi.2014.25.3.547

Projection analysis for two-way variance components  

Choi, Jaesung (Department of Statistics, Keimyung University)
Publication Information
Journal of the Korean Data and Information Science Society / v.25, no.3, 2014 , pp. 547-554 More about this Journal
Abstract
This paper discusses a method of estimating variance components for random effects model. Henderson's method I and III are discussed for the esimation of variance components. This paper shows how to use projections instead of using Henderson's methods for the calculation of sums of squares which are quadratic forms in the observations. It also discusses that eigenvalues can be used for getting the expectations of sums of squares in place of using the method of Hartley's synthesis. It shows the suggested method is much more effective than those methods.
Keywords
Eigenvalue; projection; quadratic form; random effects; variance components;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 Hartley, H. O. (1967). Expectations, variances and covariances of ANOVA mean squares by "synthesis". Biometrics, 23, 105-114.   DOI   ScienceOn
2 Choi, J. S. (2011). Type I analysis by projections. The Korean Journal of Applied Statistics, 24, 373-381.   과학기술학회마을   DOI   ScienceOn
3 Choi, J. S. (2012a). Type II analysis by projections. Journal of the Korean Data & Information Science Society, 23, 1155-1163.   과학기술학회마을   DOI   ScienceOn
4 Choi, J. S. (2013). Estimable functions of less than full rank linear model. Journal of the Korean Data & Information Science Society, 23, 333-339.
5 Corbeil, R. R. and Searle, S. R. (1976). A comparison of variance component estimators. Biometrics, 9, 226-252.
6 Graybill, F. A. (1976). Theory and application of the linear model, Wadsworth, Inc., California.
7 Henderson, C. R. (1953). Estimation of variance and covariance components. Biometrics, 32, 779-791.
8 Huynh, H., and Feldt, L. S. (1970). Conditions under which mean square ratios in repeated measures designs have exact F-distributions. Journal of the American Statistical Association, 65, 1582-1589.   DOI   ScienceOn
9 Rao, C. R. (1971). Minimum variance quadratic unbiased estimation of variance components. Journal of Multivariate Analysis, 1, 445-456.   DOI
10 Searle, S. R. (1971). Linear models, John Wiley & Sons, Inc., New York.
11 Searle, S. R., Casella, G. and McCulloch, C. E. (1992). Variance components, John Wiley & Sons, Inc., New York.
12 Milliken, G. A. and Johnson, D. E. (1984). Analysis of messy data, Van Nostrand Reinhold, New York.
13 Choi, J. S. (2012b). Esimable functions of fixed-effects model by projections. Journal of the Korean Data & Information Science Society, 23, 487-494.   DOI   ScienceOn