**DESCRIPTION OF COURSES**

**AS 604 LINEAR MODELS (2L+0P) I**

**Objective**

The students would be exposed to the theory of linear models, estimation of variance components for unbalanced data and advanced techniques for analysis of data in agriculture.

**Theory**

UNIT I

General Gauss Markoff set up, Gauss-Markoff ’s theorem, Aitken’s transformation. Theory of linear estimation, test of hypothesis in linear models. Analysis of variance, partitioning of degrees of freedom. Restricted least squares. Special cases of one and two way classifications (including disproportionate cell frequencies and interaction, cross and nested classifications).

UNIT II

Analysis of covariance. Variance components models, estimation of variance components from unbalanced data. Unified theory of least-squares, MINQUE, MIVQUE. Mixed models. LAR, LASSO.

**Suggested Readings**

- Bapat, R.B. 1993.
*Linear Algebra and Linear Models*. Springer-Verlag. - Graybill, F. A. 1976.
*Theory and Application of the Linear Model*. Duxbury, North Scituate. - Joshi, D.D. 1987.
*Linear Estimation and Design of Experiments*. Wiley Eastern. - Rao, C. R. 2001.
*Linear Inference and its Application*. Wiley Eastern. - Searle, S. R. 1998.
*Variance Components*. John Wiley. - Searle, S.R. 1971.
*Linear Models*. John Wiley. - Seber, G.A. F. 1996.
*The Linear Hypothesis: A General Theory*. Griffin, Charles and Co. Ltd. - Sheffe, H. 1999.
*Analysis of Variance*. John Wiley.