An Orthogonal Representation of Estimable Functions
| Autor: | Seong-Baek Yi |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Statistics and Probability
Discrete mathematics Rank (linear algebra) Applied Mathematics Design matrix Linear model Estimator Orthogonality Modeling and Simulation Singular value decomposition Applied mathematics Statistics Probability and Uncertainty Parametric equation Linear combination Finance Mathematics |
| Zdroj: | Communications for Statistical Applications and Methods. 15:837-842 |
| ISSN: | 2287-7843 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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