Estimability in Partitioned Linear Models

Estimability in Partitioned Linear Models

Some estimability facts for partitioned linear models with constraints are presented. For a model E(Y) = X1π1+ X2π2with constraints on π1and π2a reduced model is derived that contains all information regarding the estimability (and also regarding the blues) of parametric functions b'π2. For a m...

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Veröffentlicht in:The Annals of statistics 1980-03, Vol.8 (2), p.399-406
Hauptverfasser: Seely, Justus, Birkes, David
Format: Artikel
Sprache:eng
Schlagworte:
62J99
62K99
Covariance
Degrees of freedom
estimable linear parametric functions
Estimators
Linear models
Mathematical vectors
Matrices
Parametric models
Partitioned linear model
Regression analysis
Vector space models
Vector spaces
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Zusammenfassung:Some estimability facts for partitioned linear models with constraints are presented. For a model E(Y) = X1π1+ X2π2with constraints on π1and π2a reduced model is derived that contains all information regarding the estimability (and also regarding the blues) of parametric functions b'π2. For a model E(Y) = X0π0+ X1π1+ X2π2with constraints on π0, π1and π2, several necessary and sufficient conditions are given for when estimability of b'π2in the original model is equivalent to estimability in the simpler model E(Y) = X0π0+ X2π2.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1176344960