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150325s1995 xx |||||o 00| ||eng c |
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|a (DE-627)JST077710304
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|a (JST)25051050
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|a DE-627
|b ger
|c DE-627
|e rakwb
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|a eng
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| 100 |
1 |
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|a Bhimasankaram, P.
|e verfasserin
|4 aut
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| 245 |
1 |
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|a Recursive Inference in a General Linear Model
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| 264 |
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|c 1995
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|a Text
|b txt
|2 rdacontent
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|a Computermedien
|b c
|2 rdamedia
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|a Online-Ressource
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|a In this paper we provide exact algebraic expressions for the recalculation of the BLUE, the mean square error and several other statistical quantities of interest in a general linear model when an observation or a parameter is added or deleted. The dispersion matrix as well as the design matrix is allowed to be rank deficient by using the unified theory of least squares estimation as the point of departure. The updating formulas follow from the modifications of a generalized inverse of a symmetric matrix corresponding to the simultaneous addition or deletion of a row and a column. Statistical interpretations are given to the various special cases that arise naturally. Their relation to the changes in the rank of a key matrix is also pointed out. An extension to the mixed linear model with singular dispersion matrix is considered next. Finally we outline applications of these results in the areas of regression diagnostics and optimal design of experiments.
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| 650 |
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|a Primary 62F05
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| 650 |
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|a Secondary 62F30
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| 650 |
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|a Recursive estimation and testing
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| 650 |
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|a Generalized inverse of a matrix
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| 650 |
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4 |
|a Unified theory of linear estimation
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| 650 |
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4 |
|a Regression diagnostics
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| 650 |
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|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Cognitive processes
|x Thought processes
|x Reasoning
|x Inference
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| 650 |
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4 |
|a Information science
|x Information analysis
|x Data analysis
|x Regression analysis
|x Linear regression
|x Linear models
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| 650 |
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4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Statistical models
|x Parametric models
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| 650 |
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4 |
|a Mathematics
|x Mathematical expressions
|x Mathematical theorems
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| 650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Matrices
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| 650 |
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4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Statistical theories
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| 650 |
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4 |
|a Information science
|x Information analysis
|x Data analysis
|x Regression analysis
|x Linear regression
|x Linear models
|x General linear model
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| 650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Statistical theories
|x Estimation theory
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| 650 |
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4 |
|a Information science
|x Information analysis
|x Data analysis
|x Regression analysis
|x Linear regression
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| 650 |
|
4 |
|a Physical sciences
|x Chemistry
|x Chemical elements
|x Nonmetals
|x Carbon
|x Carbon isotopes
|x Radiocarbon
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| 655 |
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|a research-article
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| 700 |
1 |
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|a Sengupta, D.
|e verfasserin
|4 aut
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| 700 |
1 |
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|a Ramanathan, S.
|e verfasserin
|4 aut
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| 773 |
0 |
8 |
|i Enthalten in
|t Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
|d INDIAN STATISTICAL INSTITUTE, 1961
|g 57(1995), 2, Seite 227-255
|w (DE-627)328109991
|w (DE-600)2045733-9
|x 0581572X
|7 nnns
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| 773 |
1 |
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|g volume:57
|g year:1995
|g number:2
|g pages:227-255
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|u https://www.jstor.org/stable/25051050
|3 Volltext
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|d 57
|j 1995
|e 2
|h 227-255
|