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Linear estimation in models based on a graph

✍ Scribed by R.B. Bapat

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
94 KB
Volume
302-303
Category
Article
ISSN
0024-3795

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✦ Synopsis

Two natural linear models associated with a graph are considered. The GaussΒ± Markov theorem is used in one of the models to derive a combinatorial formula for the MooreΒ±Penrose inverse of the incidence matrix of a tree. An inequality involving the MooreΒ±Penrose inverse of the Laplacian matrix of a graph and its distance matrix is obtained. The case of equality is discussed. Again the main tool used in the proof is the theory of linear estimation.

πŸ“œ SIMILAR VOLUMES

Estimation in partially linear models
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✍ R.L. Eubank; E.L. Kambour; J.T. Kim; K. Klipple; C.S. Reese; M. Schimek πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 361 KB

Order n algorithms are developed for computing the estimated mean vector, regression coefficients, standard errors and smoothing parameter selection criteria for Speckman smoothing spline estimators in partially linear models. A difference type variance estimator is proposed and shown to be x/-~-con