Estimation of a Linear Transformation.

The problem which suggested this study arose in glaciology. Markers were placed in a glacier at points (xi sub c) and their positions, as measured by surveying techniques, were recorded at x sub i. Several years later a new survey was made by the same method yielding measurements y sub i of the true...

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Bibliographic Details
Main Authors: Gleser,Leon Jay, Watson,Geoffrey S.
Other Authors: PRINCETON UNIV N J DEPT OF STATISTICS
Format: Text
Language:English
Published: 1972
Subjects:
Snow
Ice and Permafrost
Statistics and Probability
(*STATISTICAL ANALYSIS
DECISION THEORY)
(*GLACIERS
MOTION)
MATHEMATICAL MODELS
STATISTICAL DISTRIBUTIONS
TRANSFORMATIONS(MATHEMATICS)
RANDOM VARIABLES
PROBABILITY
MATRICES(MATHEMATICS)
DEFORMATION
SIMULATION
MAXIMUM LIKELIHOOD ESTIMATION
NORMAL DENSITY FUNCTIONS
Eta
Ice
permafrost
Online Access:http://www.dtic.mil/docs/citations/AD0747977
http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=AD0747977
Description
Summary:The problem which suggested this study arose in glaciology. Markers were placed in a glacier at points (xi sub c) and their positions, as measured by surveying techniques, were recorded at x sub i. Several years later a new survey was made by the same method yielding measurements y sub i of the true positions eta sub i. It was assumed that eta sub i = B(xi sub i) where the matrix B describing the deformation of the glacier is the object of interest. It seemed reasonable to assume a multivariate normal distribution for the errors on both occasions with a covariance matrix (sigma squared) E, with E known and so the problem can be transformed to make E = I. This paper deals with this problem where the vectors are p dimensional.

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