Estimation of a Linear Transformation.

• 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

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.