Smoothing techniques in underdetermined linear models.
Date
1998
Authors
Sneddon, William Gary.
Journal Title
Journal ISSN
Volume Title
Publisher
Dalhousie University
Abstract
Description
In many physical processes linear models can arise from the discretization of a continuous process in order to describe behavior over an entire field. An important consequence is the models may have more parameters than observations. To alleviate this problem, one can impose a smoothness constraint on the parameters that reflects some prior knowledge of the physical process in order to obtain sensible estimates.
A linear model is developed that has random explanatory and response variables, and a smoothness penalty is imposed based on the signal-to-noise ratio of the model. Results are presented assuming the value of the ratio is fixed, and when a procedure for estimating its value is used. The estimates perform well using a prediction based criterion in both situations. Robust estimation procedures for the model are also developed.
The methods are applied to modelling temperature and salinity data in the California Current, with the goal of using shallow water observations to predict deep ocean readings.
Thesis (Ph.D.)--Dalhousie University (Canada), 1998.
A linear model is developed that has random explanatory and response variables, and a smoothness penalty is imposed based on the signal-to-noise ratio of the model. Results are presented assuming the value of the ratio is fixed, and when a procedure for estimating its value is used. The estimates perform well using a prediction based criterion in both situations. Robust estimation procedures for the model are also developed.
The methods are applied to modelling temperature and salinity data in the California Current, with the goal of using shallow water observations to predict deep ocean readings.
Thesis (Ph.D.)--Dalhousie University (Canada), 1998.
Keywords
Statistics.