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Title: Influence function approximation to estimation in linear models with generalized t- distribution noise
Keywords: Influence function, maximum likelihood estimation, data filtering, linear models, generalized t- distribution, Data Reconciliation
Issue Date: 21-Jan-2014
Citation: VU HOANG DUNG (2014-01-21). Influence function approximation to estimation in linear models with generalized t- distribution noise. ScholarBank@NUS Repository.
Abstract: Commonly made assumption of Gaussian noise is an approximation to reality. The occurrence of outliers, transient data in steady-state measurements, instrument failure, human error, process nonlinearity, etc. can all induce non-Gaussian process data. Indeed whenever the central limit theorem is invoked - the central limit theorem being a limit theorem can at most suggest approximate normality for real data. However, even high-quality process data may not fit the Gaussian distribution and the presence of a single outlier can spoil the statistical analysis completely. In this thesis, instead of assuming Gaussian distributed noise, we use the genelized t-distribution as noise model. By being a distribution superset encompassing Gaussian, uniform, t and double exponential distributions, the generalized t-distribution has the flexibility to characterize data with non-Gaussian statistical properties. We also use the influence function, a robust statistic tool, to analyze the proposed estimator. Specifically how it can predict the change in the estimate due to outliers and the variance of the estimate. Moreover, the influence function is also used to formulate a recursive algorithm that gives an approximate solution making it suitable for real-time and on-line implementation. The proposed theory is verified by simulation and experiments.
Appears in Collections:Ph.D Theses (Open)

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