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Quan Ding (University of Rhode Island), “Statistical signal processing and its applications to detection, model order selection, and classification”, adviser: Prof. Steven Kay (2011)
This dissertation has focused on topics in statistical signal processing including detection and estimation theory, information fusion, model order selection, as well as their applications to standoff detection.
In model order selection, it has been shown that the minimum description length (MDL) is consistent and the Akaike information criterion (AIC) tends to overestimate the model as the sample size goes to infinity. It is shown that for a fixed sample size, the MDL and the AIC are inconsistent as the noise variance goes to zero. The result is surprising since intuitively, a good model order selection criterion should choose the correct model when the noise is small enough. Moreover, it is proved that the embedded exponentially family (EEF) criterion is consistent as the noise variance goes to zero. In standoff detection, the author uses an autoregressive model to fit the Raman spectra, develop an unsupervised detection algorithm followed by a classification scheme, and manage to control the false alarm rate to a low level while maintaining a very good detection and classification performance. In information fusion and sensor integration, multiple sensors of the same or different types are deployed in order to obtain more information to make a better decision than with a single sensor. The maximum likelihood estimator (MLE) is the most popular method in parameter estimation. Under a misspecified model, it is well known that the MLE still converges to a well defined limit as the sample size goes to infinity. In this thesis, it is proved that under some regularity conditions, the MLE under a misspecified model also converges to a well defined limit at high signal-to-noise ratio (SNR). This result provides important performance analysis of the MLE under a misspecified model.
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