Space-Time Adaptive Processing is a signal processing technique that uses an adaptive array to help remove nonhomogeneous data points from a dataset. Since the early 1970s, STAP has been used in radar systems for their ability to "filter clutter, interference and jamming signals. One major flaw with early STAP radar systems is the reliance on non-robust estimators to estimate the noise condition. When even a single outlier is present, the earliest STAP radar systems would break down, causing the target to be missed. Many algorithms have been developed to successfully estimate the noise condition of the dataset when outliers are present. As recently as 2007, a STAP radar processing system based on Adaptive Complex Projection Statistics has been proposed and successfully"filters out the noise condition even when outliers are present. However, this algorithm requires the data to be entirely real. Radar data, which consists of amplitude and phase, is complex valued. Therefore, it must be converted into its rectangular components before processing can commence. This introduces many additional processing steps which significantly increase the computing time. The STAP radar algorithm of this thesis overcomes the problems with early radar systems. It is based on the Complex GM Wiener Filter (CGMWF) with the Minimum Covariance Determinant (MCD) for outlier detection. The robustness of the conventional Wiener "lter is enhanced by robust Huber Estimator, and using the MCD enables processing entirely in the complex domain. This results in a STAP radar algorithm with a breakdown point of nearly 35% and that enables processing entirely in the complex domain for fewer computing steps. / Master of Science

Thesis (MscEng)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: Outliers may be defined as observations that are sufficiently aberrant to arouse the suspicion of the analyst as to their origin. They could be the result of human error, in which case they should be corrected, but they may also be an interesting exception, and this would deserve further investigation. Identification of outliers typically consists of an informal inspection of a plot of the data, but this is unreliable for dimensions greater than two. A formal procedure for detecting outliers allows for consistency when classifying observations. It also enables one to automate the detection of outliers by using computers. The special case of univariate data is treated separately to introduce essential concepts, and also because it may well be of interest in its own right. We then consider techniques used for detecting multiple outliers in a multivariate normal sample, and go on to explain how these may be generalized to include cluster analysis. Multivariate outlier detection is based on the Minimum Covariance Determinant (MCD) subset, and is therefore treated in detail. Exact bivariate algorithms were refined and implemented, and the solutions were used to establish the performance of the commonly used heuristic, Fast–MCD. / AFRIKAANSE OPSOMMING: Uitskieters word gedefinieer as waarnemings wat tot s´o ’n mate afwyk van die verwagte gedrag dat die analis wantrouig is oor die oorsprong daarvan. Hierdie waarnemings mag die resultaat wees van menslike foute, in welke geval dit reggestel moet word. Dit mag egter ook ’n interressante verskynsel wees wat verdere ondersoek benodig. Die identifikasie van uitskieters word tipies informeel deur inspeksie vanaf ’n grafiese voorstelling van die data uitgevoer, maar hierdie benadering is onbetroubaar vir dimensies groter as twee. ’n Formele prosedure vir die bepaling van uitskieters sal meer konsekwente klassifisering van steekproefdata tot gevolg hˆe. Dit gee ook geleentheid vir effektiewe rekenaar implementering van die tegnieke. Aanvanklik word die spesiale geval van eenveranderlike data behandel om noodsaaklike begrippe bekend te stel, maar ook aangesien dit in eie reg ’n area van groot belang is. Verder word tegnieke vir die identifikasie van verskeie uitskieters in meerveranderlike, normaal verspreide data beskou. Daar word ook ondersoek hoe hierdie idees veralgemeen kan word om tros analise in te sluit. Die sogenaamde Minimum Covariance Determinant (MCD) subversameling is fundamenteel vir die identifikasie van meerveranderlike uitskieters, en word daarom in detail ondersoek. Deterministiese tweeveranderlike algoritmes is verfyn en ge¨ımplementeer, en gebruik om die effektiwiteit van die algemeen gebruikte heuristiese algoritme, Fast–MCD, te ondersoek.

本研究採用Lee 和Poon 所提出的隱藏常態變數模型來估計混合連續與間斷型變數之參數估計，並估計其馬式距離。此外，並利用穩健估計來估計混合型資料參數及其馬式距離，可在有離群值時解決最大蓋似估計的不穩定。 / Poon and Lee (1987) applied normal latent variable model to deal with the parameters estimation for the data mixed with continuous and discrete variables and Bedrick et al. (2000) used this idea to evaluate the Mahalanobis distance. In this thesis, we extend a similar idea to robustly estimate Multivariate Data Mixed with Continuous and Discrete Variables with the same model. Furthermore, we evaluate the Mahalanobis distance which can determine similarity of variables. The proposed method can overcome the unreliability of MLE while there exist outliers in the data.

Submitted by Gabriel Campos Pérgola (gabrielpergola@gmail.com) on 2013-02-04T12:56:43Z No. of bitstreams: 1 DissertationGabrielPergola2013.pdf: 521205 bytes, checksum: 85369078a82b0d5cc02f8248961e9214 (MD5) / Rejected by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br), reason: Prezado Gabriel, Não recebemos os arquivo em PDF. Att. Suzi 3799-7876 on 2013-02-05T18:53:00Z (GMT) / Submitted by Gabriel Campos Pérgola (gabrielpergola@gmail.com) on 2013-02-05T19:00:17Z No. of bitstreams: 2 DissertationGabrielPergola2013.pdf: 521205 bytes, checksum: 85369078a82b0d5cc02f8248961e9214 (MD5) DissertationGabrielPergola2013.pdf: 521205 bytes, checksum: 85369078a82b0d5cc02f8248961e9214 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2013-02-05T19:07:12Z (GMT) No. of bitstreams: 2 DissertationGabrielPergola2013.pdf: 521205 bytes, checksum: 85369078a82b0d5cc02f8248961e9214 (MD5) DissertationGabrielPergola2013.pdf: 521205 bytes, checksum: 85369078a82b0d5cc02f8248961e9214 (MD5) / Made available in DSpace on 2013-02-05T19:09:04Z (GMT). No. of bitstreams: 2 DissertationGabrielPergola2013.pdf: 521205 bytes, checksum: 85369078a82b0d5cc02f8248961e9214 (MD5) DissertationGabrielPergola2013.pdf: 521205 bytes, checksum: 85369078a82b0d5cc02f8248961e9214 (MD5) Previous issue date: 23-01-13 / Portfolio insurance allows a manager to limit downside risk while allowing participation in upside markets. The purpose of this dissertation is to introduce a framework to portfolio insurance optimization from a hybrid frequentist-Bayesian approach. We obtain the joint distribution of regular returns from a frequentist statistical method, once the outliers have been identified and removed from the data sample. The joint distribution of extreme returns, in its turn, is modelled by a Bayesian network, whose topology reflects the events that can significantly impact the portfolio performance. Once we link the regular and extreme distributions of returns, we simulate future scenarios for the portfolio value. The insurance subportfolio is then optimized by the Differential Evolution algorithm. We show the framework in a step by step example for a long portfolio including stocks participating in the Bovespa Index (Ibovespa), using market data from 2008 to 2012. / Seguros de carteiras proporcionam aos gestores limitar o risco de downside sem renunciar a movimentos de upside. Nesta dissertação, propomos um arcabouço de otimização de seguro de carteira a partir de um modelo híbrido frequentista-Bayesiano com uso de derivativos. Obtemos a distribuição conjunta de retornos regulares através de uma abordagem estatística frequentista, uma vez removidos os outliers da amostra. A distribuição conjunta dos retornos extremos, por sua vez, é modelada através de Redes Bayesianas, cuja topologia contempla os eventos que o gestor considera crítico ao desempenho da carteira. Unindo as distribuições de retornos regulares e extremos, simulamos cenários futuros para a carteira. O seguro é, então, otimizado através do algoritmo Evolução Diferencial. Mostramos uma aplicação passo a passo para uma carteira comprada em ações do Ibovespa, utilizando dados de mercado entre 2008 e 2012.