Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data

Uso estratégico de la deuda: un estudio a nivel de empresa para colombia 1995-2003

El presente trabajo intenta estimar si las empresas emplean estratégicamente la deuda para limitar la entrada de potenciales rivales. Mediante la metodología de Método Generalizado de Momentos (GMM) se evalúa el efecto que tienen los activos específicos, la cuota de mercado y el tamaño, como proxies de las rentas del mercado, y las barreras de entrada sobre los niveles de endeudamiento, a nivel de empresa para Colombia, durante 1995-2003. Se encuentra que las empresas utilizan los activos específicos para limitar la entrada al mercado y que el endeudamiento decrece a medida que las empresas aumentan su cuota en el mercado

Natural resource windfalls and efficiency of local government expenditures: evidence from Peru

We study the role of natural resource windfalls in explaining the efficiency of public expenditures. Using a rich dataset of expenditures and public good provision for 1,836 municipalities in Peru for period 2001-2010, we estimate a non-monotonic relationship between the efficiency of public good provision and the level of natural resource transfers. Local governments that were extremely favored by the boom of mineral prices were more efficient in using fiscal windfalls whereas those benefited with modest transfers were more inefficient. These results can be explained by the increase in political competition associated with the boom. However, the fact that increases in efficiency were related to reductions in public good provision casts doubts about the beneficial effects of political competition in promoting efficiency.

Efficient modeling and inference for event-related fMRI data

Event-related functional magnetic resonance imaging (efMRI) has emerged as a powerful technique for detecting brains' responses to presented stimuli. A primary goal in efMRI data analysis is to estimate the Hemodynamic Response Function (HRF) and to locate activated regions in human brains when specific tasks are performed. This paper develops new methodologies that are important improvements not only to parametric but also to nonparametric estimation and hypothesis testing of the HRF. First, an effective and computationally fast scheme for estimating the error covariance matrix for efMRI is proposed. Second, methodologies for estimation and hypothesis testing of the HRF are developed. Simulations support the effectiveness of our proposed methods. When applied to an efMRI dataset from an emotional control study, our method reveals more meaningful findings than the popular methods offered by AFNI and FSL. (C) 2008 Elsevier B.V. All rights reserved.

Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

Fast identification algorithms for Gaussian process model

A class identification algorithms is introduced for Gaussian process(GP)models.The fundamental approach is to propose a new kernel function which leads to a covariance matrix with low rank,a property that is consequently exploited for computational efficiency for both model parameter estimation and model predictions.The objective of either maximizing the marginal likelihood or the Kullback–Leibler (K–L) divergence between the estimated output probability density function(pdf)and the true pdf has been used as respective cost functions.For each cost function,an efficient coordinate descent algorithm is proposed to estimate the kernel parameters using a one dimensional derivative free search, and noise variance using a fast gradient descent algorithm. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

Satellite-supported flood forecasting in river networks: a real case study

Satellite-based (e.g., Synthetic Aperture Radar [SAR]) water level observations (WLOs) of the floodplain can be sequentially assimilated into a hydrodynamic model to decrease forecast uncertainty. This has the potential to keep the forecast on track, so providing an Earth Observation (EO) based flood forecast system. However, the operational applicability of such a system for floods developed over river networks requires further testing. One of the promising techniques for assimilation in this field is the family of ensemble Kalman (EnKF) filters. These filters use a limited-size ensemble representation of the forecast error covariance matrix. This representation tends to develop spurious correlations as the forecast-assimilation cycle proceeds, which is a further complication for dealing with floods in either urban areas or river junctions in rural environments. Here we evaluate the assimilation of WLOs obtained from a sequence of real SAR overpasses (the X-band COSMO-Skymed constellation) in a case study. We show that a direct application of a global Ensemble Transform Kalman Filter (ETKF) suffers from filter divergence caused by spurious correlations. However, a spatially-based filter localization provides a substantial moderation in the development of the forecast error covariance matrix, directly improving the forecast and also making it possible to further benefit from a simultaneous online inflow error estimation and correction. Additionally, we propose and evaluate a novel along-network metric for filter localization, which is physically-meaningful for the flood over a network problem. Using this metric, we further evaluate the simultaneous estimation of channel friction and spatially-variable channel bathymetry, for which the filter seems able to converge simultaneously to sensible values. Results also indicate that friction is a second order effect in flood inundation models applied to gradually varied flow in large rivers. The study is not conclusive regarding whether in an operational situation the simultaneous estimation of friction and bathymetry helps the current forecast. Overall, the results indicate the feasibility of stand-alone EO-based operational flood forecasting.

Covariance structure in the skull of Catarrhini: a case of pattern stasis and magnitude evolution

The study of the genetic variance/covariance matrix (G-matrix) is a recent and fruitful approach in evolutionary biology, providing a window of investigating for the evolution of complex characters. Although G-matrix studies were originally conducted for microevolutionary timescales, they could be extrapolated to macroevolution as long as the G-matrix remains relatively constant, or proportional, along the period of interest. A promising approach to investigating the constancy of G-matrices is to compare their phenotypic counterparts (P-matrices) in a large group of related species; if significant similarity is found among several taxa, it is very likely that the underlying G-matrices are also equivalent. Here we study the similarity of covariance and correlation structure in a broad sample of Old World monkeys and apes (Catarrhini). We made phylogenetically structured comparisons of correlation and covariance matrices derived from 39 skull traits, ranging from between species to the superfamily level. We also compared the overall magnitude of integration between skull traits (r(2)) for all Catarrhim genera. Our results show that P-matrices were not strictly constant among catarrhines, but the amount of divergence observed among taxa was generally low. There was significant and positive correlation between the amount of divergence in correlation and covariance patterns among the 30 genera and their phylogenetic distances derived from a recently proposed phylogenetic hypothesis. Our data demonstrate that the P-matrices remained relatively similar along the evolutionary history of catarrhines, and comparisons with the G-matrix available for a New World monkey genus (Saguinus) suggests that the same holds for all anthropoids. The magnitude of integration, in contrast, varied considerably among genera, indicating that evolution of the magnitude, rather than the pattern of inter-trait correlations, might have played an important role in the diversification of the catarrhine skull. (C) 2009 Elsevier Ltd. All rights reserved.

Uso da análise discriminante regularizada (RDA) no reconhecimento de padrões em imagens digitais hiperespectral de sensoriamento remoto

Em cenas naturais, ocorrem com certa freqüência classes espectralmente muito similares, isto é, os vetores média são muito próximos. Em situações como esta, dados de baixa dimensionalidade (LandSat-TM, Spot) não permitem uma classificação acurada da cena. Por outro lado, sabe-se que dados em alta dimensionalidade [FUK 90] tornam possível a separação destas classes, desde que as matrizes covariância sejam suficientemente distintas. Neste caso, o problema de natureza prática que surge é o da estimação dos parâmetros que caracterizam a distribuição de cada classe. Na medida em que a dimensionalidade dos dados cresce, aumenta o número de parâmetros a serem estimados, especialmente na matriz covariância. Contudo, é sabido que, no mundo real, a quantidade de amostras de treinamento disponíveis, é freqüentemente muito limitada, ocasionando problemas na estimação dos parâmetros necessários ao classificador, degradando portanto a acurácia do processo de classificação, na medida em que a dimensionalidade dos dados aumenta. O Efeito de Hughes, como é chamado este fenômeno, já é bem conhecido no meio científico, e estudos vêm sendo realizados com o objetivo de mitigar este efeito. Entre as alternativas propostas com a finalidade de mitigar o Efeito de Hughes, encontram-se as técnicas de regularização da matriz covariância. Deste modo, técnicas de regularização para a estimação da matriz covariância das classes, tornam-se um tópico interessante de estudo, bem como o comportamento destas técnicas em ambientes de dados de imagens digitais de alta dimensionalidade em sensoriamento remoto, como por exemplo, os dados fornecidos pelo sensor AVIRIS. Neste estudo, é feita uma contextualização em sensoriamento remoto, descrito o sistema sensor AVIRIS, os princípios da análise discriminante linear (LDA), quadrática (QDA) e regularizada (RDA) são apresentados, bem como os experimentos práticos dos métodos, usando dados reais do sensor. Os resultados mostram que, com um número limitado de amostras de treinamento, as técnicas de regularização da matriz covariância foram eficientes em reduzir o Efeito de Hughes. Quanto à acurácia, em alguns casos o modelo quadrático continua sendo o melhor, apesar do Efeito de Hughes, e em outros casos o método de regularização é superior, além de suavizar este efeito. Esta dissertação está organizada da seguinte maneira: No primeiro capítulo é feita uma introdução aos temas: sensoriamento remoto (radiação eletromagnética, espectro eletromagnético, bandas espectrais, assinatura espectral), são também descritos os conceitos, funcionamento do sensor hiperespectral AVIRIS, e os conceitos básicos de reconhecimento de padrões e da abordagem estatística. No segundo capítulo, é feita uma revisão bibliográfica sobre os problemas associados à dimensionalidade dos dados, à descrição das técnicas paramétricas citadas anteriormente, aos métodos de QDA, LDA e RDA, e testes realizados com outros tipos de dados e seus resultados.O terceiro capítulo versa sobre a metodologia que será utilizada nos dados hiperespectrais disponíveis. O quarto capítulo apresenta os testes e experimentos da Análise Discriminante Regularizada (RDA) em imagens hiperespectrais obtidos pelo sensor AVIRIS. No quinto capítulo são apresentados as conclusões e análise final. A contribuição científica deste estudo, relaciona-se à utilização de métodos de regularização da matriz covariância, originalmente propostos por Friedman [FRI 89] para classificação de dados em alta dimensionalidade (dados sintéticos, dados de enologia), para o caso especifico de dados de sensoriamento remoto em alta dimensionalidade (imagens hiperespectrais). A conclusão principal desta dissertação é que o método RDA é útil no processo de classificação de imagens com dados em alta dimensionalidade e classes com características espectrais muito próximas.

Mapping Macrophyte Species in the Amazon Floodplain Wetlands Using Fully Polarimetric ALOS/PALSAR Data

The purpose of this paper was to evaluate attributes derived from fully polarimetric PALSAR data to discriminate and map macrophyte species in the Amazon floodplain wetlands. Fieldwork was carried out almost simultaneously to the radar acquisition, and macrophyte biomass and morphological variables were measured in the field. Attributes were calculated from the covariance matrix [C] derived from the single-look complex data. Image attributes and macrophyte variables were compared and analyzed to investigate the sensitivity of the attributes for discriminating among species. Based on these analyses, a rule-based classification was applied to map macrophyte species. Other classification approaches were tested and compared to the rule-based method: a classification based on the Freeman-Durden and Cloude-Pottier decomposition models, a hybrid classification (Wishart classifier with the input classes based on the H/a plane), and a statistical-based classification (supervised classification using Wishart distance measures). The findings show that attributes derived from fully polarimetric L-band data have good potential for discriminating herbaceous plant species based on morphology and that estimation of plant biomass and productivity could be improved by using these polarimetric attributes.

Avaliação de estratégias de detecção e correção de perdas de ciclos na portadora GPS L1

To prevent large errors in the GPS positioning, cycle slips should be detected and corrected. Such procedure is not trivial, mainly for single frequency receivers, but normally it is not noticed by the users. Thus, it will be discussed some practical and more used methods for cycle slips detection and correction using just GPS single-frequency observations. In the detection, the triple (TD) and tetra differences were used. In relation to the correction, in general, each slip is corrected in the preprocessing. Otherwise, other strategies should be adopted during the processing. In this paper, the option was to the second option, and two strategies were tested. In one of them, the elements of the covariance matrix of the involved ambiguities are modified and new ambiguity estimation starts. In the one, a new ambiguity is introduced as additional unknown when a cycle slip is detected. These possibilities are discussed and compared in this paper, as well as the aspects related to the practicity, implementation and viability of each one. Some experiments were carried out using simulated data with cycle slips in different satellites and epochs of the data. This allowed assessing and comparing the results of different occurrence of cycle slip and correction in several conditions.

Line based camera calibration in machine vision dynamic applications

The problem of dynamic camera calibration considering moving objects in close range environments using straight lines as references is addressed. A mathematical model for the correspondence of a straight line in the object and image spaces is discussed. This model is based on the equivalence between the vector normal to the interpretation plane in the image space and the vector normal to the rotated interpretation plane in the object space. In order to solve the dynamic camera calibration, Kalman Filtering is applied; an iterative process based on the recursive property of the Kalman Filter is defined, using the sequentially estimated camera orientation parameters to feedback the feature extraction process in the image. For the dynamic case, e.g. an image sequence of a moving object, a state prediction and a covariance matrix for the next instant is obtained using the available estimates and the system model. Filtered state estimates can be computed from these predicted estimates using the Kalman Filtering approach and based on the system model parameters with good quality, for each instant of an image sequence. The proposed approach was tested with simulated and real data. Experiments with real data were carried out in a controlled environment, considering a sequence of images of a moving cube in a linear trajectory over a flat surface.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. © 2010 Elsevier B.V. All rights reserved.

Modelos lineares generalizados mistos e equações de estimação generalizadas para dados binário aplicados em anestesiologia veterinária

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.