Novel fast random search clustering approach for mixing matrix identification in MIMO linear blind inverse problems with sparse inputs

In this paper we propose a novel fast random search clustering (RSC) algorithm for mixing matrix identification in multiple input multiple output (MIMO) linear blind inverse problems with sparse inputs. The proposed approach is based on the clustering of the observations around the directions given by the columns of the mixing matrix that occurs typically for sparse inputs. Exploiting this fact, the RSC algorithm proceeds by parameterizing the mixing matrix using hyperspherical coordinates, randomly selecting candidate basis vectors (i.e. clustering directions) from the observations, and accepting or rejecting them according to a binary hypothesis test based on the Neyman–Pearson criterion. The RSC algorithm is not tailored to any specific distribution for the sources, can deal with an arbitrary number of inputs and outputs (thus solving the difficult under-determined problem), and is applicable to both instantaneous and convolutive mixtures. Extensive simulations for synthetic and real data with different number of inputs and outputs, data size, sparsity factors of the inputs and signal to noise ratios confirm the good performance of the proposed approach under moderate/high signal to noise ratios. RESUMEN. Método de separación ciega de fuentes para señales dispersas basado en la identificación de la matriz de mezcla mediante técnicas de "clustering" aleatorio.

Regression analysis of top of descent location for idle-thrust descents

In this paper, multiple regression analysis is used to model the top of descent (TOD) location of user-preferred descent trajectories computed by the flight management system (FMS) on over 1000 commercial flights into Melbourne, Australia. In addition to recording TOD, the cruise altitude, final altitude, cruise Mach, descent speed, wind, and engine type were also identified for use as the independent variables in the regression analysis. Both first-order and second-order models are considered, where cross-validation, hypothesis testing, and additional analysis are used to compare models. This identifies the models that should give the smallest errors if used to predict TOD location for new data in the future. A model that is linear in TOD altitude, final altitude, descent speed, and wind gives an estimated standard deviation of 3.9 nmi for TOD location given the trajectory parame- ters, which means about 80% of predictions would have error less than 5 nmi in absolute value. This accuracy is better than demonstrated by other ground automation predictions using kinetic models. Furthermore, this approach would enable online learning of the model. Additional data or further knowledge of algorithms is necessary to conclude definitively that no second-order terms are appropriate. Possible applications of the linear model are described, including enabling arriving aircraft to fly optimized descents computed by the FMS even in congested airspace.

Impacto del entorno institucional en la financiación público-privada de infraestructuras de transporte

Actualmente el sector privado posee un papel relevante en la provisión y gestión de infraestructuras de transporte en los países de ingreso medio‐bajo, principalmente a través de los proyectos de participación público‐privada (PPPs). Muchos países han impulsado este tipo de proyectos con el fin de hacer frente a la gran demanda de infraestructuras de transporte existente, debido a la escasez de recursos públicos y a la falta de eficiencia en la provisión de los servicios públicos. Como resultado, las PPPs han experimentado un crecimiento importante en las últimas dos décadas a nivel mundial. A pesar de esta tendencia creciente, muchos países no han sido capaces de atraer la participación del sector privado para la provisión de sus infraestructuras o no han logrado el nivel de participación privada que habrían requerido para alcanzar sus objetivos. Según numerosos autores, el desarrollo y el éxito de los proyectos PPP de infraestructuras de transporte de cualquier país está condicionado por una diversidad de factores, siendo uno de ellos la calidad de su entorno institucional. La presente tesis tiene como objetivo principal analizar la influencia del entorno institucional en el volumen de inversión en proyectos de participación público‐privada de infraestructuras de transporte en los países de ingreso medio‐bajo. Para acometer dicho objetivo se ha realizado un análisis empírico de 81 países distribuidos en seis regiones del mundo, durante el periodo 1996‐2013. En el análisis se han desarrollado dos modelos empíricos aplicando principalmente dos metodologías: el contraste de hipótesis y los modelos de datos de panel Tobit. El desarrollo de estos modelos ha permitido analizar de una forma exhaustiva el tema de estudio. Los resultados obtenidos aportan evidencia de que la calidad del entorno institucional posee una influencia significativa en el volumen de inversión en los proyectos PPP de transporte. En general, en esta tesis se muestran evidencias empíricas de que el sector privado ha tendido a invertir en mayor medida en países con entornos institucionales fuertes, es decir, en aquellos países en los que ha existido un mayor nivel de Estado de derecho, estabilidad política y regulatoria, efectividad del gobierno, así como un mayor control de la corrupción. Además, aquellos países donde se ha registrado una mejora en el nivel de su calidad institucional también han experimentado un incremento en el volumen de inversión en PPP de transporte. The private sector has an important role in the provision and management of transport infrastructure in countries of medium‐low income, primarily through projects of public‐private partnerships (PPPs). Many countries have developed PPP projects to meet the high demand of transport infrastructure, due to the scarcity of public resources and the lack of efficiency in the provision of public services. As a result, PPPs have experienced a significant growth, worldwide, in the past two decades. Despite this growing trend, many countries have not been able to attract private sector participation in the provision of infrastructure or have not accomplished the level of private participation that would have required to achieve its objectives. According to various authors, the development of PPP projects for transport infrastructure is determined by a number of factors, one of them being the quality of the institutional environment. The main objective of this dissertation is to analyze the influence of the institutional environment on the volume of investment, in projects of public‐private partnerships for transport infrastructure in countries of medium‐low income. In order to meet this objective, we conducted an empirical analysis of 81 countries, in six regions of the world, during the period of 1996‐2013. The analysis used two empirical models, implementing different methodologies and various statistical techniques: hypothesis testing, and Tobit model using panel data. The development of these models allowed to carry out a more comprehensive analysis. The results show that the quality of the institutional environment has a significant influence on the volume of investment in PPP projects of transport. Overall, this dissertation shows that the private sector tends to invest more in countries with stronger institutional environments, i.e. countries where there has been a higher level of Rule of Law, political and regulatory stability, and an effective control of corruption. In addition, those that have improved the level of institutional quality have also experienced an increase in the volume of investment in PPP of transport.

Descripción de parámetros glóticos basados en el modelado de los pliegues vocales para la detección de patología de la voz

Las patologías de la voz se han transformado en los últimos tiempos en una problemática social con cierto calado. La contaminación de las ciudades, hábitos como el de fumar, el uso de aparatos de aire acondicionado, etcétera, contribuyen a ello. Esto alcanza más relevancia en profesionales que utilizan su voz de manera frecuente, como, por ejemplo, locutores, cantantes, profesores o teleoperadores. Por todo ello resultan de especial interés las técnicas de ayuda al diagnóstico que son capaces de extraer conclusiones clínicas a partir de una muestra de la voz grabada con un micrófono, frente a otras invasivas que implican la exploración utilizando laringoscopios, fibroscopios o videoendoscopios, técnicas en cualquier caso mucho más molestas para los pacientes al exigir la introducción parcial del instrumental citado por la garganta, en actuaciones consideradas de tipo quirúrgico. Dentro de aquellas técnicas se ha avanzado mucho en un período de tiempo relativamente corto. En lo que se refiere al diagnóstico de patologías, hemos pasado en los últimos quince años de trabajar principalmente con parámetros extraídos de la señal de voz –tanto en el dominio del tiempo como en el de la frecuencia– y con escalas elaboradas con valoraciones subjetivas realizadas por expertos a hacerlo también con parámetros procedentes de estimaciones de la fuente glótica. La importancia de utilizar la fuente glótica reside, a grandes rasgos, en que se trata de una señal vinculada directamente al estado de la estructura laríngea del locutor y también en que está generalmente menos influida por el tracto vocal que la señal de voz. Es conocido que el tracto vocal guarda más relación con el mensaje hablado, y su presencia dificulta el proceso de detección de patología vocal. Estas estimaciones de la fuente glótica han sido obtenidas a través de técnicas de filtrado inverso desarrolladas por nuestro grupo de investigación. Hemos conseguido, además, profundizar en la naturaleza de la señal glótica: somos capaces de descomponerla y relacionarla con parámetros biomecánicos de los propios pliegues vocales, obteniendo estimaciones de elementos como la masa, la pérdida de energía o la elasticidad del cuerpo y de la cubierta del pliegue, entre otros. De las componentes de la fuente glótica surgen también los denominados parámetros biométricos, relacionados con la forma de la señal, que constituyen por sí mismos una firma biométrica del individuo. También trabajaremos con parámetros temporales, relacionados con las diferentes etapas que se observan dentro de la señal glótica durante un ciclo de fonación. Por último, consideraremos parámetros clásicos de perturbación y energía de la señal. En definitiva, contamos ahora con una considerable cantidad de parámetros glóticos que conforman una base estadística multidimensional, destinada a ser capaz de discriminar personas con voces patológicas o disfónicas de aquellas que no presentan patología en la voz o con voces sanas o normofónicas. Esta tesis doctoral se ocupa de varias cuestiones: en primer lugar, es necesario analizar cuidadosamente estos nuevos parámetros, por lo que ofreceremos una completa descripción estadística de los mismos. También estudiaremos cuestiones como la distribución de los parámetros atendiendo a criterios como el de normalidad estadística de los mismos, ocupándonos especialmente de la diferencia entre las distribuciones que presentan sujetos sanos y sujetos con patología vocal. Para todo ello emplearemos diferentes técnicas estadísticas: generación de elementos y diagramas descriptivos, pruebas de normalidad y diversos contrastes de hipótesis, tanto paramétricos como no paramétricos, que considerarán la diferencia entre los grupos de personas sanas y los grupos de personas con alguna patología relacionada con la voz. Además, nos interesa encontrar relaciones estadísticas entre los parámetros, de cara a eliminar posibles redundancias presentes en el modelo, a reducir la dimensionalidad del problema y a establecer un criterio de importancia relativa en los parámetros en cuanto a su capacidad discriminante para el criterio patológico/sano. Para ello se aplicarán técnicas estadísticas como la Correlación Lineal Bivariada y el Análisis Factorial basado en Componentes Principales. Por último, utilizaremos la conocida técnica de clasificación Análisis Discriminante, aplicada a diferentes combinaciones de parámetros y de factores, para determinar cuáles de ellas son las que ofrecen tasas de acierto más prometedoras. Para llevar a cabo la experimentación se ha utilizado una base de datos equilibrada y robusta formada por doscientos sujetos, cien de ellos pertenecientes al género femenino y los restantes cien al género masculino, con una proporción también equilibrada entre los sujetos que presentan patología vocal y aquellos que no la presentan. Una de las aplicaciones informáticas diseñada para llevar a cabo la recogida de muestras también es presentada en esta tesis. Los distintos estudios estadísticos realizados nos permitirán identificar aquellos parámetros que tienen una mayor contribución a la hora de detectar la presencia de patología vocal. Alguno de los estudios, además, nos permitirá presentar una ordenación de los parámetros en base a su importancia para realizar la detección. Por otra parte, también concluiremos que en ocasiones es conveniente realizar una reducción de la dimensionalidad de los parámetros para mejorar las tasas de detección. Por fin, las propias tasas de detección constituyen quizá la conclusión más importante del trabajo. Todos los análisis presentes en el trabajo serán realizados para cada uno de los dos géneros, de acuerdo con diversos estudios previos que demuestran que los géneros masculino y femenino deben tratarse de forma independiente debido a las diferencias orgánicas observadas entre ambos. Sin embargo, en lo referente a la detección de patología vocal contemplaremos también la posibilidad de trabajar con la base de datos unificada, comprobando que las tasas de acierto son también elevadas. Abstract Voice pathologies have become recently in a social problem that has reached a certain concern. Pollution in cities, smoking habits, air conditioning, etc. contributes to it. This problem is more relevant for professionals who use their voice frequently: speakers, singers, teachers, actors, telemarketers, etc. Therefore techniques that are capable of drawing conclusions from a sample of the recorded voice are of particular interest for the diagnosis as opposed to other invasive ones, involving exploration by laryngoscopes, fiber scopes or video endoscopes, which are techniques much less comfortable for patients. Voice quality analysis has come a long way in a relatively short period of time. In regard to the diagnosis of diseases, we have gone in the last fifteen years from working primarily with parameters extracted from the voice signal (both in time and frequency domains) and with scales drawn from subjective assessments by experts to produce more accurate evaluations with estimates derived from the glottal source. The importance of using the glottal source resides broadly in that this signal is linked to the state of the speaker's laryngeal structure. Unlike the voice signal (phonated speech) the glottal source, if conveniently reconstructed using adaptive lattices, may be less influenced by the vocal tract. As it is well known the vocal tract is related to the articulation of the spoken message and its influence complicates the process of voice pathology detection, unlike when using the reconstructed glottal source, where vocal tract influence has been almost completely removed. The estimates of the glottal source have been obtained through inverse filtering techniques developed by our research group. We have also deepened into the nature of the glottal signal, dissecting it and relating it to the biomechanical parameters of the vocal folds, obtaining several estimates of items such as mass, loss or elasticity of cover and body of the vocal fold, among others. From the components of the glottal source also arise the so-called biometric parameters, related to the shape of the signal, which are themselves a biometric signature of the individual. We will also work with temporal parameters related to the different stages that are observed in the glottal signal during a cycle of phonation. Finally, we will take into consideration classical perturbation and energy parameters. In short, we have now a considerable amount of glottal parameters in a multidimensional statistical basis, designed to be able to discriminate people with pathologic or dysphonic voices from those who do not show pathology. This thesis addresses several issues: first, a careful analysis of these new parameters is required, so we will offer a complete statistical description of them. We will also discuss issues such as distribution of the parameters, considering criteria such as their statistical normality. We will take special care in the analysis of the difference between distributions from healthy subjects and the distributions from pathological subjects. To reach these goals we will use different statistical techniques such as: generation of descriptive items and diagramas, tests for normality and hypothesis testing, both parametric and nonparametric. These latter techniques consider the difference between the groups of healthy subjects and groups of people with an illness related to voice. In addition, we are interested in finding statistical relationships between parameters. There are various reasons behind that: eliminate possible redundancies in the model, reduce the dimensionality of the problem and establish a criterion of relative importance in the parameters. The latter reason will be done in terms of discriminatory power for the criterion pathological/healthy. To this end, statistical techniques such as Bivariate Linear Correlation and Factor Analysis based on Principal Components will be applied. Finally, we will use the well-known technique of Discriminant Analysis classification applied to different combinations of parameters and factors to determine which of these combinations offers more promising success rates. To perform the experiments we have used a balanced and robust database, consisting of two hundred speakers, one hundred of them males and one hundred females. We have also used a well-balanced proportion where subjects with vocal pathology as well as subjects who don´t have a vocal pathology are equally represented. A computer application designed to carry out the collection of samples is also presented in this thesis. The different statistical analyses performed will allow us to determine which parameters contribute in a more decisive way in the detection of vocal pathology. Therefore, some of the analyses will even allow us to present a ranking of the parameters based on their importance for the detection of vocal pathology. On the other hand, we will also conclude that it is sometimes desirable to perform a dimensionality reduction in order to improve the detection rates. Finally, detection rates themselves are perhaps the most important conclusion of the work. All the analyses presented in this work have been performed for each of the two genders in agreement with previous studies showing that male and female genders should be treated independently, due to the observed functional differences between them. However, with regard to the detection of vocal pathology we will consider the possibility of working with the unified database, ensuring that the success rates obtained are also high.

Bootstrap confidence levels for phylogenetic trees

Evolutionary trees are often estimated from DNA or RNA sequence data. How much confidence should we have in the estimated trees? In 1985, Felsenstein [Felsenstein, J. (1985) Evolution 39, 783–791] suggested the use of the bootstrap to answer this question. Felsenstein’s method, which in concept is a straightforward application of the bootstrap, is widely used, but has been criticized as biased in the genetics literature. This paper concerns the use of the bootstrap in the tree problem. We show that Felsenstein’s method is not biased, but that it can be corrected to better agree with standard ideas of confidence levels and hypothesis testing. These corrections can be made by using the more elaborate bootstrap method presented here, at the expense of considerably more computation.

Patterned library analysis: A method for the quantitative assessment of hypotheses concerning the determinants of protein structure

Site-directed mutagenesis and combinatorial libraries are powerful tools for providing information about the relationship between protein sequence and structure. Here we report two extensions that expand the utility of combinatorial mutagenesis for the quantitative assessment of hypotheses about the determinants of protein structure. First, we show that resin-splitting technology, which allows the construction of arbitrarily complex libraries of degenerate oligonucleotides, can be used to construct more complex protein libraries for hypothesis testing than can be constructed from oligonucleotides limited to degenerate codons. Second, using eglin c as a model protein, we show that regression analysis of activity scores from library data can be used to assess the relative contributions to the specific activity of the amino acids that were varied in the library. The regression parameters derived from the analysis of a 455-member sample from a library wherein four solvent-exposed sites in an α-helix can contain any of nine different amino acids are highly correlated (P < 0.0001, R2 = 0.97) to the relative helix propensities for those amino acids, as estimated by a variety of biophysical and computational techniques.

Bootstrap confidence levels for phylogenetic trees.

Evolutionary trees are often estimated from DNA or RNA sequence data. How much confidence should we have in the estimated trees? In 1985, Felsenstein [Felsenstein, J. (1985) Evolution 39, 783-791] suggested the use of the bootstrap to answer this question. Felsenstein's method, which in concept is a straightforward application of the bootstrap, is widely used, but has been criticized as biased in the genetics literature. This paper concerns the use of the bootstrap in the tree problem. We show that Felsenstein's method is not biased, but that it can be corrected to better agree with standard ideas of confidence levels and hypothesis testing. These corrections can be made by using the more elaborate bootstrap method presented here, at the expense of considerably more computation.

Inferring identify from DNA profile evidence.

The controversy over the interpretation of DNA profile evidence in forensic identification can be attributed in part to confusion over the mode(s) of statistical inference appropriate to this setting. Although there has been substantial discussion in the literature of, for example, the role of population genetics issues, few authors have made explicit the inferential framework which underpins their arguments. This lack of clarity has led both to unnecessary debates over ill-posed or inappropriate questions and to the neglect of some issues which can have important consequences. We argue that the mode of statistical inference which seems to underlie the arguments of some authors, based on a hypothesis testing framework, is not appropriate for forensic identification. We propose instead a logically coherent framework in which, for example, the roles both of the population genetics issues and of the nonscientific evidence in a case are incorporated. Our analysis highlights several widely held misconceptions in the DNA profiling debate. For example, the profile frequency is not directly relevant to forensic inference. Further, very small match probabilities may in some settings be consistent with acquittal. Although DNA evidence is typically very strong, our analysis of the coherent approach highlights situations which can arise in practice where alternative methods for assessing DNA evidence may be misleading.

Sobre a evasão estudantil na Escola Politécnica da Universidade de São Paulo: identificação e possíveis causas.

A evasão estudantil afeta as universidades, privadas e públicas, no Brasil, trazendo-lhes prejuízos financeiros proporcionais à incidência, respectivamente, de 12% e de 26% no âmbito nacional e de 23% na Universidade de São Paulo (USP), razão pela qual se deve compreender as variáveis que governam o comportamento. Neste contexto, a pesquisa apresenta os prejuízos causados pela evasão e a importância de pesquisá-la na Escola Politécnica da USP (EPUSP): seção 1, desenvolve revisão bibliográfica sobre as causas da evasão (seção 2) e propõe métodos para obter as taxas de evasão a partir dos bancos de dados do Governo Federal e da USP (seção 3). Os resultados estão na seção 4. Para inferir sobre as causas da evasão na EPUSP, analisaram-se bancos de dados que, descritos e tratados na seção 5.1, contêm informações (P. Ex.: tipo de ingresso e egresso, tempo de permanência e histórico escolar) de 16.664 alunos ingressantes entre 1.970 e 2.000, bem como se propuseram modelos estatísticos e se detalharam os conceitos dos testes de hipóteses 2 e t-student (seção 5.2) utilizados na pesquisa. As estatísticas descritivas mostram que a EPUSP sofre 15% de evasão (com maior incidência no 2º ano: 24,65%), que os evadidos permanecem matriculados por 3,8 anos, que a probabilidade de evadir cresce após 6º ano e que as álgebras e os cálculos são disciplinas reprovadoras no 1º ano (seção 5.3). As estatísticas inferenciais demonstraram relação entre a evasão - modo de ingresso na EPUSP e evasão - reprovação nas disciplinas do 1º ano da EPUSP, resultados que, combinados com as estatísticas descritivas, permitiram apontar o déficit vocacional, a falta de persistência, a falta de ambientação à EPUSP e as deficiências na formação predecessora como variáveis responsáveis pela evasão (seção 5.4).

A generalized Markov sampler

A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis-Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis.

The effects of consumer knowledge on responses to event sponsorships

Research into consumer responses to event sponsorships has grown in recent years. However, the effects of consumer knowledge on sponsorship response have received little consideration. Consumers' event knowledge is examined to determine whether experts and novices differ in information processing of sponsorships and whether a sponsor's brand equity influences perceptions of sponsor-event fit. Six sponsors (three high equity/three low equity) were paired with six events. Results of hypothesis testing indicate that experts generate more total thoughts about a sponsor-event combination. Experts and novices do not differ in sponsor-event congruence for high-brand-equity sponsors, but event experts perceive less of a match between sponsor and event for low-brand-equity sponsors. (C) 2004 Wiley Periodicals, Inc.

Application of mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.

Using mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local false discovery rate is provided for each gene, and it can be implemented so that the implied global false discovery rate is bounded as with the Benjamini-Hochberg methodology based on tail areas. The latter procedure is too conservative, unless it is modified according to the prior probability that a gene is not differentially expressed. An attractive feature of the mixture model approach is that it provides a framework for the estimation of this probability and its subsequent use in forming a decision rule. The rule can also be formed to take the false negative rate into account.

Mixture models for detecting differentially expressed genes in microarrays

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.

TESTANDO A TEORIA DA PARIDADE DE PODER DE COMPRA (PPC) NO PERÍODO DE 1995 A 2010

O objetivo deste trabalho é testar a teoria da Paridade de Poder de Compra em sua versão absoluta e relativa para o Brasil no período de 1995 a 2010, utilizando procedimentos da econometria visando estabelecer através de testes de hipóteses a validação ou rejeição da teoria da Paridade do Poder de Compra. Para a verificação serão utilizados os testes de Dickey-Fuller (DF), Dickey-Fuller Ampliado (ADF) e testes de Cointegração de Engle e Granger e Joahansen. Adotamos para o estudo os países EUA e Brasil, tendo em vista o fluxo de comércio entre estes países e sua importância na economia mundial. Através dos índices de preço IPA e PPI analisarse- á a validação da teoria da Paridade de Poder de Compra em sua versão relativa e absoluta, chegando-se a conclusão de aceitação de sua versão relativa e rejeição de sua versão absoluta.