The statistical inferences about the parameters of Binomial-Poisson hierarchy model are discussed. Based on the estimators of paired observations we consider the other two cases with extra observations on both the first and second layer of the model. The MLEs of lambda and p are derived and it is also proved the MLE lambda is also the UMVUE of lambda. By using multivariate central limit theory and large sample theory, both the estimators based on extra observations on the first and second layer are obtained respectively. The performances of the estimators are compared numerically based on extensive Monte Carlo simulation. Simulation studies indicate that the performance of the estimators is more efficient than those only based on paired observations. Inference about the confidence interval for p is presented for both cases. The efficiency of the estimators is compared with condition given that same number of extra observations is provided.

Modelos com erros de medição têm recebido a atenção de vários pesquisadores das mais diversas áreas de conhecimento. O principal objetivo desta dissertação consiste no estudo de um modelo funcional com erros de medição heteroscedásticos na presença de réplicas das observações. O modelo proposto estende resultados encontrados na literatura na medida em que as réplicas são parte do modelo, ao contrário de serem utilizadas para estimação das variâncias, doravante tratadas como conhecidas. Alguns procedimentos de estimação tais como o método de máxima verossimilhança, o método dos momentos e o método de extrapolação da simulação (SIMEX) na versão empírica são apresentados. Além disso, propõe-se o teste da razão de verossimilhanças e o teste de Wald com o objetivo de testar algumas hipóteses de interesse relacionadas aos parâmetros do modelo adotado. O comportamento dos estimadores de alguns parâmetros e das estatísticas propostas (resultados assintóticos) são analisados por meio de um estudo de simulação de Monte Carlo, utilizando-se diferentes números de réplicas. Por fim, a proposta é exemplificada com um conjunto de dados reais. Toda parte computacional foi desenvolvida em linguagem R (R Development Core Team, 2011) / Measurement error models have received the attention of many researchers of several areas of knowledge. The aim of this dissertation is to study a functional heteroscedastic measurement errors model with replicated observations. The proposed model extends results from the literature in that replicas are part of the model, as opposed to being used for estimation of the variances, now treated as known. Some estimation procedures such as maximum likelihood method, the method of moments and the empirical simulation-extrapolation method (SIMEX) are presented. Moreover, it is proposed the likelihood ratio test and Wald test in order to test hypotheses of interest related to the model parameters used. The behavior of the estimators of some parameters and statistics proposed (asymptotic results) are analyzed through Monte Carlo simulation study using different numbers of replicas. Finally, the proposal is illustrated with a real data set. The computational part was developed in R language (R Development Core Team, 2011)

Modelos com erros de medição têm recebido a atenção de vários pesquisadores das mais diversas áreas de conhecimento. O principal objetivo desta dissertação consiste no estudo de um modelo funcional com erros de medição heteroscedásticos na presença de réplicas das observações. O modelo proposto estende resultados encontrados na literatura na medida em que as réplicas são parte do modelo, ao contrário de serem utilizadas para estimação das variâncias, doravante tratadas como conhecidas. Alguns procedimentos de estimação tais como o método de máxima verossimilhança, o método dos momentos e o método de extrapolação da simulação (SIMEX) na versão empírica são apresentados. Além disso, propõe-se o teste da razão de verossimilhanças e o teste de Wald com o objetivo de testar algumas hipóteses de interesse relacionadas aos parâmetros do modelo adotado. O comportamento dos estimadores de alguns parâmetros e das estatísticas propostas (resultados assintóticos) são analisados por meio de um estudo de simulação de Monte Carlo, utilizando-se diferentes números de réplicas. Por fim, a proposta é exemplificada com um conjunto de dados reais. Toda parte computacional foi desenvolvida em linguagem R (R Development Core Team, 2011) / Measurement error models have received the attention of many researchers of several areas of knowledge. The aim of this dissertation is to study a functional heteroscedastic measurement errors model with replicated observations. The proposed model extends results from the literature in that replicas are part of the model, as opposed to being used for estimation of the variances, now treated as known. Some estimation procedures such as maximum likelihood method, the method of moments and the empirical simulation-extrapolation method (SIMEX) are presented. Moreover, it is proposed the likelihood ratio test and Wald test in order to test hypotheses of interest related to the model parameters used. The behavior of the estimators of some parameters and statistics proposed (asymptotic results) are analyzed through Monte Carlo simulation study using different numbers of replicas. Finally, the proposal is illustrated with a real data set. The computational part was developed in R language (R Development Core Team, 2011)

The TRACAB Image Tracking System is used by ChyronHego for the tracking of ball and players on football fields. It requires the calibration of the cameras around the arena which is disrupted by fences and other mesh structures that are positioned between the camera and the field as a safety measure for the public. The purpose of this work was the implementation of a cycle consistent Generative Adversarial Network (cycle-GAN) for removing the fence from the image using unpaired data. Cycle-GANs are part of the state-of-the-art of image-to-image translation and can solve this kind of problem without the need of paired images. This makes it an exciting and powerful method and, according to the latest investigations in the current work, it has never been used for this kind of application before. The model was able to strongly attenuate, and in some cases completely remove, the net structure from images. To quantify the impact of the net removal a homography matching was performed. Then, it was compared with the homography associated to the baseline of blurring the image with a gaussian filter and the original image without the use of any filter. The results showed that the identification of key-points was harder on synthetic images than on the original image with or without small Gaussian filters, but it showed a better performance against images blurred with filters with a standard deviation of 3 pixels or more. Despite the performance not being better than the baseline in all the cases it always added new key-points, and sometimes, it was able to find correct homographies where the baseline could not. Therefore, the cycle-GAN model proved to complement the baseline. / TRACAB Image Tracking System används av ChyronHego för spårning av bollen och spelaren påfotbollsplaner. Detta kräver kalibrering av kamerorna runt arenan som störs av staket och andra nätstrukturer som är placerade mellan kameran och fältet som en säkerhetsåtgärd för publiken. Detta examensabrete fokuserar påimplementeringen av en cycle-GAN för borttagning av nätet från bilden med hjälp av oparade data. Cycle-GAN är en bild-till-bild-översättning state-of-the-art teknik och det kan lösa denna typ av problem utan parade bilder. Detta gör det till en spännande och kraftfull metod och enligt den senaste forskningen har det aldrig använts för denna typ av tillämpning förut. Modellen kunde kraftigt dämpa och i vissa fall helt ta bort nätstrukturen från bilder. För att kvantifiera effekterna av avlägsnandet av nätet utfördes en homografimatchning. Därefter jämfördes det med homografin associerad med baslinjen där bilden görs suddig med ett gaussiskt filter och originalbilden utan användning av något filter. Resultaten visade att identifieringen av nyckelpunkter var svårare påsyntetiska bilder än påoriginalbilder med eller utan småGauss-filter, men det visade bättre prestanda än bilder som var suddigt med filter med en standardavvikelse på 3 pixlar eller mer. Trots att prestandan inte var bättre än baslinjen i alla fall lade versionen utan nätet alltid till nya nyckelpunkter, och ibland kunde den hitta korrekta homografier där baslinjen misslyckades. Därför, cycle-GAN-modellen kompletterar baslinjen.