This paper deals with evaluating 3D-bootstrap for the mining company New Boliden in an attempt to revise their current method of calculating average gold riches in different areas. The purpose is to find one-sided 3D-bootstrap confidence bound of the average gold riches. There lacks well-defined theory behind using 3D-bootstrap, in this paper the variogram is used as an estimate of dependencies between the observations, and the block length is chosen to be higher than this estimate. In aid of this, a simulated data material is conducted to check the validity of 3D-bootstrap in a controlled area where the theoretical value is known. The results are inconclusive, and further studies are needed.

[pt] Nesta tese de mestrado, foram analisados aspectos, propriedades, utilidade e desempenho do bootstrap, um método de reamostragem, na estimação de um parâmetro relacionado à memória longa, ou longa dependência, em séries temporais. Entre outras coisas, obtém-se estimativas do desvio-padrão do estimador do parâmetro, e um teste de hipóteses para o parâmetro. O bootstrap pode conseguir propriedades de grandes amostras a partir de um número pequeno de observações. O procedimento do bootsptrap consiste de reamostrar, com reposição, da amostra original um número grande de amostras do mesmo tamanho. A longa dependência ou memória longa (long memory) pode se caracterizado por um lento decaimento das autocorrelações conforme cresce o valor do lag. A longa dependência pode ser estudada por modelos ARIMA (p,d,q.), com o parâmetro d, relativo integração a ser feita em ruídos brancos na construção da série (ARFIMA), assumindo valor fracionário. Este trabalho está relacionado com o uso do bootstrap na estimação do parâmetro d fracionário dos modelos ARFIMA (p,d,q). / [en] This thesis treats features, properties, utility and performance of the use of bootstrap, a resample techique, in the estimation of a parameter related to long memory in times. Among other things, we estimate the standard deviation of the parameter estimator and define a null hypothesis test for the parameter. With bootstrap, we can get large sample properties from a small sample. It consists of many resamples, with reposition, of the original sample, all with the same size as the original. Long memory can be featured by a small decay of the autocorrelations as the lag tends to infinity. Long memory can be studied by ARIMA (p,d,q) models with the d parameters assuming a fractional value (ARFIMA). This work concerns the use of bootstrap in the estimation of the fractional d parameter of ARFIMA (p,d,q) models.

[pt] O modelo autorregressivo periódico da família Box & Jenkins, PAR(p), é empregado na modelagem e geração das séries de vazões hidrológicas e/ou de energias naturais afluentes utilizadas no modelo de otimização do despacho hidrotérmico no Brasil. Recentemente, alguns aspectos da modelagem têm sido alvo de estudos e diversas pesquisas vêm sendo realizados. Inicialmente, este trabalho visou o estudo da fase de identificação das ordens p dos modelos, fundamental para a correta definição da estrutura de modelagem e para a geração de cenários sintéticos. Atualmente, a identificação é feita com base na avaliação da significância dos coeficientes da função de autocorrelação parcial (FACP), baseados na aproximação assintótica de Quenouille. A proposta deste estudo foi a aplicação da técnica de computação intensiva Bootstrap para estimar a real significância dos referidos coeficientes. O segundo objetivo deste trabalho foi o emprego da mesma técnica com vistas à geração de cenários. A metodologia adotada atualmente ajusta uma distribuição Lognormal com três parâmetros para a geração de ruídos aleatórios, o que parece causar uma não-linearidade indesejável ao modelo original. Neste trabalho, os próprios resíduos gerados pelo modelo PAR(p), quando aplicado às séries históricas, foram utilizados na geração dos cenários. Os resultados mostraram que o Bootstrap levou à identificação de ordens inferiores na maioria dos casos e que os cenários conservaram satisfatoriamente as propriedades estatísticas das séries originais. Finalmente, os resultados obtidos foram bastante satisfatórios, corroborando alguns pontos levantados em estudos anteriores sobre a abordagem tradicional. / [en] The periodic autoregressive model, a particular structure of the Box & Jenkins family, denoted by PAR(p), is employed to model the series of hydrological streamflow used for estimating the operational costs of the Brazilian hydro-thermal optimal dispatch. Recently, some aspects of this approach began to be studied and several researches on this topic are being developed. This work focused on the identification phase of the order "p" of the PAR(p), essential to the correct definition of the model structure, as well as to generate synthetic scenarios to be used in the optimization procedure. Nowadays, the identification is based on evaluating the significance of the estimated partial autocorrelation coefficients function (PACF), based on the asymptotic result of Quenouille. The purpose of this study was on the application of a computer-intensive technique, called Bootstrap, to estimate the real statistical significance of such the estimated. The second goal of this study was use the Bootstrap technique in order to generate synthetic scenarios. The current methodology uses an approach for noise generation through a three parameters Lognormal distribution. Such approach seems to cause an undesirable non-linearity in the model. In this work, the PAR (p) resulted noises were used during the scenarios generation. The results showed that the Bootstrap led to the identification of lower orders models, in comparison with the traditional approach, in almost all cases. In addition, the scenarios retained the statistical characteristics of the original series. The obtained results were quite satisfactory, corroborating some points raised in previous studies about the traditional approach.

No description available.

For massive data analysis, the computational bottlenecks exist in two ways. Firstly, the data could be too large that it is not easy to store and read. Secondly, the computation time could be too long. To tackle these problems, parallel computing algorithms like Divide-and-Conquer were proposed, while one of its drawbacks is that some correlations may be lost when the data is divided into chunks. Subsampling is another way to simultaneously solve the problems of the massive data analysis while taking correlation into consideration. The uniform sampling is simple and fast, but it is inefficient, see detailed discussions in Mahoney (2011) and Peng and Tan (2018). The bootstrap approach uses uniform sampling and is computing time intensive, which will be enormously challenged when data size is massive. <i>k</i>-means clustering is standard method in data analysis. This method does iterations to find centroids, which would encounter difficulty when data size is massive. In this thesis, we propose the approach of optimal subsampling for massive data bootstrapping and massive data <i>k</i>-means clustering. We seek the sampling distribution which minimize the trace of the variance co-variance matrix of the resulting subsampling estimators. This is referred to as A-optimal in the literature. We define the optimal sampling distribution by minimizing the sum of the component variances of the subsampling estimators. We show the subsampling<i> k</i>-means centroids consistently approximates the full data centroids, and prove the asymptotic normality using the empirical process theory. We perform extensive simulation to evaluate the numerical performance of the proposed optimal subsampling approach through the empirical MSE and the running times. We also applied the subsampling approach to real data. For massive data bootstrap, we conducted a large simulation study in the framework of the linear regression based on the A-optimal theory proposed by Peng and Tan (2018). We focus on the performance of confidence intervals computed from A-optimal subsampling, including coverage probabilities, interval lengths and running times. In both bootstrap and clustering we compared the A-optimal subsampling with uniform subsampling.

No description available.

Often in statistics it is of interest to investigate whether or not a trend is significant. Methods for testing such a trend depend on the assumptions of the error terms such as whether the distribution is known and also if the error terms are independent. Likelihood ratio tests may be used if the distribution is known but in some instances one may not want to make such assumptions. In a time series, these errors will not always be independent. In this case, the error terms are often modelled by an autoregressive or moving average process. There are resampling techniques for testing the hypothesis of interest when the error terms are dependent, such as, modelbased bootstrapping and the wild bootstrap, but the error terms need to be whitened. In this dissertation, a bootstrap procedure is used to test the hypothesis of no trend for variable stars when the error structure assumes a particular form. In some cases, the bootstrap to be implemented is preferred over large sample tests in terms of the level of the test. The bootstrap procedure is able to correctly identify the underlying distribution which may not be χ2.

Often in statistics it is of interest to investigate whether or not a trend is signi&#64257;cant. Methods for testing such a trend depend on the assumptions of the error terms such as whether the distribution is known and also if the error terms are independent. Likelihood ratio tests may be used if the distribution is known but in some instances one may not want to make such assumptions. In a time series, these errors will not always be independent. In this case, the error terms are often modelled by an autoregressive or moving average process. There are resampling techniques for testing the hypothesis of interest when the error terms are dependent, such as, modelbased bootstrapping and the wild bootstrap, but the error terms need to be whitened. In this dissertation, a bootstrap procedure is used to test the hypothesis of no trend for variable stars when the error structure assumes a particular form. In some cases, the bootstrap to be implemented is preferred over large sample tests in terms of the level of the test. The bootstrap procedure is able to correctly identify the underlying distribution which may not be &#967;2.

Models for mediation are widely used in psychology, behavior science and education because they help researchers understand how a causal effect happens through one or several mediating variables. And more complex mediation models that incorporate multiple mediators are increasingly being assessed. This report uses a generated dataset to provide an overview of the assessment of direct effects and indirect effects in multiple mediator models. Use of a multiple comparison-based procedure for testing a set of hypotheses simultaneously while controlling the experiment-wise type I error rate is used to calculate a confidence interval for each pairwise contrast of mediated effects. Three approaches will be used to test hypotheses concerning the contrast between pairs of mediator effects. These approaches include 1) an assumption of zero covariance between parameters from different models, 2) assumption of a non-zero covariance between parameters from different models and 3) use of bootstrapping. Results are provided and discussed. / text

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