Navegando por Autor "Maboudou-Tchao, Edgard M."
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Item Frequentist–Bayesian Monte Carlo test for mean vectors in high dimension.(2018) Silva, Ivair Ramos; Maboudou-Tchao, Edgard M.; Figueiredo, Weslei Lima deConventional methods for testing the mean vector of a P-variate Gaussian distribution require a sample size N greater than or equal to P. But, in high dimensional situations, that is when N is smaller than P, special and new adjustments are needed. Although Bayesianempirical methods are well-succeeded for testing in high dimension, their performances are strongly dependent on the actual unknown covariance matrix of the Gaussian random vector. In this paper, we introduce a hybrid frequentist–Bayesian Monte Carlo test and prove that: (i) under the null hypothesis, the performance of the proposed test is invariant with respect to the real unknown covariance matrix, and (ii) the decision rule is valid, which means that, in terms of expected loss, the performance of the proposed procedure can always be made as good as the exact Bayesian test and, in terms of type I error probability, the method is always of α level for arbitrary α ∈ (0, 1).Item Tests for mean vectors in high dimension(2013) Maboudou-Tchao, Edgard M.; Silva, Ivair RamosTraditional multivariate tests, Hotelling’s T 2 or Wilks , are designed for a test of the mean vector under the condition that the number of observations is larger than the number of variables. For high-dimensional data, where the number of features is nearly as large as or larger than the number of observations, the existing tests do not provide a satisfactory solution because of the singularity of the estimated covariance matrix. In this article, we consider a test for the mean vector of independent and identically distributed multivariate normal random vectors where the dimension is larger than or equal to the number of observations. To solve this problem, we propose a modified Hotelling statistic. Simulation results show that the proposed test is superior to other tests available in the literature. However, because we do not know the theoretical distribution of this modified statistic, Monte Carlo methods were used to reach this conclusion. Instead of using conventional Monte Carlo methods, which perform a fixed-number of simulations, we suggest using the sequential Monte Carlo test in order to decrease the number of simulations needed to reach a decision. Simulation results show that the sequential Monte Carlo test is preferable to a fixed-sample test, especially when using computationally intensive statistical methods.