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Showing 6 results for Multivariate Normal Distribution
Reza Hashemi, Ghobad Barmalzan, Abedin Haidari,
Volume 3, Issue 2 (3-2010)
Abstract
Considering the characteristics of the bivariate normal distribution, in which uncorrelation of two random variables is equivalent to their independence, it is interesting to verify this issue in other distributions in other words whether or not the multivariate normal distribution is the only distribution in which uncorrelation is equivalent to independence. This paper aims to answer this question by presenting some concepts and introduce another family in which uncorrelation is equivalent to independence.
Ahad Malekzadeh, Mina Tohidi,
Volume 4, Issue 2 (3-2011)
Abstract
Coefficient of determination is an important criterion in different applications. The problem of point estimation of this parameter has been considered by many researchers. In this paper, the class of linear estimators of R^2 was considered. Then, two new estimators were proposed, which have lower risks than other usual estimator, such as the sample coefficient of determination and its adjusted form. Also on the basis of some simulations, we show that the Jacknife estimator is an efficient estimator with lower risk, when the number of observations is small.
Hamid Karamikabir, Mohammad Arashi,
Volume 8, Issue 1 (9-2014)
Abstract
In this paper we consider of location parameter estimation in the multivariate normal distribution with unknown covariance. Two restrictions on the mean vector parameter are imposed. First we assume that all elements of mean vector are nonnegative, at the second hand assumed only a subset of elements are nonnegative. We propose a class of shrinkage estimators which dominate the minimax estimator of mean vector under the quadratic loss function.
Ghasem Rekabdar, Rahim Chinipardaz, Behzad Mansouri,
Volume 13, Issue 1 (9-2019)
Abstract
In this study, the multi-parameter exponential family of distribution has been used to approximate the distribution of indefinite quadratic forms in normal random vectors. Moments of quadratic forms can be obtained in any orders in terms of representation of the quadratic forms as weighted sum of non-central chi-square random variables. By Stein's identity in exponential family, we estimated parameters of probability density function. The method handled in some examples and we indicated this method suitable for approximating the quadratic form distribution.
Dariush Najarzadeh,
Volume 13, Issue 1 (9-2019)
Abstract
Testing the Hypothesis of independence of a p-variate vector subvectors, as a pretest for many others related tests, is always as a matter of interest. When the sample size n is much larger than the dimension p, the likelihood ratio test (LRT) with chisquare approximation, has an acceptable performance. However, for moderately high-dimensional data by which n is not much larger than p, the chisquare approximation for null distribution of the LRT statistic is no more usable. As a general case, here, a simultaneous subvectors independence testing procedure in all k p-variate normal distributions is considered. To test this hypothesis, a normal approximation for the null distribution of the LRT statistic was proposed. A simulation study was performed to show that the proposed normal approximation outperforms the chisquare approximation. Finally, the proposed testing procedure was applied on prostate cancer data.
Dariush Najarzadeh,
Volume 14, Issue 1 (8-2020)
Abstract
The hypothesis of complete independence is necessary for many statistical inferences. Classical testing procedures can not be applied to test this hypothesis in high-dimensional data. In this paper, a simple test statistic is presented for testing complete independence in multivariate high dimensional normal data. Using the theory of martingales, the asymptotic normality of the test statistic is established. In order to evaluate the performance of the proposed test and compare it with existing procedures, a simulation study was conducted. The simulation results indicate that the proposed test has an empirical type-I error rate with an average relative error less than the available tests. An application of the proposed method for gene expression clinical prostate data is presented.
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