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Showing 3 results for Najarzadeh
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.
Dariush Najarzadeh,
Volume 17, Issue 1 (9-2023)
Abstract
In multiple regression analysis, the population multiple correlation coefficient (PMCC) is widely used to measure the correlation between a variable and a set of variables. To evaluate the existence or non-existence of this type of correlation, testing the hypothesis of zero PMCC can be very useful. In high-dimensional data, due to the singularity of the sample covariance matrix, traditional testing procedures to test this hypothesis lose their applicability. A simple test statistic was proposed for zero PMCC based on a plug-in estimator of the sample covariance matrix inverse. Then, a permutation test was constructed based on the proposed test statistic to test the null hypothesis. A simulation study was carried out to evaluate the performance of the proposed test in both high-dimensional and low-dimensional normal data sets. This study was finally ended by applying the proposed approach to mice tumour volumes data.
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