Least Favorable Direction Test for Multivariate Analysis of Variance in High Dimension

Wang, Rui; Xu, Xingzhong

doi:10.5705/ss.202018.0279

Cited by 3 publications

(1 citation statement)

References 27 publications

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“…Instead, there is a common influence on the dependent variable. First, employing multi-factor variance analysis [23][24][25], the joint effect of multiple factors on dependent variables is analyzed. Quadratic interaction terms with various parameters and factors are subject to variance analysis, resulting in a table with 14 degrees of freedom.…”

Section: Resultsmentioning

confidence: 99%

A Standardized Treatment Model for Head Loss of Farmland Filters Based on Interaction Factors

Liu,

Lei,

et al. 2024

Agriculture

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A head loss model for pressureless mesh filters used in farmland irrigation was developed by integrating the four basic test factors: irrigation flow, filter cartridge speed, self-cleaning flow, and initial sand content. The model’s coefficient of determination was found to be 98.61%. Among the basic factors, the total irrigation flow accounted for only 17.20% of the relatively small self-cleaning flow. The contribution of initial sand content was found to be the smallest, with a coefficient of only 0.0166. Furthermore, the contribution rate of the flow term was significantly higher than that of the initial sand content, with a value of 159.73%. In terms of quadratic interaction, the difference between the interaction term of flushing flow and filter cartridge speed, and the interaction term of filter cartridge speed and self-cleaning flow was 38.42%. On the other hand, the difference within this level for the interaction term between initial sand content and filter cartridge speed, as well as the interaction term between irrigation flow and self-cleaning flow, was 2.82%. Finally, through joint optimization of the response surface and model, the optimal values for the irrigation flow rate, filter cartridge speed, self-cleaning flow rate, and initial sand content were determined to be 121.687 m3·h−1, 1.331 r·min−1, 19.980 m3·h−1, and 0.261 g·L−1; the measured minimum head loss was found to be 21.671 kPa. These research findings can serve as a reference for enhancing the design of farmland filters and optimizing irrigation systems.

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Section: Resultsmentioning

confidence: 99%

A Standardized Treatment Model for Head Loss of Farmland Filters Based on Interaction Factors

Liu,

Lei,

et al. 2024

Agriculture

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A generalized likelihood ratio test for linear hypothesis of k -sample means in high dimension

Cao

Liang

2022

Communications in Statistics - Theory and Methods

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A Two-Sample Test of High Dimensional Means Based on Posterior Bayes Factor

Jiang

2022

Mathematics

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In classical statistics, the primary test statistic is the likelihood ratio. However, for high dimensional data, the likelihood ratio test is no longer effective and sometimes does not work altogether. By replacing the maximum likelihood with the integral of the likelihood, the Bayes factor is obtained. The posterior Bayes factor is the ratio of the integrals of the likelihood function with respect to the posterior. In this paper, we investigate the performance of the posterior Bayes factor in high dimensional hypothesis testing through the problem of testing the equality of two multivariate normal mean vectors. The asymptotic normality of the linear function of the logarithm of the posterior Bayes factor is established. Then we construct a test with an asymptotically nominal significance level. The asymptotic power of the test is also derived. Simulation results and an application example are presented, which show good performance of the test. Hence, taking the posterior Bayes factor as a statistic in high dimensional hypothesis testing is a reasonable methodology.

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Least Favorable Direction Test for Multivariate Analysis of Variance in High Dimension

Cited by 3 publications

References 27 publications

A Standardized Treatment Model for Head Loss of Farmland Filters Based on Interaction Factors

A Standardized Treatment Model for Head Loss of Farmland Filters Based on Interaction Factors

A generalized likelihood ratio test for linear hypothesis of k -sample means in high dimension

A Two-Sample Test of High Dimensional Means Based on Posterior Bayes Factor

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