Ridgelized Hotelling’s T2 test on mean vectors of large dimension

In this paper, a ridgelized Hotelling’s [Formula: see text] test is developed for a hypothesis on a large-dimensional mean vector under certain moment conditions. It generalizes the main result of Chen et al. [A regularized Hotelling’s [Formula: see text] test for pathway analysis in proteomic studies, J. Am. Stat. Assoc. 106(496) (2011) 1345–1360.] by relaxing their Gaussian assumption. This is achieved by establishing an exact four-moment theorem that is a simplified version of Tao and Vu’s [Random matrices: universality of local statistics of eigenvalues, Ann. Probab. 40(3) (2012) 1285–1315] work. Simulation results demonstrate the superiority of the proposed test over the traditional Hotelling’s [Formula: see text] test and its several extensions in high-dimensional situations.

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Robust Multivariate Control Charts to Detect Small Shifts in Mean

Mathematical Problems in Engineering ◽

10.1155/2011/923463 ◽

2011 ◽

Vol 2011 ◽

pp. 1-19 ◽

Cited By ~ 5

Author(s):

Habshah Midi ◽

Ashkan Shabbak

Keyword(s):

Control Charts ◽

Substantial Improvement ◽

Data Set ◽

Multivariate Control Charts ◽

Mean Vectors ◽

The Mean ◽

Simulation Results ◽

Multivariate Control ◽

Mean Vector

The classical multivariate CUSUM and EWMA charts are commonly used to detect small shifts in the mean vectors. It is now evident that those charts are easily affected by outliers which may be due to small or moderate changes in the mean vector. In this paper, we propose a robust multivariate CUSUM and Robust multivariate EWMA charts to remedy the problem of small changed in scatter outliers. Both the empirical and simulation results indicate that the proposed robust multivariate CUSUM and EWMA charts offer substantial improvement over other multivariate CUSUM and EWMA charts. This article also discussed the robustness of the proposed charts, when there is a small or moderate sustained shift in the data set.

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Classification Based on Multivariate Repeated Measures with Time Effect on Mean Vector and an AR (1) Correlation Structure on the Repeated Measures

Calcutta Statistical Association Bulletin ◽

10.1177/0008068320050105 ◽

2005 ◽

Vol 57 (1-2) ◽

pp. 49-66 ◽

Cited By ~ 1

Author(s):

Anuradba Roy ◽

Ravindra Khattree

Keyword(s):

Maximum Likelihood ◽

Repeated Measures ◽

Likelihood Estimation ◽

Covariance Matrices ◽

Time Effect ◽

Population Parameters ◽

Time Effects ◽

Mean Vectors ◽

Mean Vector ◽

Over Time

In repeated measures studies how observations change over time is often of prime interest. Modelling this time effect in the context of discrimination, is the objective of this article. We study the problem of classification with multiple q-variate observations with time effect on each individual. The covariance matrices as well as mean vectors are mordelled respectively to accommodate the correlation between the successive repeated measures and to describe the time effects. Computation schemes for maximum likelihood estimation of required population parameters are provided.

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A Novel Bat Algorithm Based on Differential Operator and Lévy Flights Trajectory

Computational Intelligence and Neuroscience ◽

10.1155/2013/453812 ◽

2013 ◽

Vol 2013 ◽

pp. 1-13 ◽

Cited By ~ 63

Author(s):

Jian Xie ◽

Yongquan Zhou ◽

Huan Chen

Keyword(s):

Differential Operator ◽

Dimensional Space ◽

Bat Algorithm ◽

High Dimensional ◽

Local Minima ◽

Lévy Flights ◽

Levy Flights ◽

Mutation Strategy ◽

Differential Algorithm ◽

Simulation Results

Aiming at the phenomenon of slow convergence rate and low accuracy of bat algorithm, a novel bat algorithm based on differential operator and Lévy flights trajectory is proposed. In this paper, a differential operator is introduced to accelerate the convergence speed of proposed algorithm, which is similar to mutation strategy “DE/best/2” in differential algorithm. Lévy flights trajectory can ensure the diversity of the population against premature convergence and make the algorithm effectively jump out of local minima. 14 typical benchmark functions and an instance of nonlinear equations are tested; the simulation results not only show that the proposed algorithm is feasible and effective, but also demonstrate that this proposed algorithm has superior approximation capabilities in high-dimensional space.

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An asymptotic property of large matrices with identically distributed Boolean independent entries

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025719500243 ◽

2019 ◽

Vol 22 (04) ◽

pp. 1950024

Author(s):

Mihai Popa ◽

Zhiwei Hao

Keyword(s):

An Order-Independent Algorithm for Learning Chain Graphs

The International FLAIRS Conference Proceedings ◽

10.32473/flairs.v34i1.128365 ◽

2021 ◽

Vol 34 (1) ◽

Author(s):

Mohammad Ali Javidian ◽

Marco Valtorta ◽

Pooyan Jamshidi

Keyword(s):

Directed Acyclic Graphs ◽

High Dimensional ◽

P Values ◽

Order Dependence ◽

Error Measures ◽

Acyclic Graphs ◽

Simulation Results ◽

Improved Performance ◽

Low Dimensional ◽

Chain Graphs

LWF chain graphs combine directed acyclic graphs and undirected graphs. We propose a PC-like algorithm, called PC4LWF, that finds the structure of chain graphs under the faithfulness assumption to resolve the problem of scalability of the proposed algorithm by Studeny (1997). We prove that PC4LWF is order dependent, in the sense that the output can depend on the order in which the variables are given. This order dependence can be very pronounced in high-dimensional settings. We propose two modifications of the PC4LWF algorithm that remove part or all of this order dependence. Simulation results with different sample sizes, network sizes, and p-values demonstrate the competitive performance of the PC4LWF algorithms in comparison with the LCD algorithm proposed by Ma et al. (2008) in low-dimensional settings and improved performance (with regard to error measures) in high-dimensional settings.

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Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions

Methodology And Computing In Applied Probability ◽

10.1007/s11009-013-9370-7 ◽

2013 ◽

Vol 17 (2) ◽

pp. 419-439 ◽

Cited By ~ 11

Author(s):

Makoto Aoshima ◽

Kazuyoshi Yata

Keyword(s):

Asymptotic Normality ◽

High Dimensional ◽

Mild Conditions ◽

Mean Vectors

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Small-Deviation Inequalities for Sums of Random Matrices

Symmetry ◽

10.3390/sym11050638 ◽

2019 ◽

Vol 11 (5) ◽

pp. 638

Author(s):

Xianjie Gao ◽

Chao Zhang ◽

Hongwei Zhang

Keyword(s):

Random Matrices ◽

Large Deviation ◽

Small Deviation ◽

High Dimensional ◽

Main Research ◽

Infinite Dimensional ◽

The Matrix ◽

Largest Eigenvalues ◽

Deviation Inequalities ◽

Eigenvalues Of Random Matrices

Random matrices have played an important role in many fields including machine learning, quantum information theory, and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices. Although there are intensive studies on the large-deviation inequalities for random matrices, only a few works discuss the small-deviation behavior of random matrices. In this paper, we present the small-deviation inequalities for the largest eigenvalues of sums of random matrices. Since the resulting inequalities are independent of the matrix dimension, they are applicable to high-dimensional and even the infinite-dimensional cases.

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