Maximum-type tests for high-dimensional regression coefficients using Wilcoxon scores

Xu Kai; Zhou Yeqing

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Maximum-type tests for high-dimensional regression coefficients using Wilcoxon scores

机译：使用Wilcoxon分数的高维回归系数的最大型测试

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In this article, we develop new maximum-type tests to infer the overall significance of coefficients in high-dimensional linear models based on the Wilcoxon scores. The proposed testing procedures are free of error variance estimation and robust to heavy-tailed distributions and outliers, making them widely applicable in practice. We incorporate the dependence structure among predictors in the test statistics to enhance their powers. The limiting null distributions of the test statistics are derived to be the extreme value distribution of type I under regularity conditions. To reduce the size distortion, we further propose a multiplier bootstrap method based on the high-dimensional Gaussian approximations, which does not impose any structural assumptions on the unknown covariance matrices. We also evaluate the powers of proposed tests theoretically in comparison with two existing methods. The effectiveness of our proposed tests in the finite samples is illustrated through simulation studies and a real data application. (C) 2020 Elsevier B.V. All rights reserved.

机译：在本文中，我们开发了新的最大类型测试，以根据Wilcoxon分数推断高维线性模型中系数的总体显著性。所提出的测试方法不存在误差方差估计，对重尾分布和异常值具有鲁棒性，因此在实践中具有广泛的适用性。我们在测试统计中加入了预测因子之间的依赖结构，以增强它们的能力。在正则条件下，检验统计量的极限零分布被导出为I型极值分布。为了减少尺寸失真，我们进一步提出了一种基于高维高斯近似的乘法器自举方法，该方法不对未知协方差矩阵施加任何结构假设。我们还通过与两种现有方法的比较，从理论上评估了所提出测试的威力。通过模拟研究和实际数据应用，说明了我们提出的有限样本测试的有效性。（C） 2020爱思唯尔B.V.版权所有。

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《European Journal of Medicinal Chemistry: Chimie Therapeutique》 |2021年第1期|共20页
作者
Xu Kai; Zhou Yeqing;
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作者单位

Tongji Univ Sch Math Sci Shanghai 200092 Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类药学;
关键词
High-dimensional regression; Maximum-type test; Multiplier bootstrap; Simultaneous inference; Wilcoxon scores;

机译：高维回归;最大型式试验;乘法器引导;同时推理;威尔科克森得分;

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1. MAXIMUM TEST FOR A SEQUENCE OF QUADRATIC FORM STATISTICS ABOUT SCORE TEST IN LOGISTIC REGRESSION MODEL [J] . Qing YANG, Jiayan ZHU, Zhengbang LI 数学物理学报（英文版） . 2020,第002期
2. Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models [J] . LIU Yan, REN Mingyang, ZHANG Sanguo 系统科学与复杂性：英文版 . 2021,第003期
3. Generalized F-Test for High Dimensional Regression Coefficients of Partially Linear Models [J] . WANG Siyang, CUI Hengjian 系统科学与复杂性：英文版 . 2017,第005期
4. Maximum-type tests for high-dimensional regression coefficients using Wilcoxon scores [J] . Xu Kai, Zhou Yeqing Journal of Statistical Planning and Inference . 2021,第1期

机译：使用Wilcoxon分数的高维回归系数的最大型测试
5. Test for high-dimensional regression coefficients using refitted cross-validation variance estimation [J] . Quality Control and Applied Statistics . 2019,第5a6期

机译：使用完整的交叉验证方差估计测试高维回归系数
6. TEST FOR HIGH-DIMENSIONAL REGRESSION COEFFICIENTS USING REFITTED CROSS-VALIDATION VARIANCE ESTIMATION [J] . Cui Hengjian, Guo Wenwen, Zhong Wei The Annals of Statistics: An Official Journal of the Institute of Mathematical Statistics . 2018,第3期

机译：使用完整的交叉验证方差估计测试高维回归系数
7. The Equivalence between Mann-Whitney Wilcoxon Test and Score Test Based on the Proportional Odds Model for Ordinal Responses [C] . Yan Wang, Lu Tian International Conference on Industrial Economics System and Industrial Security Engineering . 2017

机译：基于序态响应比例赔率模型的Mann-Whitney Wilcoxon测试和得分测试的等价
8. High-dimensional Regression Models with Structured Coefficients [D] . Li, Yuan. 2018

机译：具有结构系数的高维回归模型
9. Increased correlation coefficient between the written test score and tutors’ performance test scores after training of tutors for assessment of medical students during problem-based learning course in Malaysia [O] . Heethal Jaiprakash, Aung Ko Ko Min, Sarmishtha Ghosh 2016

机译：在以问题为基础的学习课程中培训了辅导老师以评估医学生后笔试成绩和辅导员绩效考试成绩之间的相关系数增加
10. Decision-making is the process of analyzing information about a problem situation and comparing it to a specific conclusion in order to solve a specific problematic (Yıkılmaz, 2001; Miller and Byrnes, 2001). Decision-making styles are a mechanism that is influenced by the internal and external conditions that determine the direction of the decisions of the individual, the content of the decision-making process, and the outcome of the decision-making process (Payne, Bettman and Johson, 1993; Bavol’ár and Orosová, 2015). ACT is a contemporary member of the Cognitive Behavioral Therapy family. ACT (Acceptance and commitment therapy) has both similar and different directions with Behavioral Therapies and Cognitive Therapies (Herbet and Forman, 2011; Hayes, 2004). KKT responds to classical behavioral treatments using both existential and cognitive approaches in the analysis of behavior. KKT is a science wing that tries to solve human problems with a wider perspective aimed at solving problematic human behaviors (Plumb, Stewart, Dahl and Lundgren, 2009). It is seen that there is very little research about the new approach of ACT approach when the aiming country of our country is screened and it is thought that our country will contribute to the field of psychological counseling with the work done. In the scope of the research, experimental and control groups and preliminary test, post-test and follow-up measurements of 2x3 experimental design were used. The study's study group consists of a total of 24 (12 experimental and 12 control groups) university students studying in different departments and levels, continuing their education in the academic year of 2015-2016 in Ağrı province and İbrahim Chechen University in 2015-2016 academic year. The average age of participants in the experiment and control group is 20. There were 12 participants in the experimental group, 7 female and 5 male, and 12 participants, 7 female and 5 male in the control group. Personal Information Form and Decision Making Style Scale prepared by the researcher were used in the research. In order to decide on the tests to be used in the course of analyzing the data, the scores of the participant's Decision Styles Scale pre-test, which are placed primarily in the experimental and control groups, it was analyzed whether the basic expectations of parametric tests were answered. As a result of the analysis made, the scores, skewness and kurtosis coefficients obtained from the Decision Making Styles Scale were given to the experimental and control groups. It was determined that the distribution was normal in the result of Shapiro-Wilk test, in which the skewness and kurtosis coefficients of each sub-scale were ranked between -1 and +1. Participants in the experimental and control groups; homogeneity test results for decision-style pre-test measurements indicate that the data are homogeneous. According to the results of the Mauchly Globalness Test, it has been determined that working supports the hypothesis. It was determined that there was no significant difference between the pre-test scores obtained from dependent decision-making style of experiment and control groups, but the test group showed lower mean scores at the significant level within the scores of post-test and follow-up tests. Therefore, it can be said that the ACT-oriented psychoeducation program applied to the experimental group reduces the dependent decision-making style scores from the decision style sub-dimensions and the psychoeducation program has a lasting effect. It was determined that there was no significant difference between pre-test, post-test and follow-up scores obtained from the Spontaneous-Instant Decision Style of experiment and control groups. Thus, it can be said that this situation does not cause a significant difference in the Spontaneous-Decision-Making Style scores from the decision style sub-dimensions of the ACT-oriented psychoeducation program applied to the experimental group. The ACT -oriented psychoeducation program had a decline in the intuitive decision-making styles of the individuals, but this decrease did not create significant differences. Thus, it can be said that this situation does not make a meaningful difference in the intuitive decision style scores from the decision style sub-dimensions of the KKT oriented psychoeducation program applied to the experimental group. The pre-test scores obtained from the rational decision-making style of the experimental and control groups showed that there was a difference between the post-test and the follow-up scores, but this difference was not significant. As a result of the analysis, it was determined that the test group had higher levels of rational decision style than the pre - test scores in the post test and follow - up scores, whereas the post test and follow - up test scores in the control group rational decision style showed a decrease compared to the pre - test scores. the pre - test scores. Decision-making Styles Scale Avoidant Decision Making As a result of the analysis of the mean scores of the subscale scores of pre-test, post-test and follow-up measures, the group effect was found to be insignificant. It was determined that the experimental and control groups differed significantly from the pre-test scores obtained from the avoidant decision-making style but did not show any significant change within the scores of the post-test and follow-up tests. [O] . mustafa ercengiz, ali haydar şar 2018

机译：决策是分析有关问题情况的信息并将其与特定结论进行比较的过程，以解决特定的问题（Yıkılmaz，2001; Miller和Byrnes，2001）。决策风格是一种机制，受到内部和外部条件的影响，确定个人决定的方向，决策过程的内容以及决策过程的结果（PAYNE，BETTMAN和BEDNE） Johson，1993;Bavol'ár和奥萨洛瓦，2015）。法案是认知行为治疗家庭的当代成员。行为（验收和承诺治疗）具有与行为疗法和认知疗法的类似和不同方向（Herbet和Forman，2011; Hayes，2004）。 KKT在分析行为中使用存在性和认知方法来响应古典行为治疗方法。 KKT是一个科学翼，试图解决人类问题，旨在解决有问题的人类行为（铅垂，斯图尔特，Dahl和Lundgren，2009）。有人认为，当我们国家的瞄准国家进行筛选时，有关行动方法的新方法几乎没有研究，并且认为我们的国家将为完成工作做出贡献的心理咨询领域。在研究的范围内，使用实验和对照组和初步测试，使用后测试和后续测量的2x3实验设计。该研究的研究小组包括共24名（12个实验和12个对照组）大学学生在不同的部门和水平上学习，在2015-2016学术上继续进行2015-2016的学术年度2015-2016学年年。实验和对照组参与者的平均年龄是20.实验组中有12名参与者，7名女性和5名男性，12名参与者，7名女性和5名男性。研究人员准备的个人信息表格和决策制定风格规模在研究中使用。为了决定在分析数据的过程中使用的测试，参与者的决策风格刻度预测的分数主要在实验和对照组中进行，分析了参数的基本期望吗？测试得到了回答。由于对实验和对照组给出了从决策曲调标度获得的分数，偏移和峰度分子系数。确定该分布是正常的在成熟的-WILK试验结果中，其中每亚级的偏差和刚度系数在-1到+1之间排名。实验和对照组的参与者;决策式预测测量的同质性测试结果表明数据是均匀的。根据毛毛环保试验的结果，已确定工作支持假设。据确定，从依赖决策风格的实验和对照组获得的预测分数之间没有显着差异，但测试组在测试后的分数内显示出较低的平均分数和后续的分数 - 测试。因此，可以说，应用于实验组的面向活动的心理教育程序减少了决策风格子维度的依赖决策风格分数，并且心理教育程序具有持久的效果。据确定，从实验和对照组自发决策风格获得的预测试，测试后和后续评分之间没有显着差异。因此，可以说这种情况不会导致从应用于实验组的活动导向的心理教育程序的决策风格分数的自发决策风格分数显着差异。行为的心理教育计划在个人直观的决策风格下降，但这种减少并没有产生显着的差异。因此，可以说，这种情况不会在从应用于实验组的KKT导向的心理教育程序的决策风格分数中产生有意义的决策风格分数。从实验和对照组的理性决策风格获得的预测分数显示后检验后和随访评分之间存在差异，但这种差异并不重要。由于分析，确定测试组的理性决策风格较高，而不是后测试和后续分数的预测分数，而对照组合理决策风格的后测试和后续测试分数显示出与预测试分数相比的减少。预测分数。决策款式扩展避免决策由于分析了预测试，测试后和后续措施的班次评分的平均分数，发现群体效应是微不足道的。确定实验和对照组从避免决策风格获得的预测评分中显着不同，但在测试后和后续测试的分数内没有显示出任何重大变化。
11. Monte Carlo Power Study of Exponential Scores, Wilcoxon, and Normal Scores Procedures on Matched and Censored Data [R] . Michalek, J. E., Mihalko, D., White, T. J. 1985

机译：匹配和删失数据的指数分数，Wilcoxon和正态分数程序的monte Carlo幂研究

Maximum-type tests for high-dimensional regression coefficients using Wilcoxon scores

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