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A method for extracting anomaly map of Au and As using combination of u-statistic and Euclidean distance methods in Susanvar district,Iran

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Journal of Central South university 2017年第11期24卷 2693-2704页

作者： Seyyed Saeed Ghannadpour Ardeshir Hezarkhani Mostafa Sharifzadeh Department of Mining & Metallurgical Engineering Amirkabir University of Technology (Tehran Polytechnic) Department of Mining Engineering and Metallurgical Engineering Western Australia School of MineCurtin University

Quantitative descriptions of geochemical patterns and providing geochemical anomaly map are important in applied geochemistry. Several statistical methodologies are presented in order to identify and separate geochemical anomalies. The u-statistic method is one of the most important structural methods and is a kind of weighted mean that surrounding points of samples are considered in u value determination. However, it is able to separate the different anomalies based on only one variable. The main aim of the presented study is development of this method in a multivariate mode. For this purpose, u-statistic method should be combined with a multivariate method which devotes a new value to each sample based on several variables. Therefore, at the first step, the optimum p is calculated in p-norm distance and then u-statistic method is applied on p-norm distance values of the samples because p-norm distance is calculated based on several variables. This method is a combination of efficient u-statistic method and p-norm distance and is used for the first time in this research. Results show that p-norm distance of p=2(Euclidean distance) in the case of a fact that Au and As can be considered optimized p-norm distance with the lowest error. The samples indicated by the combination of these methods as anomalous are more regular, less dispersed and more accurate than using just the u-statistic or other nonstructural methods such as Mahalanobis distance. Also it was observed that the combination results are closely associated with the defined Au ore indication within the studied area. Finally, univariate and bivariate geochemical anomaly maps are provided for Au and As, which have been respectively prepared using u-statistic and its combination with Euclidean distance method.

关键词： mineral anomaly Susanvar district u-statistic method Euclidean distance bivariate anomaly map

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Testing High-Dimensional Nonparametric Behrens-Fisher Problem

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Journal of Systems Science & Complexity 2022年第3期35卷 1098-1115页

作者： MENG Zhen LI Na YuAN Ao Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China university of Chinese Academy of Sciences Beijing 100049China Department of Biostatistics Bioinformatics and BiomathematicsGeorgetown UniversityWashington 20057USA

For high-dimensional nonparametric Behrens-Fisher problem in which the data dimension is larger than the sample size,the authors propose two test statistics in which one is u-statistic Rankbased Test(uRT)and another is Cauchy Combination Test(CCT).CCT is analogous to the maximumtype test,while uRT takes into account the sum of squares of differences of ranked samples in different dimensions,which is free of shapes of distributions and robust to outliers.The asymptotic distribution of uRT is derived and the closed form for calculating the statistical significance of CCT is given.Extensive simulation studies are conducted to evaluate the finite sample power performance of the statistics by comparing with the existing method.The simulation results show that our uRT is robust and powerful method,meanwhile,its practicability and effectiveness can be illustrated by an application to the gene expression data.

关键词： Cauchy combination test nonparametric Behrens-Fisher problem rank-based test u-statistic

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High-dimensional Tests for Mean Vector: Approaches without Estimating the Mean Vector Directly

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Acta Mathematicae Applicatae Sinica 2022年第1期38卷 78-86页

作者： Bo CHEN Hai-meng WANG School of Mathematics and Information Technology Jiangsu Second Normal UniversityNanjing 211200China

Several tests for multivariate mean vector have been proposed in the recent literature.Generally,these tests are directly concerned with the mean vector of a high-dimensional distribution.The paper presents two new test procedures for testing mean vector in large dimension and small samples.We do not focus on the mean vector directly,which is a different framework from the existing choices.The first test procedure is based on the asymptotic distribution of the test statistic,where the dimension increases with the sample size.The second test procedure is based on the permutation distribution of the test statistic,where the sample size is fixed and the dimension grows to infinity.Simulations are carried out to examine the finite-sample performance of the tests and to compare them with some popular nonparametric tests available in the literature.

关键词： asymptotic distribution high-dimensional data permutation test u-statistic testing mean vector

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Local Dependence Test Between Random Vectors Based on the Robust Conditional Spearman's ρ and Kendall's τ

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Acta Mathematicae Applicatae Sinica 2023年第3期39卷 491-510页

作者： Ling-yue ZHANG Heng-jian CuI School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

This paper introduces two local conditional dependence matrices based on Spearman'sρand Kendall'sτgiven the condition that the underlying random variables belong to the intervals determined by their quantiles.The robustness is studied by means of the influence functions of conditional Spearman'sρand Kendall'sτ.using the two matrices,we construct the corresponding test statistics of local conditional dependence and derive their limit behavior including consistency,null and alternative asymptotic distributions.Simulation studies illustrate a superior power performance of the proposed Kendall-based test.Real data analysis with proposed methods provides a precise description and explanation of some financial phenomena in terms of mathematical statistics.

关键词： local dependence influence function rank correlation u-statistic

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Self-normalization:Taming a wild population in a heavy-tailed world

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Applied Mathematics(A Journal of Chinese universities) 2017年第3期32卷 253-269页

作者： SHAO Qi-man ZHOu Wen-xin Department of statistics The Chinese University of Hong Kong Department of Mathematics University of California

The past two decades have witnessed the active development of a rich probability theory of Studentized statistics or self-normalized processes, typified by Student’s t-statistic as introduced by W. S. Gosset more than a century ago, and their applications to statistical problems in high dimensions, including feature selection and ranking, large-scale multiple testing and sparse, high dimensional signal detection. Many of these applications rely on the robustness property of Studentization/self-normalization against heavy-tailed sampling distributions. This paper gives an overview of the salient progress of self-normalized limit theory, from Student’s t-statistic to more general Studentized nonlinear statistics. Prototypical examples include Studentized one- and two-sample u-statistics. Furthermore, we go beyond independence and glimpse some very recent advances in self-normalized moderate deviations under dependence.

关键词： Berry-Esseen inequality Hotelling’s T 2-statistic large deviation moderate deviation self-normalization Student’s t-statistic u-statistic

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Inference of change-point in single index models

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Science China Mathematics 2008年第10期51卷 1855-1870页

作者： CAO GuanQun WANG ZhanFeng Wu YaoHua ZHAO LinCheng Department of statistics and Finance University of Science and Technology of ChinaHefei 230026China

Single index models are widely used in medicine, econometrics and some other fields. In this paper, we consider the inference of a change point problem in single index models. Based on density-weighted average derivative estimation (ADE) method, we propose a statistic to test whether a change point exists or not. The null distribution of the test statistic is obtained using a permutation technique. The permuted statistic is rigorously shown to have the same distribution in the limiting sense under both null and alternative hypotheses. After the null hypothesis of no change point is rejected, an ADE-based estimate of the change point is proposed under assumption that the change point is unique. A simulation study confirms the theoretical results.

关键词： change point single index models density weighted average derivatives u-statistic Brownian bridges

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The abstract of doctoral dissertation‘Some research on hypothesis testing and nonparametric variable screening problems for high dimensional data’

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statistical Theory and Related Fields 2020年第2期4卷 228-229页

作者： Yongshuai Chen Hengjian Cui School of Mathematical Sciences Capital Normal UniversityBeijingPeople’s Republic of China School of statistics Capital University of Economics and BusinessBeijingPeople’s Republic of China

In this thesis,we construct test statistic for association test and independence test in high dimension,respectively,and study the corresponding theoretical properties under some regularity conditions.Meanwhile,we propose a nonparametric variable screening procedure for sparse additive model with multivariate response in untra-high dimension and established some screening properties.

关键词： High-dimensional test independence test distance correlation power enhancement association test u-statistic nonparametric variable screening additive model

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A Note on Detecting “More IFR-ness” Property of Life Distributions

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Open Journal of statistics 2012年第4期2卷 443-446页

作者： Parameshwar V.Pandit Sujatha Inginashetty Department of statistics Bangalore University Bangalore-560056 India Department of statistics Gulbarga University Gulbarga India

In this paper, a problem of testing whether one life distribution possesses ‘more IFR’ property than the other is considered. A new test procedure is proposed and the distribution of the test statistic is studied. The performance of the procedure is evaluated in terms of Pitman asymptotic relative efficiency. The consistency property of the test procedure is established. It is observed that the new procedure is better than the existing procedure in the literature.

关键词： 'More IFR' Property u-statistic Pitman ARE

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Tests for Two-Sample Location Problem Based on Subsample Quantiles

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Open Journal of statistics 2014年第1期4卷 70-74页

作者： Parameshwar V. Pandit Savitha Kumari S. B. Javali Department of Public Health Dentistry SDM College of Dental Sciences and Hospital Dharwad India Department of statistics Bangalore University Bangalor India Department of statistics SDM College Ujire India

This paper presents a new class of test procedures for two-sample location problem based on subsample quantiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests proposed is established. The asymptotic relative performance of the proposed class of test with respect to the optimal member of Xie and Priebe (2000) is studied in terms of Pitman efficiency for various underlying distributions.

关键词： u-statistic Class of Tests Two-Sample Location Problem Asymptotic Normality Pitman ARE Subsample Quantiles

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On Nonsmooth Estimating Functions via Jackknife Empirical Likelihood

On Nonsmooth Estimating Functions via Jackknife Empirical Li...

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第十届海峡两岸统计与概率研讨会

作者： Zhou Ping Li Jinfeng Xu Wang Zhou Lanzhou university university of Hong Kong National university of Singapore

In many applications, the parameters of interest are estimated by solving nonsmooth estimating functions with u-statistic structure. Since the asymptotic covariances matrix of the estimator generally involves the underlying density function, Resampling methods are often used to bypass the difficulty of nonparametric density estimation. Despite its simplicity, the resultant covariance matrix estimator depends on the nature of resampling and the method can be time-consuming when the number of replications is large. Furthermore, the inferences are based on the normal approximation which may not be accurate for practical sample sizes. In this paper, we propose a jackknife empirical likelihood-based inferential procedure for nonsmooth estimating functions. Standard chi-squared distributions are used to calculate the p-value and to construct confidence intervals. Extensive simulation studies and two real examples are provided to illustrate its practical utilities.

关键词： accelerated failure time model bootstrap jackknife empirical likelihood perturbation resampling u-statistic Wilcoxon rank regression

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