A Statistical Power Comparison of the Kolmogorov-Smirnov Two-Sample Test and the Wald Wolfowitz Test in Terms of Fixed Skewness and Fixed Kurtosis in Large Sample Sizes

In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.

Tests for Two-Sample Location Problem Based on Subsample Quantiles

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.

均值函数相等检验及在高频股指收益率中应用

针对具有相依特征的函数型数据样本,提出利用经典的Newey-West估计式对它们的长期协方差函数进行估计,从而可以得到更加准确的函数主成分,进而对独立同分布条件下的均值函数相等检验统计量进行改进,并通过模特卡罗模拟和实例分析与现有独立同分布和相依条件下的检验方法进行比较。模特卡罗模拟结果表明,相比于现有检验方法,文中所提改进方法的检验水平与显著性水平更接近,而检验功效更高。实例分析结果表明,2018年沪深300和上证180股指1分钟和5分钟累积收益率的均值函数相等,即这两个金融市场的投资收益水平相当。

Transmission Based Conditional Logistic Model for Testing Main and Interaction Effects

Transmission disequilibrium test (TDT) is a popular family based genetic association method. Under multiplicative assumption, a conditional logistic regression for matched pair, affected offspring with allele transmitted from parents and pseudo-offspring (control) with allele non-transmitted from parents, was built to detect the main effects of genes and gene-covariate interactions. When there exist genotype uncertainties, expectation-maximization (EM) algorithm was adopted to estimate the coefficients. The transmission model was applied to detect the association between M235T polymorphism in AGT gene and essential hypertension (ESH). Most of parents are not available in the 126 families from HongKong Chinese population. The results showed M235T is associated with hypertension and there is interaction between M235T and the case’s sex. The allele T is higher risk for male than female.

Distance-covariance-based tests for heteroscedasticity in nonlinear regressions

In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also derived.Numerical experiments validate the theoretical analysis.

Efficient Centralized Cooperative Spectrum Sensing Techniques for Cognitive Networks

Wireless Communication is a system for communicating information from one point to other,without utilizing any connections like wire,cable,or other physical medium.Cognitive Radio(CR)based systems and networks are a revolutionary new perception in wireless communications.Spectrum sensing is a vital task of CR to avert destructive intrusion with licensed primary or main users and discover the accessible spectrum for the efficient utilization of the spectrum.Centralized Cooperative Spectrum Sensing(CSS)is a kind of spectrum sensing.Most of the test metrics designed till now for sensing the spectrum is produced by using the Sample Covariance Matrix(SCM)of the received signal.Some of the methods that use the SCM for the process of detection are Pietra-Ricci Index Detector(PRIDe),Hadamard Ratio(HR)detector,Gini Index Detector(GID),etc.This paper presents the simulation and comparative perfor-mance analysis of PRIDe with various other detectors like GID,HR,Arithmetic to Geometric Mean(AGM),Volume-based Detector number 1(VD1),Maximum-to-Minimum Eigenvalue Detection(MMED),and Generalized Likelihood Ratio Test(GLRT)using the MATLAB software.The PRIDe provides better performance in the presence of variations in the power of the signal and the noise power with less computational complexity.

High-dimensional proportionality test of two covariance matrices and its application to gene expression data

With the development of modern science and technology, more and more high-dimensionaldata appear in the application fields. Since the high dimension can potentially increase the com-plexity of the covariance structure, comparing the covariance matrices among populations isstrongly motivated in high-dimensional data analysis. In this article, we consider the proportion-ality test of two high-dimensional covariance matrices, where the data dimension is potentiallymuch larger than the sample sizes, or even larger than the squares of the sample sizes. We devisea novel high-dimensional spatial rank test that has much-improved power than many exist-ing popular tests, especially for the data generated from some heavy-tailed distributions. Theasymptotic normality of the proposed test statistics is established under the family of ellipticallysymmetric distributions, which is a more general distribution family than the normal distribu-tion family, including numerous commonly used heavy-tailed distributions. Extensive numericalexperiments demonstrate the superiority of the proposed test in terms of both empirical sizeand power. Then, a real data analysis demonstrates the practicability of the proposed test forhigh-dimensional gene expression data.

Sphericity and Identity Test for High-dimensional Covariance Matrix Using Random Matrix Theory

This paper addresses the issue of testing sphericity and identity of high-dimensional population covariance matrix when the data dimension exceeds the sample size.The central limit theorem of the first four moments of eigenvalues of sample covariance matrix is derived using random matrix theory for generally distributed populations.Further,some desirable asymptotic properties of the proposed test statistics are provided under the null hypothesis as data dimension and sample size both tend to infinity.Simulations show that the proposed tests have a greater power than existing methods for the spiked covariance model.

Hypothesis Testing for Independence Under Blocked Compound Symmetric Covariance Structure

One type of covariance structure is known as blocked compound symmetry.Recently,Roy et al.(J Multivar Anal 144:81–90,2016)showed that,assuming this covariance structure,unbiased estimators are optimal under normality and described hypothesis testing for independence as an open problem.In this paper,we derive the distributions of unbiased estimators and consider hypothesis testing for independence.Representative test statistics such as the likelihood ratio criterion,Waldstatistic,Rao’s score statistic,and gradient statistic are derived,and we evaluate the accuracy of the test using these statistics through numerical simulations.The power of the Wald test is the largest when the dimension is high,and the power of the likelihood ratio test is the largest when the dimension is low.

Empirical likelihood test for the equality of several high-dimensional covariance mat rices

The testing covariance equality is of importance in many areas of statistical analysis,such as microarray analysis and quality control.Conventional tests for the finite-dimensional covariance do not apply to high-dimensional data in general,and tests for the high-dimensional covariance in the literature usually depend on some special structure of the matrix and whether the dimension diverges.In this paper,we propose a jackknife empirical likelihood method to test the equality of covariance matrices.The asymptotic distribution of the new test is regardless of the divergent or fixed dimension.Simulation studies show that the new test has a very stable size with respect to the dimension and it is also more powerful than the test proposed by Schott(2007)and studied by Srivastava and Yanagihara(2010).Furthermore,we illustrate the method using a breast cancer dataset.

SADDLEPOINT APPROXIMATIONS TO THETWO-SAMPLE PERMUTATION TESTS

A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall revisit the same problem from a different angle. We shall first turnthe problem into a conditional probability and then apply a Lugannani-Rice type formula to it,which was developed by Skovagard[8] for the mean of i.i.d. samples and by Jing and Robinson[5]for smooth function of vector means. Both the Lugannani-Rice type formula and Robinson'sformula achieve the same relative error of order O(n-3/2), but the former is very compact andmuch easier to use in practice. Some numerical results will be presented to compare the twoformulas.

改进的强跟踪UKF算法及其在INS/GPS组合导航中的应用

针对标准UKF缺乏对系统状态异常的自适应调整能力,导致滤波精度降低的问题,提出一种改进的强跟踪UKF算法。该算法采用假设检验的方法对异常状态进行检测,当系统状态发生异常时,对预测协方差阵引入次优渐消因子自适应的调整滤波增益,实现对系统真实状态的强跟踪。该算法中次优渐消因子的确定无需计算系统模型的雅克比矩阵,提高了传统强跟踪UKF的实用性。将提出的算法应用于INS/GPS组合导航系统进行仿真验证,并与标准UKF进行比较,结果表明,在系统状态存在异常时,提出的带单重次优渐消因子的强跟踪UKF得到的东向、北向位置误差在[-13.7 m,14.9 m]以内,带多重次优渐消因子的强跟踪UKF得到的东向、北向位置误差在[-10.0 m,12.1 m]以内,滤波性能明显优于标准UKF,提高了组合导航系统的解算精度。

WRF模式三维变分中背景误差协方差估计

利用WRF模式2008年5—10月逐日预报结果,通过NMC方法进行背景误差协方差(B)估计。给出其结构特征,进行单点数值试验,并利用不同B进行1个月的数值模拟试验,检验模拟降水效果。结果表明:通过单点数值试验验证估算的B结构合理。不同的B,资料同化过程差别较大,应用重新统计的B,同化效率更高,目标函数收敛更稳定。模式模拟降水预报效果有所差别,经过重新统计与预报模式区域和各种参数相匹配的B,模式预报效果在中雨及以上量级优于通用的B预报效果。因此,在应用三维变分同化系统时,重新统计B非常必要。

具有协变量或干扰因素的诊断试验数据的ROC分析

目的 探讨具有协变量或干扰因素的诊断试验数据的评价问题 ,建立相应的统计模型及分析方法。方法 基于ROC分析给出多变量ROC模型 ,采用有序logistic连接函数 ,利用SAS软件进行参数估计 ,得到有协变量情况下的ROC曲线方程及曲线下面积。文中结合检测动脉硬化的数据 ,说明了其用法。结果 采用文中给出的方法 ,可以有效地扣除协变量的影响 ,准确地评价诊断的作用。结论 本文提供的方法能够有效地解决诊断试验中具有干扰因素影响的问题。

叠前三参数同步反演方法及其应用

叠前三参数同步反演的优势是可以同时获得地层的纵波、横波和密度信息,进而定量描述储层的流体饱和度。提出了一种叠前三参数同步反演的新方法。该方法基于Zoeppritz近似方程和贝叶斯参数估计理论,用协方差矩阵来描述参数间的相关程度,然后用参数间的岩石物理关系对反演结果进行约束,从而得到稳定、准确、可靠的解。仿真实验和实际应用表明,该反演方法鲁棒性好,为储层的进一步识别提供了更多的物性参数。

基于Hsieh和Kljun模型的城市生态系统碳通量贡献区分析与对比

利用上海市奉贤大学城内的涡动相关通量观测站点,基于Hsieh和Kljun模型对研究区内的碳通量贡献区进行了分析。结果表明:1)随着大气稳定度的增加,各风向上的碳通量贡献区范围有增加的趋势;2)当大气处于稳定条件下时,非主风向上的碳通量贡献区范围要大于主风向;3)当大气处于不稳定状态时,主风向和非主风向上的碳通量贡献区范围相差不大;4)在各风向和各大气稳定度上Hsieh和Kljun模型所输出的碳通量贡献区范围数值不同,但无显著差异,碳通量贡献区范围形态近似椭圆;5)Hsieh和Kljun模型输出的垂直于主风向和非主风向上的碳通量贡献区的长度无显著差异;6)在迎风向上Hsieh和Kljun模型的碳通量贡献峰值所处的位置有显著差异。

临床试验中评价处理效应的协变量调整问题

临床试验设计和分析中常常包括影响疾病结果的非处理因素 ,这些因素被统称为协变量。对处理效应的评价 ,若不合理考虑协变量的影响 ,常常会导致结论的偏倚乃至错误。因此 ,在临床试验中要审慎地对待这一问题 ,在评价处理效应时应该考虑用协变量对其进行适当的调整 ,以达到处理效应的正确评价。试验设计阶段的协变量调整称为“事先调整” ,常用的方法有分层法、动态分配最小化法等。试验分析阶段的协变量调整称为“事后调整”,常用的方法有分层检验法、回归模型法等。通过协变量调整 ,一方面阐明病人特征在处理组间的不均衡并没有影响到处理效应的正确评价 ,提高临床试验结果的可信度 ;另外 ,协变量调整方法的合理运用还可提高统计效能。本文对处理效应评价协变量调整涉及的概念、方法、步骤等进行介绍和探讨 ,尤其强调了应用中的一些统计学事项。

稳态与湍流特征测试对通量数据质量的评价

应用CO_2通量、感热和潜热通量稳态测试及垂直速度积分测试相结合的湍流数据质量评价方法对锡林浩特国家气候观象台2009年全年的湍流通量观测数据进行了质量评价。结果表明,锡林浩特通量观测数据质量总体较好;80%以上数据通过质量评价为较好数据;质量评价较好的数据分布呈白天大于夜间、夏季大于冬季的特点。经过对比分析,前期数据处理能剔除大部分质量不好的数据,但应用稳态测试与湍流积分测试筛选后,数据质量仍有明显提高,能量闭合率较前期数据分析前提高2%以上。

关于协方差的U统计量检验法

讨论了两个总体协方差差异的检验问题,给出了该检验问题的U统计量.该检验方法不仅适合参数统计结构,也适用于非参数统计结构,与经典的Pearson矩相关系数检验法相比,其渐近相对效率为1.

协变量的不均衡对协方差分析的影响

目的探讨协变量的不均衡对协方差分析的影响。方法通过MonteCarlo模拟并结合临床试验实例对作协方差分析时引入不均衡的协变量来校正的前后变化作比较。结果协变量的不均衡对协方差分析的检验效能是存在一定影响的,无论协变量不均衡程度有多大,在作协方差分析时引入不均衡的协变量来校正总是有一定代价的。结论新药临床试验中常常存在病人的基线特征在处理组间不均衡从而影响对试验结果的正确评价。可以在作协方差分析时引入该不均衡的协变量去处理,但要根据协变量的不均衡程度及试验目的等实际情况加以权衡。