Modified likelihood ratio test for homogeneity in normal mixtures with two samples

This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.

Incorporating Uncertain Costs within a Series of Sequential Probability Ratio Tests

We consider an extension to Sequential Probability Ratio Tests for when we have uncertain costs, but also opportunity to learn about these in an adaptive manner. In doing so we demonstrate the effects that allowing uncertainty has on observation cost, and the costs associated with Type I and Type II error. The value of information relating to modelled uncertainties is derived and the case of statistical dependence between the parameter affecting decision outcome and the parameter affecting unknown cost is also examined. Numerical examples of the derived theory are provided, along with a simulation comparing this adaptive learning framework to the classical one.

Sequential Probability Ratio Test of Correlation Coefficient Using Fuzzy Hypothesis Testing

One of the important fields in statistics is testing hypothesis of correlation coefficient. The extension of the idea of testing correlation to fuzzy hypothesis is of great interesting. In this study, we examined the use of fuzzy hypothesis testing approach for the Sequential Probability Ratio Test (SPRT) of correlation coefficient. Use of fuzzy hypothesis testing for correlation coefficient with SPRT is illustrated by an example.

A Tiling Lemma and Its Application to the Ratio Test for Convergence of Series

We prove that any collection which tiles the positive integers must contain one of two types of sub-collections. We then use this result to prove a variation of the Ratio Test for convergence of series. This version of the Ratio Test shows the convergence of certain series for which the Root Test (which is known to be more powerful than the conventional Ratio Test) fails. This version of the Ratio Test is also used to prove a version of the Banach Contraction Principle for self-maps of a complete metric space.

Generalized Likelihood Ratio Tests for Varying-Coefficient Models with Censored Data

In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.

Multiple hypothesis tracking based on the Shiryayev sequential probability ratio test

To date, Wald sequential probability ratio test(WSPRT) has been widely applied to track management of multiple hypothesis tracking(MHT). But in a real situation, if the false alarm spatial density is much larger than the new target spatial density, the original track score will be very close to the deletion threshold of the WSPRT. Consequently, all tracks, including target tracks, may easily be deleted, which means that the tracking performance is sensitive to the tracking environment. Meanwhile, if a target exists for a long time, its track will have a high score, which will make the track survive for a long time even after the target has disappeared. In this paper, to consider the relationship between the hypotheses of the test, we adopt the Shiryayev SPRT(SSPRT) for track management in MHT. By introducing a hypothesis transition probability, the original track score can increase faster, which solves the first problem. In addition, by setting an independent SSPRT for track deletion, the track score can decrease faster, which solves the second problem. The simulation results show that the proposed SSPRT-based MHT can achieve better tracking performance than MHT based on the WSPRT under a high false alarm spatial density.

Modified likelihood ratio test for homogeneity in bivariate normal mixtures with presence of a structural parameter

This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modified likelihood ratio statistic has χ22 null limiting distribution.

A MODIFIED LIKELIHOOD RATIO TEST FOR HOMOGENEITY IN BIVARIATE NORMAL MIXTURES OF TWO SAMPLES

This paper investigates the asymptotic properties of a modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models of two samples. The asymptotic null distribution of the modified likelihood ratio statistic is found to be X2^2, where X2^2 is a chi-squared distribution with 2 degrees of freedom.

MOVING RATIO TEST FOR MULTIPLE CHANGES IN PERSISTENCE

This paper proposes a moving ratio test, which is a modified version of ratio test by involving a bandwidth parameter, to detect multiple changes in persistence, and to determine the direction of switch. The asymptotic distribution as well as its consistency are established. In order to estimate the change points, the authors propose a two step estimate approach. Simulations illustrate the performance of the test and estimate procedures in finite samples. An application to the analysis of Sweden/US foreign exchange rate demonstrates the validity of the procedure in practice.

ASYMPTOTIC DISTRIBUTION OF LIKELIHOOD RATIO STATISTIC FOR TESTING SPHERICTY IN GROWTH CURVE MODELS

In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose to the null hypothesis. These expansions are given in series form of beta distributions.

面板数据均值渐变变点的Ratio检验

为解决时间序列因观测时间较短而难以确定变点的问题,通过分析独立同分布序列面板数据,对其均值的渐变变点进行检验.假设面板数据中每条时间序列的均值在同一时刻发生变化,提出Ratio检验统计量,并分别在原假设与备择假设下给出检验统计量的极限性质.数值模拟结果表明,面板数据的检验效果优于单条时间序列,实例分析也验证了该方法的有效性与实用性.

基于Subsampling抽样的厚尾AR(p)序列趋势变点的Ratio检验

文章考虑的是厚尾AR(p)序列趋势变点检验问题。首先,在已有研究的启发下,构造了一个Ratio统计量来检验趋势变点;其次,在原假设下证明统计量的极限分布是列维过程的泛函,在备择假设下得到统计量的一致性;其次,为了避免参数的估计,采用Subsampling方法获得更为准确的临界值,数值模拟结果显示,在大样本下基于Subsampling抽样方法的Ratio检验很好地控制了经验水平,经验势也达到了比较好的效果;最后,通过一组实证数据进一步阐明理论的有效性和可行性。

Test for Homogeneity of Odds Ratios Using <i>U</i>-Statistics

There are a few statistics testing the homogeneity of odds ratios across strata. Asymptotic statistics lose their power in the “sparse-data” setting. Both asymptotic statistics and exact tests have low power when the sample sizes are small. We created a set of U statistics and compared them with some existing statistics in testing homogeneity of OR at different data settings. We evaluated their performance in terms of the empirical size and power via Monto Carlo simulations. Our results showed that two of the U-statistics under our study had higher power for testing homogeneity of odds ratios for 2 by 2 contingency tables. The application of the tests was illustrated in two real examples.

Analysis of the stress ratio of anisotropic rocks in uniaxial tests

The effect of structural discontinuities on the progressive failure process of anisotropic rocks should be paid particular attention.The crack damage stress σ_(cd),also considered as the yield strength,and the relationship between σ_(cd) and the uniaxial peak strength σ_(ucs) of anisotropic rocks for different orientations 8 of the isotropy planes with respect to the loading directions were investigated theoretically and experimentally.A theoretical relation of σ_(cd)/σ_(ucs) with the function of the shape parameter m was established.Additionally,uniaxial compression tests of shale samples were conducted for several inclinations θ.The test result of σ_(cd)/σ_(ucs) was close to the theoretical value for a given orientation.Furthermore,both experimental results and theoretical solutions of σ_(cd)/σ_(ucs) were independent of the inclination θ while σ_(cd) andσ_(ucs) were strongly affected by θ.The strength ratio σ_(cd)/σ_(ucs) may therefore be an intrinsic property of anisotropic rocks and could be used to predict the failure of rock samples.

基于极化SAR梯度和复Wishart分类器的舰船检测

舰船检测是极化SAR系统的重要应用之一。现有的舰船检测方法容易受到旁瓣泄露的干扰,使得舰船目标的形态难以提取,导致检测结果不符合真实情况。此外,在舰船过于密集、尺度不一致的情况下,相邻舰船由于旁瓣的影响有时会被认为是单个目标,从而造成漏检。针对这些问题,该文提出一种基于极化SAR梯度和复Wishart分类器的舰船检测方法。首先,将似然比检验(LRT)梯度引入对数比值梯度框架,使其适用于极化SAR数据;基于LRT梯度图进行恒虚警(CFAR)检测,提取舰船的边缘信息,消除伪影的同时抑制强旁瓣对舰船精细轮廓提取的影响。其次,利用复Wishart迭代分类器对舰船强散射部分进行检测,可排除大部分的杂波干扰且保持舰船形态细节。最后,将二者信息融合,从而可以保持舰船形态细节的同时克服旁瓣和伪信号的虚警。该文在3幅来自ALOS-2卫星的极化SAR图像上进行了对比实验,实验表明与其他方法相比,该文所提算法具有更少的虚警和漏检,且能够有效克服旁瓣泄露,保持舰船形态细节。

黄土地基阶梯型截面桩承载模型试验与计算

为研究黄土地基阶梯型截面桩的荷载传递机理,通过室内模型试验与有限元计算,分析阶梯型截面桩竖向静荷载下的桩身轴力、桩侧摩阻力、桩顶沉降和桩身不同深度荷载分担比,并探索了变径比对其工作性能的影响,并对其进行优化设计。结果表明:在相同荷载下,阶梯型截面桩的桩顶沉降明显小于等截面桩,当变径比在0.8~0.9时,沉降控制效果最佳,其材料利用率最高;若二者极限承载力相同时,阶梯型截面桩的最高材料利用率为等截面桩的1.06倍。阶梯型截面桩为摩擦型桩,变截面位置土体对桩体具有支承作用,其变径处底面土体能承担部分桩顶荷载。桩侧能够分担更多桩顶荷载,减轻桩端土体承载,当变径比在0.8~0.9时,侧摩阻力发挥程度更高。在桩体用料相同时,与等截面桩相比,阶梯型截面桩能大幅度提高承载能力。

卷积神经网提取特征的红外与可见光图像融合研究

当前红外与可见光图像融合存在一些难题,导致前红外与可见光图像精度低,误差大,而且前红外与可见光图像融合效率低,为了解决当前红外与可见光图像过程存在的问题,设计了基于卷积神经网提取特征的红外与可见光图像融合方法。首先分别采集对象的红外图像和可见光图像,并对原始图像去噪等预处理,改善图像的质量,然后采用卷积神经网络提取红外与可见光图像融合特征,根据特征得到红外与可见光图像融合结果,最后进行了仿真实验,结果表明本方法红外与可见光图像的融合结果的融合比率提高了0.24,平均梯度值提升了0.22,图像融合质量更高。

考虑孔隙比影响的堆石料湿化试验及湿化模型

对某堆石坝的坝壳料进行了不同密实状态下的单线法三轴湿化试验,分析了湿化变形随围压、应力水平以及初始孔隙比的变化规律。结果表明:在围压和应力水平相同条件下,随着初始孔隙比的减小,堆石料湿化轴向应变和体积应变均明显降低;初始孔隙比对湿化应力剪胀规律影响不大,采用对数形式的湿化剪胀方程可对不同初始孔隙比条件下的湿化应力剪胀关系进行统一描述。对指数形式的湿化轴向应变经验模型进行修正,构建了考虑初始孔隙比及应力状态影响的湿化轴向应变计算模型,并联立湿化剪胀方程推导了湿化体积应变的计算公式,通过对三轴湿化试验结果进行模拟验证了该公式的合理性。

100 V输入宽频带电压比例校验系统研究

提出一种基于数字采集装置的50 Hz~10 kHz电压比例校验系统,由电压比例变换和数字采集装置构成。数字采集装置采用了通道切换技术,极大提高数字采集装置测量比例误差的准确度。电压比例变换部分由级联型感应分压器、隔离互感器及高、低压精密电压跟随器构成。为了降低分布参数引起的附加误差,设计了采用双绞线结构的双级隔离互感器;该双级互感器在10 kHz范围内幅值误差不大于5×10^(-6),相位误差不超过10μrad。利用双封装运算放大器特性匹配特征,补偿电压跟随器电路的相位响应,显著提升了低压和高压复合型电压跟随器的相位特性,10 kHz范围内,跟随器的幅值误差不大于10×10^(-6),相位误差不大于20μrad。测量结果表明,校验系统具有较好的测量准确度,50 Hz时的测量偏差不大于1×10^(-6)和1μrad,10 kHz范围内,比值误差偏差不大于80×10^(-6),相位误差偏差不大于60μrad,可满足不同频率场景下的电压比例误差测量需求。