Profile Likelihood Tests for Common Risk Ratios in Meta-Analysis Studies

It is well-known that the power of Cochran’s Q test to assess the presence of heterogeneity among treatment effects in a clinical meta-analysis is low due to the small number of studies combined. Two modified tests (PL1, PL2) were proposed by replacing the profile maximum likelihood estimator (PMLE) into the variance formula of logarithm of risk ratio in the standard chi-square test statistic for testing the null common risk ratios across all k studies (i = 1, L, k). The simply naive test (SIM) as another comparative candidate has considerably arisen. The performance of tests in terms of type I error rate under the null hypothesis and power of test under the random effects hypothesis was done via a simulation plan with various combinations of significance levels, numbers of studies, sample sizes in treatment and control arms, and true risk ratios as effect sizes of interest. The results indicated that for moderate to large study sizes (k?≥ 16)?in combination with moderate to large sample sizes?(?≥ 50), three tests (PL1, PL2, and Q) could control type I error rates in almost all situations. Two proposed tests (PL1, PL2) performed best with the highest power when?k?≥ 16?and moderate sample sizes (= 50,100);this finding was very useful to make a recommendation to use them in practical situations. Meanwhile, the standard Q test performed best when?k?≥ 16 and large sample sizes (≥ 500). Moreover, no tests were reasonable for small sample sizes (≤ 10), regardless of study size k. The simply naive test (SIM) is recommended to be adopted with high performance when k = 4 in combination with (≥ 500).

A Likelihood-Based Multiple Change Point Algorithm for Count Data with Allowance for Over-Dispersion

Count data is almost always over-dispersed where the variance exceeds the mean. Several count data models have been proposed by researchers but the problem of over-dispersion still remains unresolved, more so in the context of change point analysis. This study develops a likelihood-based algorithm that detects and estimates multiple change points in a set of count data assumed to follow the Negative Binomial distribution. Discrete change point procedures discussed in literature work well for equi-dispersed data. The new algorithm produces reliable estimates of change points in cases of both equi-dispersed and over-dispersed count data;hence its advantage over other count data change point techniques. The Negative Binomial Multiple Change Point Algorithm was tested using simulated data for different sample sizes and varying positions of change. Changes in the distribution parameters were detected and estimated by conducting a likelihood ratio test on several partitions of data obtained through step-wise recursive binary segmentation. Critical values for the likelihood ratio test were developed and used to check for significance of the maximum likelihood estimates of the change points. The change point algorithm was found to work best for large datasets, though it also works well for small and medium-sized datasets with little to no error in the location of change points. The algorithm correctly detects changes when present and fails to detect changes when change is absent in actual sense. Power analysis of the likelihood ratio test for change was performed through Monte-Carlo simulation in the single change point setting. Sensitivity analysis of the test power showed that likelihood ratio test is the most powerful when the simulated change points are located mid-way through the sample data as opposed to when changes were located in the periphery. Further, the test is more powerful when the change was located three-quarter-way through the sample data compared to when the change point is closer (quarter-way) to the first observation.

Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models

This paper considers tests for regression coefficients in high dimensional partially linear Models.The authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly expressed.Then,the authors propose an empirical likelihood method to test regression coefficients.The authors derive the asymptotic chi-squared distribution with two degrees of freedom of the proposed test statistics under the null hypothesis.In addition,the method is extended to test with nuisance parameters.Simulations show that the proposed method have a good performance in control of type-I error rate and power.The proposed method is also employed to analyze a data of Skin Cutaneous Melanoma(SKCM).

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.

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.

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）.

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.

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。

基于时变Copula函数的多部件系统可靠性评估

针对多部件失效相关的机械系统,提出一种基于时变Copula函数的多部件系统可靠性评估方法。首先,引入非线性Wiener过程刻画性能退化过程,并采用Copula函数刻画多部件失效间的相关性;其次,基于傅里叶级数近似Copula函数的演化方程,并通过蒙特卡洛(MC)模拟验证傅里叶级数对常见时变形式的拟合效果;此外,采用似然比统计量检验时变相关性的存在性,指明时变相关性研究的必要性。算例分析结果表明,与静态相关性模型相比,时变相关性模型对数似然函数值提高4.36%、赤池信息量准则(AIC)减小3.81%,可靠性评估结果更加准确。

变化环境下珠江河口区复合洪水事件遭遇分析

受全球气候持续变暖影响,沿海城市受到上游洪水、热带气旋、天文潮等海陆要素联合驱动引发的复合洪水事件频发,严重威胁该地区人民生命财产安全。以1986—2018年间影响珠江河口区的135场台风为统计样本,采用Mann-Kendall检验法和Pettitt检验法分析复合洪水事件的发生趋势和变化情况,并通过Vine Copula拟合复合洪水事件潮位、风速、流量三变量的联合分布函数,采用Copula似然比检验法对联合分布函数相关结构进行变点检验。研究结果表明:考虑Vine Copula函数突变的情况下三个变量间的相关性增强,能更好地反映各个变量间随事件变化的相依关系,提高了复合洪水事件重现期评估的准确性。近三十年来热带气旋数量呈现出下降趋势,而风速则呈现显著增强的趋势且风速在2002年发生突变,即热带气旋事件呈现“出现次数下降、等级增强”的特性。在变化环境下“天鸽”“山竹”等极端复合洪水事件联合重现期计算结果相比传统固定参数的Copula重现期计算结果小,即未来极端复合洪水事件发生概率在增大。

高斯和非高斯平稳时间序列记忆参数的经验似然检验

本文将经验似然方法运用于高斯的和非高斯的平稳时间序列的长记忆性检验.我们从常用的长记忆模型(ARFIMA)出发,建立了记忆参数的经验似然比检验统计量.从理论上证明了所给的经验似然比渐近服从卡方分布,通过数值模拟和实例分析验证了所给的检验方法对于平稳的ARFIMA模型的长记忆参数检验的有效性.

子空间干扰加高斯杂波背景下基于GLRT的斜对称方向检测器设计

文章研究了背景为子空间干扰加高斯杂波的距离扩展目标方向检测问题。杂波是均值为零协方差矩阵未知但具有斜对称特性的高斯杂波,目标与干扰分别通过具备斜对称特性的目标子空间和干扰子空间描述。针对方向检测问题,利用上述斜对称性,根据广义似然比检验(Generalized Likeli-hood Ratio Test,GLRT)准则的一步与两步设计方法,设计了基于GLRT的一步法与两步法的距离扩展目标方向检测器。通过理论推导证明了这2种检测器相对于未知杂波协方差矩阵都具有恒虚警率。对比相同背景下已有检测器,特别是在辅助数据有限的场景下,文章提出的2个检测器表现出了优越的检测性能。

自适应Ⅱ型逐步截尾双应力恒加试验统计分析

针对传统加速寿命试验仅考虑单一加速应力和单一失效模式的问题,研究寿命服从Weibull分布且失效模式相互独立的竞争失效产品,在自适应Ⅱ型逐步截尾下建立双应力恒加试验的统计分析方法。通过Newton-Raphson迭代和渐进似然理论得到未知参数的极大似然估计和渐进置信区间。采用Gibbs抽样与M-H抽样混合算法获得参数的Bayes估计并基于MC方法构建HPD可信区间。数值模拟结果表明所提的方法具有良好的统计推断性能且失效样本数和试验时间对估计效果有显著影响。

基于嵌套剖分的位姿图分层优化算法

位姿图优化(pose graph optimization,PGO)是一种在同时定位与地图构建(simultaneous localization and mapping,SLAM)后端优化中常用的高维非凸优化算法,通常建模成极大似然估计。由于目前的PGO算法优化大规模大噪声数据集时很难在保证精度的同时提升速度,所以提出了一种基于嵌套剖分的位姿图分层优化算法。该算法首先建立不同距离度量的χ2检验模型,进而剔除异常值点。然后利用嵌套剖分算法将位姿图分割成一组子图,再从这些子图中提取出一个表示原SLAM问题的抽象拓扑的骨架图,从而优化该骨架图,完成初始化。最后在模拟和真实的位姿图数据集上进行实验评估,结果表明该算法在不影响精度的情况下,可以提高算法的计算速度,具有可伸缩性。

双应力恒加寿命试验可靠性评估模型

为了更加有效地评估高可靠长寿命产品的可靠性,针对传统双应力恒加寿命试验加速模型中只考虑各应力之间独立的问题,采用综合双应力之间相互影响的加速模型,探讨Gompertz分布型产品的可靠性评估问题,给出了产品的可靠性评估模型。基于定数截尾双应力恒加寿命试验下的数据,利用极大似然理论,计算了参数的极大似然估计,获得了与似然函数相关的Fisher信息矩阵和协方差矩阵,由此利用渐近似然理论构建了参数和可靠度的渐近置信区间。算例结果表明了所使用的方法具有可行性。

Parameters Estimation of a Bivariate Generalized Poisson Distribution with Applications to Metabolic Syndrome Data

Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.

逐步Ⅰ型混合截尾下复合Rayleigh分布竞争失效产品部分步加寿命试验的统计分析

本文在逐步Ⅰ型混合截尾下,研究复合Rayleigh分布竞争失效产品部分步加寿命试验的统计分析问题。首先,基于复合Rayleigh分布竞争失效产品和损伤失效率(TFR)模型,运用极大似然理论和渐近似然理论,给出未知参数和加速因子的极大似然估计和渐近置信区间;然后,对未知参数和加速因子选取先验,利用MH抽样算法获得参数和加速因子的Bayes估计和最大后验密度置信区间(HPD);最后,通过Monte Carlo模拟对2种估计方法进行比较。结果表明:贝叶斯估计效果整体优于极大似然估计(MLE),在相同置信水平下,基于Bayes估计的HPD置信区间长度略短于MLE的渐近置信区间长度。

Hypothesis testing analysis and unknown parameter estimation of GPS signal detection

Hypothesis testing analysis and unknown parameter estimation of both the intermediate frequency(IF) and baseband GPS signal detection are given by using the generalized likelihood ratio test(GLRT) approach,applying the model of GPS signal in white Gaussian noise,It is proved that the test statistic follows central or noncentral F distribution,It is also pointed out that the test statistic is nearly identical to central or noncentral chi-squared distribution because the processing samples are large enough to be considered as infinite in GPS acquisition problem.It is also proved that the probability of false alarm,the probability of detection and the threshold are affected largely when the hypothesis testing refers to the full pseudorandom noise(PRN) code phase and Doppler frequency search space cells instead of each individual cell.The performance of the test statistic is also given with combining the noncoherent integration.

The Latest Progress in Varying-coefficient Models

Varying-coefficient models are a useful extension of classical linear model. They are widely applied to economics, biomedicine, epidemiology, and so on. There are extensive studies on them in the latest three decade years. In this paper, many of models related to varying-coefficient models are gathered up. All kinds of the estimation procedures and theory of hypothesis test on the varying-coefficients model are summarized. Prom my opinion, some aspects waiting to study are proposed.

OUTLIER TEST IN RANDOMIZED LINEAR MODEL

In this papert we give an approach for detecting one or more outliers inrandomized linear model.The likelihood ratio test statistic and its distributions underthe null hypothesis and the alternative hypothesis are given. Furthermore,the robustnessof the test statistic in a certain sense is proved. Finally,the optimality properties of thetest are derived.