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 ...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）.展开更多
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 un...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.展开更多
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 ...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.展开更多
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 o...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.展开更多
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 d...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.展开更多
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 ...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.展开更多
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 modifi...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.展开更多
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 li...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.展开更多
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 asymptoti...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.展开更多
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 ...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.展开更多
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 th...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.展开更多
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 relati...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.展开更多
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 (...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).展开更多
因高度向分辨能力缺失,地基干涉雷达应用于建筑成像时会发生严重的高度向叠掩现象。层析合成孔径雷达(Tomographic Synthetic Aperture Radar,TomoSAR)技术具备高度向分辨能力,能够实现建筑三维成像。地基层析圆弧扫描合成孔径雷达(Grou...因高度向分辨能力缺失,地基干涉雷达应用于建筑成像时会发生严重的高度向叠掩现象。层析合成孔径雷达(Tomographic Synthetic Aperture Radar,TomoSAR)技术具备高度向分辨能力,能够实现建筑三维成像。地基层析圆弧扫描合成孔径雷达(Ground-based Tomographic Arc-scanning Synthetic Aperture Radar,GB-TomoArcSAR)通过双轴转台控制天线在不同俯仰角度的水平面内进行圆周扫描来获取高度向合成孔径,实现三维层析成像。本文提出了GB-TomoArcSAR的三维点云生成方法,首先构建了适用于高度向弧形采样条件的层析成像几何模型。其次利用基于巴特沃斯滤波器的奇异值分解(Singular Value Decomposition,SVD)方法进行谱估计,找出层析谱中的峰值及其对应的峰值位置,构成层析向目标候选集。随后利用自对消顺序广义似然比(Sequential Generalized Likelihood Ratio Test with Cancellation,SGLRTC)检测器估计散射体的数目与位置,通过设置检测门限将真实目标的峰值及对应的峰值位置从候选集中筛选出来。最后采用基于空间几何分布的点云优化方法剔除误差点,生成点云图像。文章通过点目标和面目标的仿真实验,验证了所提方法适用于GB-TomoArcSAR,能够有效解决高度向多散射体目标的叠掩问题;进一步开展了实测数据验证,基于所提方法获取了北京市一处建筑基坑的层析点云,其与实际场景几何特征一致。展开更多
基金Supported by the National Natural Science Foundation of China(10661003)the SRF for ROCS,SEM([2004]527)the NSF of Guangxi(0728092)
文摘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）.
文摘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.
文摘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.
文摘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.
文摘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.
基金supported by National Natural Science Foundation of China (Grant Nos. 61471019, 61501011)
文摘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.
基金the National Natural Science Foundation of China (Grant No. 10661003)the Natural Science Foundation of Guangxi (Grant No. 0728092) SRF for ROCS, SEM (Grant No. [2004]527)
文摘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.
基金supported by the National Natural Science Foundation of China under Grant No. 10661003SRF for ROCS, SEM under Grant No. [2004]527the Natm'aI Science Foundation of Guangxi under Grant No. 0728092
文摘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.
基金supported by the National Natural Science Foundation of China under Grant Nos.61065009 and 60972150
文摘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.
文摘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.
文摘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.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No.XDB10030302)the National Natural Science Foundation of China (No.41302233)the Project funded by China Postdoctoral Science Foundation (No.2014T70121)
文摘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.
文摘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).
文摘因高度向分辨能力缺失,地基干涉雷达应用于建筑成像时会发生严重的高度向叠掩现象。层析合成孔径雷达(Tomographic Synthetic Aperture Radar,TomoSAR)技术具备高度向分辨能力,能够实现建筑三维成像。地基层析圆弧扫描合成孔径雷达(Ground-based Tomographic Arc-scanning Synthetic Aperture Radar,GB-TomoArcSAR)通过双轴转台控制天线在不同俯仰角度的水平面内进行圆周扫描来获取高度向合成孔径,实现三维层析成像。本文提出了GB-TomoArcSAR的三维点云生成方法,首先构建了适用于高度向弧形采样条件的层析成像几何模型。其次利用基于巴特沃斯滤波器的奇异值分解(Singular Value Decomposition,SVD)方法进行谱估计,找出层析谱中的峰值及其对应的峰值位置,构成层析向目标候选集。随后利用自对消顺序广义似然比(Sequential Generalized Likelihood Ratio Test with Cancellation,SGLRTC)检测器估计散射体的数目与位置,通过设置检测门限将真实目标的峰值及对应的峰值位置从候选集中筛选出来。最后采用基于空间几何分布的点云优化方法剔除误差点,生成点云图像。文章通过点目标和面目标的仿真实验,验证了所提方法适用于GB-TomoArcSAR,能够有效解决高度向多散射体目标的叠掩问题;进一步开展了实测数据验证,基于所提方法获取了北京市一处建筑基坑的层析点云,其与实际场景几何特征一致。
