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
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,...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。展开更多
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 c...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.展开更多
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
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
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
利用球不变随机矢量(Spherically Invariant Random Vector,SIRV)描述非均匀杂波,建立了双基地多输入多输出(Multiple-Input Multiple-Qutput,MIMO)雷达距离扩展目标的信号检测模型,提出了距离扩展目标的两步广义似然比检测(Generalized...利用球不变随机矢量(Spherically Invariant Random Vector,SIRV)描述非均匀杂波,建立了双基地多输入多输出(Multiple-Input Multiple-Qutput,MIMO)雷达距离扩展目标的信号检测模型,提出了距离扩展目标的两步广义似然比检测(Generalized Likelihood Ratio Test,GLRT)算法.首先,根据目标散射系数的两种假设模型,分别推导确定型目标、高斯型目标GLRT检测器的解析表达式,然后利用固定点迭代算法估计杂波协方差矩阵,获得自适应GLRT(AD-GLRT和AG-GLRT)检测器.仿真实验表明:AD-GLRT和AG-GLRT检测器的检测性能均优于非均匀杂波背景、高斯杂波背景下点目标的检测性能,且两者的检测性能相当,并且虚拟阵元数、目标分布的距离单元数,以及信杂比越大,两者的检测性能越好.展开更多
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。
文摘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.
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.
文摘利用球不变随机矢量(Spherically Invariant Random Vector,SIRV)描述非均匀杂波,建立了双基地多输入多输出(Multiple-Input Multiple-Qutput,MIMO)雷达距离扩展目标的信号检测模型,提出了距离扩展目标的两步广义似然比检测(Generalized Likelihood Ratio Test,GLRT)算法.首先,根据目标散射系数的两种假设模型,分别推导确定型目标、高斯型目标GLRT检测器的解析表达式,然后利用固定点迭代算法估计杂波协方差矩阵,获得自适应GLRT(AD-GLRT和AG-GLRT)检测器.仿真实验表明:AD-GLRT和AG-GLRT检测器的检测性能均优于非均匀杂波背景、高斯杂波背景下点目标的检测性能,且两者的检测性能相当,并且虚拟阵元数、目标分布的距离单元数,以及信杂比越大,两者的检测性能越好.
