Asymptotic properties and expectation-maximization algorithm for maximum likelihood estimates of the parameters from Weibull-Logarithmic model

In this article, we consider a lifetime distribution, the Weibull-Logarithmic distri- bution introduced by [6]. We investigate some new statistical characterizations and properties. We develop the maximum likelihood inference using EM algorithm. Asymptotic properties of the MLEs are obtained and extensive simulations are conducted to assess the performance of parameter estimation. A numerical example is used to illustrate the application.

2-D DOA Estimation in a Cuboid Array Based on Metaheuristic Algorithms and Maximum Likelihood

This paper proposes to apply the genetic algorithm and the firefly algorithm to enhance the estimation of the direction of arrival (DOA) angle of electromagnetic signals of a smart antenna array. This estimation is essential for beamforming, where the antenna array radiating pattern is steered to provide faster and reliable data transmission with increased coverage. This work proposes using metaheuristics to improve a maximum likelihood DOA estimator for an antenna array arranged in a uniform cuboidal geometry. The DOA estimation performance of the proposed algorithm was compared to that of MUSIC on different two dimensions scenarios. The metaheuristic algorithms present better performance than the well-known MUSIC algorithm.

Genetic algorithm-based wide-band deterministic maximum likelihood direction finding algorithm

The wide-band direction finding is one of hit and difficult task in array signal processing. This paper generalizes narrow-band deterministic maximum likelihood direction finding algorithm to the wideband case, and so constructions an object function, then utilizes genetic algorithm for nonlinear global optimization. Direction of arrival is estimated without preprocessing of array data and so the algorithm eliminates the effect of pre-estimate on the final estimation. The algorithm is applied on uniform linear array and extensive simulation results prove the efficacy of the algorithm. In the process of simulation, we obtain the relation between estimation error and parameters of genetic algorithm.

A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

Maximum Likelihood Estimation of the Parameters of Exponentiated Generalized Weibull Based on Progressive Type II Censored Data

Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of the new probability distribution function are estimated by the maximum likelihood method under progressive type II censored data via expectation maximization algorithm.

Asymptotic Comparison of Method of Moments Estimators and Maximum Likelihood Estimators of Parameters in Zero-Inflated Poisson Model

This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.

Immune Clone Maximum Likelihood Estimation of Improved Non-homogeneous Poisson Process Model Parameters

Aiming at the solving problem of improved nonhomogeneous Poisson process( NHPP) model in engineering application,the immune clone maximum likelihood estimation( MLE)method for solving model parameters was proposed. The minimum negative log-likelihood function was used as the objective function to optimize instead of using iterative method to solve complex system of equations,and the problem of parameter estimation of improved NHPP model was solved by immune clone algorithm. And the interval estimation of reliability indices was given by using fisher information matrix method and delta method. An example of failure truncated data from multiple numerical control( NC) machine tools was taken to prove the method. and the results show that the algorithm has a higher convergence rate and computational accuracy, which demonstrates the feasibility of the method.

An Approximation Method for a Maximum Likelihood Equation System and Application to the Analysis of Accidents Data

There exist many iterative methods for computing the maximum likelihood estimator but most of them suffer from one or several drawbacks such as the need to inverse a Hessian matrix and the need to find good initial approximations of the parameters that are unknown in practice. In this paper, we present an estimation method without matrix inversion based on a linear approximation of the likelihood equations in a neighborhood of the constrained maximum likelihood estimator. We obtain closed-form approximations of solutions and standard errors. Then, we propose an iterative algorithm which cycles through the components of the vector parameter and updates one component at a time. The initial solution, which is necessary to start the iterative procedure, is automated. The proposed algorithm is compared to some of the best iterative optimization algorithms available on R and MATLAB software through a simulation study and applied to the statistical analysis of a road safety measure.

泰勒展开与交替投影最大似然结合的离网格DOA估计算法

针对最大似然DOA估计算法需要多维搜索、计算量大且面临着在网格估计的问题,该文提出一种基于泰勒展开的离网格交替投影最大似然算法。该方法首先利用交替投影将多维搜索转化为多个1维搜索,获得对应预设大网格的粗估计结果;再利用矩阵求导理论将1维代价函数在粗估计结果处进行2阶泰勒展开;最后通过对2阶泰勒展开求偏导并令导数等于零,求得离网参数的闭式解。与交替投影最大似然算法相比,该方法突破了搜索网格大小的限制,在保证算法精度的同时,有效减少了算法的在网格计算点数,提升了运算效率。仿真结果证明了该算法的有效性。

双边定时截尾下Pareto分布的参数的极大似然估计的EM算法

给出了当寿命分布为Pareto分布时,双边定时截尾寿命试验下形状参数的极大似然估计。由于似然方程形式较复杂,无法得到参数的显式表达式。但可证明此极大似然估计是唯一存在的,并利用EM算法求出了此参数的一种估计。

一种基于GABP神经网络的RIS辅助近场无线定位方法

可重构智能表面(RIS)是6G潜在关键技术,将其部署在无线通信系统中,可辅助基站对用户进行定位,并提高定位性能。在毫米波频段,由于频率较高,RIS面板的阵列孔径及反射单元个数较大,近场区域范围扩大,用户将大概率处于RIS的近场区域中。为此,考虑RIS辅助的无线通信系统在近场条件下对用户进行定位,将用户定位问题建模为参数估计问题,并利用最大似然估计来实现对用户三维坐标参数的估计。为求解所建立的最大似然估计问题,结合遗传算法与反向传播算法神经网络的优势,提出了一种计算效率更高的GABP算法。仿真结果表明,所提GABP算法比传统的遗传算法计算效率更高。

基于PSO和MLEM混合算法的NDP测量反演算法研究

中子深度剖面(NDP)分析技术是一种无损检测方法,能够同时测量样品中目标核素的浓度与空间信息,已被广泛应用于锂电池、半导体等产业。在NDP分析过程中,由测量能谱反演出目标核素浓度的分布信息是关键步骤。目前NDP测量反演中常用的算法为最大似然期望最大化(MLEM)算法。针对MLEM算法计算结果易陷入局部最优解的情况,本文提出了粒子群(PSO)与MLEM混合(PSO-MLEM)算法,并通过动态加速因子提高了算法的收敛速度与计算精度。应用PSO-MLEM算法、PSO算法、MLEM算法、奇异值分解求解最小二乘(SVDLS)算法对锂电池中^(6)Li的NDP模拟能谱进行反演,并对反演计算结果进行了评价。结果表明:对比PSO算法,PSO-MLEM算法的收敛效率与计算精度明显提升;对比MLEM算法,PSO-MLEM算法的全局寻优能力有效提升了反演精度,避免了局部最优解的影响;对比SVDLS算法,PSO-MLEM算法的反演精度明显提升。

面向高速PAM4有线收发机的自适应和低复杂度最大似然序列检测器

高速串行收发机是中央处理器、网卡和交换机等高性能芯片的关键部件.判决反馈均衡器(decision feedback equalization,DFE)是高速串行收发机的主要判决电路.针对传统DFE在高码间干扰(intersymbol interference,ISI)信道下的高误码率制约串行收发机速率提升的问题,提出一种面向4电平调制(4 pulse amplitude modulation,PAM4)串行收发机的自适应、低复杂度的减状态序列检测器(adaptive reduced-state sequence detector,ARSSD).ARSSD基于最大似然序列检测结构降低检测误码率;结合Viterbi算法和分区算法降低运算复杂度;采用基于迫零算法的ISI参数获取方式实现检测器参数的自适应更新.所提结构最终完成了行为仿真、电路设计以及系统验证.基于模拟前端芯片和现场可编程门阵列电路的实验结果表明,与传统DFE相比,当12~64 Gbps PAM4信号经过−8~−18 dB@16 GHz衰减信道时,32×4路并行ARSSD检测误码率降低2个数量级,与行为仿真结果一致.

一种多元均值混合正态分布参数的极大似然估计

以Madadi等提出的数学模型与概率密度函数为基础,证明了多元均值混合正态分布的性质,讨论了MMNE分布参数的极大似然估计问题,利用ECM算法对MMNE分布的位置参数、尺度参数、偏度参数进行了参数估计计算,给出了计算方法和迭代公式。实例分析表明,所提出的偏态数据下MMNE分布参数估计模型合理且实用。

基于改进帝王蝶算法的最大似然DOA估计

针对传统最大似然波达方向(maximum likelihood direction of arrival,ML-DOA)估计存在计算量大、估计精度差等问题,本文提出一种采用改进帝王蝶优化算法(improved monarch butterfly optimization algorithm,IMBO)的ML-DOA估计方法。IMBO算法通过精英反向学习策略对初始帝王蝶种群进行优化,得到适应度值较优的初始帝王蝶个体,进而能够改善帝王蝶种群的多样性;引入差分进化算法启发的变异操作以及自适应策略对帝王蝶个体的寻优方式进行改进,扩大了算法的搜索空间;引入了高斯-柯西变异算子,自适应调整变异步长,避免算法陷入局部最优。将IMBO应用于ML-DOA,实验表明,与传统的DOA估计算法相比,在不同信源数目、信噪比以及种群数量下,本文提出的算法收敛性能更好,均方根误差更低,运算量更小。

多元混合正态分布参数的极大似然估计

从层次结构的角度出发推导总结了Reinaldo B.Arellano-Vall所提出的广义多元混合正态分布公式中混合变量的相关统计性质,结合所推导的混合变量性质,运用EM算法和协方差矩阵参数化分解方法,解决多元混合正态分布在无序约束和简单树半序约束下参数的极大似然估计问题。借助MATLAB软件编程进行数据仿真模拟,并给出其协方差矩阵在简单树半序约束下的极大似然估计结果。

基于四元数表示的GraphSLAM位姿初始化算法

位姿估计问题本质上是一个非凸且NP-难问题,难以求解的原因在于位姿中包含特殊正交群,且往往拥有一个较差的初始值。针对此问题,提出了一种基于图的即时定位与建图技术位姿初始化算法。首先,使用两阶段算法将位姿估计问题构建的最大似然估计方程重新拆分为两个独立的子问题,即基于四元数表示的旋转平均问题和无约束的平移向量平均的线性方程问题。然后,通过迹松弛方式将非凸问题转化为线性方程问题。最后,结合平移向量计算出初始化的位姿。仿真实验表明,在高噪声的数据集中,所提方法比基于生成树的目标函数值降低了至少1个数量级,能够鲁棒地为位姿估计问题提供一个良好的初始值。

零一膨胀几何分布的统计分析及应用

研究了0−1膨胀几何分布模型,构造隐变量的条件分布,并设计抽样算法。在数据扩充的基础上,运用极大似然估计、期望极大(expectation maximization,EM)算法及贝叶斯方法对模型参数进行估计。设定不同的样本量和参数真值,通过数值模拟对上述方法进行性能评估。最后,对1994年美国底特律交通事故死亡数据集进行分析,研究表明,0−1膨胀几何分布模型能够较好地对该数据集进行拟合。

改进蚁群优化算法的最大似然DOA估计方法

针对将连续域蚁群优化算法应用于最大似然(maximum likelihood,ML)估计中存在计算量过大的问题,提出一种基于改进蚁群优化(modified ant colony optimization,MACO)算法的最大似然波达方向(maximum likelihood direction of arrival,ML-DOA)估计方法.采用精英反向学习策略获得较优初始解群体,结合全局跨邻域搜索和高斯核函数局部搜索对蚁群的寻优方式进行优化,扩大了算法的搜索空间并加快了收敛速度,最终得到ML估计方法的非线性全局最优解.仿真结果表明,与基于粒子群优化(particle swarm optimization,PSO)算法、蚁群优化(ant colony optimization,ACO)算法的ML估计方法相比,ML-MACO算法的收敛速度是ML-ACO算法的4倍,计算量是ML-ACO算法的1/3,分辨成功率高于ML-PSO算法和ML-ACO算法,估计误差小于ML-PSO算法和ML-ACO算法.ML-MACO算法以更低的计算量保持了ML算法的优良估计性能,收敛性能更优且估计精度更高.

复杂阵地的合成导向矢量最大似然测高

雷达在目标低仰角测高时存在严重的多径效应,复杂阵地使多径回波产生无规律反射,造成幅度与相位发生不同程度的畸变.本文引入扰动多径模型,解决经典多径模型与复杂阵地的多径回波反射不匹配问题,研究基于扰动模型的合成导向矢量最大似然(synthesized vector maximum likelihood, SVML)测高方法.该方法引入扰动参数表征复杂阵地的多径回波现象,利用基于稀疏贝叶斯学习的扰动多径(perturbational multipath sparse Bayesian learning,PSBL)算法得到扰动参数,应用于SVML算法,提高了米波雷达在复杂阵地下的测高性能.