CONVERGENCE OF ITERATION METHODS OF MAXIMUM LIKELIHOOD ESTIMATOR AND ITS APPLICATIONS

Iteration methods and their convergences of the maximum likelihoodestimator are discussed in this paper.We study Gauss-Newton method and give a set ofsufficient conditions for the convergence of asymptotic numerical stability.The modifiedGauss-Newton method is also studied and the sufficient conditions of the convergence arepresented.Two numerical examples are given to illustrate our results.

Maximum likelihood spectrum estimation method and its application in seismo－magnet－icrelation

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EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.

Maximum Likelihood Estimation of the Identification Parameters and Its Correction

By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of the identification parameters is given. In order to decrease the asymptotic error, a corrector of maximum likelihood (CML) estimation with its recursive algorithm is given. It has been proved that the corrector has smaller asymptotic error than the least square methods. A simulation example shows that the corrector of maximum likelihood estimation is of higher approximating precision to the true parameters than the least square methods.

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.

Singularity of Some Software Reliability Models and Parameter Estimation Method

According to the principle, “The failure data is the basis of software reliability analysis”, we built a software reliability expert system (SRES) by adopting the artificial intelligence technology. By reasoning out the conclusion from the fitting results of failure data of a software project, the SRES can recommend users “the most suitable model” as a software reliability measurement model. We believe that the SRES can overcome the inconsistency in applications of software reliability models well. We report investigation results of singularity and parameter estimation methods of experimental models in SRES.

基于改进权函数距离的机器人运动偏差补偿算法设计

针对机器人在组装和生产过程中,由于几何参数存在一定误差,使连杆以及关节处等不可避免地出现细微差别,对机器人运动精度产生一定影响问题,提出了基于改进权函数距离的机器人运动偏差补偿算法设计方案。在定位机器人位置前添加扭角,获取机器人两坐标系间转换矩阵,根据线性标定计算机器人运动定位的绝对误差,利用改进权函数建立机器人距离误差数学模型,初步补偿运动误差。计算机器人末端执行器中心点位置和姿态的偏差,将补偿问题转化成机器人运动优化问题,得出运动偏差优化问题目标函数,经多次迭代得出最终补偿结果。实验结果表明,所提方法的误差补偿效果佳,重心补偿后的机器人运行稳定性好。

基于多应用场景的改进DV-Hop定位模型

针对距离矢量跳(DV-Hop)定位模型定位精度低、优化策略场景依赖性强的问题,提出一种基于函数分析和模拟定参的改进DV-Hop模型——函数修正距离矢量跳(FuncDV-Hop)定位模型。首先,分析DV-Hop模型的平均跳距、距离估计和最小二乘法中的误差原因,引入待定系数优化、阶跃函数分段实验、带等效点的权重函数策略和极大似然估计修正;其次,考虑多应用场景,用控制变量法,分别将总节点数、信标节点比例、通信半径、信标节点数和待测节点数作为变量,设计对照实验;最后,进行仿真定参和整合优化测试两阶段实验,最终的改进策略较原DV-Hop模型的定位精度提高了23.70%~75.76%,平均优化率57.23%。实验结果表明,FuncDV-Hop模型的优化率最高达到了50.73%,与基于遗传算法和神经动力学改进的DV-Hop模型相比,FuncDV-Hop模型的优化率提升了0.55%~18.77%。所提模型不引入其他参量,不增加无线传感器网络(WSN)的协议开销,且有效提高定位精度。

广义指数几何分布的扩展及参数估计

在广义指数几何分布的基础上对参数进行扩展,提出了一种新的寿命分布。旨在通过这种扩展,增强模型针对一些数据的拟合能力,从而更准确地进行寿命预测和可靠性分析。采用极大似然估计法对新提出的分布进行参数估计,并通过牛顿迭代法求解复杂的参数估计问题。对选定样本数据进行估计求解,并将模型与实际观测数据进行了对比。模型的拟合优度通过AIC和BIC值与其他模型进行了比较,结果表明新提出的扩展广义指数几何分布在拟合观测数据方面表现出较好的效果。

基于威布尔分布的风功率密度计算方法比较

[目的]风功率密度是风资源评估重要参数之一,准确地计算风功率密度有赖于风频威布尔分布拟合的准确性,对它进行正确地分析和评估有助于降低投资风险和提高投资决策的可靠性。针对目前风资源评估缺少威布尔分布拟合准确性方面的研究,文章旨通过研究比较那种威布尔分布拟合具有较高的精度,从而提高风资源评估的准确性。[方法]对目前国内外采用的5种威布尔模拟风频分布的方法进行研究,引入决定系数来确定威布尔模拟的准确度,比较威布尔函数计算风功率密度与实测数据计算风功率密度绝对误差和相对误差大小。[结果]结果表明:能量因子法EPF和最大似然法MLE模拟出来的威布尔拟合决定系数高于其他方法,包括经验法(EPJ和EPL)和最小二乘法(LLSA)。用这两种方法所得的参数计算风功率密度,与实测数据计算所得的风功率密度相比较,其绝对误差和相对误差也小于其他3种方法。[结论]研究结果可为风资源评估时选择何种威布尔方法计算风功率密度提供参考依据,客观地反应风电场风资源情况,提高风资源评估的准确性。

基于树小波压缩与最大似然的超宽带信道融合估计方法

为实现无人集群智能化巡检,针对脉冲超宽带技术在山区、森林等复杂地区的应用劣势,提出应对复杂环境下多径效应影响的信道估计方法。通过理论分析与实验研究,提出一种基于树小波压缩与最大似然法融合的信道估计方法(TS-SC)。该方法在贝叶斯压缩感知(CS)模型基础上,通过小波基的稀疏矩阵与马尔可夫链蒙特卡洛抽样,建立层次贝叶斯模型,以实现低速采样下原始信号的恢复。采用最大似然估计方法(SC)对多径数量和增益进行准确估计。实验结果表明:噪声SNR为10dB时,借助低频采样数据,检测精度能达到0.5592,满足复杂环境中信道估计的需求。研究成果突破了传统信道估计方法的局限,为复杂环境下的无人机集群通信提供了有效解决方案。

长记忆时间序列的均值单变点估计

文章采用拟极大似然法估计了一类长记忆时间序列模型的单均值变点,在变点大小固定和变点收缩两种情形下分析了估计量的渐近性质。研究发现,变点大小与长记忆性之间存在一种权衡关系。具体而言,当变点大小固定时,变点估计量是不相合的,而变分点估计量是T-相合的;当变点收缩时,变点估计量的收敛速度依赖于记忆参数d,估计量的极限分布得以推导。最后,蒙特卡洛实验和实证分析验证了所提理论结果的有限样本表现。

非接触式纵梁折弯高度检测方法研究

随着变宽度车架使用越来越多,各种非接触式测量方案应用越来越广泛。借助非接触式距离测量设备,快速检测变宽度车架的Z型面高度差,在此基础上通过多点测量、统计数据极大似然估计,构建数学模型,运用最小二乘法拟合直线,并利用计算点与直线的距离来快速判断测量平面与基准平面的间距的方案。通过多次测量以及统计学分析,可实现使用低精度设备达到高精度测量的思路,系统误差约为原来的2/3。研究结果可为快速检测车架纵梁折弯高度提供依据,在大幅度提升测量效率的同时保持较高的稳定性。

Estimation for constant-stress accelerated life test from generalized half-normal distribution

In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.

On the Estimation of a Univariate Gaussian Distribution: A Comparative Approach

Estimation of the unknown mean, μ and variance, σ2 of a univariate Gaussian distribution given a single study variable x is considered. We propose an approach that does not require initialization of the sufficient unknown distribution parameters. The approach is motivated by linearizing the Gaussian distribution through differential techniques, and estimating, μ and σ2 as regression coefficients using the ordinary least squares method. Two simulated datasets on hereditary traits and morphometric analysis of housefly strains are used to evaluate the proposed method (PM), the maximum likelihood estimation (MLE), and the method of moments (MM). The methods are evaluated by re-estimating the required Gaussian parameters on both large and small samples. The root mean squared error (RMSE), mean error (ME), and the standard deviation (SD) are used to assess the accuracy of the PM and MLE;confidence intervals (CIs) are also constructed for the ME estimate. The PM compares well with both the MLE and MM approaches as they all produce estimates whose errors have good asymptotic properties, also small CIs are observed for the ME using the PM and MLE. The PM can be used symbiotically with the MLE to provide initial approximations at the expectation maximization step.

A New Modified Inverse Lomax Distribution: Properties, Estimation and Applications to Engineering and Medical Data

In this paper,a modified form of the traditional inverse Lomax distribution is proposed and its characteristics are studied.The new distribution which called modified logarithmic transformed inverse Lomax distribution is generated by adding a new shape parameter based on logarithmic transformed method.It contains two shape and one scale parameters and has different shapes of probability density and hazard rate functions.The new shape parameter increases the flexibility of the statistical properties of the traditional inverse Lomax distribution including mean,variance,skewness and kurtosis.The moments,entropies,order statistics and other properties are discussed.Six methods of estimation are considered to estimate the distribution parameters.To compare the performance of the different estimators,a simulation study is performed.To show the flexibility and applicability of the proposed distribution two real data sets to engineering and medical fields are analyzed.The simulation results and real data analysis showed that the Anderson-Darling estimates have the smallest mean square errors among all other estimates.Also,the analysis of the real data sets showed that the traditional inverse Lomax distribution and some of its generalizations have shortcomings in modeling engineering and medical data.Our proposed distribution overcomes this shortage and provides a good fit which makes it a suitable choice to model such data sets.

Parameter Estimations for Generalized RayleighDistribution under Progressively Type-I IntervalCensored Data

In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum likelihood, moment method and probability plot are derived, and their performance are compared based on simulation results in terms of the mean squared error and bias. A case application of plasma cell myeloma data is used for illustrating the proposed estimation methods.

Estimation and Forecasting Survival of Diabetic CABG Patients (Kalman Filter Smoothing Approach)

In this paper, we present a new approach (Kalman Filter Smoothing) to estimate and forecast survival of Diabetic and Non Diabetic Coronary Artery Bypass Graft Surgery (CABG) patients. Survival proportions of the patients are obtained from a lifetime representing parametric model (Weibull distribution with Kalman Filter approach). Moreover, an approach of complete population (CP) from its incomplete population (IP) of the patients with 12 years observations/follow-up is used for their survival analysis [1]. The survival proportions of the CP obtained from Kaplan Meier method are used as observed values yt?at time t (input) for Kalman Filter Smoothing process to update time varying parameters. In case of CP, the term representing censored observations may be dropped from likelihood function of the distribution. Maximum likelihood method, in-conjunction with Davidon-Fletcher-Powell (DFP) optimization method [2] and Cubic Interpolation method is used in estimation of the survivor’s proportions. The estimated and forecasted survival proportions of CP of the Diabetic and Non Diabetic CABG patients from the Kalman Filter Smoothing approach are presented in terms of statistics, survival curves, discussion and conclusion.

Quasi-Negative Binomial: Properties, Parametric Estimation, Regression Model and Application to RNA-SEQ Data

Background: The Poisson and the Negative Binomial distributions are commonly used to model count data. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial has a variance larger than the mean and therefore both models are appropriate to model over-dispersed count data. Objectives: A new two-parameter probability distribution called the Quasi-Negative Binomial Distribution (QNBD) is being studied in this paper, generalizing the well-known negative binomial distribution. This model turns out to be quite flexible for analyzing count data. Our main objectives are to estimate the parameters of the proposed distribution and to discuss its applicability to genetics data. As an application, we demonstrate that the QNBD regression representation is utilized to model genomics data sets. Results: The new distribution is shown to provide a good fit with respect to the “Akaike Information Criterion”, AIC, considered a measure of model goodness of fit. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling count data exhibiting overdispersion, arising in various fields of scientific investigation such as genomics and biomedicine.

基于改进贝叶斯的重型数控机床可靠性研究

重型数控机床在机械加工领域占据重要地位,因此提高其可靠性以及加工精度,对我国工业发展有重要意义。重型数控机床具有结构复杂、故障溯源困难、样本少、数据不足等缺点,因此对其进行可靠性研究比较困难。针对这一问题,采用双参数的威布尔分布建立机床的可靠性模型,引入贝叶斯理论对其进行参数估计,并通过马尔科夫链蒙特卡洛方法(MCMC)计算参数估计结果。对贝叶斯参数估计法中的待估参数进一步分析,得到多层次的贝叶斯模型,并通过参数仿真实验分析其准确性。采用标准均方根误差值及置信区间宽度进行模型优劣的对比,结果表明,改进后的贝叶斯方法参数估计结果精度更优,更有利于建立机床可靠性模型。