Nonlinear semiparametric AR(1) model with skew-symmetric innovations

In this paper, we expand a first-order nonlinear autoregressive (AR) model with skew normal innovations. A semiparametric method is proposed to estimate a nonlinear part of model by using the conditional least squares method for parametric estimation and the nonparametric kernel approach for the AR adjustment estimation. Then computational techniques for parameter estimation are carried out by the maximum likelihood (ML) approach using Expectation-Maximization (EM) type optimization and the explicit iterative form for the ML estimators are obtained. Furthermore, in a simulation study and a real application, the accuracy of the proposed methods is verified.     

Conditional mix-GEE models for longitudinal data with unspecified random-effects distributions

In the longitudinal studies, the mixture generalized estimation equation (mix-GEE) was proposed to improve the efficiency of the fixed-effects estimator for addressing the working correlation structure misspecification. When the subject-specific effect is one of interests, mixed-effects models were widely used to analyze longitudinal data. However, most of the existing approaches assume a normal distribution for the random effects, and this could affect the efficiency of the fixed-effects estimator. In this article, a conditional mixture generalized estimating equation (cmix-GEE) approach based on the advantage of mix-GEE and conditional quadratic inference function (CQIF) method is developed. The advantage of our new approach is that it does not require the normality assumption for random effects and can accommodate the serial correlation between observations within the same cluster. The feature of our proposed approach is that the estimators of the regression parameters are more efficient than CQIF even if the working correlation structure is not correctly specified. In addition, according to the estimates of some mixture proportions, the true working correlation matrix can be identified. We establish the asymptotic results for the fixed-effects parameter estimators. Simulation studies were conducted to evaluate our proposed method.     

Gamma lifetimes and associated inference for interval-censored cure rate model with COM–Poisson competing cause

In this article, we consider a competing cause scenario and assume the wider family of Conway–Maxwell–Poisson (COM–Poisson) distribution to model the number of competing causes. Assuming the type of the data to be interval censored, the main contribution is in developing the steps of the expectation maximization (EM) algorithm to determine the maximum likelihood estimates (MLEs) of the model parameters. A profile likelihood approach within the EM framework is proposed to estimate the COM–Poisson shape parameter. An extensive simulation study is conducted to evaluate the performance of the proposed EM algorithm. Model selection within the wider class of COM–Poisson distribution is carried out using likelihood ratio test and information-based criteria. A study to demonstrate the effect of model mis-specification is also carried out. Finally, the proposed estimation method is applied to a data on smoking cessation and a detailed analysis of the obtained results is presented.     

Estimation and prediction for an inverted exponentiated Rayleigh distribution under hybrid censoring

In this paper we consider estimation of unknown parameters of an inverted exponentiated Rayleigh distribution when it is known that data are hybrid Type I censored. The maximum likelihood and Bayes estimates are derived. In sequel interval estimates are also constructed. We further consider one- and two-sample prediction of future observations and also obtain prediction intervals. The performance of proposed methods of estimation and prediction is studied using simulations and an illustrative example is discussed in support of the suggested methods.     

A Note on “Shaved Dice” Inference

Two dice are rolled repeatedly, only their sum is registered. Have the two dice been “shaved,” so two of the six sides appear more frequently? Pavlides and Perlman discussed this somewhat complicated type of situation through curved exponential families. Here, we contrast their approach by regarding data as incomplete data from a simple exponential family. The latter, supplementary approach is in some respects simpler, it provides additional insight about the relationships among the likelihood equation, the Fisher information, and the EM algorithm, and it illustrates the information content in ancillary statistics.     

电磁导弹的初步实验

报导了电磁导弹的初步实验.实验结果表明:单频连续波在瑞利距离之后的确表现为随距离的反平方律(r~(-2))衰减;与此不同,脉冲电磁波在离源较远时具有较慢的衰减规律(如r~(-2),0<ε<1).被称为“电磁导弹”的慢衰减电磁波无论在理论上,还是在工程应用上都具有相当重要的意义.     

用复射线法分析凹槽散射

凹槽散射是开口腔结构的一种典型代表。用复射线方法十分简便地实现了凹槽结构散射宽度的预估，并用ＧＴＤ理论对复射线场在入射口面边缘上的绕射场贡献作了简化处理，计算结果与射线模式法所得结果吻合较好，但简化算法却可节省大量计算机时间。     

混合双参数指数分布的参数估计

混合指数分布是寿命数据分析中一个非常重要的分布。但是利用矩估计、极大似然估计等估计模型的参数往往比较困难。本文应用EM算法详细研究了混合双指数分布在正常工作条件下,在完全数据场合的参数估计问题。模拟说明利用EM算法来估计混合双指数分布是一种非常有效的方法,随着样本的增加,估计值离真值越来越近,估计值的方差越来越小。     

Mixture Model Analysis of Partially Rank‐Ordered Set Samples: Age Groups of Fish from Length‐Frequency Data

We present a novel methodology for estimating the parameters of a finite mixture model (FMM) based on partially rank‐ordered set (PROS) sampling and use it in a fishery application. A PROS sampling design first selects a simple random sample of fish and creates partially rank‐ordered judgement subsets by dividing units into subsets of prespecified sizes. The final measurements are then obtained from these partially ordered judgement subsets. The traditional expectation–maximization algorithm is not directly applicable for these observations. We propose a suitable expectation–maximization algorithm to estimate the parameters of the FMMs based on PROS samples. We also study the problem of classification of the PROS sample into the components of the FMM. We show that the maximum likelihood estimators based on PROS samples perform substantially better than their simple random sample counterparts even with small samples. The results are used to classify a fish population using the length‐frequency data.