关于广义压缩最小二乘估计的注记

本文研究了广义压缩最小二乘估计（ＧＳＬＳＥ）的一些性质，给出了它的均方误差（ＭＳＥ）的一个无偏估计量（ＵＥ），采用极小该ＵＥ的方法确定了ＧＳＬＳＥ的参数选取公式，并把这个统一化的方法应用于广义岭估计，岭估计、Ｍａｓｓｙ主成分估计、Ｓｔｅｉｎ型压缩估计以及根方有偏估计等，从而得到了它们的一种选取参数的方法，最后，结合Ｈａｌｄ实例进行比较分析，结果表明，本文的方法是实用的，有效的。     

增长曲线模型回归系数的广义岭估计

本文采用广义岭估计β（Ｋ）来估计增长曲线模型中回归系数β＝ｖｅｃ（Ｂ），通过Ｋ值的选取，可使其均方误差（ＭＳＥ）小于ＬＳ估计β的ＭＳＥ。同时对ＬＳ估计的任一线性变换，给出了其均方误差的一个无偏估计，并应用极小化β（Ｋ）的ＭＳＥ的无偏估计的方法，得到了确定岭参数的公式。     

相依回归模型的参数估计的风险估计

本文给出了相依回归模型的ＯＬＳ估计，ＧＬＳ估计和ＲＧＬＳ估计在二次损失和Ｆｉｓｈｅｒ损失下的风险估计不等式。     

回归系数的stein型主成分估计

对于设计阵Ｘ呈病态的线性回归模型，本文提出了一种新的关于回归系数的有偏估计─ｓｔｅｉｎ型主成分估计，并在均方误差意义下，论证了在一定条件下ｓｔｅｉｎ型主成分估计优于主成分估计，因此也优于ｓｔｅｉｎ型ＯＬＳ估计与ＯＬＳ估计，最后，我们又对偏参数的存在性，最优性进行了讨论，并得出了一些重要结论．     

协方差改进估计与相依混合效应回归方程

本文首先讨论了广义线性模型Ｙ＝Ｘβ＋ε（ε～（Ｏ，Ｖ））的系数β的最优线性无偏估计是用Ｔ２＝ＸＹ作为伴随变量对最小二乘估计Ｔ１＝（ＸＸ）－１Ｘ１Ｙ进行改进而得到的协方差改进估计．并把所得结果用于经济领域中的线性相依回归方程系统（ＳｅｅｍｉｎｇｌｙＵｎｒｅｌａｔｅｄＲｅｇｒｅｓｓｉｏｎＥｑａｕｔｉｏｎｓＳｙｓｔｅｍ）．然后关于一类线性相依混合效应回归方程系统，提出了一种优化估计方法。     

迭代函数系统的吸引子的维数估计

某些迭代函数系统（ＩＦＳ）的吸引子的Ｈａｕｓｄｏｒｆ维数的经典估计通常由求解两个非线性方程的解得到．在相同条件下，本文给出了一些显式不等式估计，使经典估计是其中的特殊情形．而且某些ＩＦＳ的吸引子的维数可以通过求解满足一定条件的非线性方程而得出     

迭代函数系统的吸收子的维数估计

某些迭代函数系统（ＩＦＳ）的吸引子的Ｈａｕｓｄｏｒｆｆ维数的经典估计通常由求解两个非线性方程的解得到。要相同条件下，本文给出卫些显示不等式估计，使经典估计是其中的特殊情形，而且某些ＩＦＳ是吸引子的维数可以通过求解满足一定条件的线性方程而得出。     

高阶Schrodinger方程的整体强解

本文首先引入高阶Ｓｃｈｒｏｄｉｎｇｅｒ方程容许对的概念，进而给出了线性亢介Ｓｃｈｒｏｄｉｎｇｅｒ方程解的空间时估计，利用空时估计及非线性函数的估计，证明了高阶非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程整体强解的存在唯一性。     

方差分量线性模型中回归系数和参数的所有可容许线性估计

对固定效应方差分量模型，在矩阵损失（ｄ－Ｓ＿τ）（ｄ－Ｓ＿τ）＇下，我们给出了线性可估函数Ｓτ的线性估计在一切估计类中可容许的充要条件；对具有两个方差分量的随机效应线性模型在矩阵损失（ｄ－Ｓα－Ｑβ）（ｄ－Ｓα－Ｑβ）＇下，我们给出了线性可估函数Ｓα＋Ｑβ的线性估计在一切估计类中可容许的充要条件。     

单位球上线性不变族的偏差定理

若Ｓ为 ｎ中的单位球Ｂｎ上的线性不变族，ｆ∈Ｓ，本文给出Ｔｒ（Ｊｆ（ｚ）Ｊｆ（ｚ））的估计，这里Ｊｆ（ｚ）为ｆ的Ｊａｃｏｂｉ矩阵，也给出了ｄｅｔ（Ｊｆ（ｚ）Ｊｆ（ｚ））的估计的一个新证明．若Ｓ为Ｂｎ上的正规化双全纯凸映照，ｆ∈Ｓ；还给出了ｆ的共变导数的估计．     

Numerically stable and efficient algorithm for vector channel parameter and frequency offset estimation

In this paper, we present a novel and numerically efficient algorithm for vector channel and calibration vector estimation, which works when frequency offset error caused by either unstable oscillator or Doppler effect is present in Spread Spectrum antenna system. We propose an estimation algorithm based on Gauss–Seidal algorithm rather than using eigen-decomposition or SVD in computing eigenvalues and eigenvectors at each iteration. The algorithm is based on the two-step procedures, one for estimating both channel and frequency offset and the other for estimating the unknown array gain and phase. Consequently, estimates of the DOAs, the multi-path impulse response of the reference signal source, and the carrier frequency offset as well as the calibration of antenna array are provided. The analytic performance improvement in multiplications number is presented. The performance of the proposed algorithm is investigated by means of computer simulations. Throughout the analytic and computer simulation, we show that the proposed algorithm reduces the number of multiplications by order of one.     

Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration

The Newton iteration is basic for solving nonlinear optimization problems and studying parameter estimation algorithms. In this letter, a maximum likelihood estimation algorithm is developed for estimating the parameters of Hammerstein nonlinear controlled autoregressive autoregressive moving average (CARARMA) systems by using the Newton iteration. A simulation example is provided to show the effectiveness of the proposed algorithm.     

An implicit least squares algorithm for nonlinear rational model parameter estimation

In this study a new insight into least squares regression is identified and immediately applied to estimating the parameters of nonlinear rational models. From the beginning the ordinary explicit expression for linear in the parameters model is expanded into an implicit expression. Then a generic algorithm in terms of least squares error is developed for the model parameter estimation. It has been proved that a nonlinear rational model can be expressed as an implicit linear in the parameters model, therefore, the developed algorithm can be comfortably revised for estimating the parameters of the rational models. The major advancement of the generic algorithm is its conciseness and efficiency in dealing with the parameter estimation problems associated with nonlinear in the parameters models. Further, the algorithm can be used to deal with those regression terms which are subject to noise. The algorithm is reduced to an ordinary least square algorithm in the case of linear or linear in the parameters models. Three simulated examples plus a realistic case study are used to test and illustrate the performance of the algorithm.     

Mixture Modeling for Longitudinal Data

In this article, we propose an unbiased estimating equation approach for a two-component mixture model with correlated response data. We adapt the mixture-of-experts model and a generalized linear model for component distribution and mixing proportion, respectively. The new approach only requires marginal distributions of both component densities and latent variables. We use serial correlations from subjects’ subgroup memberships, which improves estimation efficiency and classification accuracy, and show that estimation consistency does not depend on the choice of the working correlation matrix. The proposed estimating equation is solved by an expectation-estimating-equation (EEE) algorithm. In the E-step of the EEE algorithm, we propose a joint imputation based on the conditional linear property for the multivariate Bernoulli distribution. In addition, we establish asymptotic properties for the proposed estimators and the convergence property using the EEE algorithm. Our method is compared to an existing competitive mixture model approach in both simulation studies and an election data application. Supplementary materials for this article are available online.     

A RECURSIVE ALGORITHM AND ITS CONVERGENCE FOR PARAMETER ESTIMATION OF CONVOLUTION MODEL

In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the convergence of this algorithm is theoretically discussed, and a sufficient condition for the convergence criterion of the orthogonal procedure is given. According to this condition, the recursive algorithm is convergent to model wavelet A- = （1, α1,..., αq）.     

Limiting optimal adaptive filtering with unknown disturbance covariance

The accuracy of estimating the variance of the Kalman-Bucy filter depends essentially on disturbance covariance matrices and measurement noise. The main difficulty in filter design is the lack of necessary statistical information about the useful signal and the disturbance. Filters whose parameters are tuned during active estimation are classified with adaptive filters. The problem of adaptive filtering under parametric uncertainty conditions is studied. A method for designing limiting optimal Kalman-Bucy filters in the case of unknown disturbance covariance is presented. An adaptive algorithm for estimating disturbance covariance matrices based on stochastic approximation is described. Convergence conditions for this algorithm are investigated. The operation of a limiting adaptive filter is exemplified.     

变环境情形下Weibull分布分组数据的参数估计

本文研究了变环境情形下Weibull分布分组数据可靠性估计的参数估计问题。给出一种基于EM算法的变环境分组数据Weibull分布参数估计方法,所得估计量具有良好的收敛性,模拟结果表明方法的实践可用性。     

Estimating 2‐cycle fixed points of henon map using backpropagation neural networks

The objective of this research is the presentation of a feed‐forward neural network capable of estimating the 2‐cycle fixed points of Henon map by solving their defining nonlinear algebraic system. The network uses the back propagation algorithm and solves the aforementioned system for a set of values of the parameters α and β of Henon map. Besides the estimation of the fixed points, the paper includes the study of the network convergence and its speed for many different initial conditions. Copyright © 2013 John Wiley & Sons, Ltd.     

Variational Approximations for Generalized Linear Latent Variable Models

Generalized linear latent variable models (GLLVMs) are a powerful class of models for understanding the relationships among multiple, correlated responses. Estimation, however, presents a major challenge, as the marginal likelihood does not possess a closed form for nonnormal responses. We propose a variational approximation (VA) method for estimating GLLVMs. For the common cases of binary, ordinal, and overdispersed count data, we derive fully closed-form approximations to the marginal log-likelihood function in each case. Compared to other methods such as the expectation-maximization algorithm, estimation using VA is fast and straightforward to implement. Predictions of the latent variables and associated uncertainty estimates are also obtained as part of the estimation process. Simulations show that VA estimation performs similar to or better than some currently available methods, both at predicting the latent variables and estimating their corresponding coefficients. They also show that VA estimation offers dramatic reductions in computation time particularly if the number of correlated responses is large relative to the number of observational units. We apply the variational approach to two datasets, estimating GLLVMs to understanding the patterns of variation in youth gratitude and for constructing ordination plots in bird abundance data. R code for performing VA estimation of GLLVMs is available online. Supplementary materials for this article are available online.     

Adaptive varying-coefficient linear quantile model: a profiled estimating equations approach

We consider an estimating equations approach to parameter estimation in adaptive varying-coefficient linear quantile model. We propose estimating equations for the index vector of the model in which the unknown nonparametric functions are estimated by minimizing the check loss function, resulting in a profiled approach. The estimating equations have a bias-corrected form that makes undersmoothing of the nonparametric part unnecessary. The estimating equations approach makes it possible to obtain the estimates using a simple fixed-point algorithm. We establish asymptotic properties of the estimator using empirical process theory, with additional complication due to the nuisance nonparametric part. The finite sample performance of the new model is illustrated using simulation studies and a forest fire dataset.