Optimal adaptive estimation: Structure and parameter adaption

Optimal structure and parameter adaptive estimators have been obtained for continuous as well as discrete data Gaussian process models with linear dynamics. Specifically, the essentially nonlinear adaptive estimators are shown to be decomposable (partition theorem) into two parts, a linear nonadaptive part consisting of a bank of Kalman-Bucy filters and a nonlinear part that incorporates the adaptive nature of the estimator. The conditional-error-covariance matrix of the estimator is also obtained in a form suitable for on-line performance evaluation. The adaptive estimators are applied to the problem of state estimation with non-Gaussian initial state, to estimation under measurement uncertainty (joint detection-estimation) as well as to system identification. Examples are given of the application of the adaptive estimators to structure and parameter adaptation indicating their applicability to engineering problems.     

Sliding-mode and proportional-derivative-type motion control with radial basis function neural network based estimators for wheeled vehicles

An obstacle avoidance problem of rear-steered wheeled vehicles in consideration of the presence of uncertainties is addressed. Modelling errors and additional uncertainties are taken into consideration. Controller designs for driving and steering motors are designed. A proportional-derivative-type driving motor controller and a sliding-mode steering controller combined with radial basis function neural network (RBFNN) based estimators are proposed. The convergence properties of the RBFNN-based estimators are proven by the Stone–Weierstrass theorem. The stability of the proposed control law is proven using Lyapunov stability analysis. The obstacle avoidance strategy utilising the sliding surface adjustment to an existing navigation method is presented. It is concluded that the driving velocity and steering-angle performances of the proposed control system are satisfactory.     

考虑非标准车辆特殊行为的混合交通建模

在中国大多数的城市交通中,由机动车辆和非机动车辆组成了混合交通流。除了标准型车辆如各种出租车、私车、公交车和卡车外,还有非标准车辆如自行车、摩托车及其他改装车等。对于其中的非标准车来说,由于交通法规、道路状况和技术规范等对其约束较轻,出行的目的和路线更为灵活,不仅车辆的特性各有很大的不同,而且驾驶者的行为同标准车相比,更有着显著的差异。目前适合于分析包括非标准车在内的交通流的模型几乎没有,已有的方法将面临重大的模型改造。论文分析了混合交通流中非标准车辆的特点和驾驶者的行为特点,以及这些特殊行为对混合交通建模的影响因素。文章中讨论了采用一种模拟交通工具定位的方法并基于模糊逻辑规则控制的决策过程,并以此建立了用于混合交通的模型。该模型利用中国西安部分地区的数据来进行测试和评价。     

Algorithms for bounded-influence estimation

Bounded-influence estimation is a well developed and useful theory. It provides fairly efficient estimators which are robust to outliers and local model departures. However, its use has been limited thus far, mainly because of computational difficulties. A careful implementation in modern statistical software can effectively overcome the numerical problems of bounded-influence estimators. The proposed approach is based on general methods for solving estimating equations, together with suitable methods developed in the statistical literature, such as the delta algorithm and nested iterations. The focus is on Mallows estimation in generalized linear models and on optimal bias-robust estimation in models for independent data, such as regression models with asymmetrically distributed errors.     

Quadrotor Sensor Fault Diagnosis with Experimental Results

This paper presents a fault detection, isolation, and estimation scheme for sensor bias faults in accelerometer and gyroscope measurements of quadrotor unmanned air vehicles (UAVs). Based on sliding-mode observer techniques, a robust estimation of the quadrotor roll and pitch angles is obtained by using only accelerometer measurements. Then, a diagnostic scheme is developed for detecting, isolating, and estimating sensor bias faults in the gyroscope and accelerometer measurements. Structured residuals are generated, allowing the detection and isolation of multiple simultaneous sensor faults under consideration. After the faults are detected and isolated, two nonlinear estimators are employed to provide an estimate of the unknown fault magnitude. The stability and estimation performance properties of the nonlinear estimators are established. The sensor fault diagnosis algorithm is implemented and evaluated through experimental results using a real-time indoor quadrotor test environment.     

Multivariate distributions with proportional reversed hazard marginals

Several univariate proportional reversed hazard models have been proposed in the literature. Recently, Kundu and Gupta (2010) proposed a class of bivariate models with proportional reversed hazard marginals. It is observed that the proposed bivariate proportional reversed hazard models have a singular component. In this paper we introduce the multivariate proportional reversed hazard models along the same manner. Moreover, it is observed that the proposed multivariate proportional reversed hazard model can be obtained from the Marshall–Olkin copula. The multivariate proportional reversed hazard models also have a singular component, and their marginals have proportional reversed hazard distributions. The multivariate ageing and the dependence properties are discussed in details. We further provide some dependence measure specifically for the bivariate case. The maximum likelihood estimators of the unknown parameters cannot be expressed in explicit forms. We propose to use the EM algorithm to compute the maximum likelihood estimators. One trivariate data set has been analysed for illustrative purposes.     

Impact of unknown covariance structures in semiparametric models for longitudinal data: An application to Wisconsin diabetes data

Semiparametric models are becoming increasingly attractive for longitudinal data analysis. Often there is lack of knowledge of the covariance structure of the response variable. Although it is still possible to obtain consistent estimators for both parametric and nonparametric components of a semipatrametric model by assuming an identity structure for the covariance matrix, the resulting estimators may not be efficient. We conducted extensive simulation studies to investigate the impact of an unknown covariance structure on estimators in semiparametric models for longitudinal data. In some situations the loss of efficiency could be substantial. A two-step estimator is thus proposed to improve the efficiency. Our study was motivated by a population based data analysis to examine the temporal relationship between systolic blood pressure and urinary albumin excretion.     

Despeckling SAR-type multiplicative noise

Despeckling multiplicative noise is important in processing coherent radar images. Assuming that measurements are corrupted by multiplicative noise and that a priori values are contaminated by either multiplicative or additive noise, we have obtained Bayesian, maximum likelihood and weighted least-squares (LS) estimators, based on gamma and normal distributions. These estimators have been shown to be biased if the noise in measurements is multiplicative. A technique of bias-correction to remove biases from the estimated parameters is proposed. The bias-correction technique requires no distributions about the measurements and the a priori mean, and can be applied to eliminate bias from Bayesian, maximum likelihood and weighted LS estimators in multiplicative noise models. It theoretically provides a solid foundation for, and thus justifies some of current practice in, despeckling multiplicative noise, such as Lee's local statistics and Kuan's adaptive smoothing filter. Some despeckling measures are also proposed and simulated experiment results are reported.     

Standard errors for bagged and random forest estimators

Bagging and random forests are widely used ensemble methods. Each forms an ensemble of models by randomly perturbing the fitting of a base learner. The standard errors estimation of the resultant regression function is considered. Three estimators are discussed. One, based on the jackknife, is applicable to bagged estimators and can be computed using the bagged ensemble. The two other estimators target the bootstrap standard error estimator, and require fitting multiple ensemble estimators, one for each bootstrap sample. It is shown that these bootstrap ensemble sizes can be small, which reduces the computation involved in forming the estimator. The estimators are studied using both simulated and real data.     

Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling

Several new estimators of the marginal likelihood for complex non-Gaussian models are developed. These estimators make use of the output of auxiliary mixture sampling for count data and for binary and multinomial data. One of these estimators is based on combining Chib’s estimator with data augmentation as in auxiliary mixture sampling, while the other estimators are importance sampling and bridge sampling based on constructing an unsupervised importance density from the output of auxiliary mixture sampling. These estimators are applied to a logit regression model, to a Poisson regression model, to a binomial model with random intercept, as well as to state space modeling of count data.     

Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model

An accuracy measure (mean squared error, MSE) is necessary when small area estimators of linear parameters are provided. Even in the case when such estimators arise from the assumption of relatively simple models for the variable of interest, as linear mixed models, the analytic form of the MSE is not suitable to be calculated explicitly. Some good and widely used approximations are available for those models. For generalized linear mixed models, a rough approximation can be obtained by a linearization of the model and application of Prasad-Rao approximation for linear mixed models. Resampling methods, although computationally demanding, represent a conceptually simple alternative. Under a logistic mixed linear model for the characteristic of interest, the Prasad-Rao-type formula is compared with a bootstrap estimator obtained by a wild bootstrap designed for estimating under finite populations. A simulation study is developed in order to study the performance of both methods for estimating a small area proportion.     

On sovereign credit migration: A study of alternative estimators and rating dynamics

Different estimators of rating transition matrices have been proposed in the literature but their behaviour has been studied mainly in the context of corporate ratings. The finite-sample bias and variability of three sovereign credit migration estimators is investigated through bootstrap simulations. These are a discrete multinomial estimator and two continuous-time hazard rate methods, one of which neglects time heterogeneity in the rating process whereas the other accounts for it. Panel logit models and spectral analysis are utilized to study the properties of the rating process. The sample consists of Moody's ratings 1981-2004 for 72 industrialized and emerging economies. Hazard rate estimators yield more accurate default probabilities. The time homogeneity assumption leads to underestimating the default probability and greater migration risk is inferred upon relaxing it. There is evidence of duration dependence and downgrade momentum effects in the rating process. These findings have important implications for economic and regulatory capital allocation and for the pricing of credit sensitive instruments.     

A class of bootstrap estimators for linear system identification†

The paper deals with the identification of a process modelled by a stable, linear difference equation of known order, subject to additive output measurement noise, which is equally and independently distributed. It is shown that in the idealized situation, where the noise-free process output is assumed known, there is a set of three estimators which provide consistent estimates of the process parameters. Practical approximations to these estimators lead to on-line algorithms, in which the process parameters as well as the noise-free process outputs are estimated recursively in real time. These practical estimators are tested on simulated data obtained from time-invariant and slowly time-varying models. The performance of these estimators is compared with each other and also with some of the existing ‘bootstrap type’ estimators.     

Parameter estimation of 2-D stochastic FM model based on two step estimation procedure

This paper considers the problem of estimating the parameters of two-dimensional (2-D) stochastic FM models. First, the estimators of the parameters of 2-D stochastic FM model are obtained using two step estimation procedures by Kronecker product and least square method. Then, the asymptotic properties of the estimators are given. It is shown that the estimators are to be consistent and to have a distribution which converges to that of a normally distributed random vector under fairly general conditions. Finally, the performance of the proposed methods is illustrated by examples.     

On the estimation of the linear relation when the error variances are known

The problem of consistent estimation in measurement error models in a linear relation with not necessarily normally distributed measurement errors is considered. Three possible estimators which are constructed as different combinations of the estimators arising from direct and inverse regression are considered. The efficiency properties of these three estimators are derived and the effect of non-normally distributed measurement errors is analyzed. A Monte-Carlo experiment is conducted to study the performance of these estimators in finite samples.     

履带模型与仿真

仿真技术应用于履带车辆的研究，降低了研究成本，缩短了研制周期，有力地推动了履带车辆的发展。履带模型在履带车辆建模与仿真中是棘手问题。本文对履带车辆仿真中常见的两类履带模型-柔性履带模型和刚性履带模型的模型机理进行了分析，并分别将两类履带模型应用到履带车辆的平稳性模型中，通过仿真比较了两类履带模型的差异。     

“Extra-Ordinary” Ergonomics: How to Accommodate Small and Big Persons,the Disabled and Elderly,Expectant Mothers,and Children

Abstract

Data from a previous study of soldier driving postures and seating positions were analysed to develop statistical models for defining accommodation of driver seating positions in military vehicles. Regression models were created for seating accommodation applicable to driver positions with a fixed heel point and a range of steering wheel locations in typical tactical vehicles. The models predict the driver-selected seat position as a function of population anthropometry and vehicle layout. These models are the first driver accommodation models considering the effects of body armor and body-borne gear. The obtained results can benefit the design of military vehicles, and the methods can also be extended to be utilised in the development of seating accommodation models for other driving environments where protective equipment affects driver seating posture, such as vehicles used by law-enforcement officers and firefighters.

Practitioner Summary: A large-scale laboratory study of soldier driving posture and seating position was designed to focus on tactical vehicle (truck) designs. Regression techniques are utilised to develop accommodation models suitable for tactical vehicles. These are the first seating accommodation models based on soldier data to consider the effects of personal protective equipment and body-borne gear.     

Limited Information Estimation in Binary Factor Analysis: A Review and Extension

Based on the Bayes modal estimate of factor scores in binary latent variable models, this paper proposes two new limited information estimators for the factor analysis model with a logistic link function for binary data based on Bernoulli distributions up to the second and the third order with maximum likelihood estimation and Laplace approximations to required integrals. These estimators and two existing limited information weighted least squares estimators are studied empirically. The limited information estimators compare favorably to full information estimators based on marginal maximum likelihood, MCMC, and multinomial distribution with a Laplace approximation methodology. Among the various estimators, Maydeu-Olivares and Joe's (2005) weighted least squares limited information estimators implemented with Laplace approximations for probabilities are shown in a simulation to have the best root mean square errors.     

Generalized method of moments estimation for cointegrated vector autoregressive models

In this study, a generalized method of moments (GMM) for the estimation of nonstationary vector autoregressive models with cointegration is considered. Two iterative methods are considered: a simultaneous estimation method and a switching estimation method. The asymptotic properties of the GMM estimators of these methods are found to be the same as those of the Gaussian reduced-rank estimator. Through Monte Carlo simulation, the small-sample properties of the GMM estimators are studied and compared with those of the Gaussian reduced-rank estimator and the maximum likelihood estimator considered by other researchers. In the case of small samples, the GMM estimators are more robust to deviations from normality assumptions, particularly to outliers.     

Frequentist Model Averaging with missing observations

Model averaging or combining is often considered as an alternative to model selection. Frequentist Model Averaging (FMA) is considered extensively and strategies for the application of FMA methods in the presence of missing data based on two distinct approaches are presented. The first approach combines estimates from a set of appropriate models which are weighted by scores of a missing data adjusted criterion developed in the recent literature of model selection. The second approach averages over the estimates of a set of models with weights based on conventional model selection criteria but with the missing data replaced by imputed values prior to estimating the models. For this purpose three easy-to-use imputation methods that have been programmed in currently available statistical software are considered, and a simple recursive algorithm is further adapted to implement a generalized regression imputation in a way such that the missing values are predicted successively. The latter algorithm is found to be quite useful when one is confronted with two or more missing values simultaneously in a given row of observations. Focusing on a binary logistic regression model, the properties of the FMA estimators resulting from these strategies are explored by means of a Monte Carlo study. The results show that in many situations, averaging after imputation is preferred to averaging using weights that adjust for the missing data, and model average estimators often provide better estimates than those resulting from any single model. As an illustration, the proposed methods are applied to a dataset from a study of Duchenne muscular dystrophy detection.