用层三角变换作混合模型中的参数估计

在混合线性模型中估计方差分量,最广泛应用的方法是极大似然(ML)法和约束极大似然(REML)法.从数理统计理论的高度来看,这些方法相当完美,但从数值计算的角度来看,却比较繁琐.为克服计算上的困难,在Oefversten[1]关于推导检验方差分量变换工作的基础上,我们提出了一种新的所谓“层三角变换法”。     

Influence analyses of skew-normal/independent linear mixed models

A extension of some diagnostic procedures to skew-normal/independent linear mixed models is discussed. This class provides a useful generalization of normal (and skew-normal) linear mixed models since it is assumed that the random effects and the random error terms follow jointly a multivariate skew-normal/independent distribution. Inspired by the EM algorithm, a local influence analysis for linear mixed models, following Zhu and Lee’s approach is developed. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex and Cook’s well-known approach can be very difficult for obtaining measures of local influence. Moreover, the local influence measures obtained under this approach are invariant under reparameterization. Four specific perturbation schemes are also discussed. Finally, a real data set is analyzed in order to illustrate the usefulness of the proposed methodology.     

Estimation and inference in functional mixed-effects models

Functional mixed-effects models are very useful in analyzing functional data. A general functional mixed-effects model that inherits the flexibility of linear mixed-effects models in handling complex designs and correlation structures is considered. A wavelet decomposition approach is used to model both fixed-effects and random-effects in the same functional space, meaning that the population-average curve and the subject-specific curves have the same smoothness property. A linear mixed-effects representation is then obtained that is used for estimation and inference in the general functional mixed-effects model. Adapting recent methodologies in linear mixed-effects and nonparametric regression models, hypothesis testing procedures for both fixed-effects and random-effects are provided. Using classical linear mixed-effects estimation techniques, the linear mixed-effects representation is also used to obtain wavelet-based estimates for both fixed-effects and random-effects in the general functional mixed-effects model. The usefulness of the proposed estimation and hypothesis testing procedures is illustrated by means of a small simulation study and a real-life dataset arising from physiology.     

Componentwise ultimate bound and invariant set computation for switched linear systems

We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form of polyhedral and/or mixed ellipsoidal/polyhedral sets, is completely systematic once the aforementioned transformation is obtained, and provides a new sufficient condition for practical stability. We show that the transformation required by our method can easily be found in the well-known case where the subsystem matrices generate a solvable Lie algebra, and we provide an algorithm to seek such transformation in the general case. An example comparing the bounds obtained by the proposed method with those obtained from a common quadratic Lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases.     

Influence diagnostics for random effect survival models: Application to a recurrent infection study for kidney patients on portable dialysis

In modeling multivariate failure time data, a class of survival model with random effects is applicable. It incorporates the random effect terms in the linear predictor and includes various random effect survival models as special cases, such as the random effect model assuming Cox's proportional hazards, with Weibull baseline hazards and with power family of transformation in the relative risk function. Residual maximum likelihood (REML) estimation of parameters is achieved by adopting the generalised linear mixed models (GLMM) approach. Accordingly, influence diagnostics are developed as sensitivity measures for the REML estimation of model parameters. A data set of recurrent infections of kidney patients on portable dialysis illustrates the usefulness of the influence diagnostics. A simulation study is carried out to examine the performance of the proposed influence diagnostics.     

Assessment of local influence in elliptical linear models with longitudinal structure

The aim of this paper is to derive local influence curvatures under various perturbation schemes for elliptical linear models with longitudinal structure. The elliptical class provides a useful generalization of the normal model since it covers both light- and heavy-tailed distributions for the errors, such as Student-t, power exponential, contaminated normal, among others. It is well known that elliptical models with longer-than-normal tails may present robust parameter estimates against outlying observations. However, little has been investigated on the robustness aspects of the parameter estimates against perturbation schemes. We use appropriate derivative operators to express the normal curvatures in tractable forms for any correlation structure. Estimation procedures for the position and variance-covariance parameters are also presented. A data set previously analyzed under a normal linear mixed model is reanalyzed under elliptical models. Local influence graphics are used to select less sensitive models with respect to some perturbation schemes.     

线性模型中变量和变换的同时选择

变量选择和变换选择是线性模型中的两个不同的问题.把这两个过程结合起来同时进行,将是很有意义的.由于近来在计算技术方面的发展,这种同时进行的过程现在是可行的.本文提出了在线性模型中的变数和变换同时进行选择的两个方法.节(?)个方法是(?)个纯粹的同时选择过程.第二个方法适用于具有较多预报因子的数据集,也提出了(?)个对于同时选择的向后删除过程.这两个方法皆以贝叶斯模型选择准则为基础.用(?)个实例来说明这(?)方法.     

A Quasi-ARMAX approach to modelling of non-linear systems

This paper proposes a class of quasi-ARMAX models for non-linear systems. Similar to ordinary non-linear ARMAX models, the quasi-ARMAX models are flexible black-box models, but they have various linearity properties similar to those of linear ARMAX models. A modelling scheme is introduced to construct models consisting of two parts: a macro-part and a kernel-part. By using Taylor expansion and other mathematical transformation techniques, it is first constructed as a class of quasi-ARMAX interfaces (macro-parts) that have various linearity properties but contain some complicated coefficients. MIMO neurofuzzy models (kernel-parts) are then introduced to represent the complicated coefficients. It is shown that the proposed quasi-ARMAX models have both good approximation ability and some easy-to-use properties. The proposed models have been successfully applied to prediction, fault detection and adaptive control of non-linear systems.     

Size and power of tests for a zero random effect variance or polynomial regression in additive and linear mixed models

Several tests for a zero random effect variance in linear mixed models are compared. This testing problem is non-regular because the tested parameter is on the boundary of the parameter space. Size and power of the different tests are investigated in an extensive simulation study that covers a variety of important settings. These include testing for polynomial regression versus a general smooth alternative using penalized splines. Among the test procedures considered, three are based on the restricted likelihood ratio test statistic (RLRT), while six are different extensions of the linear model F-test to the linear mixed model. Four of the tests with unknown null distributions are based on a parametric bootstrap, the other tests rely on approximate or asymptotic distributions. The parametric bootstrap-based tests all have a similar performance. Tests based on approximate F-distributions are usually the least powerful among the tests under consideration. The chi-square mixture approximation for the RLRT is confirmed to be conservative, with corresponding loss in power. A recently developed approximation to the distribution of the RLRT is identified as a rapid, powerful and reliable alternative to computationally intensive parametric bootstrap procedures. This novel method extends the exact distribution available for models with one random effect to models with several random effects.     

Balanced truncation for temporal- and spatial-LPV interconnected systems based on the full block S-procedure

This paper presents a technique for model order reduction of exponentially stable temporal- and spatial-LPV (Linear Parameter Varying) interconnected systems represented in linear fractional transformation form, based on the application of full block S-procedure. The first stage of the proposed technique is to balance the system. The balancing transformation is applied to the nominal system; the reduced system is connected with the same scheduling block as the original system. The reduced models preserve exponential stability and the spatial structure of the system. The proposed approach simplifies the problem of model order reduction for LPV systems in the sense of avoiding gridding over the scheduling parameter range. The results are illustrated with the application to an experimentally identified spatially interconnected model of an actuated beam. In addition, extended reachability and observability matrices are presented.     

Flexible modelling of random effects in linear mixed models—A Bayesian approach

Flexible modelling of random effects in linear mixed models has attracted some attention recently. In this paper, we propose the use of finite Gaussian mixtures as in Verbeke and Lesaffre [A linear mixed model with heterogeneity in the random-effects population, J. Amu. Statist. Assoc. 91, 217-221]. We adopt a fully Bayesian hierarchical framework that allows simultaneous estimation of the number of mixture components together with other model parameters. The technique employed is the Reversible Jump MCMC algorithm (Richardson and Green [On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion). J. Roy. Statist. Soc. Ser. B 59, 731-792]). This approach has the advantage of producing a direct comparison of different mixture models through posterior probabilities from a single run of the MCMC algorithm. Moreover, the Bayesian setting allows us to integrate over different mixture models to obtain a more robust density estimate of the random effects. We focus on linear mixed models with a random intercept and a random slope. Numerical results on simulated data sets and a real data set are provided to demonstrate the usefulness of the proposed method.     

Modelling the semivariograms and cross-semivariograms required in downscaling cokriging by numerical convolution–deconvolution

A practical problem of interest in remote sensing is to increase the spatial resolution of a coarse spatial resolution image by fusing the information of that image with another fine spatial resolution image (from the same sensor or from sensors on different satellites). Thus, the problem is how to introduce spatial ‘detail’ into a coarse spatial resolution image (decrease the pixel size) such that it is coherent with the spectral information of the image. Cokriging provides a geostatistical solution to the problem and has several interesting advantages: it is a sound statistical method by being unbiased and minimizing a prediction variance (c.f. ad hoc procedures), it takes into account the effect of pixel size, and also autocorrelation in each image as well as the cross-correlation between images, it may be extended to incorporate extra information from other sources and it provides an estimation of the uncertainty of the final predictions. When formulating the cokriging system, semivariograms and cross-semivariograms (or covariances and cross-covariances) appear, some of which cannot be estimated from data directly. Cross-variograms between different variables as well as cross-semivariograms between different supports for the same variable are required. The problem is solved by using linear systems theory in which any variable for any pixel size is seen as the output of a linear system when the input is the same variable on a point support. In remote-sensing applications, the linear system is specified by the point-spread function (or impulse response) of the sensor. Linear systems theory provides the theoretical relations between the different semivariograms and cross-semivariograms. Overall, one must ensure that the whole set of covariances and cross-covariances is positive-definite and models must be estimated for non-observed semivariograms and cross-semivariograms. The models must also be realistic, taking into account, for example, the parabolic behaviour close to the origin presented in regularized semivariograms and cross-semivariograms. The solution proposed is to find by numerical deconvolution a positive-definite set of point covariances and cross-covariances and then any required model may be obtained by numerical convolution of the corresponding point model. The first step implies several numerical deconvolutions where some model parameters are fixed, while others are estimated using the available experimental semivariograms and cross-semivariograms, and some goodness-of-fit measure. The details of the proposed procedure are presented and illustrated with an example from remote sensing.     

Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis

A mixed integer linear model for selecting the best decision making unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying the most efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi’s. The proposed alternative MILP models can make full use of input and output information without the need of specifying any assurance regions for input and output weights to avoid zero weights, can make correct selections without being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of the most efficient DMU. The potential applications of the proposed alternative MILP models and their effectiveness are illustrated with four numerical examples.     

A comparison of linear and nonlinear statistical techniques inperformance attribution

Performance attribution is usually conducted under the linear framework of multifactor models. Although commonly used by practitioners in finance, linear multifactor models are known to be less than satisfactory in many situations. After a brief survey of nonlinear methods, nonlinear statistical techniques are applied to performance attribution of a portfolio constructed from a fixed universe of stocks using factors derived from some commonly used cross sectional linear multifactor models. By rebalancing this portfolio monthly, the cumulative returns for procedures based on standard linear multifactor model and three nonlinear techniques-model selection, additive models, and neural networks-are calculated and compared. It is found that the first two nonlinear techniques, especially in combination, outperform the standard linear model. The results in the neural-network case are inconclusive because of the great variety of possible models. Although these methods are more complicated and may require some tuning, toolboxes are developed and suggestions on calibration are proposed. This paper demonstrates the usefulness of modern nonlinear statistical techniques in performance attribution.     

Testing transformations for the linear mixed model

Transformation of the response of a linear model is a popular method in practice when attempting to satisfy the assumptions of the model. Environmental research routinely uses log-transformations due to the nature of the observed data. The choice of the transformation is often made based upon previous experience or on the comparison of models with different transformed responses. Often a transformation parameter is estimated when fitting a model to a set of data. However, in practice interpretability becomes an issue, as it is only desired to know if a particular transformation is appropriate. Thus, inference tools for a hypothesized value of the transformation, such as the log-transformation in environmental exposure models, have their merit. An examination of hypothesis tests of the transformation parameter in the general linear mixed model will be beneficial due to its practical applications, particularly for areas of environmental research. The effect of outliers on inference about the transformation parameter is also studied.     

Influence diagnostics for random effect survival models: Application to a recurrent infection study for kidney patients on portable dialysis

In modeling multivariate failure time data, a class of survival model with random effects is applicable. It incorporates the random effect terms in the linear predictor and includes various random effect survival models as special cases, such as the random effect model assuming Cox's proportional hazards, with Weibull baseline hazards and with power family of transformation in the relative risk function. Residual maximum likelihood (REML) estimation of parameters is achieved by adopting the generalised linear mixed models (GLMM) approach. Accordingly, influence diagnostics are developed as sensitivity measures for the REML estimation of model parameters. A data set of recurrent infections of kidney patients on portable dialysis illustrates the usefulness of the influence diagnostics. A simulation study is carried out to examine the performance of the proposed influence diagnostics.     

Computational relaxed TP model transformation: restricting the computation to subspaces of the dynamic model

The tensor‐product (TP) model transformation is a recently proposed numerical method capable of transforming linear parameter varying state‐space models to the higher order singular value decomposition (HOSVD) based canonical form of polytopic models. It is also capable of generating various types of convex TP models, a type of polytop models, for linear matrix inequality based controller design. The crucial point of the TP model transformation is that its computational load exponentially explodes with the dimensionality of the parameter vector of the parameter‐varying state‐space model. In this paper we propose a modified TP model transformation that leads to considerable reduction of the computation. The key idea of the method is that instead of transforming the whole system matrix at once in the whole parameter space, we decompose the problem and perform the transformation element wise and restrict the computation to the subspace where the given element of the model varies. The modified TP model transformation can readily be executed in higher dimensional cases when the original TP model transformation fails. The effectiveness of the new method is illustrated with numerical examples. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Structural shape sensitivity analysis for nonlinear material models with strain softening

This paper describes some considerations around the analytical structural shape sensitivity analysis when the structural behaviour is computed using the finite element method with a nonlinear constitutive material model. Traditionally, the structural sensitivity analysis is computed using an incremental approach based on the incremental procedures for the solution of the structural equilibrium problem. In this work, a direct (nonincremental) formulation for computing these structural sensitivities, that is valid for some specific nonlinear material models, is proposed. The material models for which the presented approach is valid are characterized by the fact that the stresses at any timet can be expressed in terms of the strains at the timet and, in some cases, the strains at a specific past timet ^u (t ^u <t). This is the case of elasticity (linear as well as nonlinear), perfect plasticity and damage models. A special strategy is also proposed for material models with strain softening.For the cases where it is applicable, the sensitivity analysis proposed here allows us to compute the structural sensitivities around any structural equilibrium point after finishing the solution process and it is completely independent of the numerical scheme used to solve the structural equilibrium problem. This possibility is particularized for the case of a damage model considering a strain-softening behaviour. Finally, the quality and reliability of the proposed approach is assessed through its application to some examples.     

Mixed H2/H∞ fuzzy output feedbackcontrol design for nonlinear dynamic systems: an LMI approach

This study introduces a mixed H₂/H_∞ fuzzy output feedback control design method for nonlinear systems with guaranteed control performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based mixed H₂/H_∞ controller is developed to achieve the suboptimal H₂ control performance with a desired H_∞ disturbance rejection constraint. A robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure. By the proposed decoupling technique and two-stage procedure, the outcome of the fuzzy observer-based mixed H₂/H_∞ control problem is parametrized in terms of the two eigenvalue problems (EVPs): one for observer and the other for controller. The EVPs can be solved very efficiently using the linear matrix inequality (LMI) optimization techniques. A simulation example is given to illustrate the design procedures and performances of the proposed method     

Alternative solutions for classifying inputs and outputs in data envelopment analysis

In conventional data envelopment analysis (DEA) models, a performance measure whether as an input or output usually has to be known. Nevertheless, in some cases, the type of a performance measure is not clear and some models are introduced to accommodate such flexible measures. In this paper, it is shown that alternative optimal solutions of these models has to be considered to deal with the flexible measures, otherwise incorrect results might occur. Practically, the efficiency scores of a DMU could be equal when the flexible measure is considered either as input or output. These cases are introduced and referred as share cases in this study specifically. It is duplicated that share cases must not be taken into account for classifying inputs and outputs. A new mixed integer linear programming (MILP) model is proposed to overcome the problem of not considering the alternative optimal solutions of classifier models. Finally, the applicability of the proposed model is illustrated by a real data set.