technical communique adaptive ilc for a class of discrete time systems with iteration varying trajectory and random initial condition in this work we present a discrete time adaptive iterative learning control ailc scheme to deal with systems with time varying parametric uncertainties using the analogy between the discrete time axis and the iterative learning axis the new adaptive ilc can incorporate a recursive least squares rls algorithm hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis when the initial states are random and the reference trajectory is iteration varying the new ailc can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis

decentralized and adaptive nonlinear tracking of large scale systems via output feedback presents a solution to the problem of decentralized adaptive asymptotic tracking for a class of large scale systems using nonlinear output feedback the proposed constructive approach does not require any matching conditions on the parametric uncertainties nor growth conditions of any kind on the subsystem and interacting output nonlinearities any decentralized system in the family may have an unknown nonzero equilibrium point partially decentralized reduced order filters are presented to recover the unmeasured states the recursive decentralized output feedback design procedure is illustrated in a practical example of two inverted pendulums on carts without velocity measurements the effectiveness of the decentralized algorithm is supported by simulation results

a discrete time event history approach to informative drop out in mixed latent markov models with covariates summary mixed latent markov mlm models represent an important tool of analysis of longitudinal data when response variables are affected by time fixed and time varying unobserved heterogeneity in which the latter is accounted for by a hidden markov chain in order to avoid bias when using a model of this type in the presence of informative drop out we propose an event history eh extension of the latent markov approach that may be used with multivariate longitudinal data in which one or more outcomes of a different nature are observed at each time occasion the eh component of the resulting model is referred to the interval censored drop out and bias in mlm modeling is avoided by correlated random effects included in the different model components which follow common latent distributions in order to perform maximum likelihood estimation of the proposed model by the expectation maximization algorithm we extend the usual forward backward recursions of baum and welch the algorithm has the same complexity as the one adopted in cases of non informative drop out we illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest one continuous and the other binary

a synthetic approach for robust constrained iterative learning control of piecewise affine batch processes for industrial nonlinear batch processes that can be practically divided into a series of piecewise affine operating regions a two dimensional 2d closed loop iterative learning control ilc method is proposed for robust tracking of the set point profile against cycle to cycle process uncertainties and load disturbances both state feedback and output feedback are considered for the control design together with the process input and output constraints for implementation based on a 2d system description for the batch operation a few synthetic performance and robust control objectives are proposed for developing the 2d ilc schemes in combination with the 2d lyapunov krasovskii functions that can guarantee monotonic state energy or output error decrease in both the time during a cycle and batch from cycle to cycle directions both the polyhedral and norm bounded descriptions of process uncertainties are considered to derive the corresponding linear matrix inequality lmi conditions for the closed loop ilc system robust stability an important merit of these lmi conditions is that there are adjustable convergence indices prescribed for both the time and batch directions and an adjustable robust control performance level for the closed loop system by specifying optimizing these adjustable parameters to solve these lmi conditions the 2d ilc controller can be explicitly derived for implementation the application to a highly nonlinear continuous stirred tank reactor cstr is shown to illustrate the effectiveness and merits of the proposed ilc method

iterative learning control for a class of nonlinear systems abstract for precise tracking control of a class of nonlinear systems over a finite time interval an iterative learning control method using the relative degree of a system is proposed the class of nonlinear systems where the iterative learning control is applied can be extended by using the proposed method a sufficient condition is derived for guaranteeing a uniform convergence of the output to the desired output the results obtained for a class of nonlinear systems are shown to be a generalization of the existing results for linear time invariant systems

on d type and p type ilc designs and anticipatory approach many schemes of iterative learning control ilc have been developed for continuous time non linear dynamic systems to improve tracking performance two schemes d type and p type have been the bases for many ilc designs recently the anticipatory ilc scheme has been introduced on the basis of a different approach wang 1998a 1999 in this paper these basic schemes are compared from both analysis and implementation view points the anticipatory ilc scheme is designed on the basis of a causal pair of the action taken and its resulting state variables this approach has the anticipatory characteristics of the d type ilc and the simplicity for implementation of p type ilcs a sampled data ilc scheme is presented as another form of this anticipatory ilc scheme furthermore control device saturation is taken into account and tracking error convergence results are established with proofs the convergence results are also provided in the presence of uncertainties disturbances and measurement noises ex

on asymptotic normality of limiting density functions with bayesian implications walker 1969 presented a straightforward approach to asymptotic normality of posterior distributions based on independent and identically distributed i i d observations dawid 1970 extended this work by providing a weaker set of conditions to cover some distributions whose ranges depend on the parameters of interest more recently heyde and johnstone 1979 simplified walker s conditions for stochastic processes in this paper we introduce three basic normality conditions for limiting density functions in the bayesian context our approach is data determined and is nonprobabilistic in nature nevertheless the results thus obtained can be easily converted to probabilistic ones when compared with those given by other investigators it is shown that our conditions as a whole have a greater generality and flexibility than those previously assumed either by dawid or heyde and johnstone in particular for the i i d case the commonly assumed wald type uniform boundedness condition for tail behaviours is shown to be unnecessary for asymptotic normality section 3 3 the advantage of our approach is further exemplified by a simple proof of the asymptotic normality of distributions conjugate to the exponential family

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

adaptive iterative learning control for linear systems with binary valued observations this brief presents a novel adaptive iterative learning control ilc algorithm for a class of single parameter systems with binary valued observations using the certainty equivalence principle the adaptive ilc algorithm is designed by employing a projection identification algorithm along the iteration axis it is shown that even though the available system information is very limited and the desired trajectory is iteration varying the proposed adaptive ilc algorithm can guarantee the convergence of parameter estimation over a finite time interval along the iterative axis meanwhile the tracking error is pointwise convergence asymptotically two examples are given to validate the effectiveness of the algorithm

bayesian hypothesis testing in latent variable models hypothesis testing using bayes factors bfs is known not to be well defined under the improper prior in the context of latent variable models an additional problem with bfs is that they are difficult to compute in this paper a new bayesian method based on the decision theory and the em algorithm is introduced to test a point hypothesis in latent variable models the new statistic is a by product of the bayesian mcmc output and hence easy to compute it is shown that the new statistic is appropriately defined under improper priors because the method employs a continuous loss function in addition it is easy to interpret the method is illustrated using a one factor asset pricing model and a stochastic volatility model with jumps

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

iterative learning of model reference adaptive controller for uncertain nonlinear systems with only output measurement in this paper a model reference adaptive control strategy is used to design an iterative learning controller for a class of repeatable nonlinear systems with uncertain parameters high relative degree initial output resetting error input disturbance and output noise the class of nonlinear systems should satisfy some differential geometric conditions such that the plant can be transformed via a state transformation into an output feedback canonical form a suitable error model is derived based on signals filtered from plant input and output the learning controller compensates for the unknown parameters uncertainties and nonlinearity via projection type adaptation laws which update control parameters along the iteration domain it is shown that the internal signals remain bounded for all iterations the output tracking error will converge to a profile which can be tuned by design parameters and the learning speed is improved if the learning gain is large

output feedback control of markovian jump repeated scalar nonlinear systems this paper is concerned with the induced l2 dynamic output feedback controller dofc design problem for discrete time markovian jump repeated scalar nonlinear systems by employing both the switching sequence dependent lyapunov function approach and the positive definite diagonally dominant lyapunov function technique a sufficient condition is first established which guarantees the underlying system to be stochastically stable with an induced l2 disturbance attenuation performance then the desired full or reduced order dofcs are designed by using projection approach cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem finally a numerical example is presented to show the effectiveness of the proposed methods

decentralized dynamic output feedback control of nonlinear interconnected systems the problem of robust stabilization is considered for a class of nonlinear interconnected systems which consist of linear subsystems coupled by nonlinear interconnections that are unknown and quadratically bounded a decentralized dynamic output feedback based linear controller is proposed where the feedback gain matrices of local controllers are obtained by solving an optimization problem subject to linear matrix inequalities local sliding mode observers are employed to asymptotically estimate the subsystems states and at the same time to reconstruct the unknown nonlinear interconnections the closed loop system driven by the proposed decentralized dynamic output feedback controller is guaranteed to be connectively stable with maximized interconnection bounds

a mixture model for multivariate extremes this thesis is a contribution to multivariate extreme value statistics the tail of a multivariate distribution function is characterized by its spectral distribution for which we propose a new semi parametric model based on mixtures of dirichlet distributions to estimate the components of this model reversible jump monte carlo markov chain and em algorithms are developed their performances are illustrated on real and simulated data obtained using new representations of the extremal logistic and dirichlet models in parallel with the estimation of the spectral distribution extreme value statistic machinery requires the selection of a threshold in order to classify data as extreme or not this selection is achieved by a new method based on heuristic arguments it allows a selection independent of the dimension of the data its performance is illustrated on real and simulated data primal scientific interests behind a multivariate extreme value analysis reside in the estimation of quantiles of rare events and in the exploration of the dependence structure for which the estimation of the spectral measure is a means rather than an end these two issues are addressed for the first a monte carlo method is developed based on simulation of extremes it is compared with classical and new methods of the literature for the second one an original conditional dependence analysis is proposed which enlightens various aspects of the dependence structure of the data examples using real data sets are given in the last part the semi parametric model and the presented methods are extended to spatial extremes it is made possible by considering the spectral distribution as the distribution of a random probability an original viewpoint adopted throughout this thesis classical multivariate extremes are extended to extremes of random measures the application is illustrated on rainfall data in china

stability of learning control with disturbances and uncertain initial conditions the authors investigate the effects of state disturbances output noise and errors in initial conditions on a class of learning control algorithms they present a simple learning algorithm and exhibit via a concise proof bounds on the asymptotic trajectory errors for the learned input and the corresponding state and output trajectories furthermore these bounds are continuous functions of the bounds on the initial condition errors state disturbances and output noise and the bounds are zero in the absence of these disturbances

a frequentist approach to bayesian asymptotics abstract ergodic theorem shows that ergodic averages of the posterior draws converge in probability to the posterior mean under the stationarity assumption the literature also shows that the posterior distribution is asymptotically normal when the sample size of the original data considered goes to infinity to the best of our knowledge there is little discussion on the large sample behaviour of the posterior mean in this paper we aim to fill this gap in particular we extend the posterior mean idea to the conditional mean case which is conditioning on a given vector of summary statistics of the original data we establish a new asymptotic theory for the conditional mean estimator for the case when both the sample size of the original data concerned and the number of markov chain monte carlo iterations go to infinity simulation studies show that this conditional mean estimator has very good finite sample performance in addition we employ the conditional mean estimator to estimate a garch 1 1 model for s p 500 stock returns and find that the conditional mean estimator performs better than quasi maximum likelihood estimation in terms of out of sample forecasting

tests for the error component model in the presence of local misspecification it is well known that most of the standard specification tests are not valid when the alternative hypothesis is misspecified this is particularly true in the error component model when one tests for either random effects or serial correlation without taking account of the presence of the other effect in this paper we study the size and power of the standard rao s score tests analytically and by simulation when the data are contaminated by local misspecification these tests are adversely affected under misspecification we suggest simple procedures to test for random effects or serial correlation in the presence of local serial correlation or random effects and these tests require ordinary least squares residuals only our monte carlo results demonstrate that the suggested tests have good finite sample properties for local misspecification and in some cases even for far distant misspecification our tests are also capable of detecting the right direction of the departure from the null hypothesis we also provide some empirical illustrations to highlight the usefulness of our tests

on the p type learning control sufficient conditions for the robustness and convergence of p type learning control algorithms for a class of time varying nonlinear systems are presented the authors prove the uniform boundedness of the system state and the input control with respect to the existence of errors of initialization measurement noises and fluctuations of system dynamics furthermore the system output converges uniformly to the desired one in absence of all disturbances finally specialization of the results to linear systems are presented

deviance information criterion for latent variable models and misspecified models abstract deviance information criterion dic has been widely used for bayesian model comparison especially after markov chain monte carlo mcmc is used to estimate candidate models this paper first studies the problem of using dic to compare latent variable models when dic is calculated from the conditional likelihood in particular it is shown that the conditional likelihood approach undermines theoretical underpinnings of dic a new version of dic namely dic l is proposed to compare latent variable models the large sample properties of dic l are studied a frequentist justification of dic l is provided like aic dic l provides an asymptotically unbiased estimator to the expected kullback leibler kl divergence between the dgp and a predictive distribution some popular algorithms such as the em kalman and particle filtering algorithms are introduced to compute dic l for latent variable models moreover this paper studies the problem of using dic to compare misspecified models a new version of dic namely dic m is proposed and it can be regarded as a bayesian version of tic a frequentist justification of dic m is provided under misspecification dic l and dic m are illustrated using asset pricing models and stochastic volatility models

extending the state space model to accommodate missing values in responses and covariates this article proposes an extended state space model for accommodating multivariate panel data the novel aspect of this contribution is an adjustment to the classical model for multiple subjects that allows missingness in the covariates in addition to the responses missing covariate data are handled by a second state space model nested inside the first to represent unobserved exogenous information relevant kalman filter equations are derived and explicit expressions are provided for both the e and m steps of an expectation maximization em algorithm to obtain maximum gaussian likelihood estimates of all model parameters in the presence of missing data the resulting em algorithm becomes computationally intractable but a simplification of the m step leads to a new procedure that is shown to be an expectation conditional maximization ecm algorithm under exogeneity of the covariates simulation studies reveal that the approach appears to be relatively robust to moderate percentages of missing dat

asymptotic relative efficiency of the classical test statistics under misspecification abstract asymptotic properties of the three classical test statistics the likelihood ratio lagrange multiplier efficient score and wald statistics are studied in the case of two types of misspecification the first misspecification is that the alternative used to construct the test is different from the true nonnull model in the second case the alternative hypothesis is correct but some of the nuisance parameters satisfy restrictions which are not taken into account in the test pitman s local alternatives and the concept of asymptotic relative efficiency are used to derive the asymptotic distributions of the test statistics and to examine the effects of the misspecifications the general results of the paper are illustrated by an example on the dynamic specification of a regression model

technical communique limit or limit superior observations on the convergence of some iterative learning control schemes in this paper we survey the convergence properties of a number of iterative learning control schemes from the past decade we observe a common technical error that appeared in these papers point out how the results should be corrected and finally consider the significance of these corrections with regard to the effectiveness of the schemes concerned

stochastic volatility with leverage fast and efficient likelihood inference this paper is concerned with the bayesian analysis of stochastic volatility sv models with leverage specifically the paper shows how the often used kim et al 1998 stochastic volatility likelihood inference and comparison with arch models review of economic studies 65 361 393 method that was developed for sv models without leverage can be extended to models with leverage the approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten component mixture of bivariate normal distributions the resulting posterior distribution is summarized by mcmc methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure the overall procedure is fast and highly efficient we illustrate the ideas on daily returns of the tokyo stock price index finally extensions of the method are described for superposition models where the log volatility is made up of a linear combination of heterogenous and independent autoregressions and heavy tailed error distributions student and log normal

large sample properties of posterior densities bayesian information criterion and the likelihood principle in nonstationary time series models asymptotic normality of the posterior is a well understood result for dynamic as well as nondynamic models based on sets of abstract conditions whose actual applicability is hardly known especially for the case of nonstationarity in this paper we provide a set of conditions by which we can relatively easily prove the asymptotic posterior normality under quite general situations of possible nonstationarity this result reinforces and generalizes the point of sims and uhlig 1991 that inference based on the likelihood principle explained by berger and wolpert 1988 will be unchanged regardless of whether the data are generated by a stationary process or by a unit root process on the other hand our conditions allow us to generalize the bayesian information criterion known as the schwarz criterion to the case of possible nonstationarity in addition we have shown that consistency of the maximum likelihood estimator not the asymptotic normality of the estimator with some minor additional assumptions is sufficient for asymptotic posterior normality

interval estimation for log linear models with one variable subject to non ignorable non response log linear models for multiway contingency tables where one variable is subject to non ignorable non response will often yield boundary solutions with the probability of non respondents being classified in some cells of the table estimated as 0 the paper considers the effect of this non standard behaviour on two methods of interval estimation based on the distribution of the maximum likelihood estimator the first method relies on the estimator being approximately normally distributed with variance equal to the inverse of the information matrix it is shown that the information matrix is singular for boundary solutions but intervals can be calculated after a simple transformation for the second method based on the bootstrap asymptotic results suggest that the coverage properties may be poor for boundary solutions both methods are compared with profile likelihood intervals in a simulation study based on data from the british general election panel study the results of this study indicate that all three methods perform poorly for a parameter of the non response model whereas they all perform well for a parameter of the margin model irrespective of whether or not there is a boundary solution

multilevel latent class models with dirichlet mixing distribution summary latent class analysis lca and latent class regression lcr are widely used for modeling multivariate categorical outcomes in social science and biomedical studies standard analyses assume data of different respondents to be mutually independent excluding application of the methods to familial and other designs in which participants are clustered in this article we consider multilevel latent class models in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common dirichlet distribution we apply the expectation maximization em algorithm for model fitting by maximum likelihood ml this approach works well but is computationally intensive when either the number of classes or the cluster size is large we propose a maximum pairwise likelihood mpl approach via a modified em algorithm for this case we also show that a simple latent class analysis combined with robust standard errors provides another consistent robust but less efficient inferential procedure simulation studies suggest that the three methods work well in finite samples and that the mpl estimates often enjoy comparable precision as the ml estimates we apply our methods to the analysis of comorbid symptoms in the obsessive compulsive disorder study our models random effects structure has more straightforward interpretation than those of competing methods thus should usefully augment tools available for lca of multilevel data

on the application of robust regression based diagnostics to models of conditional means and conditional variances abstract a strategy is proposed for applying a class of robust regression based diagnostics to nonlinear models of conditional means and conditional variances for cross section or time series data the distinguishing feature of the current approach which builds on already popular residual based procedures is that no auxiliary assumptions are imposed at any testing stage consequently the statistics are guaranteed to have the correct asymptotic size under the relevant null hypothesis several new regression based conditional mean and conditional variance diagnostics are proposed the case of incompletely specified dynamics in time series models is explicitly covered

a bayesian chi squared test for hypothesis testing abstract a new bayesian test statistic is proposed to test a point null hypothesis based on a quadratic loss the proposed test statistic may be regarded as the bayesian version of the lagrange multiplier test its asymptotic distribution is obtained based on a set of regular conditions and follows a chi squared distribution when the null hypothesis is correct the new statistic has several important advantages that make it appealing in practical applications first it is well defined under improper prior distributions second it avoids jeffrey lindley s paradox third it always takes a non negative value and is relatively easy to compute even for models with latent variables fourth its numerical standard error is relatively easy to obtain finally it is asymptotically pivotal and its threshold values can be obtained from the chi squared distribution the method is illustrated using some real examples in economics and finance

brief adaptive robust iterative learning control with dead zone scheme an adaptive robust iterative learning control method based on a new dead zone scheme is presented for the control of nonlinear uncertain systems the new dead zone scheme ceases both learning and adaptation whenever the previous iteration error enters a pre specified error bound in the sequel enhances the robustness of the control system and meanwhile achieves arbitrary tracking accuracy for guaranteed stability it is indicated that the system will converge to the error bound within finite iterations and stay inside it and that the boundedness of the system signals for any iteration is ensured no finite escape time iterative learning control ilc and adaptive robust control are synthesized to achieve a new control paradigm the iterative learning control strategy is applied directly to deal with structured system uncertainties unknown time functions which are invariant over iterations the adaptive robust control strategy is used to handle non periodic system uncertainties associated with partially known bounding functions where the unknown parameters in the upper bounding functions are estimated with adaptation by integrating learning adaptation robust control and the new dead zone scheme using lyapunov s direct method the proposed scheme is able to handle fairly broad classes of nonlinear uncertain systems

standard errors for em estimates in generalized linear models with random effects a procedure is derived for computing standard errors of em estimates in generalized linear models with random effects quadrature formulas are used to approximate the integrals in the em algorithm where two different approaches are pursued i e gauss hermite quadrature in the case of gaussian random effects and nonparametric maximum likelihood estimation for an unspecified random effect distribution an approximation of the expected fisher information matrix is derived from an expansion of the em estimating equations this allows for inferential arguments based on em estimates as demonstrated by an example and simulations

a unified adaptive iterative learning control framework for uncertain nonlinear systems in this note we propose a unified framework for adaptive iterative learning control design for uncertain nonlinear systems it is shown that if a lyapunov based adaptive control law is available for the system under consideration and the lyapunov function satisfies certain conditions it is straightforward to extend the adaptive controller to handle repetitive systems operating over a finite time interval according to the value of a certain parameter the parametric adaptation law can be a pure time domain adaptation a pure iteration domain adaptation or a combination of both a pure iteration domain adaptation is described by a difference equation a pure time domain adaptation is described by a differential equation and a combination of both is described by a differential difference equation the advantages and disadvantages of the three possible adaptation types are discussed and some illustrative examples are given

decentralized adaptive control of interconnected systems the adaptive control of a class of large scale systems formed of an arbitrary interconnection of subsystems with unknown parameters nonlinearities and bounded disturbances is investigated it is first shown that no matter how weak the interconnections are a decentralized adaptive control scheme can become unstable approaches are then developed for stabilization and tracking using new decentralized adaptive controllers in the case where the relative degree n of the transfer function of each decoupled subsystem is less than or equal to two sufficient conditions are established which guarantee boundedness and exponential convergence of the state and parameter errors to bounded residual sets in the absence of disturbances and interconnections the decentralized adaptive control schemes guarantee exact convergence of the tracking errors to zero the effectiveness of the proposed adaptive schemes is demonstrated using a simple example

adaptive learning control of nonlinear systems by output error feedback this paper addresses the problem of designing an output error feedback control for single input single output nonlinear systems with uncertain smooth output dependent nonlinearities whose local lipschitz constants are known the considered systems are required to be observable minimum phase with known relative degree and known high frequency gain sign linear systems are included the reference output signal is assumed to be smooth and periodic with known period by developing in fourier series expansion a suitable periodic input reference signal an output error feedback adaptive learning control is designed which ldquolearnsrdquo the input reference signal by identifying its fourier coefficients bounded closed loop signals and exponential tracking of both input and output reference signals are obtained when the fourier series expansion is finite while arbitrary small tracking errors are exponentially achieved otherwise the resulting control is not model based is independent of the system order and depends only on the relative degree the reference signal period and the high frequency gain sign

a novel approach to output feedback control of fuzzy stochastic systems this paper investigates the problem of hankel norm output feedback controller design for a class of t s fuzzy stochastic systems the full order output feedback controller design technique with the hankel norm performance is proposed by the fuzzy basis dependent lyapunov function approach and the conversion on the hankel norm controller parameters sufficient conditions are established to design the controllers such that the resulting closed loop system is stochastically stable and satisfies a prescribed performance the desired output feedback controller can be obtained by solving a convex optimization problem which can be efficiently solved by standard numerical algorithms finally a henon map system is used to illustrate the effectiveness of the proposed techniques

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

a bayesian robust chi squared test for testing simple hypotheses abstract in this paper we introduce a new bayesian chi squared test based on an adjusted quadratic loss function for testing a simple null hypothesis we show that the asymptotic null distribution of our suggested test is a central chi squared distribution under some assumptions required for the bayesian large sample theory we refer to our test as the bayesian robust chi squared test since it is robust to parametric misspecification in the alternative model that is the limiting null distribution of our test is a central chi squared distribution irrespective of parametric misspecification in the alternative model in addition to being robust to parametric misspecification our test also shares properties of the test suggested by li et al 2015 based on a quadratic loss function we provide four examples to illustrate the implementation of our suggested bayesian test statistic

statistical inference for discretely observed markov jump processes summary likelihood inference for discretely observed markov jump processes with finite state space is investigated the existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated this topic is closely related to the imbedding problem for markov chains it is demonstrated that the maximum likelihood estimator can be found either by the em algorithm or by a markov chain monte carlo procedure when the maximum likelihood estimator does not exist an estimator can be obtained by using a penalized likelihood function or by the markov chain monte carlo procedure with a suitable prior the methodology and its implementation are illustrated by examples and simulation studies

a new approach to bayesian hypothesis testing abstract in this paper a new bayesian approach is proposed to test a point null hypothesis based on the deviance in a decision theoretical framework the proposed test statistic may be regarded as the bayesian version of the likelihood ratio test and appeals in practical applications with three desirable properties first it is immune to jeffreys concern about the use of improper priors second it avoids jeffreys lindley s paradox third it is easy to compute and its threshold value is easily derived facilitating the implementation in practice the method is illustrated using some real examples in economics and finance it is found that the leverage effect is insignificant in an exchange time series and that the fama french three factor model is rejected

estimation for general birth death processes birth death processes bdps are continuous time markov chains that track the number of particles in a system over time while widely used in population biology genetics and ecology statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear bdps in which per particle birth and death rates are constant researchers often observe the number of particles at discrete times necessitating data augmentation procedures such as expectation maximization em to find maximum likelihood estimates mles for bdps on finite state spaces there are powerful matrix methods for computing the conditional expectations needed for the e step of the em algorithm for bdps on infinite state spaces closed form solutions for the e step are available for some linear models but most previous work has resorted to time consuming simulation remarkably we show that the e step conditional expectations can be expressed as convolutions of computable transition probabi

direct calculation of the information matrix via the em algorithm summary a simple explicit formula is provided for the matrix of second derivatives of the observed data log likelihood in terms of derivatives of the criterion function the conditional expectation of the complete data log likelihood given the observed data invoked by the em algorithm

direct calculation of the information matrix via the em a simple explicit formula is provided for the matrix of second derivatives of the observed data log likelihood in terms of derivatives of the criterion function conditional expectation of the complete data log likelihood given the observed data invoked by the em algorithm

controller synthesis for networked control systems this paper presents a discrete time model for networked control systems ncss that incorporates all network phenomena time varying sampling intervals packet dropouts and time varying delays that may be both smaller and larger than the sampling interval based on this model constructive lmi conditions for controller synthesis are derived such that stabilizing state feedback controllers can be designed besides the proposed controller synthesis conditions a comparison is made between the use of parameter dependent lyapunov functions and lyapunov krasovskii functions for stability analysis several examples illustrate the effectiveness of the developed theory

inference based on the em algorithm for the competing risks model with masked causes of failure summary in this paper we propose inference methods based on the em algorithm for estimating the parameters of a weakly parameterised competing risks model with masked causes of failure and second stage data with a carefully chosen definition of complete data the maximum likelihood estimation of the cause specific hazard functions and of the masking probabilities is performed via an em algorithm both the e and m steps can be solved in closed form under the full model and under some restricted models of interest we illustrate the flexibility of the method by showing how grouped data and tests of common hypotheses in the literature on missing cause of death can be handled the method is applied to a real dataset and the asymptotic and robustness properties of the estimators are investigated through simulation

on leverage in a stochastic volatility model this paper is concerned with the specification for modelling financial leverage effect in the context of stochastic volatility sv models two alternative specifications co exist in the literature one is the euler approximation to the well known continuous time sv model with leverage effect and the other is the discrete time sv model of jacquier et al j econometrics 122 2004 185 using a gaussian nonlinear state space form with uncorrelated measurement and transition errors i show that it is easy to interpret the leverage effect in the conventional model whereas it is not clear how to obtain and interpret the leverage effect in the model of jacquier et al empirical comparisons of these two models via bayesian markov chain monte carlo mcmc methods further reveal that the specification of jacquier et al is inferior simulation experiments are conducted to study the sampling properties of bayes mcmc for the conventional model

brief sampled data iterative learning control for nonlinear systems with arbitrary relative degree in this paper a sampled daata iterative learning control method is proposed for nonlinear systems without restriction on system relative degree the learning algorithm does not require numerical differentiations of any order from the tracking error a sufficient condition is derived to guarantee the convergence of the system output at each sampling instant to the desired trajectory numerical simulation is conducted to demonstrate the theoretical result

a fast improvement to the em algorithm on its own terms the em algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models it is easy to apply in many problems and is stable but slow the algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the louis method is performed newton type or other gradient methods are faster and provide error estimates but tend to be unstable and require the analytical evaluation of likelihoods to derive expressions for the score function and at least approximations to the fisher information matrix the purpose of this paper is to expand on a result by fisher that permits a unification of em methodology and newton methods the evaluation of the individual observation by observation score functions of the incomplete data is a byproduct of the application of the e step of the em algorithm once these become available the fisher information matrix may be consistently estimated and the m step may be replaced by a fast newton type step

testing ar 1 against ma 1 disturbances in an error component model this paper derives three lm statistics for an error component model with first order serially correlated errors the first lm statistic jointly tests for zero first order serial correlation and random individual effects the second lm statistic tests for zero first order serial correlation assuming fixed individual effects and the third lm statistic tests for zero first order serial correlation assuming random individual effects in all three cases the corresponding lm statistic is the same whether the alternative is ar 1 or ma 1 this paper also derives two extensions of the burke godfrey and termayne 1990 test from the time series to the panel data literature the first tests the null of ar 1 disturbances against ma 1 disturbances and the second tests the null of ma 1 disturbances against ar 1 disturbances in an error component model these tests are computationally simple requiring only ols or within residuals the small sample performance of these tests are studied using monte carlo experiments

decentralized quantized control for ncss under periodic protocol this paper is concerned with the problem of designing decentralized quantized controller for networked control systems ncss that are subject to time varying transmission intervals packet dropout communication constraints and limited bandwidth the convex overapproximation method proposed in donkers and heemels 2011 is used to handle with time varying transmission intervals packet dropout process in this paper is modeled as both independent identically distributed process and homogeneous markov jumping process the uniform quantizer is adopted here to deal with limited bandwidth in quantization strategy which switches between zooming out and zooming in modes a variable called proportionality coefficient of saturation value is used to handle with the complex coupling relationship between system states and quantized variables periodic protocol is used here to deal with communication constraints under which only one node can access the network and send its information per transmission within this setup we derive stability results in terms of linear matrix inequalities lmis an illustrative example is given to show the usefulness of the proposed framework for the stability analysis of some classes of ncss

implicit alternatives and the local power of test statistics the local power of test statistics is analyzed by extending the notion of pitman sequences to sequences of data generating processes dgp s that approach the null hypothesis without necessarily satisfying the alternative a space of probability densities is defined and endowed with the structure of an infinite dimensional hilbert manifold which permits a geometrical interpretation of hypothesis testing the three classical test statistics lr wald and lm are shown to tend asymptotically to the same random variable under all sequences of local dgp s the power of these statistics is seen to depend on the null the alternative and the sequence of dgp s in a simple and geometrically intuitive way moreover for any test statistic that is asymptotically chi squared under the null there exists an implicit alternative hypothesis against which that statistic will have highest power and which coincides with the explicit alternative for the classical test statistics

network decentralized control strategies for stabilization we consider the problem of stabilizing a class of systems formed by a set of decoupled subsystems nodes interconnected through a set of controllers arcs controllers are network decentralized i e they use information exclusively from the nodes they interconnect this condition requires a block structured feedback matrix having the same structure as the transpose of the overall input matrix of the system if the subsystems do not have common unstable eigenvalues we demonstrate that the problem is solvable in the general case we provide sufficient conditions for solvability when subsystems are identical and each input agent controls a pair of subsystems with input matrices having opposite sign flow networks we prove that stabilization is possible if and only if the system is connected with the external environment our proofs are constructive and lead to structured linear matrix inequalities lmis

a combined adaptive law for fuzzy iterative learning control of nonlinear systems with varying control tasks to deal with the iterative control of uncertain nonlinear systems with varying control tasks nonzero initial resetting state errors and nonrepeatable mismatched input disturbance a new adaptive fuzzy iterative learning controller is proposed in this paper the main structure of this learning controller is constructed by a fuzzy learning component and a robust learning component for the fuzzy learning component a fuzzy system used as an approximator is designed to compensate for the plant nonlinearity for the robust learning component a sliding mode like strategy is applied to overcome the nonlinear input gain input disturbance and fuzzy approximation error both designs are based on a time varying boundary layer which is introduced not only to solve the problem of initial state errors but also to eliminate the possible undesirable chattering behavior a new adaptive law combining time and iteration domain adaptation is derived to search for suitable values of control parameters and then guarantee the closed loop stability and error convergence this adaptive algorithm is designed without using projection or deadzone mechanism with a suitable choice of the weighting gain the memory size for the storage of parameter profiles can be greatly reduced it is shown that all the adjustable parameters as well as internal signals remain bounded for all iterations moreover the norm of tracking state error vector will asymptotically converge to a tunable residual set even when the desired tracking trajectory is varying between successive iterations

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

a hidden seasonal switching model for high resolution breakpoint rainfall data 1 a nonhomogeneous hidden semi markov model nhsmm for breakpoint rainfall data is proposed which extends the homogeneous hidden semi markov model hsmm of sansom and thomson 2001 to incorporate stochastic seasonality the nhsmm model is able to switch seasons at times that are earlier or later than expected and in this way is able to explain additional seasonal variability due to varying length seasons the model s hidden rainfall states align with precipitation mechanisms that are seasonally invariant but the state dynamics are assumed to vary with season recursions for constructing the likelihood are developed and the em algorithm used to fit the parameters of the model an application of the model to breakpoint rainfall measurements from invercargill new zealand is discussed and the results of fitting a number of different nhsmms are compared to those from fitting the non seasonal homogeneous hsmm

bayesian analysis of stochastic volatility models with fat tails and correlated errors abstract the basic univariate stochastic volatility model specifies that conditional volatility follows a log normal auto regressive model with innovations assumed to be independent of the innovations in the conditional mean equation since the introduction of practical methods for inference in the basic volatility model j business econom statist 12 4 371 it has been observed that the basic model is too restrictive for many financial series we extend the basic svol to allow for a so called leverage effect via correlation between the volatility and mean innovations and for fat tails in the mean equation innovation a bayesian markov chain monte carlo algorithm is developed for the extended volatility model thus far likelihood based inference for the correlated svol model has not appeared in the literature we develop bayes factors to assess the importance of the leverage and fat tail extensions sampling experiments reveal little loss in precision from adding the model extensions but a large loss from using the basic model in the presence of mis specification there is overwhelming evidence of a leverage effect for weekly and daily equity indices the evidence in favor of fat tails is very strong for daily exchange rate and equity indices but less so for weekly data we also find that volatility estimates from the extended model are markedly different from those produced by the basic svol