bias correction of two state latent markov process parameter estimates under misclassification a discretely observed two state process may misclassify the state of an unobservable continuous time two state markov process we examine the behaviour of maximum likelihood transition probability estimates as functions of known misclassification probabilities since maximum likelihood estimators are not available in closed form we provide two alternatives for bias adjusted estimation in the case of large samples the asymptotic bias is quantified and estimators are constructed iteratively using transition counts and specified misclassification probabilities for finite samples we provide an approximation based on partial derivatives estimators that are bias adjusted to a first approximation are easily constructed and may serve well when misclassification probabilities are known to be small simulation studies reveal the effect of misclassification on estimation repeated diagnostic testing data illustrate the approaches

stochastic stabilization and destabilization of nonlinear differential equations abstract this paper is concerned with the stochastic stabilization and destabilization of nonlinear differential equations which more precisely further develops the general theory of stochastic stabilization and destabilization that was studied by mao 1994 4 and appleby et al 2008 1 the proposed results are of substantial improvements and reveal the more fundamental principle for stochastic stabilization and destabilization of dynamical systems which is also verified with examples of application to mass action systems

stabilization of hybrid stochastic differential equations by feedback control based on discrete time state observations recently mao 2013 discusses the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations mao 2013 also obtains an upper bound on the duration between two consecutive state observations however it is due to the general technique used there that the bound on is not very sharp in this paper we will consider a couple of important classes of hybrid sdes making full use of their special features we will be able to establish a better bound on our new theory enables us to observe the system state less frequently so costs less but still to be able to design the feedback control based on the discrete time state observations to stabilize the given hybrid sdes in the sense of mean square exponential stability

stochastic maximum principle for stochastic recursive optimal control problem under volatility ambiguity we study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by g brownian motion some of the economic and financial optimization problems with volatility ambiguity can be formulated as such problems unlike the classical variational approach we establish the maximum principle by the linearization and weak convergence methods

estimation of operating characteristics for dependent diagnostic tests based on latent markov models we describe a method for making inferences about the joint operating characteristics of multiple diagnostic tests applied longitudinally and in the absence of a definitive reference test log linear models are adopted for the classification distributions conditional on the latent state where inclusion of appropriate interaction terms accommodates conditional dependencies among the tests a marginal likelihood is constructed by marginalizing over a latent two state markov process specific latent processes we consider include a first order markov model a second order markov model and a time nonhomogeneous markov model although the method is described in full generality adaptations to handle missing data are described model diagnostics are considered based on the bootstrap distribution of conditional residuals the methods are illustrated by application to a study of diffuse bilateral infiltrates among patients in intensive care wards in which the objective was to assess aspects of validity and clinical agreement

marginal methods for correlated binary data with misclassified responses misclassification is a longstanding concern in medical research although there has been much research concerning error prone covariates relatively little work has been directed to problems with response variables subject to error in this paper we focus on misclassification in clustered or longitudinal outcomes we propose marginal analysis methods to handle binary responses which are subject to misclassification the proposed methods have several appealing features including simultaneous inference for both marginal mean and association parameters and they can handle misclassified responses for a number of practical scenarios such as the case with a validation subsample or replicates furthermore the proposed methods are robust to model misspecification in a sense that no full distributional assumptions are required numerical studies demonstrate satisfactory performance of the proposed methods under a variety of settings copyright 2011 oxford university press

seemingly unrelated regressions under additive heteroscedasticity theory and share equation applications abstract we derive consistent asymptotically efficient and asymptotically normal estimators for sur systems that have additive heteroscedastic contemporaneous correlation both our estimator for the location vector and the parameters of the covariance matrix possess these properties the procedure is superior to other methods because we use gls to estimate the parameters of the covariance matrix our method also permits the use of cross equation parameter restrictions we discuss how this type of heteroscedasticity arises naturally in share equation systems and random coefficient models and how these models can be uniquely estimated with our two step estimation technique

stabilisation of hybrid stochastic systems with levy noise by discrete time feedback control this paper is devoted to deal with the stabilisation problems of continuous time hybrid stochastic systems often described by stochastic differential equations with markovian switching with levy

almost sure exponential stabilization by discrete time stochastic feedback control given an unstable linear scalar differential equation dot x t alpha x t alpha 0 we will show that the discrete time stochastic feedback control sigma x t tau tau db t can stabilize it that is we will show that the stochastically controlled system dx t alpha x t dt sigma x t tau tau db t is almost surely exponentially stable when sigma 2 2 alpha and tau 0 is sufficiently small where b t is a brownian motion and t tau is the integer part of t tau we will also discuss the nonlinear stabilization problem by a discrete time stochastic feedback control the reason why we consider the discrete time stochastic feedback control is because that the state of the given system is in fact observed only at discrete times say 0 tau 2 tau ldots for example where tau 0 is the duration between two consecutive observations accordingly the stochastic feedback control should be designed based on these discrete time observations namely the stochastic feedback control should be of the form sigma x t tau tau db t from the point of control cost it is cheaper if one only needs to observe the state less frequently it is therefore useful to give a bound on tau from below as larger as better

the analysis of panel data under a markov assumption abstract methods for the analysis of panel data under a continuous time markov model are proposed we present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models and for other process characteristics such as mean sojourn times and equilibrium distributions generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented and an example based on a longitudinal study of the smoking habits of school children is discussed questions of embeddability and estimation are examined

estimation of parasitic infection dynamics when detectability is imperfect the simultaneous estimation of infection rate cure rate and detectability of parasitic infections is considered a new method for this estimation based on a simple statistical model assuming constant transition rates between parasite states is proposed repeated observations on the infection status of the same individuals is required for this method a maximum likelihood approach is used for parameter estimation and the calculation of standard errors of the estimates the method is illustrated by a longitudinal study of the presence of giardia lamblia infection in kenyan children

technical communique stabilization of continuous time hybrid stochastic differential equations by discrete time feedback control in this paper we are concerned with the mean square exponential stabilization of continuous time hybrid stochastic differential equations also known as stochastic differential equations with the markovian switching by discrete time feedback controls although the stabilization by continuous time feedback controls for such equations has been discussed by several authors see e g ji and chizeck 1990 mao lam and huang 2008 mao yin and yuan 2007 wu shi and gao 2010 wu su and shi 2012 there is so far no result on the stabilization by discrete time feedback controls our aim here is to initiate the study in this area by establishing some new results

quasi sure exponential stabilization of stochastic systems induced by g brownian motion with discrete time feedback control abstract in this paper we aim to study quasi sure exponential stabilization of stochastic systems induced by g brownian motion with discrete time feedback control as for an unstable system we use discrete stochastic feedback control to stabilize it if stochastic differential equation driven g brownian motion g sde in short is quasi sure exponential stability it reveals that there exist the discrete step size h 0 and a positive constant h with h h and the responding stochastically controlled system is also quasi sure exponential stability finally a simple example is also provided to show the validity of the control strategy

almost sure exponential stabilization of hybrid stochastic coupled systems via intermittent noises a higher order nonlinear growth condition abstract in this paper the almost sure exponential stabilization problem of hybrid coupled systems with two independent noises is investigated wherein one of the noises exists periodically intermittently different from existing literature on coupled systems the functions in the system we addressed are nonlinear without the linear growth condition by employing graph theory and lyapunov method almost sure exponential stabilization criterion of hybrid coupled systems with two independent noises is derived the criterion is closely associated with the noise strength the number of vertex systems the coupling strength the existence interval and period of intermittent noises meanwhile the theoretical results are applied to a higher order nonlinear stochastic coupled electronic oscillators system and the corresponding numerical example is presented

sample path properties of g brownian motion abstract the present article is devoted to careful study of sample pathwise properties of g brownian motion i e those which quasi surely hold for all paths we develop a comparison machinery to analyze the irregular functional of g brownian paths and to characterize their zero sets the key ingredient of our approach is an estimate of solutions to g heat equations as a result we prove that the g brownian motion path is nowhere differentiable

stochastic stabilization and destabilization it is shown in this paper that any nonlinear systems dot x t f x t t in rd can be stabilized by brownian motion provided f hook x t k x for some k 0 on the other hand this system can also be destabilized by brownian motion if the dimension d 2 similar results are also obtained for any given stochastic differential equation dx t f hook x t t g x t t dw t

stochastic stabilization of hybrid differential equations this paper aims to determine whether or not a stochastic state feedback control can stabilize a given linear or nonlinear hybrid system new methods are developed and sufficient conditions on the stability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization by stochastic feedback controls two types of structure controls namely state feedback and output injection are discussed our stabilization criteria are in terms of linear matrix inequalities lmis whence the feedback controls can be designed more easily in practice a couple of examples and computer simulations are worked out to illustrate our theory

lyapunov type conditions and stochastic differential equations driven by g brownian motion abstract this paper studies the solvability and the stability of stochastic differential equations driven by g brownian motion gsdes in particular the existence and uniqueness of the solution for locally lipschitz gsdes are obtained by localization methods also the stability of such gsdes is discussed with lyapunov type conditions

semi markov models with phase type sojourn distributions continuous time multistate models are widely used for categorical response data particularly in the modeling of chronic diseases however inference is difficult when the process is only observed at discrete time points with no information about the times or types of events between observation times unless a markov assumption is made this assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state such a formulation results in a semi markov model we show that the computational problems associated with fitting semi markov models to panel observed data can be alleviated by considering a class of semi markov models with phase type sojourn distributions this allows methods for hidden markov models to be applied in addition extensions to models where observed states are subject to classification error are given the methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post lung transplantation patients

stabilisation of hybrid stochastic differential equations by delay feedback control this paper is concerned with the exponential mean square stabilisation of hybrid stochastic differential equations also known as stochastic differential equations with markovian switching by delay feedback controls although the stabilisation by non delay feedback controls for such equations has been discussed by several authors there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap to make our theory more understandable as well as to avoid complicated notations we will restrict our underlying hybrid stochastic differential equations to a relatively simple form however our theory can certainly be developed to cope with much more general equations without any difficulty

stochastic stabilisation of functional differential equations in this paper we investigate the problem of stochastic stabilisation for a general nonlinear functional differential equation given an unstable functional differential equation dx t dt f t xt we stochastically perturb it into a stochastic functional differential equation dx t f t xt dt x t db t where is a matrix and b t a brownian motion while xt x t 0 under the condition that f satisfies the local lipschitz condition and obeys the one side linear bound we show that if the time lag is sufficiently small there are many matrices for which the stochastic functional differential equation is almost surely exponentially stable while the corresponding functional differential equation dx t dt f t xt may be unstable

asymptotic distribution of the hildreth houck estimator abstract hildreth and houck 1968 discussed a random coefficients regression model and proposed several weighted least squares estimators with estimated weights they conjectured that the estimators are asymptotically equivalent to the weighted least squares estimator with known weights in this article the conjecture is verified providing the first correct proof that hildreth houck estimators are asymptotically normal one of hildreth and houck s conditions is eliminated an easily applied version of a broadly applicable theorem of carroll and ruppert 1982 is stated

stabilization of hybrid systems by feedback control based on discrete time state observations recently mao automatica j ifac 49 2013 pp 3677 3681 initiated the study the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations in the same paper mao also obtains an upper bound on the duration tau between two consecutive state observations however it is due to the general technique used there that the bound on tau is not very sharp in this paper we will be able to establish a better bound on tau making use of lyapunov functionals we will discuss the stabilization not only in the sense of exponential stability as mao does in automatica j ifac 49 2013 pp 3677 3681 but also in other sense that of h infty stability or asymptotic stability we will consider not only the mean square stability but also the almost sure stability

correcting for misclassification for a monotone disease process with an application in dental research motivated by a longitudinal oral health study we evaluate the performance of binary markov models in which the response variable is subject to an unconstrained misclassification process and follows a monotone or progressive behavior theoretical and empirical arguments show that the simple version of the model can be used to estimate the prevalence incidences and misclassification parameters without the need of external information and that the incidence estimators associated with the model outperformed approaches previously proposed in the literature we propose an extension of the simple version of the binary markov model to describe the relationship between the covariates and the prevalence and incidence allowing for different classifiers we implemented a bayesian version of the extended model and show that under the settings of our motivating example the parameters can be estimated without any external information finally the analyses of the motivating problem are presented

quasi sure exponential stability and stabilisation of stochastic delay differential equations under g expectation framework in this work we obtain the sufficient conditions to examine quasi sure exponential stability of stochastic delay differential equation under g expectation framework in short g sdde our argumen

brief paper almost sure exponential stabilisation of stochastic systems by state feedback control so far a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean square stability this paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean square sense the results are expressed in terms of linear matrix inequalities lmis which are easy to be checked in practice by using matlab toolbox moreover the control structure in this paper appears not only in the drift part but also in the diffusion part of the underlying stochastic system

stabilization of stochastic differential equations driven by g brownian motion with feedback control based on discrete time state observation abstract this paper mainly concerns the stability of the solutions for stochastic differential equations driven by g brownian motion g sdes via feedback control based on discrete time state observation more precisely the discrete time state feedback control is included in the drift coefficient of the g sdes by constructing an appropriate g lyapunov function a set of conditions is obtained for the h stability asymptotic stability and mean square exponential stability of the controlled systems finally an example with numerical simulation is presented to illustrate the effectiveness of the proposed control design technique

robust estimation in heteroscedastic linear models we consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter theta we propose robust estimates for the regression parameter beta and show that as long as a reasonable starting estimate of theta is available our estimates of beta are asymptotically equivalent to the natural estimate obtained with known variances a particular method for estimating theta is proposed and shown by monte carlo to work quite well especially in power and exponential models for the variances we also briefly discuss a feedback estimate of beta

stabilization and destabilization of hybrid systems of stochastic differential equations this paper aims to determine whether or not a stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system new methods are developed and sufficient conditions on the stability and instability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization and destabilization

modeling of multivariate monotone disease processes in the presence of misclassification motivated by a longitudinal oral health study the signal tandmobiel study we propose a multivariate binary inhomogeneous markov model in which unobserved correlated response variables are subject to an unconstrained misclassification process and have a monotone behavior the multivariate baseline distributions and markov transition matrices of the unobserved processes are defined as a function of covariates through the specification of compatible full conditional distributions distinct misclassification models are discussed in all cases the possibility that different examiners were involved in the scoring of the responses of a given subject across time is taken into account a full bayesian implementation of the model is described and its performance is evaluated using simulated data we provide theoretical and empirical evidence that the parameters can be estimated without any external information about the misclassification parameters finally the analyses of the motivating study are presented a

bias and efficiency loss due to misclassified responses in binary regression summary methods that ignore errors in binary responses yield biased estimators of the associations of covariates with response this paper derives general expressions for the magnitude of the bias due to errors in the response and shows that unless both the sensitivity and specificity are very high ignoring errors in the responses will yield highly biased covariate effect estimators when the true error free response follows a generalised linear model and misclassification probabilities are known and independent of covariate values responses observed with error also follow such a model with a modified link function we describe a simple method to obtain consistent estimators of covariate effects and associated errors in this case and derive an expression for the asymptotic relative efficiency of covariate effect estimators from the correct likelihood for the responses with errors with respect to estimates based on the true error free responses this expression shows that errors in the response can lead to substantial losses of information about covariate effects data from a study on infection with human papilloma virus among women and simulation studies motivate this work and illustrate the findings

comparison of variance estimation approaches in a two state markov model for longitudinal data with misclassification we examine the behaviour of the variance covariance parameter estimates in an alternating binary markov model with misclassification transition probabilities specify the state transitions for a process that is not directly observable the state of an observable process which may not correctly classify the state of the unobservable process is obtained at discrete time points misclassification probabilities capture the two types of classification errors variance components of the estimated transition parameters are calculated with three estimation procedures observed information jackknife and bootstrap techniques simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation the three approaches generally provide similar variance estimates for large samples and moderate misclassification in these situations the resampling methods are reasonable alternatives when programming partial derivatives is not appealing with smaller chains or higher misclassification probabilities the bootstrap method appears to be the best choice

mean square convergence of explicit two step methods for highly nonlinear stochastic differential equations abstract in this paper we propose the projected two step euler maruyama method and the projected two step milstein method for highly nonlinear stochastic differential equations under a global monotonicity condition we first examine the strong convergence in mean square sense for these two explicit schemes based on the notions of stochastic stability and b consistency for two step methods we prove that the convergence rates of the projected two step euler maruyama method and the projected two step milstein method are 1 2 and 1 respectively in particular our results can be applied to equations with super linearly growing drift and diffusion coefficients finally we numerically verify the optimal mean square convergence orders of these two schemes by a series of examples