partial synchronization from symmetry towards stability abstract in this paper we study the existence and stability of linear invariant manifolds in a network of coupled identical dynamical systems symmetry under permutation of different units of the network is helpful to construct explicit formulae for linear invariant manifolds of the network in order to classify them and to examine their stability through lyapunov s direct method

order selection in finite mixture models with a nonsmooth penalty order selection is a fundamental and challenging problem in the application of finite mixture models in this article we develop a new penalized likelihood approach the new method modified smoothly clipped absolute deviation mscad deviates from information based methods such as akaike information criterion aic and bayesian information criterion bic by introducing two penalty functions that depend on the mixing proportions and the component parameters it is consistent at estimating both the order of the mixture model and the mixing distribution simulations show that mscad has much better performance than a number of existing methods two real data examples are examined to illustrate the performance of mscad

detecting features in spatial point processes with clutter via model based clustering abstract we consider the problem of detecting features such as minefields or seismic faults in spatial point processes when there is substantial clutter we use model based clustering based on a mixture model for the process in which features are assumed to generate points according to highly linear multivariate normal densities and the clutter arises according to a spatial poisson process nonlinear features are represented by several densities giving a piecewise linear representation hierarchical model based clustering provides a first estimate of the features and this is then refined using the em algorithm the number of features is estimated from an approximation to its posterior distribution the method gives good results for the minefield and seismic fault problems software to implement it is available on the world wide web

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

synchronization conditions and desynchronizing patterns in coupled limit cycle and chaotic systems many coupling schemes for both limit cycle and chaotic systems involve adding linear combinations of dynamical variables from various oscillators in an array of identical oscillators to each oscillator node of the array examples of such couplings are nearest neighbor diffusive coupling all to all coupling star coupling and random linear couplings we show that for a given oscillator type and a given choice of oscillator variables to use in the coupling arrangement the stability of each linear coupling scheme can be calculated from the stability of any other for symmetric coupling schemes in particular when there are desynchronization bifurcations our approach reveals interesting patterns and relations between desynchronous modes including the situation in which for some systems there is a limit on the number of oscillators that can be coupled and still retain synchronous chaotic behavior

mixture models with a prior on the number of components abstracta natural bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric dirichlet weights and put a prior on the number of components that is to use a mixture of finite mixtures mfm the most commonly used method of inference for mfms is reversible jump markov chain monte carlo but it can be nontrivial to design good reversible jump moves especially in high dimensional spaces meanwhile there are samplers for dirichlet process mixture dpm models that are relatively simple and are easily adapted to new applications it turns out that in fact many of the essential properties of dpms are also exhibited by mfms an exchangeable partition distribution restaurant process random measure representation and stick breaking representation and crucially the mfm analogues are simple enough that they can be used much like the corresponding dpm properties consequently many of the powerful methods developed for inference in dpms

mixture of regression models with varying mixing proportions a semiparametric approach in this article we study a class of semiparametric mixtures of regression models in which the regression functions are linear functions of the predictors but the mixing proportions are smoothing functions of a covariate we propose a one step backfitting estimation procedure to achieve the optimal convergence rates for both regression parameters and the nonparametric functions of mixing proportions we derive the asymptotic bias and variance of the one step estimate and further establish its asymptotic normality a modified expectation maximization type em type estimation procedure is investigated we show that the modified em algorithms preserve the asymptotic ascent property numerical simulations are conducted to examine the finite sample performance of the estimation procedures the proposed methodology is further illustrated via an analysis of a real dataset

extending the akaike information criterion to mixture regression models we examine the problem of jointly selecting the number of components and variables in finite mixture regression models we find that the akaike information criterion is unsatisfactory for this purpose because it overestimates the number of components which in turn results in incorrect variables being retained in the model therefore we derive a new information criterion the mixture regression criterion mrc that yields marked improvement in model selection due to what we call the clustering penalty function moreover we prove the asymptotic efficiency of the mrc we show that it performs well in monte carlo studies for the same or different covariates across components with equal or unequal sample sizes we also present an empirical example on sales territory management to illustrate the application and efficacy of the mrc finally we generalize the mrc to mixture quasi likelihood and mixture autoregressive models thus extending its applicability to non gaussian models discrete responses and d

on the unfolding of a blowout bifurcation abstract suppose a chaotic attractor a in an invariant subspace loses stability on varying a parameter at the point of loss of stability the most positive lyapunov exponent of the natural measure on a crosses zero at what has been called a blowout bifurcation we introduce the notion of an essential basin of an attractor a this is the set of points x such that accumulation points of the sequence of measures 1 n n 1 k 0 f k x are supported on a we characterise supercritical and subcritical scenarios according to whether the lebesgue measure of the essential basin of a is positive or zero we study a drift diffusion model and a model class of piecewise linear mappings of the plane in the supercritical case we find examples where a lyapunov exponent of the branch of attractors may be positive hyperchaos or negative depending purely on the dynamics far from the invariant subspace for the mappings we find asymptotically linear scaling of lyapunov exponents average distance from the subspace and basin size on varying a parameter we conjecture that these are general characteristics of blowout bifurcations

a constrained formulation of maximum likelihood estimation for normal mixture distributions in this context the normal densities are sometimes referred to as component densities the log likelihood function l zy corresponding to a random sample xl xnj is defined by l ty ek 1 10g pm xk y the first problem associated with maximum likelihood estimation arises from the unboundedness of l qy on r day 1969 a global maximum likelihood estimate always fails to exist in addition the unboundedness of l y causes failures of optimization algorithms of both the em redner and walker 1984 and quasi newton fowlkes 1979 types in spite of the unboundedness of l 4y statistical theory kiefer 1978 guarantees that a particular local maximizer of l y is strongly consistent and asymptotically efficient several local maximizers can exist for a given sample and the other major maximum likelihood difficulty is in determining when the correct one has been found day 1969 noted that spurious maximizers corresponding to parameter points having some component standard deviations very small relative to others are generated by any small number of sample points grouped sufficiently close together the spurious maximizers like the unboundedness of l zy can create difflculties when using the em or quasi newton algorithms the constrained maximum likelihood formulation presented in the next section avoids the unconstrained problems of singularities and spurious maximizers of the type noted by day section 3 contains the statement and proof of a consistency result for the corresponding constrained estimator

optimal periodic orbits of chaotic systems occur at low period invariant sets embedded in a chaotic attractor can generate time averages that differ from the average generated by typical orbits on the attractor motivated by two different topics namely controlling chaos and riddled basins of attraction we consider the question of which invariant set yields the largest optimal value of an average of a given smooth function of the system state we present numerical evidence and analysis that indicate that the optimal average is typically achieved by a low period unstable periodic orbit embedded in the chaotic attractor in particular our results indicate that if we consider that the function to be optimized depends on a parameter gamma then the lebesgue measure in gamma corresponding to optimal periodic orbits of period ital p or greater decreases exponentially with increasing ital p furthermore the set of parameter values for which optimal orbits are nonperiodic typically has zero lebesgue measure copyright ital 1996 the american physical society

time and causality a monte carlo assessment of the timing of events approach we present new monte carlo evidence regarding the feasibility of separating causality from selection within non experimental duration data by means of the non parametric maximum likelihood estimator npmle key findings are i the npmle is extremely reliable and it accurately separates the causal effects of treatment and duration dependence from sorting effects almost regardless of the true unobserved heterogeneity distribution ii the npmle is normally distributed and standard errors can be computed directly from the optimally selected model and iii unjustified restrictions on the heterogeneity distribution e g in terms of a pre specified number of support points may cause substantial bias

mixtures of exponential distributions arbitrary nonparametric mixtures of exponential and weibull fixed shape distributions are considered as possible models for a lifetime distribution a characterization of such distributions is given by the well known characterization of laplace transforms the maximum likelihood estimate of the mixing distribution is investigated and found to be supported on a finite number of points it is shown to be unique and weakly convergent to the true mixing measure with probability one a practical algorithm for computing the maximum likelihood estimate is described its performance is briefly discussed and some illustrative examples given

gaussian distributions on riemannian symmetric spaces statistical learning with structured covariance matrices the riemannian geometry of covariance matrices has been essential to several successful applications in computer vision biomedical signal and image processing and radar data processing for these applications an important ongoing challenge is to develop riemannian geometric tools which are adapted to structured covariance matrices this paper proposes to meet this challenge by introducing a new class of probability distributions gaussian distributions of structured covariance matrices these are riemannian analogs of gaussian distributions which only sample from covariance matrices having a preassigned structure such as complex toeplitz or block toeplitz the usefulness of these distributions stems from three features 1 they are completely tractable analytically or numerically when dealing with large covariance matrices 2 they provide a statistical foundation to the concept of structured riemannian barycentre i e frechet or geometric mean and 3 they lead to efficient statistical learning algorithms which realise among others density estimation and classification of structured covariance matrices this paper starts from the observation that several spaces of structured covariance matrices considered from a geometric point of view are riemannian symmetric spaces accordingly it develops an original theory of gaussian distributions on riemannian symmetric spaces of their statistical inference and of their relationship to the concept of riemannian barycentre then it uses this original theory to give a detailed description of gaussian distributions of three kinds of structured covariance matrices complex toeplitz and block toeplitz finally it describes algorithms for density estimation and classification of structured covariance matrices based on gaussian distribution mixture models

duration dependence and nonparametric heterogeneity a monte carlo study we examine the behaviour of the nonparametric maximum likelihood estimator npmle for a discrete duration model with unobserved heterogeneity and unknown duration dependence we find that a nonparametric specification of either the duration dependence or unobserved heterogeneity when the other feature of the hazard is known to be absent leads to estimators that are well behaved even in modestly sized samples in contrast there is a large and systematic bias in the parameters of these components when both are specified nonparametrically as well as a complementary bias in the coefficients on observed heterogeneity furthermore these biases diminish very gradually as sample size increases we find that a minor modification of the quasilikelihood that penalizes specifications with many points of support leads to a dramatic improvement

testing the order of a model this paper deals with order identification for nested models in the i i d framework we study the asymptotic efficiency of two generalized likelihood ratio tests of the order they are based on two estimators which are proved to be strongly consistent a version of stein s lemma yields an optimal underestimation error exponent the lemma also implies that the overestimation error exponent is necessarily trivial our tests admit non trivial underestimation error exponents the optimal underestimation error exponent is achieved in some situations the overestimation error can decay exponentially fast with respect to a positive power of the number of observations these results are proved under mild assumptions by relating the underestimation resp overestimation error to large resp moderate deviations of the log likelihood process in particular it is not necessary that the classical cramer condition be satisfied namely the log densities are not required to admit every exponential moment three benchmark examples with specific difficulties location mixture of normal distributions abrupt changes and various regressions are detailed so as to illustrate the generality of our results

testing for a finite mixture model with two components summary we consider a finite mixture model with k components and a kernel distribution from a general one parameter family the problem of testing the hypothesis k 2 versus k 3 is studied there has been no general statistical testing procedure for this problem we propose a modified likelihood ratio statistic where under the null and the alternative hypotheses the estimates of the parameters are obtained from a modified likelihood function it is shown that estimators of the support points are consistent the asymptotic null distribution of the modified likelihood ratio test proposed is derived and found to be relatively simple and easily applied simulation studies for the asymptotic modified likelihood ratio test based on finite mixture models with normal binomial and poisson kernels suggest that the test proposed performs well simulation studies are also conducted for a bootstrap method with normal kernels an example involving foetal movement data from a medical study illustrates the testing procedure

hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems the paper presents a qualitative analysis of an array of diffusively coupled identical continuous time dynamical systems the effects of full partial anti phase and in phase anti phase chaotic synchronization are investigated via the linear invariant manifolds of the corresponding differential equations existence of various invariant manifolds a self similar behavior a hierarchy and embedding of the manifolds of the coupled system are discovered sufficient conditions for the stability of the invariant manifolds are obtained via the method of lyapunov functions conditions under which full global synchronization can not be achieved even for the largest coupling constant are defined the general rigorous results are illustrated through examples of coupled lorenz like and coupled rossler systems

consistency of a recursive estimate of mixing distributions mixture models have received considerable attention recently and newton sankhy ser a 64 2002 306 322 proposed a fast recursive algorithm for estimating a mixing distribution we prove almost sure consistency of this recursive estimate in the weak topology under mild conditions on the family of densities being mixed this recursive estimate depends on the data ordering and a permutation invariant modification is proposed which is an average of the original over permutations of the data sequence a rao blackwell argument is used to prove consistency in probability of this alternative estimate several simulations are presented comparing the finite sample performance of the recursive estimate and a monte carlo approximation to the permutation invariant alternative along with that of the nonparametric maximum likelihood estimate and a nonparametric bayes estimate

robust estimation of mixture complexity in many applications it is important to find the mixture with fewest number of components known as the mixture complexity that provides a satisfactory fit to the data this article focuses on developing an estimator of mixture complexity that is consistent when the form of component densities are unknown but are postulated to be members of some parametric family and is simultaneously robust against model misspecification we treat the estimation of mixture complexity as a model selection problem and construct an estimator of mixture complexity as a byproduct of minimizing a hellinger information criterion this estimator is shown to be consistent for any parametric family of mixtures when the model is correctly specified monte carlo simulations for a wide variety of normal mixtures show that our estimator is very competitive with several others in the literature in correctly identifying the true mixture complexity the basic construction being firmly rooted in the minimum hellinger distance approach

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

non parametric estimation of finite mixtures from repeated measurements this paper provides methods to estimate finite mixtures from data with repeated measurements non parametrically we present a constructive identification argument and use it to develop simple two step estimators of the component distributions and all their functionals we discuss a computationally efficient method for estimation and derive asymptotic theory simulation experiments suggest that our theory provides confidence intervals with good coverage in small samples

semiparametric estimation of a two component mixture model suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter such a model is known to be nonidentifiable from a nonparametric viewpoint however if we assume that the unknown mixed distribution is symmetric we obtain the identifiability of this model which is then defined by four unknown parameters the mixing proportion two location parameters and the cumulative distribution function of the symmetric mixed distribution we propose estimators for these four parameters when no training data is available our estimators are shown to be strongly consistent under mild regularity assumptions and their convergence rates are studied their finite sample properties are illustrated by a monte carlo study and our method is applied to real data

non parametric identification and estimation of the number of components in multivariate mixtures this article analyzes the identiability of the number of components in k variate mcomponent nite mixture models in which each component distribution has independent marginals including models in latent class analysis without making parametric assumptions on the component distributions we investigate how one can identify the number of components from the distribution function of the observed data when k 2 a lower bound on the number of components m is nonparametrically identiable from the rank of a matrix constructed from the distribution function of the observed variables building on this identication condition we develop a procedure to consistently estimate a lower bound on the number of components

nonparametric identification and maximum likelihood estimation for hidden markov models nonparametric identification and maximum likelihood estimation for finite state hidden markov models are investigated we obtain identification of the parameters as well as the order of the markov chain if the transition probability matrices have full rank and are ergodic and if the state dependent distributions are all distinct but not necessarily linearly independent based on this identification result we develop a nonparametric maximum likelihood estimation theory first we show that the asymptotic contrast the kullback leibler divergence of the hidden markov model also identifies the true parameter vector nonparametrically second for classes of state dependent densities which are arbitrary mixtures of a parametric family we establish the consistency of the nonparametric maximum likelihood estimator here identification of the mixing distributions need not be assumed numerical properties of the estimates and of nonparametric goodness of fit tests are investigated in a simulation study

bounds for bayesian order identification with application to mixtures the efficiency of two bayesian order estimators is studied by using nonparametric techniques we prove new underestimation and overestimation bounds the results apply to various models including mixture models in this case the errors are shown to be o e an and o log n b p n a b 0 respectively 1 introduction order identification deals with the estimation and test of a structural parameter which indexes the complexity of a model in other words the most economical representation of a random phenomenon is sought this problem is encountered in many situations including mixture models 13 19 with an unknown number of components cluster analysis 9 when the number of clusters is unknown autoregressive models 1 when the process memory is not known this paper is devoted to the study of two bayesian estimators of the order of a model frequentist properties of efficiency are particularly investigated we obtain new efficiency bounds under mild assumptions providing a theoretical answer to the questions raised for instance in 7 see their section 4

a mixed non homogeneous hidden markov model for categorical data with application to alcohol consumption hidden markov models hmms are frequently used to analyse longitudinal data where the same set of subjects is repeatedly observed over time in this context several sources of heterogeneity may arise at individual and or time level which affect the hidden process that is the transition probabilities between the hidden states in this paper we propose the use of a finite mixture of non homogeneous hmms nh hmms to face the heterogeneity problem the non homogeneity of the model allows us to take into account observed sources of heterogeneity by means of a proper set of covariates time and or individual dependent explaining the variations in the transition probabilities moreover we handle the unobserved sources of heterogeneity at the individual level due to for example omitted covariates by introducing a random term with a discrete distribution the resulting model is a finite mixture of nh hmm that can be used to classify individuals according to their dynamic behaviour or to estimate a mixed nh hmm without any assumption regarding the distribution of the random term following the non parametric maximum likelihood approach we test the effectiveness of the proposal through a simulation study and an application to real data on alcohol abuse

nonparametric inference in multivariate mixtures summary we consider mixture models in which the components of data vectors from any given subpopulation are statistically independent or independent in blocks we argue that if under this condition of independence we take a nonparametric view of the problem and allow the number of subpopulations to be quite general the distributions and mixing proportions can often be estimated root n consistently indeed we show that if the data are k variate and there are p subpopulations then for each p 2 there is a minimal value of k kp say such that the mixture problem is always nonparametrically identifiable and all distributions and mixture proportions are nonparametrically identifiable when k kp we treat the case p 2 in detail and there we show how to construct explicit distribution density and mixture proportion estimators converging at conventional rates other values of p can be addressed using a similar approach although the methodology becomes rapidly more complex as p increases

loss of synchronization in coupled rossler systems this paper considers the loss of synchronization for a system of two coupled rossler oscillators bifurcation curves for the transverse destabilization of low periodic orbits embedded in the synchronized chaotic state are obtained and we show that desynchronization for a pair of symmetrically coupled identical rossler systems is associated with different orbits undergoing transverse pitchfork or period doubling bifurcations the transverse destabilization of the period 1 orbit is examined in detail and we follow the sequence of bifurcations that the asynchronous periodic cycles undergo in the presence of an asymmetry in the coupling the transverse period doubling bifurcation remains essentially the same the transverse pitchfork bifurcation on the other hand is transformed into a transcritical riddling bifurcation if the interacting rossler oscillators have different parameter values the non generic character of the pitchfork bifurcation leads it to be replaced by a saddle node bifurcation occurring off the symmetric sub space finally we show how the transverse stability properties of the equilibrium point can be used to obtain approximative analytical results for the transverse stability of the coupled chaotic oscillators 2001 elsevier science b v all rights reserved

on choosing mixture components via non local priors choosing the number of mixture components remains an elusive challenge model selection criteria can be either overly liberal or conservative and return poorly separated components of limited practical use we formalize non local priors nlps for mixtures and show how they lead to well separated components with non negligible weight interpretable as distinct subpopulations we also propose an estimator for posterior model probabilities under local priors and nlps showing that bayes factors are ratios of posterior to prior empty cluster probabilities the estimator is widely applicable and helps to set thresholds to drop unoccupied components in overfitted mixtures we suggest default prior parameters based on multimodality for normal t mixtures and minimal informativeness for categorical outcomes we characterize theoretically the nlp induced sparsity derive tractable expressions and algorithms we fully develop normal binomial and product binomial mixtures but the theory computation and principles hold more generally we observed a serious lack of sensitivity of the bayesian information criterion insufficient parsimony of the akaike information criterion and a local prior and a mixed behaviour of the singular bayesian information criterion we also considered overfitted mixtures their performance was competitive but depended on tuning parameters under our default prior elicitation nlps offered a good compromise between sparsity and power to detect meaningfully separated components

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

parametric latent class joint model for a longitudinal biomarker and recurrent events a joint model for a longitudinal biomarker and recurrent events is proposed this general model accommodates the effects of covariates on the biomarker and event processes the effects of accumulating event occurrences and effects caused by interventions after each event occurrence association between the biomarker and recurrent event processes is captured through a latent class structure which also serves to handle an underlying heterogeneous population we use the em algorithm for maximum likelihood estimation of the model parameters and a penalized likelihood measure to determine the number of latent classes this joint model is validated by simulation and illustrated with a data set from epileptic seizure study

spectral curves and the mass of hyperbolic monopoles the moduli spaces of hyperbolic monopoles are naturally fibred by the monopole mass and this leads to a nontrivial mass dependence of the holomorphic data spectral curves rational maps holomorphic spheres associated to hyperbolic multi monopoles in this paper we obtain an explicit description of this dependence for general hyperbolic monopoles of magnetic charge two in addition we show how to compute the monopole mass of higher charge spectral curves with tetrahedral and octahedral symmetries spectral curves of euclidean monopoles are recovered from our results via an infinite mass limit

multilevel functional clustering analysis in this article we investigate clustering methods for multilevel functional data which consist of repeated random functions observed for a large number of units e g genes at multiple subunits e g bacteria types to describe the within and between variability induced by the hierarchical structure in the data we take a multilevel functional principal component analysis mfpca approach we develop and compare a hard clustering method applied to the scores derived from the mfpca and a soft clustering method using an mfpca decomposition in a simulation study we assess the estimation accuracy of the clustering membership and the cluster patterns under a series of settings small versus moderate number of time points various noise levels and varying number of subunits per unit we demonstrate the applicability of the clustering analysis to a real data set consisting of expression profiles from genes activated by immunity system cells prevalent response patterns are identified by clustering the expression profiles using our multilevel clustering analysis

discovering subpopulation structure with latent class mixed models the linear mixed model is a well known method for incorporating heterogeneity for example subject to subject variation into a statistical analysis for continuous responses however heterogeneity cannot always be fully captured by the usual assumptions of normally distributed random effects latent class mixed models offer a way of incorporating additional heterogeneity which can be used to uncover distinct subpopulations to incorporate correlated non normally distributed outcomes and to classify individuals the methodology is motivated with examples in health care studies and a detailed illustration is drawn from the nutritional prevention of cancer trials latent class models are used with longitudinal data on prostate specific antigen psa as well as incidence of prostate cancer the models are extended to accommodate prostate cancer as a survival endpoint this is compared to treating it as a binary endpoint four subpopulations are identified which differ both with regard to their psa trajectories and their incidence rates of prostate cancer

inference on the order of a normal mixture finite normal mixture models are used in a wide range of applications hypothesis testing on the order of the normal mixture is an important yet unsolved problem existing procedures often lack a rigorous theoretical foundation many are also hard to implement numerically in this article we develop a new method to fill the void in this important area an effective expectation maximization em test is invented for testing the null hypothesis of arbitrary order m 0 under a finite normal mixture model for any positive integer m 0 2 the limiting distribution of the proposed test statistic is we also use a novel computer experiment to provide empirical formulas for the tuning parameter selection the finite sample performance of the test is examined through simulation studies real data examples are provided the procedure has been implemented in r code the p values for testing the null order of m 0 2 or m 0 3 can be calculated with a single command this article has supplementary materials avail

nonparametric identification of finite mixture models of dynamic discrete choices in dynamic discrete choice analysis controlling for unobserved heterogeneity is an important issue and finite mixture models provide flexible ways to account for it this paper studies nonparametric identifiability of type probabilities and type specific component distributions in finite mixture models of dynamic discrete choices we derive sucient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work under dierent assumptions on the markov property stationarity and type invariance in the transition process three elements emerge as the important determinants of identification the time dimension of panel data the number of values the covariates can take and the heterogeneity of the response of dierent types to changes in the co

asymptotic stabilization of minimum phase nonlinear systems how a class of multivariable nonlinear systems can be stabilized about an equilibrium via smooth state feedback is shown more precisely conditions under which for every compact set of initial states it is possible to design a feedback law which drives to the equilibrium all initial states in this compact set are described the theory includes the development of globally defined transformations of the system equations to their global normal form

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

equivalence of truncated count mixture distributions and mixtures of truncated count distributions summary this article is about modeling count data with zero truncation a parametric count density family is considered the truncated mixture of densities from this family is different from the mixture of truncated densities from the same family whereas the former model is more natural to formulate and to interpret the latter model is theoretically easier to treat it is shown that for any mixing distribution leading to a truncated mixture a usually different mixing distribution can be found so that the associated mixture of truncated densities equals the truncated mixture and vice versa this implies that the likelihood surfaces for both situations agree and in this sense both models are equivalent zero truncated count data models are used frequently in the capture recapture setting to estimate population size and it can be shown that the two horvitz thompson estimators associated with the two models agree in particular it is possible to achieve strong results for mixtures of truncated poisson densities including reliable global construction of the unique npmle nonparametric maximum likelihood estimator of the mixing distribution implying a unique estimator for the population size the benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities which is less appealing for the practitioner but theoretically easier mixtures of truncated count densities form a convex linear model for which a developed theory exists including global maximum likelihood theory as well as algorithmic approaches once the problem has been solved in this class it might readily be transformed back to the original problem by means of an explicitly given mapping applications of these ideas are given particularly in the case of the truncated poisson family

markov switching model selection using kullback leibler divergence abstract in markov switching regression models we use kullback leibler kl divergence between the true and candidate models to select the number of states and variables simultaneously specifically we derive a new information criterion markov switching criterion msc which is an estimate of kl divergence msc imposes an appropriate penalty to mitigate the over retention of states in the markov chain and it performs well in monte carlo studies with single and multiple states small and large samples and low and high noise we illustrate the usefulness of msc via applications to the u s business cycle and to media advertising

mixed poisson regression models with covariate dependent rates this paper studies a class of poisson mixture models that includes covariates in rates this model contains poisson regression and independent poisson mixtures as special cases estimation methods based on the em and quasi newton algorithms properties of these estimates a model selection procedure residual analysis and goodness of fit test are discussed a monte carlo study investigates implementation and model choice issues this methodology is used to analyze seizure frequency and ames salmonella assay data

exponential feedback passivity and stabilizability of nonlinear systems abstract motivated by n krasovskii s characterisation of exponential stability the concept of exponential passivity is introduced it is shown that to make a nonlinear system with factorisable high frequency gain matrix exponentially passive via either state or output feedback exponential minimum phaseness and invertibility conditions are necessary and sufficient these conditions also guarantee exponential output feedback stabilisability this result extends previous results concerning linear systems

on the bayes optimality of f measure maximizers the f measure which has originally been introduced in information retrieval is nowadays routinely used as a performance metric for problems such as binary classification multi label classification and structured output prediction optimizing this measure is a statistically and computationally challenging problem since no closed form solution exists adopting a decision theoretic perspective this article provides a formal and experimental analysis of different approaches for maximizing the f measure we start with a bayes risk analysis of related loss functions such as hamming loss and subset zero one loss showing that optimizing such losses as a surrogate of the f measure leads to a high worst case regret subsequently we perform a similar type of analysis for f measure maximizing algorithms showing that such algorithms are approximate while relying on additional assumptions regarding the statistical distribution of the binary response variables furthermore we present a new algorithm which is not only computationally efficient but also bayes optimal regardless of the underlying distribution to this end the algorithm requires only a quadratic with respect to the number of binary responses number of parameters of the joint distribution we illustrate the practical performance of all analyzed methods by means of experiments with multi label classification problems

partial synchronization and spontaneous spatial ordering in coupled chaotic systems a model of many symmetrically and locally coupled chaotic oscillators is studied partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated very rich patterns of the system are revealed based on partial synchronization analysis the stabilities of different partially synchronous spatiotemporal structures and some dynamical behaviors of these states are discussed both numerically and analytically

consistent estimation of mixture complexity the consistent estimation of mixture complexity is of fundamental importance in many applications of finite mixture models an enormous body of literature exists regarding the application computational issues and theoretical aspects of mixture models when the number of components is known but estimating the unknown number of components remains an area of intense research effort this article presents a semiparametric methodology yielding almost sure convergence of the estimated number of components to the true but unknown number of components the scope of application is vast as mixture models are routinely employed across the entire diverse application range of statistics including nearly all of the social and experimental sciences

automatic control of phase synchronization in coupled complex oscillators abstract we present an automatic control method for phase locking of regular and chaotic nonidentical oscillations when all subsystems interact via feedback this method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering in contrast to unidirectional and bidirectional coupling the approach presented here supposes the existence of a special controller which allows to change the parameters of the controlled systems first we discuss general principles of automatic phase synchronization ps for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator we demonstrate the effectiveness of our approach for controlled ps on several examples i two coupled regular oscillators ii coupled regular and chaotic oscillators iii two coupled chaotic rossler oscillators iv two coupled foodweb models v coupled chaotic rossler and lorenz oscillators vi ensembles of locally coupled regular oscillators vii ensembles of locally coupled chaotic oscillators and viii ensembles of globally coupled chaotic oscillators

maximum penalized likelihood estimation for independent and markov dependent mixture models summary this paper concerns the use and implementation of maximum penalized likelihood procedures for choosing the number of mixing components and estimating the parameters in independent and markov dependent mixture models computation of the estimates is achieved via algorithms for the automatic generation of starting values for the em algorithm computation of the information matrix is also discussed poisson mixture models are applied to a sequence of counts of movements by a fetal lamb in utero obtained by ultrasound the resulting estimates are seen to provide plausible mechanisms for the physiological process the analysis of count data that are overdispersed relative to the poisson distribution i e variance mean has received considerable recent attention such data might arise in a clinical study in which overdispersion is caused by unexplained or random subject effects alternatively we might observe a time series of counts in which temporal patterns in the data suggest that a poisson model and its implied randomness are inappropriate this paper is motivated by analysis of a time series of overdispersed count data generated in a study of central nervous system development in fetal lambs our data set consists of observed movement counts in 240 consecutive 5 second intervals obtained from a single animal in analysing these data we focus on the use of poisson mixture models assuming independent observations and also markov dependent mixture models or hidden markov models these models assume that the counts follow independent poisson distributions conditional on the rates which are generated from a mixing distribution either independently or with markov dependence we believe finite mixture models are particularly attractive because they provide plausible explanations for variation in the data this paper will emphasize the following issues concerning estimation inference and application of mixture models i choosing the number of model components ii applying the em algorithm to obtain parameter estimates iii generating sufficiently many starting values to identify a global maximum of the likelihood iv avoiding numerical instability

nonparametric mixture of regression models motivated by an analysis of u s house price index hpi data we propose nonparametric finite mixture of regression models we study the identifiability issue of the proposed models and develop an estimation procedure by employing kernel regression we further systematically study the sampling properties of the proposed estimators and establish their asymptotic normality a modified em algorithm is proposed to carry out the estimation procedure we show that our algorithm preserves the ascent property of the em algorithm in an asymptotic sense monte carlo simulations are conducted to examine the finite sample performance of the proposed estimation procedure an empirical analysis of the u s hpi data is illustrated for the proposed methodology

bayesian model selection in finite mixtures by marginal density decompositions we consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture model in which d is bounded by some fixed finite number n our approach relies on the use of a prior over the space of mixing distributions with at most n components by decomposing the resulting marginal density under this prior we discover a weighted bayes factor method for consistently estimating d that can be implemented by an iid generalized weighted chinese restaurant gwcr monte carlo algorithm we also discuss a gibbs sampling method the blocked gibbs sampler for estimating d and also the mixing distribution we show that our resulting posterior is consistent and achieves the frequentist optimal op n 1 4 rate of estimation we compare the performance of the new gwcr model selection procedure with that of the akaike information criterion and the bayes information criterion implemented through an em algorithm applications of our methods to five real datasets and simulation

almost nonparametric inference for repeated measures in mixture models summary we consider ways to estimate the mixing proportions in a finite mixture distribution or to estimate the number of components of the mixture distribution without making parametric assumptions about the component distributions we require a vector of observations on each subject this vector is mapped into a vector of os and 1 s and summed the resulting distribution of sums can be modelled as a mixture of binomials we then work with the binomial mixture the efficiency and robustness of this method are compared with the strategy of assuming multivariate normal mixtures when typically the true underlying mixture distribution is different it is shown that in many cases the approach based on simple binomial mixtures is superior let pi x and p2 x be probability distributions with ai and a2 positive real numbers that sum to 1 then p x al pi x a2 p2 x defines a two component mixture distribution with com ponents pl x and p2 x and mixture weights al and a2 mixture distributions arise when observations come from different populations each with a different distribution and the population sampled is unobserved interesting examples include those in the social sciences in which important variables are latent and unobserved as an example consider the problem of trying to infer the solution strategies which young children employ in solving a cognitive task when different solution strategies can be employed a group of same age children can be considered a sample from a mixture distribution in which the components correspond to the various strategies see thomas and horton 1997 recently there has been an expanding interest in mixtures and there is now a large literature examples and theory may be found in many sources including lindsay 1995 mclachlan and basford 1988 titterington et al 1985 and everitt and hand 1981 computational issues in estimating the model parameters rely mainly on the em algorithm see mclachlan and krishnan 1997 for a detailed account two main issues remain unresolved in applications of mixtures one is the specification of the number of components although there may sometimes be substantive theory to guide this specification in exploratory settings