the use of mixed logit models to reflect heterogeneity in capture recapture studies summary we examine issues in estimating population size n with capture recapture models when there is variable catchability among subjects we focus on a logistic normal mixed model for which the logit of the probability of capture is an additive function of a random subject and a fixed sampling occasion parameter when the probability of capture is small or the degree of heterogeneity is large the log likelihood surface is relatively flat and it is difficult to obtain much information about n we also discuss a latent class model and a log linear model that account for heterogeneity and show that the log linear model has greater scope models assuming homogeneity provide much narrower intervals for n but are usually highly overly optimistic the actual coverage probability being much lower than the nominal level

stable adaptive regulation of arbitrary nth order plants this paper presents an algorithm for adaptively stabilizing and asymptotically regulating an arbitrary single input single output linear time invariant plant which is controllable and observable of known order n and has unknown parameters no further assumptions are made no external probing signal is required

a robust indirect adaptive control approach this paper considers the robust design of an indirect adaptive control approach which is applicable when the unknown parameters of a linear time invariant plant lie in a known convex set throughout which no unstable pole zero cancellation occurs in order to achieve the robustness the use of a relative dead zone in the adaptive law is proposed it is shown that with a suitably designed relative dead zone the adaptive control system is globally stable even in the presence of small unmodeled plant uncertainties

the study of pareto equilibria for multiobjective games by fixed point and ky fan minimax inequality methods abstract in this paper we present two ways to study the existence of weight nash equilibria and pareto equilibria for multiobjective games one is the fixed point method which is well known and the second is the application of ky fan minimax inequality which is not often used in the study of optimization game theory and mathematical programming as results several existence theorems for weight nash equilibria and pareto equilibria are established which improve and unify the corresponding results in the recently existing literatures

on the statistical analysis of capture experiments summary a procedure is given for estimating the size of a closed population in the presence of heterogeneous capture probabilities using capture recapture data when it is possible to model the capture probabilities of individuals in the population using covariates the results include the estimation of the parameters associated with the model of the capture probabilities and the use of these estimated capture probabilities to estimate the population size confidence intervals for the population size using both the asymptotic normality of the estimator and a bootstrap procedure for small samples are given

brief interval excitation through impulse sequences a technical lemma we present a technical lemma that establishes in a general framework an interval excitation property using a specific class of impulse sequences according to such an interval excitation property an impulse applied within a time interval generates excitation within the same interval this property does not hold for arbitrary exciting sequences the lemma is a unified statement of previous results corresponding to particular choices of the exciting sequence

global stability of adaptive pole placement algorithms this paper presents direct and indirect adaptive control schemes for assigning the closed loop poles of a single input single output system in both the continuous and discrete time cases the resulting closed loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids in particular persistent excitation of the potentially unbounded closed loop input output data and hence convergence of a sequential least squares identification algorithm is proved the results are applicable to standard sequential least squares and least squares with covariance reset

nonidentifiability of population size from capture recapture data with heterogeneous detection probabilities heterogeneity in detection probabilities has long been recognized as problematic in mark recapture studies and numerous models developed to accommodate its effects individual heterogeneity is especially problematic in that reasonable alternative models may predict essentially identical observations from populations of substantially different sizes thus even with very large samples the analyst will not be able to distinguish among reasonable models of heterogeneity even though these yield quite distinct inferences about population size the problem is illustrated with models for closed and open populations

on some equilibrium problems for multimaps abstract in this paper we first establish the continuity property for multimaps and generalized berge s theorem for multimaps then we apply these results and the fan browder fixed point theorem to establish the existence theorems of quasi equilibrium problems and generalized quasi equilibrium problems for multimaps

nash type equilibrium theorems and competitive nash type equilibrium theorems abstract in this paper we consider two types of equilibrium problems we study the constrained nash type equilibrium problems with multivalued payoff functions we also study the competitive nash type equilibrium problems with multivalued payoff functions in these two equilibrium problems we want to find a strategy combination such that each player wishes to find a minimal loss from his multivalued payoff function we use a fixed point theorem of park to prove the existence results of these two types of equilibrium problems

logistic regression in capture recapture models the effect of population heterogeneity in capture recapture or dual registration models is discussed an estimator of the unknown population size based on a logistic regression model is introduced the model allows different capture probabilities across individuals and across capture times the probabilities are estimated from the observed data using conditional maximum likelihood the resulting population estimator is shown to be consistent and asymptotically normal a variance estimator under population heterogeneity is derived the finite sample properties of the estimators are studied via simulation an application to finnish occupational disease registration data is presented

bifurcation in model reference adaptive control systems abstract we study the effect of unmodeled dynamics on the performance of a simple model reference adaptive control mechanism exact stability boundaries are computed and different routes to chaotic behavior and global instability are described typically we observed a region of period doubling and hopf bifurcations similar to those observed in the ziegler nichols approach to pid control design the analysis applies to higher order and certain nonlinear systems as well

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

robust pole placement direct adaptive control a pole placement direct adaptive control for not necessarily minimum phase plants is presented which is robust with respect to unmodeled dynamics and bounded disturbances the robustness is achieved by using both a normalized least squares algorithm with dead zone and appropriate nonlinear feedback the resulting closed loop system is shown to be globally stable subject to standard assumptions

global adaptive pole positioning adaptive pole positioning for linear time invariant discrete time systems is considered under the constraint that the controller consists of an identifier the gains in which do not go to zero an observer and a state feedback law the latter two elements being viewed in transfer function form a globally convergent algorithm is presented for achieving a prescribed set of closed loop poles persistency of excitation of an external input is required together with an underbound on the magnitude of the sylvester resultant of the plant numerator and denominator polynomials this in effect being an underbound on the product of a measure of pole zero separation and a generalized gain

towards a link between the factorization approach and mimo robust adaptive control based on a doubly coprime factorization theorem nett et al 1984 an adaptive controller for discrete time mimo systems consisting of a not necessarily minimum phase modelled part and fraction type unmodelled dynamics which are not necessarily stable non linear and time varying is developed then by virtue of a stability result which is itself of interest it is shown that the adaptive closed loop system is bibo stable even in the presence of small but not necessarily stable unmodelled dynamics and arbitrarily bounded initial conditions consequently an initial but important step for applying the factorization approach to mimo robust adaptive control is completely established

on adaptive state regulation an indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed in a rigorous analysis lyapunov stability of the resulting closed loop system without the need for external excitation possible global instabilities as well as global convergence subject to sufficient excitation are shown moreover the behavior of the closed loop system is analyzed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order contains slight nonlinearities and time variation effects and is subject to plant and measurement disturbances

multinomial poisson homogeneous models for contingency tables a unified approach to maximum likelihood inference for a broad new class of contingency table models is presented the model class comprises multinomial poisson homogeneous mph models which can be characterized by an independent sampling plan and a system of homogeneous constraints h m 0 where m is the vector of expected table counts maximum likelihood ml fitting and large sample inference for mph models are described the mph models are partitioned into well defined equivalence classes and explicit comparisons of the large sample behaviors of ml estimators of equivalent models are given the equivalence theory not only unifies a large collection of previously known results it also leads to useful generalizations and many new results the practical computational implication is that ml fit results for any particular mph model can be obtained directly from the ml fit results for any conveniently chosen equivalent model issues of hypothesis testability and parameter estimability are also addressed to illustrate an example based on statistics journal citation patterns is given for which the data can be used to test the hypothesis that a certain model holds but they cannot be used to estimate any of that model s parameters

stable adaptive control of non minimum phase systems abstract an adaptive pole placement design for not necessarily minimum phase systems is analyzed with respect to stability conditions are given for boundedness of closed loop signals when the process is subject to bounded disturbances the most restrictive one can be avoided in a local stability result

existence of pareto equilibria for constrained multiobjective games in h space abstract in this paper we introduce and study a new class of constrained multiobjective games in h spaces without linear structure an existence theorem of solutions for quasi equilibrium problems is first proved in noncompact h spaces then as applications of the quasi equilibrium existence theorem several existence theorems of weighted nash equilibria and pareto equilibria for the constrained multiobjective games are established in noncompact h spaces these theorem improve unify and generalize the corresponding results of the multiobjective games in recent literature

singularity free adaptive pole placement without resorting to persistency of excitation detailed analysis for first order systems abstract this paper presents a novel approach to avoid singularities in adaptive pole placement control algorithms the control scheme is applicable to either minimum or nonminimum phase plants and the closed loop stability is guaranteed in spite of bounded disturbances the algorithm uses a least squares identification algorithm with a particular dead zone that allows the definition of modified estimate that retain the convergence properties of the original estimates explicit modification to the parameters estimates is given that secures well conditioned matrices in the adaptive control law detailed analysis is given for one pole one zero systems

a general class of recapture models based on the conditional capture probabilities we propose an mhotb model for population size estimation in capture recapture studies the tb part is based on equality constraints for the conditional capture probabilities leading to an extremely rich model class observed and unobserved heterogeneity are dealt with by means of a logistic parameterization in order to explore the model class we introduce a penalized version of the likelihood the conditional likelihood and penalized conditional likelihood are maximized by means of efficient em algorithms simulations and two real data examples illustrate the approach

adaptive stabilization of nonminimum phase first order continuous time systems presents an adaptive control scheme for first order systems of the form y spl dot a y b sub 0 u spl dot b sub 1 u which may possibly be a nonminimum phase the control scheme achieves asymptotical stabilization without any a priori knowledge on the plant parameters the adaptive scheme is free from singularities in the sense that the plant estimated model is always controllable the singularity has been overcome through a suitable modification of the parameter estimates which is based on standard least squares covariance matrix properties and the use of a hysteresis switching function

brief paper stability analysis of adaptively controlled systems subject to bounded disturbances an approach for studying stability of adaptively controlled systems subject to bounded disturbances with unknown statistics is given a shorter proof of some results established for minimum phase systems is also given new results are established for nonminimum phase systems in each case the uniform boundedness of all signals is proven under a condition that is discussed examples of adaptive schemes that can be treated with this approach are given

robustness of discrete time adaptive controllers an input output approach a general input output approach that can be used for the design and analysis of robust discrete time adaptive control schemes is presented in particular a model reference adaptive controller is considered the design approach involves the use of the certainty equivalence principle to combine a robust control structure with a robust adaptive law using exponentially weighted i sub 2 norms and exploiting the properties of the adaptive law and the control structure robust stability is established for the closed loop adaptive control scheme

on the nonidentifiability of population sizes summary when a nonparametric mixture model is adopted to deal with the heterogeneity among individual capture probabilities the population size is nonidentifiable link 2003 biometrics59 1123 1130 holzmann munk and zucchini 2006 biometrics62 934 936 discussed the conditions under which a subfamily of mixing distributions is identifiable link 2006 biometrics92 936 939 found that the nonidentifiability occurs across identifiable subfamilies it is shown that there is a subfamily in which each mixing distribution is determined by its mixture and the population size admits estimable lower bounds that can be used to construct lower confidence limits

reformulation of the parameter identification problem for systems with bounded disturbances abstract the problem of deriving parameter identification algorithms that incorporate prior knowledge of a bound on the disturbance is studied particular emphasis is given to the following aspects firstly to motivate from geometrical and optimization considerations the modifications dead zones required to cope with the disturbances secondly to guarantee the convergence properties which are essential in the establishment of stability of identification based adaptive control systems projection and least squares algorithms are studied in both cases an interpretation is given to the new dead zone that has proven to be a key ingredient in recent robustness studies e g goodwin et al 1986 automatica 22 199 207 kreisselmeier and anderson 1985 ieee trans aut control 31 127 133 and lozano leal and ortega 1986 2nd ifac workshop on adapt syst in control and signal proc lund sweden

persistency of excitation in the presence of possibly unbounded signals this note develops an explicit characterization of the concept of persistency of excitation for time invariant linear systems in the presence of possibly unbounded signals this result can be used to establish exponential convergence for a range of adaptive control algorithms a feature of our proof is a particular technique for dealing with the initial condition response

robust adaptive regulation with minimal prior knowledge a robust adaptive regulator is designed under minimal prior knowledge namely the order of a nominal plant model in a well defined sense the involved robustness means that the closed loop stability is guaranteed in the presence of some class of time varying parameters and unmodeled dynamics the main design feature of the proposed adaptive regulator consists in its self excitation capability together with an appropriate identification stabilization time splitting unlike in the available literature concerning robust adaptive control the involved self excitation is established independently of the parameter estimator properties the use of the robustness oriented modifications as deadzone and parameter projection or contraction which are aimed at achieving the parameter estimates boundedness is no longer required beforehand thereby reducing the underlying prior knowledge

on identifiability in capture recapture models we study the issue of identifiability of mixture models in the context of capture recapture abundance estimation for closed populations such models are used to take account of individual heterogeneity in capture probabilities but their validity was recently questioned by link 2003 biometrics 59 1123 1130 on the basis of their nonidentifiability we give a general criterion for identifiability of the mixing distribution and apply it to establish identifiability within families of mixing distributions that are commonly used in this context including finite and beta mixtures our analysis covers binomial and geometrically distributed outcomes in an example we highlight the difference between the identifiability issue considered here and that in classical binomial mixture models

simultaneous factor selection and collapsing levels in anova when performing an analysis of variance the investigator often has two main goals to determine which of the factors have a significant effect on the response and to detect differences among the levels of the significant factors level comparisons are done via a post hoc analysis based on pairwise differences this article proposes a novel constrained regression approach to simultaneously accomplish both goals via shrinkage within a single automated procedure the form of this shrinkage has the ability to collapse levels within a factor by setting their effects to be equal while also achieving factor selection by zeroing out entire factors using this approach also leads to the identification of a structure within each factor as levels can be automatically collapsed to form groups in contrast to the traditional pairwise comparison methods these groups are necessarily nonoverlapping so that the results are interpretable in terms of distinct subsets of levels the proposed procedure is shown to have the oracle property in that asymptotically it performs as well as if the exact structure were known beforehand a simulation and real data examples show the strong performance of the method

stable model reference adaptive control in the presence of bounded disturbances the adaptive control of a linear time invariant plant in the presence of bounded disturbances is considered in addition to the usual assumptions made regarding the plant transfer function it is also assumed that the high frequency gain k p of the plant and an upper bound on the magnitude of the controller parameters are known under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system

random effects modeling of multiple binomial responses using the multivariate binomial logit normal distribution summary the multivariate binomial logit normal distribution is a mixture distribution for which i conditional on a set of success probabilities and sample size indices a vector of counts is independent binomial variates and ii the vector of logits of the parameters has a multivariate normal distribution we use this distribution to model multivariate binomial type responses using a vector of random effects the vector of logits of parameters has a mean that is a linear function of explanatory variables and has an unspecified or partly specified covariance matrix the model generalizes and provides greater flexibility than the univariate model that uses a normal random effect to account for positive correlations in clustered data the multivariate model is useful when different elements of the response vector refer to different characteristics each of which may naturally have its own random effect it is also useful for repeated binary measurement of a single response when there is a nonexchangeable association structure such as one often expects with longitudinal data or when negative association exists for at least one pair of responses we apply the model to an influenza study with repeated responses in which some pairs are negatively associated and to a developmental toxicity study with continuation ratio logits applied to an ordinal response with clustered observations

recapture models under equality constraints for the conditional capture probabilities alessio farcomeni uniroma1 it summary we introduce a general class of capture recapture models in which capture probabilities depend on the previous capture history we discuss constrained versions of the saturated model based on equality constraints despite the seeming complexity inference can be performed through a simple estimating equation the approach is illustrated on a data set about the population of great copper butterflies in willamette valley of o regon it has long been recognized that in capture recapture exper iments the previous capture history may influence capture probabilities and failure to acknowl edge this fact may lead to biased estimates of the unknown population size one of the first model s used denoted by mb included behavioural response to capture by using different probabi lities before and after first capture otis et al 1978 pollock 1991 other examples are given by the markov chain models of yang chao 2005 and the persistence models detailed in ramsey usner 2003 and ramsey severns 2010 in this paper we propose a general class of models which are based on conditional capture probabilities we restrict the satura ted model through equality constraints arguing that the resulting class of models is rich enough to s ummarize a plethora of real data situations the restricted class can be also defined through partitions of the capture histories where capture probabilities conditional on different hist ories belonging to the same partition are equal surprisingly enough the approach based on maximizing the conditional likelihood leads to a straightforward inference based on a simple estimating equation an interesting feature of the proposed model class is that the previous capture histor y can be allowed to influence the capture probability in very flexible ways different models can be fitted and compared through information criteria or likelihood ratio tests

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

singularity free adaptive pole placement for second order systems abstract this paper proposes a new adaptive pole placement control scheme which overcomes the crucial singularity problem in indirect adaptive control that is it guarantees the controllability of the estimated plant model allowing the calculation of the controller parameters without introducing persistency of excitation into the system the control scheme is applicable to either minimum or non minimum phase systems and guarantees the closed loop stability of the controlled system detailed analysis is given for second order systems

a generalization of chao s estimator for covariate information this note generalizes chao s estimator of population size for closed capture recapture studies if covariates are available chao s estimator was developed under unobserved heterogeneity in which case it represents a lower bound of the population size if observed heterogeneity is available in form of covariates we show how this information can be used to reduce the bias of chao s estimator the key element in this development is the understanding and placement of chao s estimator in a truncated poisson likelihood it is shown that a truncated poisson likelihood with log link with all counts truncated besides ones and twos is equivalent to a binomial likelihood with logit link this enables the development of a generalized chao estimator as the estimated expected value of the frequency of zero counts under a truncated all counts truncated except ones and twos poisson regression model if the regression model accounts for the heterogeneity entirely the generalized chao estimator is asymptotically unbiased a simulation study illustrates the potential in gain of bias reduction comparisons of the generalized chao estimator with the homogeneous zero truncated poisson regression approach are supplied as well the method is applied to a surveillance study on the completeness of farm submissions in great britain