estimation in capture recapture models when covariates are subject to measurement errors nous considerons les problemes d estimation des modeles de capture recapture quand les covariables ou les variables auxilliaires sont mesurees avec erreur nous trouvons que l approche naive qui ignore les erreurs de mesure est inacceptable pour l estimation des parametres de regression et de la taille de la population elle donne des estimateurs biaises de manieere croissante avec l amplitude des erreurs et des intervalles de confiance fausses pour tenir compte des erreurs de mesure nous proposons un estimateur des parametres de regression par une methode de calibration et developpons des estimateurs modifies de la taille de la population une etude de simulation montre que les estimateurs resultants sont plus satisfaisant que ceux de l approche naive ou de la methode d extrapolation simulation simex des donnees de l espece d oiseau primia flaviventris a hong kong sont analysees avec et sans l hypothese d erreur de mesure pour demontrer l effet des erreurs sur les estimations

finite time stabilization of linear time varying continuous systems in this technical note the problem of finite time stabilization of linear time varying continuous systems is considered necessary and sufficient conditions based upon the solution to some lyapunov differential matrix equations are proposed for particular cases of interest from these conditions the design of time varying state feedback controller guaranteeing the finite time closed loop stability is presented numerical experiments illustrate the potentialities of the approach

inference for capture recapture experiments in continuous time with variable capture rates summary a two step procedure based on a partial likelihood is proposed to estimate the size of a closed population for multiple recapture studies in continuous time when the capture rates are permitted to depend on covariates associated with individuals the asymptotic and small sample properties of the resulting estimators are investigated the analysis of capture recapture experiments is often based on the assumption that capture probabilities are equal for all individuals in the population being caught it has long been recognised that this assumption is often violated indeed equal capture probability is only a convenient mathematical assumption with no empirical justification manly 1970 gilbert 1973 and carothers 1973 have shown that heterogeneity can cause substantial bias in commonly used estimators burnham overton 1978 and yip 1991 assumed a beta distribution to model the individual capture probabilities chao lee 1992 provided an estimator for a heterogeneous population using sample coverage seber 1982 and otis et al 1978 have pointed out that catchability may vary with characteristics of the individual such as age with physical conditions or with environmental factors for the discrete case with distinct capture occasions huggins 1989 used covariates to model heterogeneity a conditional argument to estimate the parameters associated with the model for the capture probabilities and a method of moments to estimate the population size here we employ a similar two step process in continuous time first using a partial likelihood applied to the counting processes of recaptures of individuals already captured to estimate the parameters in the model for the capture intensity then a method of moments to estimate the population size the work here fits into the model ih classification of pollock 1993 also lee chao 1994 recently suggested a coverage estimator for the population size with heterogeneous and time dependent and behaviour dependent capture probabilities to motivate our work consider a continuous time capture recapture experiment for a closed population of a certain type of bird where the capture intensities depend on covariates assumed to be time independent during the experimental period simulated data from a population of 50 birds with captures occurring over a two unit period where the capture intensities depend on

a semiparametric method for estimating population size for capture recapture experiments with random covariates in continuous time a semiparametric estimation procedure is proposed to model capture recapture data with the aim of estimating the population size for a closed population individuals covariates are possibly time dependent and missing at noncaptured times and may be measured with error a set of estimating equations ees based on covariate process and capture recapture data is constructed to estimate the relevant parameters and the population size these ees can be solved by an algorithm similar to an em algorithm simulation results show that the proposed procedures work better than the naive estimate in some cases they are even better than ideal estimates for which the true values of covariates are available for all captured subjects over the entire experimental period we apply the method to a capture recapture experiment on the bird species prinia flaviventris in hong kong

horvitz thompson estimators for double platform line transect surveys summary horvitz thompson estimators based on estimated inclusion probabilities are developed for line transect surveys in which some of the central assumptions of conventional line transect theory fail the estimators are designed to accommodate uncertain detection of animals in the observers path simultaneously with dependence of detection probabilities on explanatory variables other than perpendicular distance they require that data be collected by two observer teams simultaneously searching the survey region recording for each detection both positional data and details of any other variables that may affect detectability one of the estimators is designed to correct for responsive animal movement this method requires that the primary observer team searches independently of the secondary team whereas the second estimator requires both observer teams to search independently of each other the methods can be viewed as specific forms of mark recapture experiments in which individual capture probabilities are modelled as functions of observable explanatory variables and in which animals detected by both observer teams correspond to recaptures they differ from existing mark recapture horvitz thompson estimators primarily in that they use an assumption about the distribution of perpendicular distances that is implicit in conventional

total error in pes estimates of population abstract we describe a methodology for estimating the accuracy of dual systems estimates dse s of population census estimates of population and estimates of undercount in the census the dse s are based on the census and a post enumeration survey pes we apply the methodology to the 1988 dress rehearsal census of st louis and east central missouri and we discuss its applicability to the 1990 census and pes the methodology is based on decompositions of the total or net error into components such as sampling error matching error and other nonsampling errors limited information about the accuracy of certain components of error notably failure of assumptions in the capture recapture model but others as well lead us to offer tentative estimates of the errors of the census dse and undercount estimates for 1988 improved estimates are anticipated for 1990

a unified parametric regression model for recapture studies with random removals in continuous time nous combinons la vraisemblance conditionnelle dans des processus de comptage avec l estimateur de horvitz thompson pour obtenir un estimateur de la taille de la population plus efficient que les estimateurs existants des suppressions aleatoires peuvent etre introduites dans le processus de recapture on presente des etudes de simulation pour determiner la performance des estimateurs proposes on donne des exemples sur une repartition d oiseaux et une petite etude de recapture de mammiferes

full likelihood inference for abundance from continuous time capture recapture data capture recapture experiments are widely used cost effective sampling techniques for estimating population sizes or abundances in biology ecology demography epidemiology and reliability studies for continuous time capture recapture data existing estimation methods are based on conditional likelihoods and an inverse weighting estimating equation the corresponding wald type confidence intervals for the abundance may have severe undercoverage and their lower limits can be below the number of individuals captured we propose a full likelihood inference approach by combining a parametric or partial likelihood with the empirical likelihood under both parametric and semiparametric intensity models we demonstrate that the maximum likelihood estimator attains the semiparametric efficiency lower bound and that the full likelihood ratio statistic for the abundance is asymptotically 2 with 1 degree of freedom simulations indicate that compared with conditional likelihood based methods the maximum full likelihood estimator has a smaller mean square error and the likelihood ratio confidence intervals often have remarkable gains in coverage probability we illustrate the advantages of the proposed approach by analysing illegal immigrant data for the netherlands and prinia flaviventris data from hong kong

parametric regression models for continuous time removal and recapture studies we use a class of parametric counting process regression models that are commonly employed in the analysis of failure time data to formulate the subject specific capture probabilities for removal and recapture studies conducted in continuous time we estimate the regression parameters by modifying the conventional likelihood score function for left truncated and right censored data to accommodate an unknown population size and missing covariates on uncaptured subjects and we subsequently estimate the population size by a martingale based estimating function the resultant estimators for the regression parameters and population size are consistent and asymptotically normal under appropriate regularity conditions we assess the small sample properties of the proposed estimators through monte carlo simulation and we present an application to a bird banding exercise

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

dispersing billiards with cusps slow decay of correlations dispersing billiards introduced by sinai are uniformly hyperbolic and have strong statistical properties exponential decay of correlations and various limit theorems however if the billiard table has cusps corner points with zero interior angles then its hyperbolicity is nonuniform and statistical properties deteriorate until now only heuristic and experimental results existed predicting the decay of correlations as mathcal o 1 n we present a first rigorous analysis of correlations for dispersing billiards with cusps

stratified capture recapture estimation of the size of a closed population this paper considers the estimation of the size of a closed population in a stratified capturerecapture experiment using the stratified petersen lincoln model introduced by darroch 1961 biometrika 48 241 260 a generalization of darroch s model where the tagging or the recovery probabilities depend on explanatory variables possibly related to the capture mechanism is proposed a simple scoring algorithm for the estimation of the nuisance parameters i e the vectors of tagging and of recovery probabilities and the matrix for the distribution of the units in the capturerecapture area is derived this algorithm is based on a new closed form expression for the inverse of the fisher information matrix of the conditional likelihood for the estimation of the nuisance parameters large sample tests for the tagging and the recovery probabilities are obtained pooling of adjacent recovery strata with equal capture probabilities is proposed as a method for getting accurate estimators of the size of the population conditional and unconditional estimators of the size of the population are proposed analyses of data on smolt migration illustrate the methodology presented in this paper

an algorithm based on discrete response regression models suitable to correct the bias of non response in surveys with several capture tries the use of survey plans which contemplate several tries or call backs when endeavouring to capture individual data may supply unarguable information in certain sampling situations with non ignorable non response this paper presents an algorithm whose final aim is the estimation of the individual non response probabilities from a general perspective of discrete response regression models which includes the well known probit and logit models it will be assumed that the respondents supply all the variables of interest when they are captured nevertheless the call backs continue even after previous captures for a small number of tries r which has been fixed beforehand only for estimating purposes the different retries or call backs are supposed to be carried out with different capture intensities as mentioned above the response probabilities which may vary from one individual to another are sought by discrete response regression models whose parameters are estimated from conditioned likelihoods evaluated on the respondents only the algorithm quick and easy to implement may be used even when the capture indicator matrix has been partially recorded finally the practical performance of the proposed procedure is tested and evaluated from empirical simulations whose results are undoubtedly encouraging

inadmissibility of the maximum likelihood estimator in the sequential estimation of the size of a population summary for the sequential estimation of the size of a finite population the maximum likelihood estimator is a commonly used estimator but has no explicit expression in this paper it is shown that the maximum likelihood estimator is inadmissible an estimator which is simple in form and dominates the maximum likelihood estimator asymptotically is proposed to study the optimality property of the estimator for the stopping rule sb from a decision theoretical approach we investigate the admissibility of the estimator under a general weighted squared error loss function although the maximum likelihood estimator and its risk have no closed form expression the estimator will be shown to be inadmissible by means of a general theorem that we establish later as theorem 2 1 in this paper we only consider the simple capture capture model discussed by samuel 1968 more complex and realistic capture recapture models have been developed subsequently pollack otto 1983 pickands raghavachari 1987 bonett woodward bentler 1987 cormack 1989 huggins 1989 we conjecture that many of the

robust design and the use of auxiliary variables in estimating population size for an open population nous considerons le probleme de l estimation de la taille d une population ouverte ou les donnees sont collectees sur une deuxieme periode a l interieur d une periode primaire selon un plan robuste propose par pollock 1982 une vraisemblance conditionnelle est utilisee pour estimer les parametres associes a un modele lineaire generalise pour lequel la probabilite de capture est supposee suivre une loi logistique qui depend de covariables individuelles un estimateur de type horvitz thompson est utilise pour estimer la taille de la population pour chaque periode primaire et les probabilites du survie entre les periodes primaires les proprietes asymptotiques de l estimateur propose explorees par simulation ont de bonnes proprietes un jeu de donnee attache a une etude de capture recapture de petits mammiferes conduite selon un plan robuste a dummy bottom au sein du browns park national wildlife refuge est analyse

estimating heterogeneity in the probabilities of enumeration for dual system estimation abstract we show how conditional logistic regression can be used to estimate the probability of being enumerated in a census and apply the model to the 1990 post enumeration survey pes in the united states the estimates can be used in the estimation of population size and the estimation of correlation bias for example unlike the classical stratification approach the logistic approach permits the use of continuous explanatory variables model choice can be based on the standard techniques of the generalized linear models we discuss some special problems caused by the fact that the pes sample area is open to migration between the captures we also consider the effect of data errors in estimation we characterize hard to enumerate populations and give some tentative estimates of correlation bias

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

spatially explicit maximum likelihood methods for capture recapture studies live trapping capture recapture studies of animal populations with fixed trap locations inevitably have a spatial component animals close to traps are more likely to be caught than those far away this is not addressed in conventional closed population estimates of abundance and without the spatial component rigorous estimates of density cannot be obtained we propose new flexible capture recapture models that use the capture locations to estimate animal locations and spatially referenced capture probability the models are likelihood based and hence allow use of akaike s information criterion or other likelihood based methods of model selection density is an explicit parameter and the evaluation of its dependence on spatial or temporal covariates is therefore straightforward additional nonspatial variation in capture probability may be modeled as in conventional capture recapture the method is tested by simulation using a model in which capture probability depends only on location relative to traps point estimators are found to be unbiased and standard error estimators almost unbiased the method is used to estimate the density of red eyed vireos vireo olivaceus from mist netting data from the patuxent research refuge maryland u s a estimates agree well with those from an existing spatially explicit method based on inverse prediction a variety of additional spatially explicit models are fitted these include models with temporal stratification behavioral response and heterogeneous animal home ranges

estimation in closed capture recapture models when covariates are missing at random individual covariates are commonly used in capture recapture models as they can provide important information for population size estimation however in practice one or more covariates may be missing at random for some individuals which can lead to unreliable inference if records with missing data are treated as missing completely at random we show that in general such a naive complete case analysis in closed capture recapture models with some covariates missing at random underestimates the population size we develop methods for estimating regression parameters and population size using regression calibration inverse probability weighting and multiple imputation without any distributional assumptions about the covariates we show that the inverse probability weighting and multiple imputation approaches are asymptotically equivalent we present a simulation study to investigate the effects of missing covariates and to evaluate the performance of the proposed methods we also illustrate an analysis using data on the bird species yellow bellied prinia collected in hong kong

the analysis of group truncated binary data with random effects injury severity in motor vehicle accidents the analysis of group truncated binary data has been previously considered by o neill and barry 1995b biometrics 51 533 541 where the analysis assumed that responses within each group were independent in this paper we consider the analysis of such data when there is group level heterogeneity a generalized linear mixed model is hypothesized to model the response and maximum likelihood estimates are derived for the truncated case a score test is derived to test for heterogeneity finally the method is applied to a set of traffic accident data

parametric and semiparametric models for recapture and removal studies a likelihood approach summary capture recapture processes are biased samplings of recurrent event processes which can be modelled by the andersen gill intensity model the intensity function is assumed to be a function of time covariates and a parameter we derive the maximum likelihood estimators of both the parameter and the population size and show the consistency and asymptotic normality of the estimators for both recapture and removal studies the estimators are asymptotically efficient and their theoretical asymptotic relative efficiencies with respect to the existing estimators of yip and co workers can be as large as oo the variance estimation and a numerical example are also presented

estimating population size for a continuous time frailty model with covariates in a capture recapture study a continuous time frailty capture recapture model is proposed for estimating population size of a closed population with the use of observed covariates to explain individuals heterogeneity in presence of a random effect a conditional likelihood approach is used to derive the estimate of parameters and the horvitz thompson estimator is adopted to estimate the unknown population size asymptotic normality of the estimates is obtained simulation results and a real example show that the proposed method works satisfactorily

a general theory for modeling capture recapture data from a closed population a general theory for estimating the size of a closed population from multiple recapture data is presented this theory is easily extended to open population models for multiple recapture data estimation is based on a log linear model developed for modeling dependent capture recapture data when capture probabilities vary temporally with behavioral response and are heterogeneous among animals models for complete capture history data are developed along with the first log linear models for removal data the maximum likelihood estimator of the model parameters along with the estimated covariance matrix are presented

mixture models for estimating the size of a closed population when capture rates vary among individuals nous developpons une parametrisation du melange de lois beta et binomiale qui fournit un cadre inferentiel approprie pour estimer l effectif d une population fermee lorsque les probabilites de capture ou de detection varient entre individus nous ajustons trois classes de modeles de melange beta binomiale logistique normale et modele a classes latentes d une part a des donnees de recapture de lievres d amerique pour en estimer l abondance et d autre part a des comptages d especes d oiseaux pour estimer la richesse specifique dans les deux jeux de donnees les taux de detection varient davantage entre individus lievres ou especes qu entre occasions ou lieux de capture les estimateurs de l effectif de la population et de la richesse specifique sont sensibles aux hypotheses faites sur la distribution sous jacente des probabilites individuelles de detection nous montrons par simulations que les outils habituels d evaluation de la qualite du modele comme la deviance ne sont pas fiables pour choisir entre des modeles de melanges celui qui fournit une inference correcte de l effectif de la population lorsqu elles existent des connaissances a priori sur les causes d heterogeneite des taux de detection doivent etre utilisees pour aider a choisir quelle classe de modeles de melanges utiliser pour l inference

open capture recapture models with heterogeneity ii jolly seber model summary estimation of abundance is important in both open and closed population capture recapture analysis but unmodeled heterogeneity of capture probability leads to negative bias in abundance estimates this article defines and develops a suite of open population capture recapture models using finite mixtures to model heterogeneity of capture and survival probabilities model comparisons and parameter estimation use likelihood based methods a real example is analyzed and simulations are used to check the main features of the heterogeneous models especially the quality of estimation of abundance survival recruitment and turnover the two major advances in this article are the provision of realistic abundance estimates that take account of heterogenetiy of capture and an appraisal of the amount of overestimation of survival arising from conditioning on the first capture when heterogeneity of survival is present

adjusting for nonresponse bias using logistic regression summary a method of adjustment for nonresponse is considered no information about the nonrespondents is required but the respondents are assumed to answer all questions of interest one or more call backs are assumed the probabilities of response are represented by a logistic regression model in which variables in the survey are explanatory variables the probabilities are estimated using a modified conditional maximum likelihood approach based on the respondents the estimated probabilities are used in a horvitzthompson type estimator to reduce bias in the estimation of sample moments simulations suggest that the method reduces the mean squared error of estimation when response probabilities depend strongly on variables in the survey

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

accommodating unmodeled heterogeneity in double observer distance sampling surveys mark recapture models applied to double observer distance sampling data neglect the information on relative detectability of objects contained in the distribution of observed distances a difference between the observed distribution and that predicted by the mark recapture model is symptomatic of a failure of the assumption of zero correlation between detection probabilities implicit in the mark recapture model we develop a mark recapture based model that uses the observed distribution to relax this assumption to zero correlation at only one distance we demonstrate its usefulness in coping with unmodeled heterogeneity using data from an aerial survey of crabeater seals in the antarctic

maximum empirical likelihood estimation for abundance in a closed population from capture recapture data summarycapture recapture experiments are widely used to collect data needed for estimating the abundance of a closed population to account for heterogeneity in the capture probabilities huggins 1989 and alho 1990 proposed a semiparametric model in which the capture probabilities are modelled parametrically and the distribution of individual characteristics is left unspecified a conditional likelihood method was then proposed to obtain point estimates and wald type confidence intervals for the abundance empirical studies show that the small sample distribution of the maximum conditional likelihood estimator is strongly skewed to the right which may produce wald type confidence intervals with lower limits that are less than the number of captured individuals or even are negative in this paper we propose a full empirical likelihood approach based on huggins and alho s model we show that the null distribution of the empirical likelihood ratio for the abundance is asymptotically chi squared with one degree of freedom and that the maximum empirical likelihood estimator achieves semiparametric efficiency simulation studies show that the empirical likelihood based method is superior to the conditional likelihood based method its confidence interval has much better coverage and the maximum empirical likelihood estimator has a smaller mean square error we analyse three datasets to illustrate the advantages of our empirical likelihood approach

simple capture recapture models permitting unequal catchability and variable sampling effort we consider two capture recapture models that imply that the logit of the probability of capture is an additive function of an animal catchability parameter and a parameter reflecting the sampling effort the models are special cases of the rasch model and satisfy the property of quasi symmetry one model is log linear and the other is a latent class model for the log linear model point and interval estimates of the population size are easily obtained using standard software such as glim

mixture regression models for closed population capture recapture data in capture recapture studies the use of individual covariates has been recommended to get stable population estimates however some residual heterogeneity might still exist and ignoring such heterogeneity could lead to underestimating the population size n in this work we explore two new models with capture probabilities depending on both covariates and unobserved random effects to estimate the size of a population inference techniques including horvitz thompson estimate and confidence intervals for the population size are derived the selection of a particular model is carried out using the akaike information criterion aic first we extend the random effect model of darroch et al 1993 journal of american statistical association 88 1137 1148 to handle unit level covariates and discuss its limitations the second approach is a generalization of the traditional zero truncated binomial model that includes a random effect to account for an unobserved heterogeneity this approach provides useful tools for inference about n since key quantities such as moments likelihood functions and estimates of n and their standard errors have closed form expressions several models for the unobserved heterogeneity are available and the marginal capture probability is expressed using the logit and the complementary log log link functions the sensitivity of the inference to the specification of a model is also investigated through simulations a numerical example is presented we compare the performance of the proposed estimator with that obtained under model mh of huggins 1989 biometrika 76 130 140

unified maximum likelihood estimates for closed capture recapture models using mixtures summary agresti 1994 biometrics50 494 500 and norris and pollock 1996a biometrics52 639 649 suggested using methods of finite mixtures to partition the animals in a closed capture recapture experiment into two or more groups with relatively homogeneous capture probabilities this enabled them to fit the models mh mbh norris and pollock and mth agresti of otis et al 1978 wildlife monographs62 1 135 in this article finite mixture partitions of animals and or samples are used to give a unified linear logistic framework for fitting all eight models of otis et al by maximum likelihood likelihood ratio tests are available for model comparisons for many data sets a simple dichotomy of animals is enough to substantially correct for heterogeneity induced bias in the estimation of population size although there is the option of fitting more than two groups if the data warrant it

some practical aspects of a conditional likelihood approach to capture experiments the use of conditional likelihood methods in the analysis of capture data allows the modeling of capture probabilities in terms of observable characteristics of the captured individuals and the trapping occasions the resulting models may then be used to estimate the size of the population here the use of conditional likelihood procedures to construct models for capture probabilities is discussed and illustrated by an example