survival analysis using a scale change random effects model abstract frailty models are effective in broadening the class of survival models and inducing dependence in multivariate survival distributions in proportional hazards the random effect multiplies the hazard function the scale change model incorporates unobserved heterogeneity through a random effect that enters the baseline hazard function to change the time scale we interpret this random effect as frailty or other unobserved risks that create heterogeneity in the population this model produces a wide range of shapes for univariate survival and hazard functions we extend this model to multivariate survival data by assuming that members of a group share a common random effect this structure induces association among the survival times in a group and provides alternative association structures to the proportional hazards frailty model we present parametric and semiparametric estimation techniques and illustrate these methods with an example

detrended fluctuation analysis of intertrade durations abstract the intraday pattern long memory and multifractal nature of the intertrade durations which are defined as the waiting times between two consecutive transactions are investigated based upon the limit order book data and order flows of 23 liquid chinese stocks listed on the shenzhen stock exchange in 2003 an inverse u shaped intraday pattern in the intertrade durations with an abrupt drop in the first minute of the afternoon trading is observed based on a detrended fluctuation analysis we find a crossover of power law scaling behaviors for small box sizes trade numbers in boxes and large box sizes and strong evidence in favor of long memory in both regimes in addition the multifractal nature of intertrade durations in both regimes is confirmed by a multifractal detrended fluctuation analysis for individual stocks with a few exceptions in the small duration regime the intraday pattern has little influence on the long memory and multifractality

interval censored data a note on the nonparametric maximum likelihood estimator of the distribution function summary gentleman geyer 1994 discuss the analysis of interval censored data and present results based on standard convex optimisation theory here this problem is viewed from the perspective of a mixing problem of indicator functions using an analogy with the problem of mixture distributions a variety of results are easily derived including a characterisation theorem for the maximum likelihood estimator and various reliably convergent algorithms software for the analysis of mixture distributions can be used to find the nonparametric estimate of the distribution function of the interval censored survival time examples are provided to demonstrate the theory

identifiability and rates of estimation for scale parameters in location mixture models in this paper we consider the problem of identifiability and estimation for the scale parameter 0 in the location mixture model 0 x y where x has a known distribution independent of the y whose distribution is unknown identification of 0 is ensured by constraining y based on the tail behavior of the distribution for x rates for estimation are described for those x which can be written as a square summable series of exponential variables as a special case our analysis shows that the structural parameters in the weibull semiparametric mixture heckman and singer are not estimable at the usual parametric op 1 xn rate the exact relationship between identifying constraints and achievable rates is explained 1 introduction heckman and singer 1984 studied economic theories concerning continuous durations of occupancy of states in order to properly estimate structural parameters in the presence of population heterogeneity they proposed the use of a semiparametric mixture model as a method for modeling duration data the model they proposed was the weibull semiparametric mixture

information in semiparametric mixtures of exponential families in a class of semiparametric mixture models the score function and consequently the effective information for a finite dimensional parameter can be made arbitrarily small depending upon the direction taken in the parameter space this result holds for a broad range of semiparametric mixtures over exponential families and includes examples such as the gamma semiparametric mixture the normal mean mixture the weibull semiparametric mixture and the negative binomial mixture the near zero information rules out the usual parametric n rate for the finite dimensional parameter but even more surprising is that the rate continues to be unattainable even when the mixing distribution is constrained to be countably discrete two key conditions which lead to a loss of information are the smoothness of the underlying density and whether a sufficient statistic is invertible

activity spectrum from waiting time distribution in high frequency financial data not only returns but also waiting times between trades are random variables in this work we analyze the spectra of the waiting time processes for tick by tick trades the numerical problem strictly related with the real inversion of laplace transforms is analyzed by using tikhonov s regularization method we also analyze these spectra by a rough method using a comb of dirac s delta functions

an algorithm for computing the nonparametric mle of a mixing distribution abstract a fast algorithm for calculating the nonparametric maximum likelihood estimate mle of a mixing distribution g in a mixture model is discussed the literature contains several methods for computing the nonparametric mle of g but these methods are slow in this article we develop an algorithm for maximizing the log likelihood l g over the family of all distribution functions that yields the nonparametric mle of g in some semiparametric problems a structural or fixed parameter is of interest and we are interested in computing profile likelihood sup gl g for a grid of values of the algorithm that we propose is fast enough for this purpose examples illustrate and compare the algorithms one taken from an article by laird the common mean problem and one taken from the literature on optimal experimental design it is also noted that routines from the literature on semi infinite programming may be used to compute the profile log likelihood

objective bayesian survival analysis using shape mixtures of log normal distributions survival models such as the weibull or log normal lead to inference that is not robust to the presence of outliers they also assume that all heterogeneity between individuals can be modeled through covariates this article considers the use of infinite mixtures of lifetime distributions as a solution for these two issues this can be interpreted as the introduction of a random effect in the survival distribution we introduce the family of shape mixtures of log normal distributions which covers a wide range of density and hazard functions bayesian inference under nonsubjective priors based on the jeffreys rule is examined and conditions for posterior propriety are established the existence of the posterior distribution on the basis of a sample of point observations is not always guaranteed and a solution through set observations is implemented in addition we propose a method for outlier detection based on the mixture structure a simulation study illustrates the performance of our methods under dif

around effros theorem some stronger versions of the effros theorem are discussed in the paper not only for homeomorphisms but also for some other mappings e g for open ones equivalent formulations of the theorem are presented as the e push property and the existence of a so called effros metric

weighted nonparametric maximum likelihood estimate of a mixing distribution in nonrandomized clinical trials hierarchical models have a variety of applications including multi center clinical trials local estimation of disease rates longitudinal studies risk assessment and meta analysis in a hierarchical model observations are sampled conditional on individual unit specific parameters and these parameters are sampled from a mixing distribution in observational studies or nonrandomized clinical trails observations may be biased samples from a population and heterogeneous with respect to some confounding factors without controlling the heterogeneity in the sample the standard estimation of the mixing distribution may lead to inaccurate statistical inferences in this article we propose a weighted nonparametric maximum likelihood estimate npmle of the mixing distribution and its smoothed version via weighted smoothing by roughening the proposed estimator reduces bias by assigning a weight to each subject in the sample the weighted npmle is shown to be weighted self consistent and therefore can be easily calculated through a recursive approach simulation studies were conducted to evaluate the performance of the proposed estimator we applied this method to clinical trial data evaluating a new treatment for stress urinary incontinence

on spline regularized inversion of noisy laplace transforms abstract in this paper we have converted the laplace transform to an integral equation of the first kind of convolution type which is an ill posed problem and used the spline regularization method to solve it inversion of perturbed laplace transforms also plays an important role in system theory the method is applied to several test examples taken from 1 3 8 11 22 it gives a good approximation to the true solution and compares well with the methods discussed in 1 3 8 11 22 the results are shown in table 1 and respective diagrams

sieve m inference on irregular parameters abstract this paper presents sieve inferences on possibly irregular i e slower than root n estimable functionals of semi nonparametric models with i i d data we provide a simple consistent variance estimator of the plug in sieve m estimator of a possibly irregular functional and the asymptotic standard normality of the sieve t statistic we show that for hypothesis testing of irregular functionals the sieve likelihood ratio statistic is asymptotically chi square distributed these results are useful in inference on structural parameters that may have singular semiparametric efficiency bounds a simulation study and an empirical application of heckman and singer 1984 duration model are presented

the open mapping principle for partial actions of polish groups abstract we present a extension of the classical open mapping principle and effros theorem for polish group actions to the context of partial group actions

estimation of a k monotone density limit distribution theory and the spline connection we study the asymptotic behavior of the maximum likelihood and least squares estimators of a kmonotone density g0 at a fixed point x0 when k 2 we find that the jth derivative of the estima tors at x0 converges at the rate n k j 2k 1 for j 0 k 1 the limiting distribution depends on an almost surely uniquely de fined stochastic process hk that stays above below the k fold in tegral of brownian motion plus a deterministic drift when k is even odd both the mle and lse are known to be splines of degree k 1 with simple knots establishing the order of the random gap n n where n denote two successive knots is a key ingredient of the proof of the main results we show that this gap problem can be solved if a conjecture about the upper bound on the error in a particular hermite interpolation via odd degree splines holds

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

a homogeneous arcwise connected non locally connected curve given a homogeneous compactum x a general method of constructing homogeneous compacta as inverse limit spaces lim x n b n is introduced where x n are covering spaces for x and b n are covering mappings if inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i is the menger universal curve a variant of this construction provides a homogeneous arcwise connected non locally connected curve this answers a question of k kuperberg

alternative models for the heterogeneity of mortality risks among the aged abstract to develop a model to estimate the degree of unobserved heterogeneity in morality risks in a population it is necessary to specify two types of functions one describing the age specific rate of increase of mortality risks for individuals and the other describing the distribution of mortality risks across individuals there has been considerable interest in the question of how sensitive the estimates of heterogeneity are to the choices of these functions to explore this question high quality data were obtained from published medicare mortality rates for the period 1968 1978 for analysis of total mortality among the aged in addition national vital statistics data for the period 1950 1977 were used to analyze adult lung cancer mortality for these data the estimates of structural parameters were less sensitive to reasonable choices of the heterogeneity distribution gamma vs inverse gaussian than to reasonable choices of the hazard rate function gompertz vs weibull

semiparametric estimation of a proportional hazard model with unobserved heterogeneity the proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity this paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically the baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known finite dimensional parametric families existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family thus the estimators presented here are more general than existing ones

statistical models for intercepted data abstract consider a population of replaceable items of different ages and suppose that for each item there is a certain measurable attribute that is a monotone function perhaps random of the item s age to fix ideas we refer to this attribute as deterioration and we assume that as items age their level of deterioration increases we further assume that as the level of deterioration hits a certain threshold value perhaps unknown the item dies and disappears from the population so it is not available for sampling any more since items that deteriorate at a slower rate live longer any sample obtained over a short period of time would overrepresent slowly deteriorating items consequently under such circumstances longitudinal studies are often needed to statistically study deterioration as a function of age this article presents a statistical model that enables us to study the deterioration function from a single cross section snapshot of the population or some random parts of it specifically

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

triple goal estimates in two stage hierarchical models the beauty of the bayesian approach is its ability to structure complicated models inferential goals and analyses to take full advantage of it methods should be linked to an inferential goal via a loss function for example in the two stage compound sampling model the posterior means are optimal under squared error loss however they can perform poorly in estimating the histogram of the parameters or in ranking them triple goal estimates are motivated by the desire to have a set of estimates that produce good ranks a good parameter histogram and good co ordinate specific estimates no set of estimates can simultaneously optimize these three goals and we seek a set that strikes an effective trade off we evaluate and compare three candidate approaches the posterior means the constrained bayes estimates of louis and ghosh and a new approach that optimizes estimation of the histogram and the ranks mathematical and simulation based analyses support the superiority of the new approach and document its excellent performance for the three inferential goals

nonparametric mle under two closed capture recapture models with heterogeneity we conduct nonparametric maximum likelihood estimation under two common heterogeneous closed population capture recapture models our models specify mixture models as did previous researchers models which have a common generating distribution say f for the capture probabilities using lindsay and roeder s 1992 journal of the american statistical association 87 785 794 mixture model results and the em algorithm a nonparametric maximum likelihood estimator mle of f for any specified population size n is obtained then the nonparametric mle of the n f pair and thus for n is determined perhaps most importantly since our mle pair maximizes the likelihood under the entire nonparametric probability model it provides an excellent foundation for estimating properties of estimators conducting a goodness of fit test and performing a likelihood ratio test these are illustrated in the paper

testing the mixture of exponentials hypothesis and estimating the mixing distribution by the method of moments abstract this article presents nonparametric methods for testing the hypothesis that duration data can be represented by a mixture of exponential distributions both bayesian and classical tests are developed a variety of apparently distinct models can be written in mixture of exponentials form this raises a fundamental identification problem a consistent estimator for the number of points of support of a discrete mixture is developed a consistent method of moments estimator for the mixing distribution is derived from the testing criteria and is evaluated in a monte carlo study

the geometry of mixture likelihoods a general theory in this paper certain fundamental properties of the maximum likelihood estimator of a mixing distribution are shown to be geometric properties of the likelihood set the existence support size likelihood equations and uniqueness of the estimator are revealed to be directly related to the properties of the convex hull of the likelihood set and the support hyperplanes of that hull it is shown using geometric techniques that the estimator exists under quite general conditions with a support size no larger than the number of distinct observations analysis of the convex dual of the likelihood set leads to a dual maximization problem a convergent algorithm is described the defining equations for the estimator are compared with the usual parametric likelihood equations for finite mixtures sufficient conditions for uniqueness are given part ii will deal with a special theory for exponential family mixtures

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

binomial mixtures geometric estimation of the mixing distribution given a mixture of binomial distributions how do we estimate the unknown mixing distribution we build on earlier work of lindsay and further elucidate the geometry underlying this question exploring the approximating role played by cyclic polytopes convergence of a resulting maximum likelihood fitting algorithm is proved and numerical examples given problems over the lack of identifiability of the mixing distribution in part disappear

a simple nonparametric approach to estimating the distribution of random coefficients in structural models abstract we explore least squares and likelihood nonparametric mixtures estimators of the joint distribution of random coefficients in structural models the estimators fix a grid of heterogeneous parameters and estimate only the weights on the grid points an approach that is computationally attractive compared to alternative nonparametric estimators we provide conditions under which the estimated distribution function converges to the true distribution in the weak topology on the space of distributions we verify most of the consistency conditions for three discrete choice models we also derive the convergence rates of the least squares nonparametric mixtures estimator under additional restrictions we perform a monte carlo study on a dynamic programming model

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

the cyclic connectivity of homogeneous arcwise connected continua a continuum is cyclicly connected provided each pair of its points lie together on some simple closed curve in 1927 g t whyburn proved that a locally connected plane continuum is cycicly connected if and only if it contains no separating points this theorem was fundamental in his original treatment of cyclic element theory since then numerous authors have obtained extensions of whybum s theorem in this paper we characterize cyclic connectedness in the class of all hausdorff continua theorem the hausdorff continuum x is cyclicly connected if and only if for each point x e x x lies in the relative interior of some arc in x and x x is arcwise connected we then prove that arcwise connected homogeneous metric continua are cycicly connected introduction in his ph d dissertation 14 r l wilson proved that no uniquely arcwise connected hausdorff continuum supports the structure of a topological group since he used mainly algebraic techniques his proof revealed little about the topological nature of such continua indeed in private conversation with the authors wilson asked whether uniquely arcwise connected hausdorff continua can be homogeneous in this paper we characterize cyclicly connected continua i e continua in which each pair of points lie together on a simple closed curve arcwise connected homogeneous metric continua are then shown to be cyclicly connected this yields a negative answer to wilson s question for metric continua the nonmetric case remains open the authors wish to thank g r gordh jr for many helpful discussions and suggestions during the preparation of this paper a cyclic connectedness theorem the continuum x is cyclicly connected 12 provided each pair of points in x lie together on some simple closed curve in x received by the editors february 19 1979 1980 mathematics subject classification primary 54f20 secondary 54f65 a portion of this paper was presented to the american mathematical society under the title arcwise connected homogeneous continua contain simple closed curves at the 1980 national meeting 2the first author was supported during the latter stages of this research by nsf grant number mcs 7908413 3this research was begun while the second author was a visitor at the university of delaware in 1978 79 he wishes to thank the members of the mathematical sciences department there for their hospitality during that year c 1981 american mathematical society 0002 9947 81 0000 0352 03 00

on fast computation of the non parametric maximum likelihood estimate of a mixing distribution summary a fast algorithm for computing the non parametric maximum likelihood estimate of a mixing distribution is presented at each iteration the algorithm adds new important points to the support set as guided by the gradient function updates all mixing proportions via a quadratically convergent method and discards redundant support points straightaway with its convergence being theoretically established numerical studies show that it is very fast and stable compared with several other algorithms that are available in the literature

theory of earthquakes interevent times applied to financial markets abstract we analyze the probability density function pdf of waiting times between financial loss exceedances the empirical pdfs are fitted with the self excited hawkes conditional poisson process with a long power law memory kernel the hawkes process is the simplest extension of the poisson process that takes into account how past events influence the occurrence of future events by analyzing the empirical data for 15 different financial assets we show that the formalism of the hawkes process used for earthquakes can successfully model the pdf of interevent times between successive market losses

nonparametric estimation of nonstationary spatial covariance structure abstract estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks we introduce a nonparametric approach to global estimation of the spatial covariance structure of a random function z x t observed repeatedly at times ti i 1 t at a finite number of sampling stations xi i 1 2 n in the plane our analyses assume temporal stationarity but do not assume spatial stationarity or isotropy we analyze the spatial dispersions var z xi t z xj t as a natural metric for the spatial covariance structure and model these as a general smooth function of the geographic coordinates of station pairs xi xj the model is constructed in two steps first using nonmetric multidimensional scaling mds we compute a two dimensional representation of the sampling stations for which a monotone function of interpoint distances ij approximates the spatial dispersions mds transforms the problem

uncoupled continuous time random walk finite jump length probability density function in this work the uncoupled continuous time random walk model with the exponential jump length probability density function pdf is considered exact solutions for the pdf and second moment are obtained and investigated for different kinds of waiting time pdf

likelihood inference for mixtures geometrical and other constructions of monotone step length algorithms summary this paper considers algorithms for the maximum likelihood estimator of the mixing distribution of a family of parametric densities specific interest is devoted to the monotonicity of the step length of the solution in 2 we introduce the idea of estimating the area above the second derivative curve and in theorem 1 we relate area overestimation to the monotonicity of the associated algorithm in 3 we apply theorem 1 to the monotonicity analysis of well known algorithms as well as to the construction of a new class of monotone step length choices which is particularly simple in the mixture setting numerical comparisons and refinements in keeping the monotonic step length from becoming too conservative are given theorem 3 characterizes conditions under which the newton raphson step is monotonic and if these conditions fail to hold states that the regula falsi step is monotonic

semiparametric estimation of normal mixture densities a semiparametric method for estimating densities of normal mean mixtures is presented this consistent data driven method of estimation is based on probability spacings the estimation technique involves iteratively fixing the standard deviation of the normal kernel that serves as a smoothing parameter and then maximizing a function of the probability spacings over all mixing distributions based on the distribution of uniform spacings a distribution free goodness of fit criterion is developed to guide the selection of the smoothing parameter the result is a set of consistent estimators indexed by a range of smoothing parameters empirical process results are used to prove consistency

estimating the number of classes estimating the unknown number of classes in a population has numerous important applications in a poisson mixture model the problem is reduced to estimating the odds that a class is undetected in a sample the discontinuity of the odds prevents the existence of locally unbiased and informative estimators and restricts confidence intervals to be one sided confidence intervals for the number of classes are also necessarily one sided a sequence of lower bounds to the odds is developed and used to define pseudo maximum likelihood estimators for the number of classes

semi terminal continua in kelley spaces a continuum k in a space x is said to be semi terminal if at least one out of every two disjoint continua in x intersecting k is contained in k based on this concept new structural results on kelley continua are obtained in particular two decomposition theorems for kelley continua are presented one of these theorems is an improved version of the aposyndetic decomposition theorem for kelley continua

autoregressive conditional duration a new model for irregularly spaced transaction data this paper proposes a new statistical model for the analysis of data which arrive at irregular intervals the model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates the conditional intensity is developed and compared with other self exciting processes because the model focuses on the expected duration between events it is called the autoregressive conditional duration acd model asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to arch model results strong evidence is provided for duration clustering for the financial transaction data analyzed both deterministic time of day effects and stochastic effects are important the model is applied to the arrival times of trades and therefore is a model of transaction volume and also to the arrival of other events such as price changes models for the volatility of prices are estimated with price based durations and examined from a market microstructure point of view

predicting the conditional probability of discovering a new class consider a population comprising disjoint classes an important problem arising from various fields is prediction of the random conditional probability of discovering a new class the asymptotic normality of the discovery probability is established in a poisson model where the number of individuals from each class is a poisson process with a class specific rate a new derivation is presented for the well known good toulmin predictor as a moment based estimator for the asymptotic limit of the discovery probability the good toulmin predictor is also shown to be a nonparametric empirical bayes estimator for the expectation of the discovery probability given the rates of the poisson processes and an approximation to an unbiased estimator only for the identifiable part of the expectation of the discovery probability in a multinomial model the properties of the moment based estimator are investigated so that confidence and prediction intervals can be constructed the good toulmin predictor and the discovery

the maximum number of infected individuals in sis epidemic models computational techniques and quasi stationary distributions we study the maximum number of infected individuals observed during an epidemic for a susceptible infected susceptible sis model which corresponds to a birth death process with an absorbing state we develop computational schemes for the corresponding distributions in a transient regime and till absorption moreover we study the distribution of the current number of infected individuals given that the maximum number during the epidemic has not exceeded a given threshold in this sense some quasi stationary distributions of a related process are also discussed

a fixed point theorem for weakly chainable plane continua in this paper the fixed point theorem is proven for every plane acyclic continuum x with the property that every indecomposable continuum in the boundary of x is contained in a weakly chainable subcontinuum of x

on the number of births and deaths during an extinction cycle and the survival of a certain individual in a competition process competition processes as discussed by iglehart 1964 26 and reuter 1961 25 have been frequently used in biology to describe the dynamics of population models involving some kind of interaction among various species our interest is in the stochastic model of a competition process analyzed by ridler rowe 1978 23 which is related to an ecosystem of two species the ecosystem is closed in the sense that no immigration or emigration is supposed to take place individuals compete either directly or indirectly for common resources and consequently births and deaths depend on the population sizes of one or both of the species in this paper we focus on the number of births and deaths during an extinction cycle specifically we discuss an approximation method inspired from the use of the maximum size distribution which is equally applicable to the survival of a certain individual we analyze three models defined in terms of the way individuals within each species are selected to die our results are illustrated with reference to simulated data

simple estimation of a duration model with unobserved heterogeneity this paper presents a simple estimator of the shape parameter in a weibull duration model with unobserved heterogeneity the estimator is consistent and asymptotically normal under mild conditions and a consistent estimator of the asymptotic variance is available a monte carlo study indicates that the asymptotic distribution of the estimator provides a good approximation to the finite sample distribution the estimation strategy can be extended to a model with regressors and to a log logistic model with unobserved heterogeneity the advantages of the estimator are that it is easy to calculate and that its asymptotic distribution can be derived copyright 1990 by the econometric society

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

renewal sums under mixtures of exponentials abstract we start with applying two methods to derive formulas of a mixture of exponential process i e a renewal process whose inter arrival time follows a mixture of exponentials further stochastic order properties are discussed when comparing this process to a poisson process with the same expectation of inter arrival times based on these properties formulas and ordering properties are given for the non discounted compound process as well as the discounted one explicit formulas for the density functions are also provided for both cases under the discounted compound case several new results are derived for heavy tailed distributions finally the laguerre series approximation is proposed and tested for various common actuarial indices e g var cte and stop loss premium

scaling in the distribution of intertrade durations of chinese stocks abstract the distribution of intertrade durations defined as the waiting times between two consecutive transactions is investigated based upon the limit order book data of 23 liquid chinese stocks listed on the shenzhen stock exchange in the whole year 2003 a scaling pattern is observed in the distributions of intertrade durations where the empirical density functions of the normalized intertrade durations of all 23 stocks collapse onto a single curve the scaling pattern is also observed in the intertrade duration distributions for filled and partially filled trades and in the conditional distributions the ensemble distributions for all stocks are modeled by the weibull and the tsallis q exponential distributions maximum likelihood estimation shows that the weibull distribution outperforms the q exponential for not too large intertrade durations which account for more than 98 5 of the data alternatively nonlinear least squares estimation selects the q exponential as a better model in which the optimization is conducted on the distance between empirical and theoretical values of the logarithmic probability densities the distribution of intertrade durations is weibull followed by a power law tail with an asymptotic tail exponent close to 3

residual diagnostics for mixture models abstract a sample is commonly modeled by a mixture distribution if the observations follow a common distribution but the parameter of interest differs between observations for example we observe the lengths but not the ages of a sample offish it may be reasonable to assume that length is normally distributed about an unknown mean that depends on the age of the fish provided there is more than one age class in the sample then the data are distributed as a mixture of normals in this article we assume that the data are a random sample from a mixture of exponential family distributions and that for each observation the parameter of interest is sampled independently from an unknown mixing distribution q the adequacy of a fitted mixture model can be assessed by examining residuals based on the ratio of the observed to expected fit residuals based on the homogeneity model in which q is a one point distribution display a convexity property when the data follow a mixture model this becomes the basis fo

outlet points and homogeneous continua i a proof is presented for bing s conjecture that homogeneous treelike continua are hereditarily indecomposable as a consequence each ho mogeneous curve admits the continuous decomposition into the maximal termi nal homeomorphic homogeneous hereditarily indecomposable treelike sub continua 2 a homogeneous hereditarily unicoherent continuum contains either an arc or arbitrarily small nondegenerate indecomposable subcontinua 3 a treelike continuum with property k which is homogeneous with respect to confluent light mappings contains no two nondegenerate subcontinua with the one point intersection

the singularity of the information matrix of the mixed proportional hazard model this paper presents new identification conditions for the mixed proportional hazard model in particular the baseline hazard is assumed to be bounded away from 0 and near t 0 these conditions ensure that the information matrix is nonsingular the paper also presents an estimator for the mixed proportional hazard model that converges at rate n 1 2

pseudo path connected homogeneous continua abstract the main result of this paper states that every homogeneous pseudo path connected continuum is weakly chainable or equivalently every homogeneous continuum connected by continuous images of the pseudo arc is itself a continuous image of the pseudo arc we notice that even though there exist homogeneous path connected continua that are not continuous images of an arc prajs 2002 they all are continuous images of the pseudo arc

a semiparametric mixture approach to case control studies with errors in covariables abstract methods are devised for estimating the parameters of a prospective logistic model in a case control study with dichotomous response d that depends on a covariate x for a portion of the sample both the gold standard x and a surrogate covariate w are available however for the greater portion of the data only the surrogate covariate w is available by using a mixture model the relationship between the true covariate and the response can be modeled appropriately for both types of data the likelihood depends on the marginal distribution of x and the measurement error density w x d the latter is modeled parametrically based on the validation sample the marginal distribution of the true covariate is modeled using a nonparametric mixture distribution in this way we can improve the efficiency and reduce the bias of the parameter estimates the results also apply when there is no validation data provided the error distribution is known or estimated from an independent data source many of the

maximum likelihood estimation with partially censored data suppose one observes independent samples of size n from both the mixture density int p x mid z d eta z and from the distribution eta the kernel p x mid z is known we show asymptotic normality and efficiency of the maximum likelihood estimator for eta

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

heterogeneity and selection in dynamic panel data abstract the data generating process dgp for generic dynamic panel data consists of a law of state dynamics g a selection or attrition rule h and an initial condition f i study nonparametric identifiability of this complete dgp g h f using short unbalanced panel data allowing for nonseparability between observed states and unobserved heterogeneity in each of g h and f for t 3 the dgp is identified by using a proxy variable for t 6 the three additional periods construct a proxy and thus the dgp is identified without an auxiliary variable

extensions of estimation methods using the em algorithm abstract the em algorithm described by dempster laid and rubin 1977 is reviewed with the purpose of clarifying several misconceptions in the statistical and econometric literature the clarifications lead to several applications of the algorithm to models that have appeared to be less tractable the relationship between the em algorithm and the method of scoring is also explained providing estimators of the score and the information from the em algorithm the em algorithm is extended to missing data problems and an estimation method based on simulations

nonparametric estimation of component distributions in a multivariate mixture suppose k variate data are drawn from a mixture of two distributions each having independent components it is desired to estimate the univariate marginal distributions in each of the products as well as the mixing proportion this is the setting of two class fully parametrized latent models that has been proposed for estimating the distributions of medical test results when disease status is unavailable the problem is one of inference in a mixture of distributions without training data and until now it has been tackled only in a fully parametric setting we investigate the possibility of using nonparametric methods of course when k 1 the problem is not identifiable from a nonparametric viewpoint we show that the problem is almost identifiable when k 2 there the set of all possible representations can be expressed in terms of any one of those representations as a two parameter family furthermore it is proved that when k geq3 the problem is nonparametrically identifiable under particularly mild regularity conditions in this case we introduce root n consistent nonparametric estimators of the 2k univariate marginal distributions and the mixing proportion finite sample and asymptotic properties of the estimators are described

sensitivity of dynamical systems to banach space parameters we consider general nonlinear dynamical systems in a banach space with dependence on parameters in a second banach space an abstract theoretical framework for sensitivity equations is developed an application to measure dependent delay differential systems arising in a class of hiv models is presented

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

kernel estimation of hazard functions when observations have dependent and common covariates abstract we propose a hazard model where dependence between events is achieved by assuming dependence between covariates this model allows for correlated variables specific to observations as well as macro variables which all observations share this setup better fits many economic and financial applications where events are not independent nonparametric estimation of the hazard function is then studied kernel estimators proposed in nielsen and linton 1995 and linton et al 2003 are shown to have similar asymptotic properties compared with the i i d case mixing conditions ensure the asymptotic results follow these results depend on adjustments to bandwidth conditions simulations are conducted which verify the impact of dependence on estimators bandwidth selection accounting for dependence is shown to improve performance in an empirical application trade intensity in high frequency financial data is estimated

long term correlations and multifractal nature in the intertrade durations of a liquid chinese stock and its warrant abstract the intertrade duration of equities is an important financial measure characterizing trading activities it is defined as the waiting time between successive trades of an equity using the ultrahigh frequency data of a liquid chinese stock and its associated warrant we perform a comparative investigation of the statistical properties of their intertrade duration time series the distributions of the two equities can be better described by the shifted power law form than the weibull form and their scaled distributions do not collapse onto a single curve although the intertrade durations of the two equities have very different magnitude their intraday patterns exhibit very similar shapes both detrended fluctuation analysis dfa and detrending moving average analysis dma show that the 1 min intertrade duration time series of the two equities are strongly correlated in addition both multifractal detrended fluctuation analysis mfdfa and multifractal detrending moving average analysis mfdma unveil that the 1 min intertrade durations possess multifractal nature however the difference between the two singularity spectra of the two equities obtained from the mfdma is much smaller than that from the mfdfa

modeling heaped duration data an application to neonatal mortality in 2005 the indian government launched a conditional cash incentive program to encourage institutional delivery this paper studies the effects of the program on neonatal mortality using district level household survey data we model mortality using survival analysis paying special attention to substantial heaping a form of measurement error present in the data the main objective of this paper is to provide a set of sufficient conditions for identification and consistent estimation of the discretized baseline hazard accounting for heaping and unobserved heterogeneity our identification strategy requires neither administrative data nor multiple measurements but a correctly reported duration point and the presence of some flat segment s in the baseline hazard we establish the asymptotic properties of the maximum likelihood estimator and derive a set of specification tests that allow among other things to test for the presence of heaping and to compare different heaping mechanisms our empirical findings do not suggest a significant reduction of mortality in treated districts however they do indicate that accounting for heaping matters for the estimation of the hazard parameters

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

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

mixed hitting time models we study mixed hitting time models that specify durations as the first time a levy process a continuous time process with stationary and independent increments crosses a heterogeneous threshold such models are of substantial interest because they can be deduced from optimal stopping models with heterogeneous agents that do not naturally produce a mixed proportional hazards structure we show how strategies for analyzing the identifiability of the mixed proportional hazards model can be adapted to prove identifiability of a hitting time model with observed covariates and unobserved heterogeneity we discuss inference from censored data and give examples of structural applications we conclude by discussing the relative merits of both models as complementary frameworks for econometric duration analysis

uniform rates of estimation in the semiparametric weibull mixture model this paper presents a uniform estimator for a finite dimensional parameter in the semiparametric weibull mixture model the rates achieved by the estimator hold uniformly over shrinking sequences of models much more general than traditional sequences that are required to satisfy a hellinger differentiable property we show that these rates are optimal in a class of identified models constrained by a moment condition on the nonparametric mixing distribution

efficient greedy learning of gaussian mixture models this article concerns the greedy learning of gaussian mixtures in the greedy approach mixture components are inserted into the mixture one after the other we propose a heuristic for searching for the optimal component to insert in a randomized manner a set of candidate new components is generated for each of these candidates we find the locally optimal new component and insert it into the existing mixture the resulting algorithm resolves the sensitivity to initialization of state of the art methods like expectation maximization and has running time linear in the number of data points and quadratic in the final number of mixture components due to its greedy nature the algorithm can be particularly useful when the optimal number of mixture components is unknown experimental results comparing the proposed algorithm to other methods on density estimation and texture segmentation are provided

lifetime and reproduction of a marked individual in a two species competition process the interest is in a stochastic model for the competition of two species which was first introduced by reuter 18 and iglehart 11 and then analyzed by ridler rowe 19 the model is related to the two species autonomous competitive model zeeman 24 where individuals compete either directly or indirectly for a limited food supply and consequently birth and death rates depend on the population size of one or both of the species the aim is to complement the treatment of the model we started in 8 9 by focusing here on probabilistic descriptors that are inherently linked to an individual its residual lifetime and the number of direct descendants we present an approximating model based on the maximum size distribution and we discuss on various models defined in terms of the underlying killing and reproductive strategies numerical examples are presented to show the effects of the killing and reproductive strategies on the behavior of an individual and how the impact of these strategies on the descriptors vanishes in highly competitive ecosystems