on the lebesgue measure of li yorke pairs for interval maps we investigate the prevalence of li yorke pairs for c2 and c3 multimodal maps f with non flat critical points we show that every measurable scrambled set has zero lebesgue measure and that all strongly wandering sets have zero lebesgue measure as does the set of pairs of asymptotic but not asymptotically periodic points

time consistent equilibrium reinsurance investment strategy for n competitive insurers under a new interaction mechanism and a general investment framework abstract we propose a new interaction mechanism for n 2 competitive insurers under which we investigate the time consistent equilibrium reinsurance investment strategy for n insurers each insurer can purchase reinsurance for reducing the claim risk and invest in the financial market for increasing his wealth we consider a general investment framework which includes typical diversified and concentrated investment patterns in the literature the objective of each insurer is to find a time consistent equilibrium reinsurance investment strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth by using the stochastic control technique we obtain the explicit time consistent equilibrium reinsurance investment strategies and corresponding equilibrium value functions through analyzing the general investment strategy we find the criterion of whether the insurer should invest in a specific risky asset furthermore we examine theoretically and numerically how the price parameters of risky assets affect the concrete investment pattern we find that when the appreciation rate of one risky asset exceeds some times as those of other risky assets the insurer will only invest in this asset otherwise the insurer will adopt the diversified investment pattern we also numerically examine the influences of the number of insurers and the surplus jump on the time consistent equilibrium reinsurance strategy

an evaluation of some methods for fitting dose response models to quantal response developmental toxicology data the analysis of quantal response developmental toxicology data by dose response modeling is discussed with emphasis on methods that avoid exact distributional assumptions these methods quasi likelihood bootstrapping and jackknifing are contrasted with analyses based on the beta binomial distribution for the resampling procedures dose response models are fit under a binomial likelihood a justification for this choice of estimator in resampling plans is given based on an extension of the standard results for asymptotic normality and consistency of maximum likelihood estimators this justification depends only on the true distribution of the data having the usual binomial expectation a quasi likelihood approach is also considered in which simple assumptions about the intralitter correlation structure are made quasi likelihood methods are in theory asymptotically robust to misspecification of the intralitter correlation structure the practical implications of these asymptotic results are evaluated in a simulation study

renormalization methods for higher order differential equations we adapt methodology of statistical mechanics and quantum field theory to approximate solutions to an arbitrary order ordinary differential equation boundary value problem by a second order equation in particular we study equations involving the derivative of a double well potential such as u u3 or u 2u3 using momentum fourier space variables we average over short length scales and demonstrate that the higher order derivatives can be neglected within the first cumulant approximation once length is properly renormalized yielding an approximation to solutions of the higher order equation from the second order the results are confirmed using numerical computations additional numerics confirm that the main role of the higher order derivatives is in rescaling the length

axiom a maps are dense in the space of unimodal maps in the ck topology in this paper we prove c k structural stability conjecture for unimodal maps in other words we shall prove that axiom a maps are dense in the space of c k unimodal maps in the c k topology here k can be 1 2 1 1 the structural stability conjecture the structural stability conjecture was and remains one of the most interesting and important open problems in the theory of dynamical systems this conjecture states that a dynamical system is structurally stable if and only if it satisfies axiom a and the transversality condition in this paper we prove this conjecture in the simplest nontrivial case in the case of smooth unimodal maps these are maps of an interval with just one critical turning point to be more specific let us recall the definition of axiom a maps definition 1 1 let x be an interval we say that a c k map f x satisfies the axiom a conditions if f has finitely many hyperbolic periodic attractors the set f x f i sh yperbolic where f i sa union of the

test of marginal compatibility and smoothing methods for exchangeable binary data with unequal cluster sizes exchangeable binary data are often collected in developmental toxicity and other studies and a whole host of parametric distributions for fitting this kind of data have been proposed in the literature while these distributions can be matched to have the same marginal probability and intra cluster correlation they can be quite different in terms of shape and higher order quantities of interest such as the litter level risk of having at least one malformed fetus a sensible alternative is to fit a saturated model bowman and george 1995 journal of the american statistical association 90 871 879 using the expectation maximization em algorithm proposed by stefanescu and turnbull 2003 biometrics 59 18 24 the assumption of compatibility of marginal distributions is often made to link up the distributions for different cluster sizes so that estimation can be based on the combined data stefanescu and turnbull proposed a modified trend test to test this assumption their test however fails to take into account the variability of an estimated null expectation and as a result leads to inaccurate p values this drawback is rectified in this article when the data are sparse the probability function estimated using a saturated model can be very jagged and some kind of smoothing is needed we extend the penalized likelihood method simonoff 1983 annals of statistics 11 208 218 to the present case of unequal cluster sizes and implement the method using an em type algorithm in the presence of covariate we propose a penalized kernel method that performs smoothing in both the covariate and response space the proposed methods are illustrated using several data sets and the sampling and robustness properties of the resulting estimators are evaluated by simulations

modelling and analysing exchangeable binary data with random cluster sizes correlated binary data occur very frequently in cluster sample surveys dependent repeated cancer screening teratological experiments ophthalmologic and otolaryngologic studies and other clinical trials the standard methods to analyse these data include the use of beta binomial models and generalized estimating equations with third and fourth moments specified by working matrices however in many applications it is reasonable to assume that the data from the same cluster are exchangeable when all sampled clusters have equal sizes bowman and george introduced maximum likelihood estimates mles of the population parameters such as the marginal means moments and correlations of order two and higher they also extended their approach to sampled clusters with unequal sizes it seems that their extension has a gap this paper points out the source of this gap and shows that estimates introduced by bowman and george are not the mles of the parameters which are used to identify the joint distribution of correlated binary data we show that the mles of the population parameters have no closed form in general and should be calculated by numerical methods we apply our results and a generalized estimating equation procedure to a data set from a double blind randomized clinical trial comparing two antibiotics cefaclor and amoxicillin used for the treatment of acute otitis media to see the performance of the mles with small or moderate sample sizes several simulation studies are also conducted

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

dose response models for teratological experiments in a recent paper hereinafter referred to as rvr rai and van ryzin 1985 propose a dose response model for use in low dose extrapolation from teratological experiments involving quantal responses suppose n litters are divided into m 1 dose groups the ith group consisting of ni litters exposed to dose di o do di dn the group i 0 being a zero dose control let sij denote the size of the jth litter in the ith group j 1 ni and let rij denote the number of foetuses or pups in the litter exhibiting the toxic response of interest the model proposed by rvr assumes that the conditional distribution of rij given sij sij is binomial sij p1j where

getting rid of the negative schwarzian derivative condition in this paper we will show that the assumption on the negative schwarzian derivative is redundant in the case of c 3 unimodal maps with a non at critical point the following theorem will be proved for any c 3 unimodal map of an interval with a non at critical point there exists an interval around the critical value such that the flrst entry map to this interval has negative schwarzian derivative another theorem proved in the paper provides useful cross ratio estimates thus all theorems proved only for unimodal maps with negative schwarzian derivative can be easily generalized

solutions of asymptotically linear operator equations via morse theory abstract in this paper we use the classical morse theory of critical points to study the existence and multiplicity of solutions of a class of asymptotically linear operator equations as special cases we include multiplicity results for semilinear elliptic bvp s as well as existence and multiplicity of periodic solutions of semilinear wave equation and of hamiltonian systems these results simplify and complement recent work of amann zehnder and castro lazer author

regular or stochastic dynamics in real analytic families of unimodal maps in this paper we prove that in any non trivial real analytic family of quasiquadratic maps almost any map is either regular i e it has an attracting cycle or stochastic i e it has an absolutely continuous invariant measure to this end we show that the space of analytic maps is foliated by codimension one analytic submanifolds hybrid classes this allows us to transfer the regular or stochastic property of the quadratic family to any non trivial real analytic family

likelihood inference for exchangeable binary data with varying cluster sizes ce papier etudie l estimation au maximum de vraisemblance dans des modeles satures et insatures pour des donnees binaires correlees echangeables lorsqu on dispose d un echantillon de clusters independants de tailles variables nous discutons plusieurs parametrisations de ces modeles et nous proposons l utilisation de l algorithme em pour obtenir des estimations du maximum de vraisemblance la methodologie est illustree par des applications a une etude d agregation familiale de maladie et a la construction d un essai randomise par groupe pour la prevention du cancer

the impact of litter effects on dose response modeling in teratology the fitting of dose response models to teratology data involving littermates in order to generate estimates of teratogenic risk is receiving increasing attention as a potential alternative to the safety factor approach to risk estimation in this paper we utilize the beta binomial distribution to introduce varying degrees of intralitter correlation and for purposes of illustration consider a logistic dose response model that describes the logit of risk as a straight line function of ln dose the biases and exact and asymptotic variances of the maximum likelihood estimators of the intercept and slope are studied by simulation as a function of the intralitter correlation structure

real bounds ergodicity and negative schwarzian for multimodal maps over the last 20 years many of the most spectacular results in the field of dynamical systems dealt specifically with interval and circle maps or perturbations and complex extensions of such maps primarily this is because in the one dimensional case much better distortion control can be obtained than for general dynamical systems however many of these spectacular results were obtained so far only for unimodal maps the aim of this paper is to provide all the tools for studying general multimodal maps of an interval or a circle by obtaining real bounds controlling the geometry of domains of certain first return maps and providing a new and we believe much simpler proof of absense of wandering intervals provided certain combinatorial conditions are satisfied large real bounds implying that certain first return maps are almost linear koebe distortion controlling the distortion of high iterates of the map and negative schwarzian derivative for certain return maps showing that the usual assumption of negative schwarzian derivative is unnecessary control of distortion of certain first return maps ergodic properties such as sharp bounds for the number of ergodic components

complex bounds for real maps in this paper we prove complex bounds also referred to as a priori bounds for c 3 and in particular for analytic maps of the interval any c 3 mapping of the interval has an asymptotically holomorphic extension to a neighbourhood of the interval we associate to such a map a complex box mapping which provides a kind of markov structure for the dynamics moreover we prove universal geometric bounds on the shape of the domains and on the moduli between components of the range and domain such bounds show that the first return maps to these domains are well controlled and consequently such bounds form one of the corner stones in many recent results in one dimensional dynamics for example renormalization theory rigidity density of hyperbolicity and local connectivity of julia sets

estimation bias using the beta binomial distribution in teratology kupper et al 1986 biometrics 42 85 98 considered the fitting of dose response regressions to litter proportions in teratology experiments they found that the estimators which maximise the beta binomial likelihood become biased when the intralitter correlation is incorrectly assumed to be homogeneous this paper considers the nature of this bias and its implications for the analysis of litter proportions in toxicology

computing finite time non ruin probability and some joint distributions in discrete time risk model with exchangeable claim occurrences abstract in this paper we study a discrete time risk model based on exchangeable dependent claim occurrences in particular we obtain expressions for the finite time non ruin probability and the joint distribution of the time to ruin the surplus immediately before ruin and the deficit at ruin an illustration of the results is given and some implications of the results are provided comparisons are made with the corresponding results for the classical compound binomial model of independent and identically distributed claim occurrences

mean variance portfolio selection under a non markovian regime switching model abstract in this paper we investigate the mean variance portfolio selection problem in a continuous time setting we assume that the coefficients in the model are random and adapted to the filtration generated by a markov chain instead of using the embedding approach which is widely adopted in the existing literature we study the problem from the viewpoint of mean field formulation and provide a distinctive and straightforward approach by introducing and discussing a new system of mean field backward stochastic differential equations driven by a markov chain we obtain both the optimal strategy and the efficient frontier in explicit forms in particular we revisit the markovian regime switching model in which the coefficients are deterministic functions of the markov chain

the palais smale condition versus coercivity possesses a convergent subsequence and cp is said to satisfy ps if ir satisfies ps for every c e ir recently among other results in critical point theory shujie i i showed that if a c functional p x k is bounded from below and satisfies the condition ps then p is coercive shujie s proof uses a gradient flow approach through the so called deformation theorem cf 3 io and for that he needs the notion of a pseudo gradient vector field tjassociated with the functional cp whose existence is guaranteed for c functionals by palais 8 in this paper we present some new results which relate the palais smale condition and the notion of coercivity and are based on the well known variational principle due to ekeland 5 61 in particular a new proof of the above mentioned result of shujie is given it should be pointed out that throughout the paper the given functional p could be assumed to be only gateaux differentiable rather than c and in addition to being conceptually simpler this approach could be used in more general situations where the functional is not even differentiable cf 4 the strong form of ekeland s variational principle to be repeatedly used is given in the following theorem

on success runs of a fixed length in bernoulli sequences exact and asymptotic results consider a sequence of n bernoulli success failure or 1 0 trials the exact and limiting distribution of the random variable e n k denoting the number of success runs of a fixed length k email protected email protected n is derived along with its mean and variance an associated waiting time is examined as well the exact distribution is given in terms of binomial coefficients and an extension of it covering exchangeable sequences is also discussed limiting distributions of e n k are obtained using poisson and normal approximations the exact mean and variance of e n k which are given in explicit forms are also used to derive bounds and an additional approximation of the distribution of e n k numbers associated with e n k and related random variables counting binary strings and runs of 1 s useful in applications of computer science are provided the overall study is illustrated by an extensive numerical experimentation

time consistent reinsurance investment strategy for an insurer and a reinsurer with mean variance criterion under the cev model this paper is devoted to derive the time consistent reinsurance investment strategy for an insurer and a reinsurer under mean variance criterion we aim to maximize the weighted sum of the insurer s and the reinsurer s objectives with different risk averse coefficients the claim process is assumed to follow a brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer moreover both the insurer and the reinsurer are allowed to invest in a risk free asset and a risky asset respectively in order to reduce risks the insurer and the reinsurer can invest in different risky assets whose price processes are described by the constant elasticity of variance cev models consideration of the cev model and the profits of both the insurer and the reinsurer the proof of the verification theorem becomes difficult and the solution becomes complex we first formulate a general problem and prove the verification theorem by solving an extended hamilton jacobi bellman hjb equation we obtain the time consistent reinsurance investment strategy and the corresponding value function explicitly finally sensitivity analysis and numerical simulation are presented to show the effects of parameters on the time consistent strategy and illustrate the economic meaning

a shared response model for clustered binary data in developmental toxicity studies summary existing distributions for modeling fetal response data in developmental toxicology such as the beta binomial distribution have a tendency of inflating the probability of no malformed fetuses and hence understating the risk of having at least one malformed fetus within a litter as opposed to a shared probability extra binomial model we advocate a shared response model that allows a random number of fetuses within the same litter to share a common response an explicit formula is given for the probability function and graphical plots suggest that it does not suffer from the problem of assigning too much probability to the event of no malformed fetuses the em algorithm can be used to estimate the model parameters results of a simulation study show that the em estimates are nearly unbiased and the associated confidence intervals based on the usual standard error estimates have coverage close to the nominal level simulation results also suggest that the shared response model estimates of the marginal malformation probabilities are robust to misspecification of the distributional form but not so for the estimates of intralitter correlation and the litter level probability of having at least one malformed fetus the proposed model is fitted to a set of data from the u s national toxicology program for the same dose response relationship the fit based on the shared response distribution is superior to that based on the beta binomial and comparable to that based on the recently proposed q power distribution kuk 2004 applied statistics53 369 386 an advantage of the shared response model over the q power distribution is that it is more interpretable and can be extended more easily to the multivariate case to illustrate this a bivariate shared response model is fitted to fetal response data involving visceral and skeletal malformation

a dose response model for teratological experiments involving quantal responses this paper introduces a dose response model for teratological quantal response data where the probability of response for an offspring from a female at a given dose varies with the litter size the maximum likelihood estimators for the parameters of the model are given as the solution of a nonlinear iterative algorithm two methods of low dose extrapolation are presented one based on the litter size distribution and the other a conservative method the resulting procedures are then applied to a teratological data set from the literature

a simple numerical solution for an optimal investment strategy for a dc pension plan in a jump diffusion model abstract in this paper we study an optimal investment strategy for a fund manager of a dc pension who wants to maximise the expected exponential utility of the terminal wealth in a market where the stock is a jump diffusion process using stochastic control theory we derive a hamilton jacobi bellman equation since the market is not complete the optimal strategy cannot be found in closed as is done in most literature on dc pension plans we characterise the optimal strategy as a solution of an integro ordinary differential equation which can easily be solved by a simple numerical method we investigate the impact of different jump parameters through numerical experiments using a familiar distribution of jumps

path connected yang mills moduli spaces on utilise des techniques de min max dans le calcul des variations pour demontrer que les espaces modules des connexions auto duales sur des fibres principaux su 2 ou su 3 sur s 4 sont chemin connexe

existence for a semilinear sixth order ode abstract in this paper we study the existence and multiplicity of nontrivial solutions for a boundary value problem associated with a semilinear sixth order ordinary differential equation arising in the study of spatial patterns our treatment is based on variational tools including two brezis nirenberg s linking theorems

periodic and homoclinic solutions of extended fisher kolmogorov equations in this paper we study the existence of periodic solutions of the fourth order equations uiv pu a x u b x u3 0 and uiv pu a x u b x u3 0 where p is a positive constant and a x and b x are continuous positive 2l periodic functions the boundary value problems p1 and p2 for these equations are considered respectively with the boundary conditions u 0 u l u 0 u l 0 existence of nontrivial solutions for p1 is proved using a minimization theorem and a multiplicity result using clark s theorem existence of nontrivial solutions for p2 is proved using the symmetric mountain pass theorem we study also the homoclinic solutions for the fourth order equation uiv pu a x u b x u2 c x u3 0 where p is a constant and a x b x and c x are periodic functions the mountain pass theorem of brezis and nirenberg and concentration compactness arguments are used

hausdorff dimension of cantor attractors in one dimensional dynamics in this paper we study the hausdorff dimension of cantor attractors of smooth interval maps with non flat critical points we prove that the hausdorff dimension is bounded from above by a constant less than 1 which depends only on the number and order of the critical points

compound markov negative binomial distribution abstract let y i i 1 be a sequence of 0 1 variables which forms a markov chain with a given initial probability distribution and one step transition probability matrix define n n to be the number of trials until the n th success 1 in y i i 1 in this paper we study the distribution of the random variable t i 1 n n x i where x i i 1 is a sequence of independent and identically distributed random variables having a common phase type distribution the distribution of t is obtained by means of phase type distributions

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

inference procedures for assessing interobserver agreement among multiple raters summary we propose a new procedure for constructing inferences about a measure of interobserver agreement in studies involving a binary outcome and multiple raters the proposed procedure based on a chi square goodness of fit test as applied to the correlated binomial model bahadur 1961 in studies in item analysis and prediction 158 176 is an extension of the goodness of fit procedure developed by donner and eliasziw 1992 statistics in medicine11 1511 1519 for the case of two raters the new procedure is shown to provide confidence interval coverage levels that are close to nominal over a wide range of parameter combinations the procedure also provides a sample size formula that may be used to determine the required number of subjects and raters for such studies

preconditioning markov chain monte carlo simulations using coarse scale models we study the preconditioning of markov chain monte carlo mcmc methods using coarse scale models with applications to subsurface characterization the purpose of preconditioning is to reduce the fine scale computational cost and increase the acceptance rate in the mcmc sampling this goal is achieved by generating markov chains based on two stage computations in the first stage a new proposal is first tested by the coarse scale model based on multiscale finite volume methods the full fine scale computation will be conducted only if the proposal passes the coarse scale screening for more efficient simulations an approximation of the full fine scale computation using precomputed multiscale basis functions can also be used comparing with the regular mcmc method the preconditioned mcmc method generates a modified markov chain by incorporating the coarse scale information of the problem the conditions under which the modified markov chain will converge to the correct posterior distribution are stated in the paper the validity of these assumptions for our application and the conditions which would guarantee a high acceptance rate are also discussed we would like to note that coarse scale models used in the simulations need to be inexpensive but not necessarily very accurate as our analysis and numerical simulations demonstrate we present numerical examples for sampling permeability fields using two point geostatistics the karhunen loeve expansion is used to represent the realizations of the permeability field conditioned to the dynamic data such as production data as well as some static data our numerical examples show that the acceptance rate can be increased by more than 10 times if mcmc simulations are preconditioned using coarse scale models

hyperbolicity sinks and measure in one dimensional dynamics letf be ac2 map of the circle or the interval and let f denote the complement of the basins of attraction of the attracting periodic orbits we prove that f is a hyperbolic expanding set if and obviously only if every periodic point is hyperbolic and f doesn t contain the critical point this is the real one dimensional version of fatou s hyperbolicity criteria for holomorphic endomorphisms of the riemann sphere we also explore other applications of the techniques used for the result above proving for instance that for everyc2 immersionf of the circle i e a map of the circle onto itself without critical points either its julia set has measure zero or it is the whole circle and thenf is ergodic i e positively invariant borel sets have zero or full measure

statistical inference for familial disease clusters in many epidemiologic studies the first indication of an environmental or genetic contribution to the disease is the way in which the diseased cases cluster within the same family units the concept of clustering is contrasted with incidence we assume that all individuals are exchangeable except for their disease status this assumption is used to provide an exact test of the initial hypothesis of no familial link with the disease conditional on the number of diseased cases and the distribution of the sizes of the various family units new parametric generalizations of binomial sampling models are described to provide measures of the effect size of the disease clustering we consider models and an example that takes covariates into account ascertainment bias is described and the appropriate sampling distribution is demonstrated four numerical examples with real data illustrate these methods

a mountain pass theorem 143 in other words the mountain separating 0 and e may even be assumed of zero altitude and the conclusion is still true moreover as we shall show if c a the critical point can be chosen with llx ll r it is interesting to ask whether this extension of the ambrosetti rabinowitz theorem remains true in the infinite dimensional case we prove here that if 1 is strengthened a little to the form 1 there exist real numbers u r r such that 0 a for every x e a x e x y a moreover if c a the critical point can be chosen with r i x0 i r roughly speaking in brief the mountain pass theorem continues to hold for a mountain of zero altitude provided it also has non zero thickness in addition if c a the pass itself occurs precisely on the mountain i e satisfying r llroll r there are two interesting and immediate corollaries the first one says that a c function which has iwo local minimum points also has a third critical point the second states that a u periodic c function with a local minimum e has a critical point x e ku k 0 1 2 the precise statements of the above results will be given in the next sec tions the proof depends upon a lemma of clark 3 formulated here in a version suitable to our purpose in section 3 some applications are presen ted for the forced pendulum equation 2

on bivariate compound sums abstract the study of compound sums have always been very popular in the literature many models in insurance and engineering have been represented and solved by compound sums in this paper two different bivariate compound sums are proposed and studied the phase type distribution is applied to obtain the probability generating function of the bivariate sum

on hausdorff dimension of unimodal attractors there exists a universal constant 1 such that every attractor of every c 4 unimodal map with a non degenerate critical point is an analytic manifold or its hausdorff dimension is equal to or less than

a variational approach to discontinuous problems with critical sobolev exponents abstract we employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form u h x h u a uq u2 1 in rn where a 0 are parameters h x is both nonnegative and integrable on rn h is the heaviside function 2 is the critical sobolev exponent and 0 q

decay of geometry for unimodal maps an elementary proof we prove that a nonrenormalizable smooth unimodal interval map with critical order between 1 and 2 displays decay of geometry by an elementary and purely real argument this completes a real approach to milnor s attractor problem for smooth unimodal maps with critical order not greater than 2

tests of independence treatment heterogeneity dose related trend with exchangeable binary data abstract existing methods of testing for treatment effects for clustered binary data include the beta binomial quasilikelihood gee procedures all of these methods revolve around the mean response and the second order correlation however these two parameters alone do not fully determine the effect of treatment this article develops nonparametric likelihood ratio procedures to test for independence heterogeneity dose related trend in dose response studies involving exchangeable binary data the hypotheses of independence heterogeneity trend are expressed in terms of joint probabilities of similar responses among cluster mates constrained maximum likelihood estimates of these probabilities are computed and used to construct test statistics unlike the test statistics for independence and heterogeneity the asymptotic distribution of the likelihood ratio test for trend is not exactly a chi square however an upper bound of its p value is obtained by using a chi squared distribution a set of clustere

hypothesis testing for proportions with overdispersion summary the properties of likelihood ratio tests and simpler t tests are investigated by simulation under an assumed beta binomial model for parameter values typically found in toxicological studies it is found that likelihood ratio methods are at least as powerful as the simpler approaches and in certain situations can be significantly more powerful

on the metric properties of multimodal interval maps and c 2 density of axiom a in this paper we shall prove that axiom a maps are dense in the space of c 2 interval maps endowed with the c 2 topology as a step of the proof we shall prove real and complex a priori bounds for first return maps to certain small neighborhoods of the critical points of real analytic multimodal interval maps with non degenerate critical points we shall also discuss rigidity for interval maps without large bounds

a full likelihood procedure for analysing exchangeable binary data a full likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability the binomial and beta binomial models are shown to occur as special cases correspondingly respectively to the choice of degenerate and beta mixing distributions for a finite exchangeable binary sequence of random variables expressions for the joint distribution moments and correlations of all orders are derived maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster in an application to developmental toxicology data analysis the procedure introduced is compared with a beta binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose

the existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method abstract in this paper we study the existence and multiplicity of classical solutions for a second order impulsive differential equation with periodic boundary conditions by using a variational method and critical point theory we give some new criteria to guarantee that the impulsive problem has at least one solution two solutions and infinitely many solutions when the parameter pair c lies in different intervals respectively some examples are given in this paper to illustrate the main results

a unified approach for analyzing exchangeable binary data with applications to developmental toxicity studies in this article we present a general procedure to analyze exchangeable binary data that may also be viewed as realizations of binomial mixtures our approach unifies existing models and is practical and computationally easy resulting from completely monotonic functions we introduce a rich family of parametric parsimonious binomial mixtures including the incomplete beta gamma normal and poisson binomial generalizing the beta binomial we show that the family is closed under convex linear combinations products and composites we also give the moments and the markov property of the family with such distributions we can perform statistical inference on correlated binary data and in particular overdispersed data we propose a regression procedure that generalizes logistic regression we provide a forward model selection procedure we run a small simulation to validate the inclusion of the binomial distribution finally we apply the proposed procedure to analyze the 2 4 5 trichlorophenoxyacetic acid and e2 data and compare the results with existing procedures copyright 2009 john wiley sons ltd

a compound negative binomial distribution with mutative termination conditions based on a change point abstract in this paper an extended negative binomial distribution called nbm is proposed by considering mutative termination conditions based on a change point if the condition a is satisfied before the occurrence of the change point the trial is terminated according to condition a otherwise if the condition a does not happen and the change point is satisfied the termination condition of the trial changes from condition a to condition b we consider the conditions under which the resulting distribution can be degenerated to the existing negative binomial distributions and other new negative binomial distributions the finite markov chain imbedding approach is employed to derive the new negative binomial distribution nbm and to obtain the related probabilistic indexes furthermore we study the distribution of the compound negative binomial distribution with mutative termination conditions based on a change point cnbm by means of phase type representations

on exchangeable multinomial distributions we derive an expression for the joint distribution of exchangeable multinomial random variables which generalizes the multinomial distribution based on independent trials while retaining some of its important properties unlike de finneti s representation theorem for a binary sequence the exchangeable multinomial distribution derived here does not require that the finite set of random variables under consideration be a subset of an infinite sequence using expressions for higher moments and correlations we show that the covariance matrix for exchangeable multinomial data has a different form from that usually assumed in the literature and we analyse data from developmental toxicology studies the proposed analyses have been implemented in r and are available on cran in the corrbin package

a saturated model for analyzing exchangeable binary data applications to clinical and developmental toxicity studies abstract correlated binary data occur very frequently in statistical practice in many applications it is reasonable to assume that data from the same cluster are exchangeable such data are commonly encountered in cluster sample surveys teratological experiments ophthalmologic and otolaryngologic studies and other clinical trials the standard methods of analyzing these data include the use of beta binomial models and generalized estimating equations with third and fourth moments specified by working matrices the focus of these procedures is an estimation of the mean and variance parameters more information can be obtained when data are exchangeable by expressing the joint distribution of a set of exchangeable binary random variables in terms of the probability of similar response within cluster this article introduces a procedure for obtaining maximum likelihood estimates of population parameters such as the marginal means moments and correlations of orders two and higher applications are m

optimal time consistent reinsurance investment strategy with delay for an insurer under a defaultable market abstract in this paper we consider a reinsurance investment problem with delay for an insurer under the mean variance criterion in a defaultable market the financial market consists of a risk free bond a stock and a defaultable bond the insurer s surplus process is described by a jump diffusion risk model and the price process of the stock is assumed to follow a constant elasticity of variance cev model in particular we take the delay of feedback time for strategy into account applying stochastic control approach we derive the time consistent reinsurance investment strategy in post default case and pre default case explicitly via a game theoretic framework respectively finally numerical examples and sensitivity analyses are provided to show the impact of financial parameters on the optimal strategies