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

transversal waves in beams via the network simulation method abstract in this paper the network simulation method nsm is proposed as a tool for solving the transverse motion of thin beams resulting from a bending action the reliability and robustness of the proposed technique is demonstrated with two examples in which a pinned pinned beam and a clamped mass load beam are respectively submitted to different flexural forces the nsm is a numerical technique for the solution of linear and non linear problems which are defined by a mathematical model assuming that the electrical variables of voltage and current are equivalent respectively to the displacement and the spatial variation of the displacement a network model for each volume element is designed such that electrical equations are formally equivalent to the spatial discretised equations of the mechanical model the whole network model including the devices associated with the boundary conditions is solved by the numerical computer code pspice the numerical results have been compared with those obtained by the mode superposition method the agreement between them is impressive the temporal behaviour of each quantity involved in the problem is obtained without transform complications since the whole study has been conducted in the time domain with the possibility of obtaining the corresponding spectral content at the end of calculation the main contribution of the present paper therefore is to employ the nsm numerical method in order to arrive at solutions in the time domain of dynamic mechanical problems one must also emphasize that nsm has not previously been used by other authors to solve physical problems like the ones presented here

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

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

bifurcation analysis of a delayed epidemic model in this paper hopf bifurcation for a delayed sis epidemic model with stage structure and nonlinear incidence rate is investigated through theoretical analysis we show the positive equilibrium stability and the conditions that hopf bifurcation occurs applying the normal form theory and the center manifold argument we derive the explicit formulas determining the properties of the bifurcating periodic solutions in addition we also study the effect of the inhibition effect on the properties of the bifurcating periodic solutions to illustrate our theoretical analysis some numerical simulations are also included

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

the automatic robustness of minimum distance functionals on montre que les estimateurs de distance minimale forment une classe d estimateurs automatiquement robustes dans le meme sens que l estimateur du maximum de vraisemblance

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

approximation dans les espaces metriques et theorie de l estimation we investigate the relations between the speed of estimation and the metric structure of the parameter space especially in the case when its metric dimension is infinite given some distance d on generally hellinger distance in the case of n i i d variables we consider the minimax risk for n observations r n q mathop inf sup limits t n theta in theta text ie theta d q theta t n t n being any estimate of we shall look for functions r such that for positive constants c 1 q and c 2 q c 1 r q n r n q c2 r q n r n is the speed of estimation and we shall show under fairly general conditions including i i d variables and regular cases of markov chains and stationnary gaussian processes that r n is determined up to multiplicative constants by the metric structure of we shall also give a construction for some sort of universal estimates the risk of which is bounded by c 2 r q n in all cases where the preceding theory applies

the construction of trend free run orders of two level factorial designs abstract in experimental situations where a factorial design with all factors occurring at two levels is to be run in a time sequence the usual advice given to the experimenter is that the order of runs should be randomized before the experiment is performed however randomization may lead to an undesirable run order for example in a factory experiment there may be a certain learning process that occurs over time as a result of making level changes in the factors being studied or there may be equipment wear out in either case the observations obtained will be affected by uncontrollable variables that are highly correlated with the time or position in which they occur and randomization may lead to a run order in which the estimates of factor effects are adversely effected by the presence of the trend joiner and campbell 1976 gave some more specific examples as to when trend effects can occur in sequential experiments therefore it is important to consider systematic designs in which the estimat

dimensionless characterization of salt intrusion benchmark scenarios in anisotropic media the governing equations of salt intrusion scenarios the henry benchmark problem in hydrogeology is discriminately nondimensionalized to derive the dimensionless groups which define the steady state patterns of iso concentration and iso stream function lines assuming that both hydraulic conductivity and permeability are not isotropic the use of discrimination leads to lowest number of dimensionless groups which have inherent physical characteristics that those derived from classical procedures do not have the new discriminated groups have a clear physical meaning in terms of balance between quantities that counteract the problem in the applied domain in addition they are of an order of magnitude of unity numerical simulations by the network method are presented to discuss the worthiness of henry s problem on the basis of these results

a bahadur type representation for empirical quantiles of a large class of stationary possibly infinite variance linear processes bahadur has obtained an asymptotic almost sure representation for empirical quantiles of independent and identically distributed random variables in this paper we present an analogous result for a large class of stationary linear processes

improving the worthiness of the henry problem as a benchmark for density dependent groundwater flow models 1 this study considers the worthiness of the henry saltwater intrusion problem as a test case to benchmark density dependent groundwater flow models previously published results from a coupled versus uncoupled analysis indicate that the flow patterns associated with the standard henry problem are largely dictated by the boundary forcing and not necessarily a result of density dependent effects simpson and clement 2003 results in this study show that the worthiness of henry s problem can be improved by decreasing the freshwater recharge this modification maintains the usual benefits of the standard test case while at the same time increasing the influence of the density dependent effects the numerical results for the modified henry problem are rigorously tested against a new set of semianalytical results the semianalytical result for the modified problem offers an additional improvement over the standard henry problem that has typically only been tested using intercode comparisons

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

richardson extrapolation and the bootstrap abstract simulation methods particularly efron s 1979 bootstrap are being applied more and more frequently in statistical inference given data x 1 xn distributed according to p which belongs to a hypothesized model p the basic goal is to estimate the distribution l p of a function tn x 1 xn p the bootstrap presupposes the existence of an estimate and involves estimating l p by the distribution l n of where x 1 xn is distributed according to the method is of particular interest when ln though known in principle can realistically only be computed by simulation such computation can be expensive if n is large and tn is complex e g see the multivariate goodness of fit tests of beran and millar 1986 even when bootstrap application to a single data set is not excessively expensive monte carlo studies of the bootstrap are another matter we propose a method based on the classical ideas of richardson extrapolation for reducing the computational cost inherent in bootstra

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

a lower bound for the risk in estimating the value of a probability density abstract this article considers estimation of f 0 of a density function satisfying a lipshitz condition in a neighborhood of 0 a nonstandard use of the cramer rao inequality yields numerical lower bounds on the minimax squared error risk of any estimator these bounds are then compared with the minimax risk of the asymptotically optimal kernel type estimator the asymptotic bounds obtained as the sample size n are not quite as good as those in donoho and liu in press a b but bounds are presented here also for finite values of n and that paper contains no such bounds for this problem the numerical results reported in table 1 show that the asymptotically optimal kernel estimator performs within a factor of 3 of the minimax bound even for sample size n 30 as n increases the relative performance improves to its limiting value although the convergence is fairly slow

a predator prey system with stage structure for predator abstract this paper studies the asymptotoc behavior of a predator prey model with stage structure it is found that an orbitally asymptotically stable periodic orbit exists in that model when time delay due to gestation of predator and time delay from crowding effect of prey are incorporated we establish the condition for the permanence of populations and sufficient conditions under which positive equilibrium of the model is globally stable

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

qualitative analysis of an sir epidemic model with stage structure abstract an sir epidemic model with stage structure consisting immature and mature stages is investigated the global stability of epidemic equilibrium and disease free equilibrium is proved meanwhile we obtained that global dynamics is completely determined by the basic reproduction number if 1 the disease free equilibrium is globally stable and the disease dies out if 1 a unique endemic equilibrium is globally stable in the interior of a feasible region and the disease persists at endemic equilibrium

geometrizing rates of convergence ii consider estimating a functional t f of an unknown distribution f in mathbf f from data x 1 cdots x n i i d f let omega varepsilon denote the modulus of continuity of the functional t over mathbf f computed with respect to hellinger distance for well behaved loss functions l t we show that inf t n sup mathbf f e fl t n t f is equivalent to l omega n 1 2 to within constants whenever t is linear and mathbf f is convex the same conclusion holds in three nonlinear cases estimating the rate of decay of a density estimating the mode and robust nonparametric regression we study the difficulty of testing between the composite infinite dimensional hypotheses h 0 t f leq t and h 1 t f geq t delta our results hold in the cases studied because the difficulty of the full infinite dimensional composite testing problem is comparable to the difficulty of the hardest simple two point testing subproblem

large sample theory of estimation in biased sampling regression models i biased sampling regression models were introduced by jewell generalizing the truncated regression model studied by bhattacharya chernoff and yang if the independent variable takes on only a finite number of values as does the stratum variable we show 1 that if the slope of the underlying regression model is assumed known then the nonparametric maximum likelihood estimates of the distribution of the independent and dependent variables a can be calculated from ordinary m estimates b are asymptotically efficient 2 how to construct m estimates of the slope which are always sqrt n consistent asymptotically gaussian and are efficient locally for example if the error distribution is gaussian we support our asymptotics with a small simulation

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

estimating the stable index alpha in order to measure tail thickness a critique stable laws are often fit to outlier prone data and if the index alpha is estimated to be much less than two then the normal law is rejected in favor of an infinite variance stable law this paper derives the theoretical properties of such a procedure when the true distribution is stable the distribution of the m l e of alpha is non regular if alpha 2 when the true distribution is not stable the estimate of alpha is not a robust measure of the rate of decrease of the tail probabilities a more robust procedure is developed and a statistic for describing and comparing the tail shapes of arbitrary samples is proposed

the henry problem for saltwater intrusion previous solutions of the idealized saltwater intrusion problem known as the henry problem are discussed and possible reasons for the observed discrepancies between them are given high accuracy finite difference techniques are used to solve the nondimensionalized equations governing the problem and a fine grid is used so that the solutions obtained contain only very small truncation errors such errors are investigated by means of grid refinement comparison of past results with the present solutions indicate first the presence of significant inaccuracy in certain earlier results and second the effects of numerical dispersion in other previous solutions calculated using relatively few grid points