direct estimation of the mean outcome on treatment when treatment assignment and discontinuation compete several authors have investigated the challenges of statistical analyses and inference in the presence of early treatment termination including a loss of efficiency in randomized controlled trials and a connection to dynamic regimes in observational studies popular estimation strategies for causal estimands in dynamic regimes lend themselves to studies where treatment is assigned at a finite number of points and the extension to continuous treatment assignment is nontrivial we re examine this from a different perspective and propose a new estimator for the mean outcome of a target treatment length policy that does not involve a treatment model because this strategy avoids modelling the treatment assignment mechanism the estimator works for both discrete and continuous treatment length data and eschews bias and imprecision that arise as a result of coarsening continuous time data into intervals we show how the competition of treatment length assignment and terminating event lead to a competing risks problem we exemplify the direct estimator through numerical studies and the analysis of two real datasets when all modelling assumptions for both the direct and inverse weighted estimators are correct our simulation studies suggest that the direct estimator is more precise

transient properties of a bistable kinetic model with correlations between additive and multiplicative noises mean first passage time the transient properties of a bistable system with correlations between additive and multiplicative noise terms are investigated the explicit expressions of the mean first passage time mfpt are obtained the numerical computations show that the mfpt of the system is affected by ensuremath lambda the strength of correlations between additive intensity ensuremath alpha and multiplicative intensity d noise terms for the case of perfectly correlated noises ensuremath lambda 1 the mfpt corresponding to ensuremath alpha ensuremath gtrsim d and ensuremath alpha d exhibits very different behaviors and the mfpt for ensuremath alpha d diverges to infinity textcopyright 1996 the american physical society

partially linear models with missing response variables and error prone covariates we consider partially linear models of the form y x t beta nu z epsilon when the response variable y is sometimes missing with missingness probability pi depending on x z and the covariate x is measured with error where nu z is an unspecified smooth function the missingness structure is therefore missing not at random rather than the usual missing at random we propose a class of semiparametric estimators for the parameter of interest beta as well as for the population mean e y the resulting estimators are shown to be consistent and asymptotically normal under general assumptions to construct a confidence region for beta we also propose an empirical likelihood based statistic which is shown to have a chi squared distribution asymptotically the proposed methods are applied to an aids clinical trial dataset a simulation study is also reported

equipercentile equating via data imputation techniques in the design of common item equating two groups of examinees are administered separate test forms and each test form contains a common subset of items we consider test equating under this situation as an incomplete data problem that is examinees have observed scores on one test form and missing scores on the other through the use of statistical data imputation techniques the missing scores can be replaced by reasonable estimates and consequently the forms may be directly equated as if both forms were administered to both groups in this paper we discuss different data imputation techniques that are useful for equipercentile equating we also use empirical data to evaluate the accuracy of these techniques as compared with chained equipercentile equating

delay fokker planck equations perturbation theory and data analysis for nonlinear stochastic systems with time delays we study nonlinear stochastic systems with time delayed feedback using the concept of delay fokker planck equations introduced by guillouzic l heureux and longtin we derive an analytical expression for stationary distributions using first order perturbation theory we demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data in addition we show that the fokker planck perspective for stochastic systems with time delays is consistent with the so called extended phase space approach to time delayed systems

local multiple imputation dealing with missing data via parametric multiple imputation methods usually implies stating several strong assumptions both about the distribution of the data and about underlying regression relationships if such parametric assumptions do not hold the multiply imputed data are not appropriate and might produce inconsistent estimators and thus misleading results in this paper a fully nonparametric and a semiparametric imputation method are studied both based on local resampling principles it is shown that the final estimator based on these local imputations is consistent under fewer or no parametric assumptions asymptotic expressions for bias variance and mean squared error are derived showing the theoretical impact of the different smoothing parameters simulations illustrate the usefulness and applicability of the method

globally efficient non parametric inference of average treatment effects by empirical balancing calibration weighting the estimation of average treatment effects based on observational data is extremely important in practice and has been studied by generations of statisticians under different frameworks existing globally efficient estimators require non parametric estimation of a propensity score function an outcome regression function or both but their performance can be poor in practical sample sizes without explicitly estimating either functions we consider a wide class calibration weights constructed to attain an exact three way balance of the moments of observed covariates among the treated the control and the combined group the wide class includes exponential tilting empirical likelihood and generalized regression as important special cases and extends survey calibration estimators to different statistical problems and with important distinctions global semiparametric efficiency for the estimation of average treatment effects is established for this general class of calibration estimators the results show that efficiency can be achieved by solely balancing the covariate distributions without resorting to direct estimation of propensity score or outcome regression function we also propose a consistent estimator for the efficient asymptotic variance which does not involve additional functional estimation of either the propensity score or the outcome regression functions the proposed variance estimator outperforms existing estimators that require a direct approximation of the efficient influence function

nonparametric estimation of mean functionals with data missing at random abstract this article considers a distribution free estimation procedure for a basic pattern of missing data that often arises from the wellknown double sampling in survey methodology without parametric modeling of the missing mechanism or the joint distribution kernel regression estimators are used to estimate mean functionals through empirical estimation of the missing pattern a generalization of the method of cheng and wei is verified under the assumption of missing at random asymptotic distributions are derived for estimating the mean of the incomplete data and for estimating the mean treatment difference in a nonrandomized observational study the nonparametric method is compared with a naive pairwise deletion method and a linear regression method via the asymptotic relative efficiencies and a simulation study the comparison shows that the proposed nonparametric estimators attain reliable performances in general

efficient estimation of population level summaries in general semiparametric regression models this article considers a wide class of semiparametric regression models in which interest focuses on population level quantities that combine both the parametric and the nonparametric parts of the model special cases in this approach include generalized partially linear models generalized partially linear single index models structural measurement error models and many others for estimating the parametric part of the model efficiently profile likelihood kernel estimation methods are well established in the literature here our focus is on estimating general population level quantities that combine the parametric and nonparametric parts of the model e g population mean probabilities etc we place this problem in a general context provide a general kernel based methodology and derive the asymptotic distributions of estimates of these population level quantities showing that in many cases the estimates are semiparametric efficient for estimating the population mean with no missing data we s

semiparametric regression analysis with missing response at random we develop inference tools in a semiparametric partially linear regression model with missing response data a class of estimators is defined that includes as special cases a semiparametric regression imputation estimator a marginal average estimator and a marginal propensity score weighted estimator we show that any of our class of estimators is asymptotically normal the three special estimators have the same asymptotic variance they achieve the semiparametric efficiency bound in the homoscedastic gaussian case we show that the jackknife method can be used to consistently estimate the asymptotic variance our model and estimators are defined with a view to avoid the curse of dimensionality which severely limits the applicability of existing methods the empirical likelihood method is developed it is shown that when missing responses are imputed using the semiparametric regression method the empirical log likelihood is asymptotically a scaled chi squared variable an adjusted empirical log likel

data driven local bandwidth selection for additive models with missing data this paper deals in the nonparametric estimation of additive models in the presence of missing data in the response variable specifically in the case of additive models estimated by the backfitting algorithm with local polynomial smoothers 1 three estimators are presented one based on the available data and two based on a complete sample from imputation techniques we also develop a data driven local bandwidth selector based on a wild bootstrap approximation of the mean squared error of the estimators the performance of the estimators and the local bootstrap bandwidth selection method are explored through simulation experiments

double stochastic resonance in an insect ecosystem with time delays abstract considering additive and multiplicative periodic signals we have investigated the stochastic resonance sr phenomenon in an insect ecosystem with two different types of time delays at which the insect dynamics is assumed to be disturbed by both additive and multiplicative noises the signal to noise ratio snr is calculated when two different weak periodic signals are added to the insect system it is shown from the snr that the additive and multiplicative periodic signals can cause the sr and double sr in the case of time delays in the stochastic and deterministic force respectively a detailed study of the snr depending on various noise characteristics is performed and the main results about sr are compared for two different cases of time delays

analytical approach for the floquet theory of delay differential equations we present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states to this end we start with approximately determining such reference states by extending the poincare lindstedt and the shohat expansions which were originally developed for ordinary differential equations then we systematically elaborate a linear stability analysis around a time periodic reference state this allows us to approximately calculate the floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions

role of the noise on the transient dynamics of an ecosystem of interacting species abstract we analyze the transient dynamics of an ecosystem described by generalized lotka volterra equations in the presence of a multiplicative noise and a random interaction parameter between the species we consider specifically three cases i two competing species ii three interacting species one predator two preys iii n interacting species the interaction parameter in case i is a stochastic process which obeys a stochastic differential equation we find noise delayed extinction of one of two species which is akin to the noise enhanced stability phenomenon other two noise induced effects found are temporal oscillations and spatial patterns of the two competing species in case ii the noise induces correlated spatial patterns of the predator and of the two preys concentrations finally in case iii we find the asymptotic behavior of the time average of the ith population when the ecosystem is composed of a great number of interacting species

conditional moment models with data missing at random summarywe consider a general statistical model defined by moment restrictions when data are missing at random using inverse probability weighting we show that such a model is equivalent to a model for the observed variables only augmented by a moment condition defined by the missingness mechanism our framework covers parametric and semiparametric mean regressions and quantile regressions we allow for missing responses missing covariates and any combination of them the equivalence result sheds new light on various aspects of missing data and provides guidelines for building efficient estimators

delay induced instabilities in nonlinear feedback systems extending general methods developed in synergetics to construct order parameter equations we work out a systematic elimination procedure for the stable modes in nonlinear delay systems it will be shown that in the vicinity of an instability the dynamical behavior of the infinite dimensional delay system is approximately governed by a low dimensional set of order parameter equations which turn out to be of the form of ordinary differential equations i e they no longer contain memory terms the general formalism will then be compared with experimental data obtained from the nonlinear operation of a phase locked loop where the finite propagation time of the signal in the feedback loop is taken into account

bistable kinetic model driven by correlated noises steady state analysis a simple rule to obtain the fokker planck equation for a general one dimensional system driven by correlated gaussian white noises is proved by the functional method the fokker planck equation obtained in this paper is applied to the bistable kinetic model we find the following for the steady state 1 in the ensuremath alpha d parameter plane ensuremath alpha is the strength of the additive noise and d is the multiplicative noise strength the critical curve separating the unimodal and bimodal regions of the stationary probability distribution spd of the model is shown to be affected by ensuremath lambda the degree of correlation of the noises as ensuremath lambda is increased the area of the bimodal region in the ensuremath alpha d plane is contracted 2 when we take a point fixed in the ensuremath alpha d plane and increase ensuremath lambda the form of the spd changes from a bimodal to a unimodal structure 3 the positions of the extreme value of the spd of the model sensitively depend on the strength of the multiplicative noise and weakly depend on the additive noise strength 4 for ensuremath lambda 1 the case of perfectly correlated noises when the parameters ensuremath alpha and d take values in the neighborhood of the line ensuremath alpha d in the ensuremath alpha d plane the spd s corresponding to the points ensuremath alpha dg1 and ensuremath alpha d1 exhibit a very different shape of divergence therefore the ratio ensuremath alpha d 1 plays the role of a critical ratio

stochastic resonance in linear systems subject to multiplicative and additive noise exact expressions have been found for the first two moments and the correlation function for an overdamped linear system subject to an external periodic field as well as to multiplicative and additive noise stochastic resonance is absent for gaussian white noise however when the multiplicative noise has the form of an asymmetric dichotomous noise the signal to noise ratio snr becomes a nonmonotonic function of the correlation time and the asymmetry of noise moreover the snr turns out to be a nonmonotonic function of the frequency of the external field as well as strongly depending on the strength of the cross correlation between multiplicative and additive noise

subcritical hopf bifurcation in dynamical systems described by a scalar nonlinear delay differential equation a subcritical hopf bifurcation in a dynamical system modeled by a scalar nonlinear delay differential equation is studied theoretically and experimentally the subcritical hopf bifurcation leads to a significant domain of bistability where stable steady and time periodic states coexist

stochastic resonance in extended bistable systems the role of potential symmetry we study the role of potential symmetry in a three field reaction diffusion system presenting bistability by means of a two state theory for stochastic resonance in general asymmetric systems by analyzing the influence of different parameters in the optimization of the signal to noise ratio we observe that this magnitude always increases with the symmetry of the system s potential indicating that it is this feature which governs the optimization of the system s response to periodic signals

the effects of time delay on stochastic resonance in a bistable system with correlated noises the effects of time delay on stochastic resonance sr in a bistable system with time delay correlated noises and periodic signal are studied by using the theory of signal to noise ratio snr the expression of the snr is derived under the adiabatic limit and the small delay time approximation it is found that i for the case of no correlations between multiplicative and additive noise the delay time can enhance the snr as a function of the multiplicative noise intensity and it can restrain the snr as a function of the additive noise intensity d ii for the case of correlations between multiplicative and additive noise can induce a minimum and maximum in curve of the snr as a function of and can intensively restrain the snr as a function of the d and there is a critical value of delay tim c 0 1 in the height of the snr peak with change of i e when takes value blow c t he boosts up the snr as a function of the strength of correlations between multiplicative and additive noise however when takes value above c t he restrains that

the time delay restraining the herd behavior with bayesian approach abstract we explore the herd behavior of stock prices influenced by the time delay in a finance system with the delayed heston model on the basis of a bayesian approach for delayed heston model that we proposed and parameter bayesian estimation we simulate the absolute deviation between mean residence time of positive and negative returns to characterize the herd behavior in the plots of absolute deviation against the mean reversion long run variance of volatility or cross correlation between two wiener processes of stock price and volatility the results demonstrate an increasing phenomenon of herd behavior with increasing delay time in the plot of absolute deviation against the amplitude of volatility fluctuations the result indicates an optimal delay time matching minimum herd behavior i e the time delay restrains the herd behavior also the optimal mean reversion long run variance of volatility and cross correlation concerning minimum herd behavior can be observed

regression smoothing parameters that are not far from their optimum abstract it is well known that data driven regression smoothing parameters based on cross validation and related methods exhibit a slow rate of convergence to their optimum in an earlier article we showed that this rate can be as slow as n 1 10 that is for a bandwidth 0 optimizing the averaged squared error n 1 10 0 0 tends to an asymptotic normal distribution in this article we consider mean averaged squared error optimal bandwidths h 0 this nonrandom smoothing parameter can be approximated much faster we use the technique of double smoothing to show that there is an such that under certain conditions n 1 2 h 0 h 0 tends to an asymptotic normal distribution

estimation of mean response via the effective balancing score we introduce effective balancing scores for estimation of the mean response under a missing at random mechanism unlike conventional balancing scores the effective balancing scores are constructed via dimension reduction free of model specification three types of effective balancing scores are introduced those that carry the covariate information about the missingness the response or both they lead to consistent estimation with little or no loss in efficiency compared to existing estimators the effective balancing score based estimator relieves the burden of model specification and is the most robust it is a near automatic procedure which is most appealing when high dimensional covariates are involved we investigate both the asymptotic and the numerical properties and demonstrate the proposed method in a study on human immunodeficiency virus disease

semiparametric double balancing score estimation for incomplete data with ignorable missingness when estimating the marginal mean response with missing observations a critical issue is robustness to model misspecification in this article we propose a semiparametric estimation method with extended double robustness that attains the optimal efficiency under less stringent requirement for model specifications than the doubly robust estimators in this semiparametric estimation covariate information is collapsed into a two dimensional score s with one dimension for i the pattern of missingness and the other for ii the pattern of response both estimated from some working parametric models the mean response e y is then estimated by the sample mean of e y s which is estimated via nonparametric regression the semiparametric estimator is consistent if either the core of i or the core of ii is captured by s and attains the optimal efficiency if both are captured by s as the cores can be obtained without correctly specifying the full parametric models for i or ii the proposed es

mann whitney test with adjustments to pretreatment variables for missing values and observational study the conventional wilcoxon mann whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies this is because the missingness of the outcomes or the participation in the treatments may depend on certain pre treatment variables we propose an approach to adjust the mann whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the pre treatment variables we also propose semiparametric extensions of the adjusted mann whitney test which leads to dimension reduction for high dimensional covariate a novel bootstrap procedure is devised to approximate the null distribution of the test statistics for practical implementations results from simulation studies and an economic observational study data analysis are presented to demonstrate the performance of the proposed approach

stochastic resonance in a trapping overdamped monostable system the response of a trapping overdamped monostable system to a harmonic perturbation is analyzed in the context of stochastic resonance phenomenon we consider the dynamics of a brownian particle moving in a piecewise linear potential with a white gaussian noise source based on linear response theory and laplace transform technique analytical expressions of signal to noise ratio snr and signal power amplification spa are obtained we find that the snr is a nonmonotonic function of the noise intensity while the spa is monotonic theoretical results are compared with numerical simulations

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

nonparametric analysis of factorial designs with random missingness bivariate data we propose a nonparametric approach to the analysis of factorial designs where each subject is observed at two time points and both observations are subject to missingness the procedures are fully nonparametric in that they do not require continuity and do not impose models to describe the relation of the response distribution in different factor level combinations the approach for estimating and testing treatment and time effects is based on a method which we introduce for estimating a distribution function the method requires a pattern mixture type assumption on the missingness mechanism which is weaker than the missing completely at random assumption but neither weaker nor stronger than the missing at random assumption this missingness assumption is the minimal requirement for nonparametric analysis comparisons with normal based likelihood ratio tests indicate that the proposed tests fare well when the data are normal and homoscedastic and outperform them in many other cases simulations also

a flexible and fast method for automatic smoothing abstract the choice of smoothing parameter or bandwidth is crucial when applying nonparametric regression estimators such as kernel estimators the optimal choice depends on the data at hand a data driven bandwidth selection close to the optimal one would make these curve estimators objective more reliable and easier to use minimizing residual mean squared error criteria such as cross validation have been frequently proposed to estimate the optimal smoothing parameter empirical and theoretical evidence indicates that cross validation rules and related methods lead to rather variable estimated optimal bandwidths the method presented here builds on estimating the asymptotically optimal bandwidth from the data since estimators for the residual variance and for an asymptotic expression for the bias are plugged into the asymptotic formula such selection rules are called plug in estimators the functional that quantifies bias is approximated by the integrated squared second derivative of the regre

stochastic resonance in a bistable system subject to multiplicative and additive noise the stochastic resonance sr phenomenon in a bistable system under the simultaneous action of multiplicative and additive noise and periodic signal is studied by using the theory of signal to noise ratio snr in the adiabatic limit two cases have been considered the case of no correlations between multiplicative and additive noise and the case of correlations between two noises the expressions of the snr for both cases are obtained the effects of intensity of multiplicative and additive noise and the intensity of the correlations between noises on the snr are discussed for both cases respectively it is found that the existence of a maximum in the snr is the identifying characteristic of the sr phenomenon in the case of no correlations between multiplicative and additive noise the snr is independent of the initial condition of the system however the snr is not only dependent on the intensity of correlations between noises but also on the initial condition of the system in the presence of correlations between two noises

estimation in partially linear models with missing covariates the partially linear model y xt z has been studied extensively when data are completely observed in this article we consider the case where the covariate x is sometimes missing with missingness probability depending on y z new methods are developed for estimating and our methods are shown to outperform asymptotically methods based only on the complete data asymptotic efficiency is discussed and the semiparametric efficient score function is derived justification of the use of the nonparametric bootstrap in this context is sketched the proposed estimators are extended to a working independence analysis of longitudinal clustered data and applied to analyze an aids clinical trial dataset the results of a simulation experiment are also given to illustrate our approach

using a monotone single index model to stabilize the propensity score in missing data problems and causal inference the augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems an important component of this method is the propensity score popular parametric models for the propensity score include the logistic probit and complementary log log models a common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables to avoid the need to choose a model we model the propensity score via a semiparametric single index model in which the score is an unknown monotonic nondecreasing function of the given single index under this new model the augmented inverse weighting estimator aiwe of the mean of the response is asymptotically linear semiparametrically efficient and more robust than existing estimators moreover we have made a surprising observation the inverse probability weighting and aiwes based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model a heuristic explanation of this phenomenon is provided a real data example is used to illustrate the proposed methods

on variance estimation in nonparametric regression a simple explicit estimator of variance in nonparametric regression is suggested based on the mean square of a sequence of residuals the estimator is valid for general error distributions has elementary bias and variance properties and is optimal to both first and second orders

on the structure of unitary conformal field theory ii representation theoretic approach two dimensional unitary rational conformal field theory is studied from the point of view of the representation theory of chiral algebras chiral algebras are equipped with a family of co multiplications which serve to define tensor product representations chiral vertices arise as clebsch gordan operators from tensor product representations to irreducible subrepresentations of a chiral algebra the algebra of chiral vertices is studied and shown to give rise to representations of the braid groups determined by yang baxter braid matrices chiral fusion is analyzed it is shown that the braid and fusion matrices determine invariants of knots and links connections between the representation theories of chiral algebras and of quantum groups are sketched finally it is shown how the local fields of a conformal field theory can be reconstructed from the chiral vertices of two chiral algebras

estimating equations inference with missing data there is a large and growing body of literature on estimating equation ee as an estimation approach one basic property of ee that has been universally adopted in practice is that of unbiasedness and there are deep conceptual reasons why unbiasedness is a desirable ee characteristic this article deals with inference from ees when data are missing at random the investigation is motivated by the observation that direct imputation of missing data in ees generally leads to ees that are biased and thus violates a basic assumption of the ee approach the main contribution of this article is that it goes beyond existing imputation methods and proposes a procedure whereby one mitigates the effects of missing data through a reformulation of ees imputed through a kernel regression method these modified ees then constitute a basis for inference by the generalized method of moments gmm and empirical likelihood el asymptotic properties of the gmm and el estimators of the unknown parameters are derived a

efficiency bounds for missing data models with semiparametric restrictions this paper shows that the semiparametric efficiency bound for a parameter identified by an unconditional moment restriction with data missing at random mar coincides with that of a particular augmented moment condition problem the augmented system consists of the inverse probability weighted ipw original moment restriction and an additional conditional moment restriction which exhausts all other implications of the mar assumption the paper also investigates the value of additional semiparametric restrictions on the conditional expectation function cef of the original moment function given always observed covariates in the program evaluation context for example such restrictions are implied by semiparametric models for the potential outcome cefs given baseline covariates the efficiency bound associated with this model is shown to also coincide with that of a particular moment condition problem some implications of these results for estimation are briefly discussed

efficient and doubly robust imputation for covariate dependent missing responses in this article we study a well known response missing data problem missing data is an ubiquitous problem in medical and social science studies imputation is one of the most popular methods for dealing with missing data the most commonly used imputation that makes use of covariates is regression imputation in which the regression model can be parametric semiparametric or nonparametric parametric regression imputation is efficient but is not robust against misspecification of the regression model although nonparametric regression imputation such as nearest neighbor imputation and kernel regression imputation is model free it is not efficient especially if the dimension of covariate vector is high the well known problem of curse of dimensionality semiparametric regression imputation such as partially linear regression imputation can reduce the dimension of the covariate in nonparametric regression fitting but is not robust against misspecification of the linear component in the regression

joint sufficient dimension reduction and estimation of conditional and average treatment effects the estimation of treatment effects based on observational data usually involves multiple confounders and dimension reduction is often desirable and sometimes inevitable we first clarify the definition of a central subspace that is relevant for the efficient estimation of average treatment effects a criterion is then proposed to simultaneously estimate the structural dimension the basis matrix of the joint central subspace and the optimal bandwidth for estimating the conditional treatment effects the method can easily be implemented by forward selection semiparametric efficient estimation of average treatment effects can be achieved by averaging the conditional treatment effects with a different data adaptive bandwidth to ensure optimal undersmoothing asymptotic properties of the estimated joint central subspace and the corresponding estimator of average treatment effects are studied the proposed methods are applied to a nutritional study where the covariate dimension is reduced from 11 to an effective dimension of one

stochastic resonance and noise delayed extinction in a model of two competing species abstract we study the role of the noise in the dynamics of two competing species we consider generalized lotka volterra equations in the presence of a multiplicative noise which models the interaction between the species and the environment the interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term which accounts for the environment temperature variation we find noise induced periodic oscillations of the species concentrations and stochastic resonance phenomenon we find also a nonmonotonic behavior of the mean extinction time of one of the two competing species as a function of the additive noise intensity

use of regression functions for improved estimation of means summary suppose one has a random sample from a distribution fy x the goal being to estimate u4 the unconditional mean of y if the regression function of y on x is of a known parametric form one might consider estimating u by the average of the estimated regression function values at the sample points it is shown here that such an estimator can offer substantial improvement over the sample mean of y and that in no case does the former estimator have larger asymptotic variance than the latter estimator applications of this asymptotic distribution theory to the double sampling setting are also given

dynamics of two competing species in the presence of levy noise sources we consider a lotka volterra system of two competing species subject to multiplicative stable levy noise the interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive stable levy noise we study the species dynamics which is characterized by two different regimes exclusion of one species and coexistence of both we find quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species analyzing the role of the levy noise sources

information transmission in parallel threshold arrays suprathreshold stochastic resonance the information transmitted through a parallel summing array of noisy threshold elements with a common threshold is considered in particular using theoretical and numerical analysis a recently reported n g stocks phys rev lett 84 2310 2000 form of stochastic resonance termed suprathreshold stochastic resonance ssr is studied in detail ssr is observed to occur in arrays with two or more elements and unlike stochastic resonance sr in a single element gives rise to noise induced information gains that occur independent of the setting of the threshold or the size of the signal the transmitted information is maximized when all thresholds are set to coincide with the signal mean in this situation and for large arrays the noise can enhance performance up to approximately half the theoretical noiseless channel capacity the theory is tested against digital simulation

stochastic resonance driven by time modulated correlated white noise sources we analyze the effects caused by the simultaneous presence of correlated additive and multiplicative noises for stochastic resonance besides the standard potential modulation we also consider a time periodic variation of the correlation between the two noise sources as a foremost result we find that stochastic resonance as characterized by the signal to noise ratio and the spectral amplification becomes characteristically broadened the broadening can be controlled by varying the relative phase shift between the two types of modulation force

handling estimating equation with nonignorably missing data based on sir algorithm abstract in this paper the estimation of parameters in estimating equation with nonignorably missing data is considered based on a logistic regression model for the response mechanism and an assumed parametric model for the distribution of respondents we propose to use the sampling importance resampling sir algorithm to calculate the conditional expectation for non respondents the proposed method can avoid the difficulty of high dimensional kernel smoothing on calculating the conditional expectation under nonignorably missing data based on the sir algorithm we derive a modified estimating equation to facilitate comparison we apply the empirical likelihood method to derive the parameters estimator some numerical simulation results based on linear and nonlinear models show that the proposed method is robust and performs the best among the compared existing methods so we extend the estimation method of e g y using sir algorithm with nonignorably missing response to the estimation of parameters in generalized estimating equation and obtain a new and more robust estimation method

stochastic resonance in threshold systems we consider signal processing in simple threshold systems with nonstationary additive and or multiplicative noise a discrete time process with a small periodical signal masked by noise represents an input the systems convert sampled input data to a nonstationary random point event flow carrying some information on an input signal as it is shown in our previous study m m alibegov astron lett 22 564 1996 the rayleigh spectral function of a random point event train estimates a signal to noise ratio snr at selected frequencies based on these results we compute a system response at signal frequencies as a function of threshold and input noise intensity the threshold systems are shown to reveal stochastic resonance sr i e output snr exhibits a maximum at resonant noise intensity intensities and threshold s at rather common conditions we show that sr and rayleigh spectral technique allow us to carry out numerical signal detection in data sets with noise

doubly robust type estimation for covariate adjustment in latent variable modeling due to the difficulty in achieving a random assignment a quasi experimental or observational study design is frequently used in the behavioral and social sciences if a nonrandom assignment depends on the covariates multiple group structural equation modeling that includes the regression function of the dependent variables on the covariates that determine the assignment can provide reasonable estimates under the condition of correct specification of the regression function however it is usually difficult to specify the correct regression function because the dimensions of the dependent variables and covariates are typically large therefore the propensity score adjustment methods have been proposed since they do not require the specification of the regression function and have been applied to several applied studies however these methods produce biased estimates if the assignment mechanism is incorrectly specified in order to make a more robust inference it would be more useful to develop an estimation method that integrates the regression approach with the propensity score methodology in this study we propose a doubly robust type estimation method for marginal multiple group structural equation modeling this method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified a simulation study indicates that the proposed estimation method is more robust than the existing methods

empirical likelihood based inference under imputation for missing response data inference under kernel regression imputation for missing response data is considered an adjusted empirical likelihood approach to inference for the mean of the response variable is developed a nonparametric version of wilks theorem is proved for the adjusted empirical log likelihood ratio by showing that it has an asymptotic standard chi squared distribution and the corresponding empirical likelihood confidence interval for the mean is constructed with auxiliary information an empirical likelihood based estimator is defined and an adjusted empirical log likelihood ratio is derived asymptotic normality of the estimator is proved also it is shown that the adjusted empirical log likelihood ratio obeys wilks theorem a simulation study is conducted to compare the adjusted empirical likelihood and the normal approximation methods in terms of coverage accuracies and average lengths of confidence intervals based on biases and standard errors a comparision is also made by simulation between the empirical likelihood based estimator and related estimators our simulation indicates that the adjusted empirical likelihood method performs competitively and that the use of auxiliary information provides improved inferences

parameter estimation for nonlinear time delay systems with noisy output measurements this paper considers the problem of using noisy output data to estimate unknown time delays and unknown system parameters in a general nonlinear time delay system we formulate the problem as a dynamic optimization problem in which the unknown quantities are decision variables to be chosen optimally with the cost function penalizing the mean and variance of the least squares error between actual and predicted system output since the time delays and system parameters influence the cost function implicitly through the governing time delay system the cost function s gradient which is required to solve the problem using gradient based optimization techniques cannot be computed analytically using standard differentiation rules we instead develop two computational methods for evaluating this gradient one involves solving an auxiliary time delay system forward in time the other involves solving an auxiliary time advance system backward in time on this basis we propose an efficient optimization algorithm for determining optimal estimates for the time delays and system parameters we conclude the paper by examining the performance of this algorithm on a dynamic model of a continuously stirred tank reactor

semiparametric model based inference in the presence of missing responses summary we consider a semiparametric model that parameterizes the conditional density ofthe response given covariates but allows the marginal distribution of the covariates to be completely arbitrary responses may be missing a likelihood based imputation estimator and a semi empirical likelihood based estimator for the parameter vector describing the conditional density are defined and proved to be asymptotically normal semi empirical loglikelihood functions for the parameter vector and the response mean are derived it is shown that the two semi empirical loglikelihood functions are distributed asymptotically as weighted x2 and scaled x2 respectively

a propensity score adjustment for multiple group structural equation modeling in the behavioral and social sciences quasi experimental and observational studies are used due to the difficulty achieving a random assignment however the estimation of differences between groups in observational studies frequently suffers from bias due to differences in the distributions of covariates to estimate average treatment effects when the treatment variable is binary rosenbaum and rubin 1983a proposed adjustment methods for pretreatment variables using the propensity score

different delays induced regime shifts in a stochastic insect outbreak dynamics abstract considering time delays in the deterministic and stochastic forces we construct stochastic delayed differential equations to investigate the regime shifts in an insect ecosystem the stationary probability distribution spd and mean first passage time mfpt are obtained respectively our main results show i the multiplicative noise positive cross correlation noise between two noises and time delays can induce the regime shifts from the boom outbreak state to the bust one but the additive noise and negative cross correlation can induce the regime shifts from the bust outbreak state to the boom one ii for the negative cross correlation the mfpt as a function of noise strengths exhibits one maximum which shows the characteristic of the noise delayed switching for the boom outbreak state but for the no cross correlation or positive cross correlation the mfpt decreases with the noise strengths iii two different types of time delays play same roles on the maximal mfpt with additive noise and play opposite roles on the maximal mfpt with multiplicative noise the mechanisms for noises and delays induced regime shifts between two states can be explained physically through the effective potential of ecological model

semiparametric dimension reduction estimation for mean response with missing data model misspecification can be a concern for high dimensional data nonparametric regression obviates model specification but is impeded by the curse of dimensionality this paper focuses on the estimation of the marginal mean response when there is missingness in the response and multiple covariates are available we propose estimating the mean response through nonparametric functional estimation where the dimension is reduced by a parametric working index the proposed semiparametric estimator is robust to model misspecification it is consistent for any working index if the missing mechanism of the response is known or correctly specified up to unknown parameters even with misspecification in the missing mechanism it is consistent so long as the working index can recover e y x the conditional mean response given the covariates in addition when the missing mechanism is correctly specified the semiparametric estimator attains the optimal efficiency if e y x is recoverable through the working index robustness and efficiency of the proposed estimator is further investigated by simulations we apply the proposed method to a clinical trial for hiv