asymptotic properties of an estimator in nonlinear functional errors in variables models with dependent error terms nonlinear functional errors in variables models with error terms satisfying mixing conditions are studied it is pointed out that under certain conditions the least squares estimator of regression parameters is not consistent an alternative estimator for regression parameters is proposed the consistency of the alternative estimator is established

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

reducing measurement error in student achievement estimation the achievement level is a variable measured with error that can be estimated by means of the rasch model teacher grades also measure the achievement level but they are expressed on a different scale this paper proposes a method for combining these two scores to obtain a synthetic measure of the achievement level based on the theory developed for regression with covariate measurement error in particular the focus is on ordinal scaled grades using the simex method for measurement error correction the result is a measure comparable across subjects with smaller measurement error variance an empirical application illustrates the method

nonlinear and nonparametric regression and instrumental variables we consider regression when the predictor is measured with error and an instrumental variable iv is available the regression function can be modeled linearly nonlinearly or nonparametrically our major new result shows that the regression function and all parameters in the measurement error model are identified under relatively weak conditions much weaker than previously known to imply identifiability in addition we exploit a characterization of the iv estimator as a classical correction for attenuation method based on a particular estimate of the variance of the measurement error this estimate of the measurement error variance allows us to construct functional nonparametric regression estimators making no assumptions about the distribution of the unobserved predictor and structural estimators that use parametric assumptions about this distribution the functional estimators uses simulation extrapolation or deconvolution kernels and the structural method uses bayesian markov chain monte carlo

the limiting distribution of least squares in an errors in variables regression model abstract there is a substantial literature concerning linear regression when some of the predictors independent variables are measured with error such models are of importance in econometrics instrumental variables models psychometrics correction for attenuation models of change and in instrumental calibration studies in medicine and industry recent theoretical work concerning maximum likelihood estimation in such models appears in healy 1980 fuller 1980 and anderson 1984 while reilly and patino leal 1981 take a bayesian approach in an applied context an investigator may either overlook the measurement errors in the predictors or choose the classical ordinary least squares ols estimator of the parameters because of its familiarity and ease of use certainly the methodology of classical least squares theory confidence intervals multiple comparisons tests of hypotheses residual analysis is considerably more developed than the corresponding errors in variables methodology particularly in samples of moderate size in this paper it is shown that under reasonable regularity conditions such linear combinations are jointly asymptotically normally distributed

nonparametric regression in the presence of measurement error summary in many regression applications the independent variable is measured with error when this happens conventional parametric and nonparametric regression techniques are no longer valid we consider two diverent approaches to nonparametric regression the first uses the simex simulation extrapolation method and makes no assumption about the distribution of the unobserved error prone predictor for this approach we derive an asymptotic theory for kernel regression which has some surprising implications penalised regression splines are also considered for fixed number of known knots the second approach assumes that the error prone predictor has a distribution of a mixture of normals with an unknown number of components and uses regression splines simulations illustrate the results

bias analysis and simex approach in generalized linear mixed measurement error models abstract we consider generalized linear mixed models glmms for clustered data when one of the predictors is measured with error when the measurement error is additive and normally distributed and the error prone predictor is itself normally distributed we show that the observed data also follow a glmm but with a different fixed effects structure from the original model a different and more complex random effects structure and restrictions on the parameters this characterization enables us to compute the biases that result in common glmms when one ignores measurement error for instance in one common situation the biases in parameter estimates become larger as the number of observations within a cluster increases both for regression coefficients and for variance components parameter estimation is described using the simex method a relatively new functional method that makes no assumptions about the structure of the unobservable predictors simulations and an example illustrate the results

asymptotic properties of an estimator in errors in variables models in the presence of validation data abstract structural errors in variables models with dependent spatial observations are studied the presence of validation data is assumed an estimator for regression parameters proposed by lee and sepanski 1 is studied consistency and asymptotic normality of the estimator are established in the case of increasing domain infill asymptotic properties are described simulation results are also presented

exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method the authors present a systematic and formal approach toward finding solitary wave solutions of nonlinear evolution and wave equations from the real exponential solutions of the underlying linear equations the physical concept is one of the mixing of these elementary solutions through the nonlinearities in the system the emphasis is however on the mathematical aspects i e the formal procedure necessary to find single solitary wave solutions by means of examples it is shown how various cases of pulse type and kink type solutions are to be obtained by this method an exhaustive list of equations so treated is presented in tabular form together with the particular intermediate relations necessary for deriving their solutions the extension of the technique to construct n soliton solutions and indicate connections with other existing methods is outlined

stochastic three dimensional rotating navier stokes equations averaging convergence and regularity we consider stochastic three dimensional rotating navier stokes equations and prove averaging theorems for stochastic problems in the case of strong rotation regularity results are established by bootstrapping from global regularity of the limit stochastic equations and convergence theorems

approximate quasi likelihood estimation in models with surrogate predictors abstract we consider quasi likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error we review and extend four approaches to estimation in this problem all of them based on small measurement error approximations a taxonomy of the data sets likely to be available in measurement error studies is developed an asymptotic theory based on this taxonomy is obtained and includes measurement error and berkson error models as special cases

time filtered leapfrog integration of maxwell equations using unstaggered temporal grids a finite difference time domain method for integration of maxwell equations is presented the computational algorithm is based on the leapfrog time stepping scheme with unstaggered temporal grids it uses a fourth order implicit time filter that reduces computational modes and fourth order finite difference approximations for spatial derivatives the method can be applied within both staggered and collocated spatial grids it has the advantage of allowing explicit treatment of terms involving electric current density and application of selective numerical smoothing which can be used to smooth out errors generated by finite differencing in addition the method does not require iteration of the electric constitutive relation in nonlinear electromagnetic propagation problems the numerical method is shown to be effective and stable when employed within perfectly matched layers pml stability analysis demonstrates that the proposed method is effective in stabilizing and controlling numerical instabilities of computational modes arising in wave propagation problems with physical damping and artificial smoothing terms while maintaining higher accuracy for the physical modes comparison of simulation results obtained from the proposed method and those computed by the classical time filtered leapfrog where maxwell equations are integrated for a lossy medium within pml regions and for kerr nonlinear media show that the proposed method is robust and accurate the performance of the computational algorithm is also verified by analyzing parametric four wave mixing in an optical nonlinear kerr medium the algorithm is found to accurately predict frequencies and amplitudes of nonlinearly converted waves under realistic conditions proposed in the literature

a family of exact travelling wave solutions to nonlinear evolution and wave equations a family q of the multicomponent special functions is defined for obtaining the exact travelling wave solutions to nonlinear evolution and wave equations it is shown that the functions qn from q for some n 2 4 are closely related to the special unitary groups su n the necessary and sufficient conditions for existence of a family of the exact multicomponent travelling wave solutions to a quasilinear evolution equation are given an efficiency of the method based on q functions is demonstrated on several classes of the nonlinear partial differential equations

cocaine dependence treatment data methods for measurement error problems with predictors derived from stationary stochastic processes in a cocaine dependence treatment study we use linear and nonlinear regression models to model posttreatment cocaine craving scores and first cocaine relapse time a subset of the covariates are summary statistics derived from baseline daily cocaine use trajectories such as baseline cocaine use frequency and average daily use amount these summary statistics are subject to estimation error and can therefore cause biased estimators for the regression coefficients unlike classical measurement error problems the error we encounter here is heteroscedastic with an unknown distribution and there are no replicates for the error prone variables or instrumental variables we propose two robust methods to correct for the bias a computationally efficient method of moments based method for linear regression models and a subsampling extrapolation method that is generally applicable to both linear and nonlinear regression models simulations and an application to the cocaine dependence treatment data are used to

long time solvability of the navier stokes equations in a rotating frame with spatially almost periodic large data we consider existence of solutions for large times to the navier stokes equations in a rotating frame with spatially almost periodic large data provided by a sufficiently large coriolis force the coriolis force appears in almost all of the models of meteorology and geophysics dealing with large scale phenomena to show existence of solutions for large times we use the l 1 norm of amplitudes existence for large times is proven by means of techniques of fast singular oscillating limits and bootstrapping from a global in time unique solution to the limit equation

backlund transformations and abundant exact explicit solutions of the sharma tasso olver equation abstract by using an extension of the homogeneous balance method and maple the backlund transformations for the sharma tasso olver equation are derived the connections between the sharma tasso olver equation and some linear partial differential equations are found with the aid of the transformations given here and the computer program maple 12 abundant exact explicit special solutions to the sharma tasso olver equation are constructed in addition to all known solutions re deriving in a systematic way several entirely new and more general exact explicit solitary wave solutions can also be obtained these solutions include a the algebraic solitary wave solution of rational function b single soliton solutions c double soliton solutions d n soliton solutions e singular traveling solutions f the periodic wave solutions of trigonometric function type and g many non traveling solutions by using the airy s function and the backlund transformations obtained here the exact explicit solution of the initial value problem for the sto equation is presented the variety of the structure of the solutions for the sharma tasso olver equation is illustrated

random kick forced 3d navier stokes equations in a thin domain we consider the navier stokes equations in the thin 3d domain mathbb t 2 times 0 epsilon where mathbb t 2 is a two dimensional torus the equation is perturbed by a non degenerate random kick force we establish that firstly when e 1 the equation has a unique stationary measure and secondly after averaging in the thin direction this measure converges as e 0 to a unique stationary measure for the navier stokes equation on mathbb t 2 thus the 2d navier stokes equations on surfaces describe asymptotic in time and limiting in e statistical properties of 3d solutions in thin 3d domains

exact solutions of some nonlinear partial differential equations abstract we implemented a generalized tanh function method for approximating the solution of the combined korteweg de vries ckdv equation and sharma tasso olver equation by using this scheme we found some exact solutions of the ckdv equation and sharma tasso olver equation for the further investigation of the method some exact solutions of the boussinesq equation and the complexly coupled kdv equations have been obtained

functional inference in frailty measurement error models for clustered survival data using the simex approach we consider frailty models for clustered survival data in the presence of measurement errors in covariates we first show that when the measurement error is accounted for in a full likelihood analysis but the distribution of the unobserved covariate is misspecified the maximum likelihood estimators are asymptotically biased especially for the variance component whose bias can be substantial we then discuss making inference using functional estimation via the simex method where no distribution of the unobserved error prone covariate is assumed the simex method is easy to implement by repeatedly fitting standard frailty models we study the asymptotic properties of the simex estimates and show that they are consistent and asymptotically normal in simulation studies we compare the simex method and the likelihood method in terms of efficiency and robustness we also propose a simex score test for the variance component to test for the within cluster correlation and evaluate its performance through simu

irreducibility of the 3 d stochastic navier stokes equation abstract a 3 dimensional navier stokes equation with random force is investigated a form of irreducibility of interest in ergodic theory is proved under a full noise assumption the basic tool is the fact that even if the equation is a priori non well posed the solutions depend continuously on the noise around regular solutions

extended least correlation estimates for errors in variables non linear models this paper introduces a method of parameter estimation working on errors in variables polynomial non linear models in which all measurements are corrupted by noise the first step is to develop the linear regression models which are equivalent to polynomial non linear systems a main idea is to extend the parameter vector by even order components of noise and to augment the regression vector by appropriate constants or measurements applying the method of least correlation which has a capability to cope with errors in variables linear models to the equivalent model with extended parameters and augmented regressors yields an extended least correlation estimator analysis shows that for non linear systems with third or lower order polynomials the parameters estimated by the proposed method asymptotically converge to the true values numerical examples also support analytical results applications of the approach to volterra models hammerstein models and weiner non linear systems are included

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

simex variance component tests in generalized linear mixed measurement error models in the analysis of clustered data with covariates measured with error a problem of common interest is to test for correlation within clusters and heterogeneity across clusters we examined this problem in the framework of generalized linear mixed measurement error models we propose using the simex method to construct a score test for the null hypothesis that all variance components are zero a key feature of this simex score test is that no assumptions need to be made regarding the distributions of the random eects and the unobserved covariates we illustrate this test by analyzing framingham heart disease data and evaluate its performance by simulation we also propose individual simex score tests for testing the variance components separately both tests can be easily implemented using existing statistical software

hamiltonian formulation of odd burgers hierarchy the derivation of the odd burgers hierarchy is revisited a first hamiltonian formulation of the basic equation of the hierarchy is presented in relation with its linear counterpart the generalized poisson bracket is given explicitly it contains exponentials of integrals of the dynamic variable it verifies jacobi identity by construction and through direct calculations a second hamiltonian formulation is also presented it means that the equation as expected is bi hamiltonian this property permits as usual the construction of all the hierarchy extension to matrix burgers systems is suggested

measurement error instrumental variables and corrections for attenuation with applications to meta analyses macmahon et al present a meta analysis of the effect of blood pressure on coronary heart disease as well as new methods for estimation in measurement error models for the case when a replicate or second measurement is made of the fallible predictor the correction for attenuation used by these authors is compared to others already existing in the literature as well as to a new instrumental variable method the assumptions justifying the various methods are examined and their efficiencies are studied via simulation compared to the methods we discuss the method of macmahon et al may have bias in some circumstances because it does not take into account i possible correlations among the predictors within a study ii possible bias in the second measurement or iii possibly differing marginal distributions of the predictors or measurement errors across studies a unifying asymptotic theory using estimating equations is also presented

additive partial linear models with measurement errors we consider statistical inference for additive partial linear models when the linear covariate is measured with error we propose attenuation to correction and simex estimators of the parameter of interest it is shown that the first resulting estimator is asymptotically normal and requires no undersmoothing this is an advantage of our estimator over existing backfitting based estimators for semiparametric additive models which require undersmoothing of the nonparametric component in order for the estimator of the parametric component be root n consistent this feature stems from a decrease of the bias of the resulting estimator which is appropriately derived using a profile procedure a similar characteristic in semiparametric partially linear models was obtained by wang et al 2005 we also discuss the asymptotics of the proposed simex approach finite sample performance of the proposed estimators is assessed by simulation experiments the proposed methods are applied to a dataset from a semen study

asymptotics for the simex estimator in nonlinear measurement error models abstract cook and stefanski have described a computer intensive method the simex method for approximately consistent estimation in regression problems with additive measurement error in this article we derive the asymptotic distribution of their estimators and show how to compute estimated standard errors these standard error estimators can either be used alone or as prepivoting devices in a bootstrap analysis we also give theoretical justification to some of the phenomena observed by cook and stefanski in their simulations

low order approximations in deconvolution and regression with errors in variables summary we suggest two new methods which are applicable to both deconvolution and regression with errors in explanatory variables for nonparametric inference the two approaches involve kernel or orthogonal series methods they are based on defining a low order approximation to the problem at hand and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently of course both techniques could be employed to construct consistent estimators but in many contexts of importance e g those where the errors are gaussian consistency is from a practical viewpoint an unattainable goal we rephrase the problem in a form where an explicit interpretable low order approximation is available the information that we require about the error distribution the error in variables distribution in the case of regression is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors e g through repeated measurements in particular we do not need to estimate a function such as a characteristic function which expresses detailed properties of the error distribution this feature of our methods coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages means that the methods are particularly economical in computing time

variance estimation in the analysis of microarray data microarrays are one of the most widely used high throughput technologies one of the main problems in the area is that conventional estimates of the variances that are required in the t statistic and other statistics are unreliable owing to the small number of replications various methods have been proposed in the literature to overcome this lack of degrees of freedom problem in this context it is commonly observed that the variance increases proportionally with the intensity level which has led many researchers to assume that the variance is a function of the mean here we concentrate on estimation of the variance as a function of an unknown mean in two models the constant coefficient of variation model and the quadratic variance mean model because the means are unknown and estimated with few degrees of freedom naive methods that use the sample mean in place of the true mean are generally biased because of the errors in variables phenomenon we propose three methods for overcoming this bias the first two are variations on the theme of the so called heteroscedastic simulation extrapolation estimator modified to estimate the variance function consistently the third class of estimators is entirely different being based on semiparametric information calculations simulations show the power of our methods and their lack of bias compared with the naive method that ignores the measurement error the methodology is illustrated by using microarray data from leukaemia patients

partial regularity for the stochastic navier stokes equations the effects of random forces on the emergence of singularities in the navier stokes equations are investigated in spite of the presence of white noise the paths of a martingale suitable weak solution have a set of singular points of one dimensional hausdorff measure zero furthermore statistically stationary solutions with finite mean dissipation rate are analysed for these stationary solutions it is proved that at any time t the set of singular points is empty the same result holds true for every martingale solution starting from 0 a e initial condition u 0 where 0 is the law at time zero of a stationary solution finally the previous result is non trivial when the noise is sufficiently non degenerate since for any stationary solution the measure 0 is supported on the whole space h of initial conditions

estimation of linear and nonlinear errors in variables models using validation data abstract consistent estimators for linear and nonlinear regression models with measurement errors in variables in the presence of validation data are proposed the estimation procedures are based on least squares methods with regression functions replaced by wide sense conditional expectation functions the methods do not depend on distributional assumptions and are robust against the misspecification of a measurement error model they are computationally and analytically simpler than semiparametric methods based on nonparametric regression or density functions

averaging principle for a class of stochastic reaction diffusion equations we consider the averaging principle for stochastic reaction diffusion equations under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component we calculate limiting slow motion the study of solvability of kolmogorov equations in hilbert spaces and the analysis of regularity properties of solutions allow to generalize the classical approach to finite dimensional problems of this type in the case of spde s

abundant exact and explicit solitary wave and periodic wave solutions to the sharma tasso olver equation abstract this paper is concerned with a double nonlinear dispersive equation the sharma tasso olver equation the extended hyperbolic function method is employed to investigate the solitary and periodic travelling waves in this equation with the aid of mathematica and wu elimination method the abundant exact explicit solutions of the nonlinear sharma tasso olver equation are derived the solutions obtained in this paper include a solitary wave solutions b the singular travelling wave solutions and c periodic travelling wave solutions of triangle function types several entirely new exact solutions to the equation are explicitly obtained in addition to deriving all known solutions in a systematic way this work can be regard as an extension to the recent work by wazwaz

parameter estimation for differential equation models using a framework of measurement error in regression models differential equation de models are widely used in many scientific fields including engineering physics and biomedical sciences the so called forward problem the problem of simulations and predictions of state variables for given parameter values in the de models has been extensively studied by mathematicians physicists engineers and other scientists however the inverse problem the problem of parameter estimation based on the measurements of output variables has not been well explored using modern statistical methods although some least squares based approaches have been proposed and studied in this article we propose parameter estimation methods for ordinary differential equation ode models based on the local smoothing approach and a pseudo least squares psls principle under a framework of measurement error in regression models the asymptotic properties of the proposed psls estimator are established we also compare the psls method to the corresponding simulation extrapolation

symmetries and exact solutions of the sharma tass olver equation abstract the simple symmetry reduction procedure is repeatedly used to obtain infinitely many symmetries as well as exact solutions of the sharma tass olver sto equation some sets of exact solutions such as singular rational complexitons and both analytical and singular rational negaton positons with new soliton fission and fusion phenomena are obtained

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

inference in a survival cure model with mismeasured covariates using a simulation extrapolation approach in many situations in survival analysis it may happen that a fraction of individuals will never experience the event of interest they are considered to be cured the promotion time cure model takes this into account we consider the case where one or more explanatory variables in the model are subject to measurement error which should be taken into account to avoid biased estimators a general approach is the simulation extrapolation algorithm a method based on simulations which allows one to estimate the effect of measurement error on the bias of the estimators and to reduce this bias we extend this approach to the promotion time cure model we explain how the algorithm works and we show that the proposed estimator is approximately consistent and asymptotically normally distributed and that it performs well in finite samples finally we analyse a database in cardiology among the explanatory variables of interest is the ejection fraction which is known to be measured with error

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

new solitons and kinks solutions to the sharma tasso olver equation abstract in this work the sharma tasso olver sto equation is investigated the tanh method the extended tanh method and other ansatze involving hyperbolic and exponential functions are efficiently used for analytic study of this equation new solitons and kinks solutions are formally derived the proposed schemes are reliable and manageable

travelling wave solutions to nonlinear evolution and wave equations we have studied a series of ansatze ordinary differential equations of the first order which correspond to the travelling and or solitary wave solutions of some nonlinear partial differential equations we have investigated the conditions under which the nonlinear partial differential equations have certain kinds of travelling and or solitary wave solutions as a consequence of applications we can take the trial procedures to obtain the travelling wave solutions which is a very efficient method for solving several classes of nonlinear partial differential equations

measurement error in covariates in the marginal hazards model for multivariate failure time data nous nous interessons aux erreurs de mesure des covariables dans un modele marginal du risque pour des donnees de survie multivariees nous examinons le biais genere par une erreur de mesure additive normalesans faire d hypothese de distribution pour la vraie covariable sous jacente pour corriger le biais genere par les erreurs de mesures dans l estimation du coefficient de regression du modele marginal nous proposons d utiliser la methode simex et etudions ses proprietes pour des grands et petits echantillons en supposant la variance des erreurs de mesure soit connue soit estimee nous illustrons cette methode avec des donnees de l essai de prevention primaire coronaire des centres de recherche sur les lipides le cholesterol total est la covariable mesuree avec erreur et les delais d apparition d une angine de poitrine et d un infarctus du myocarde sont les criteres correles etudies

nonparametric methods for solving the berkson errors in variables problem summary it is common in errors in variables problems in regression to assume that the errors are incurred after the experiment in that the observed value of the explanatory variable is an independent perturbation of its true value however if the errors are incurred before the experiment then the true value of the explanatory variable equals a perturbation of its observed value this is the context of the berkson model which is increasingly attracting attention in parametric and semiparametric settings we introduce and discuss nonparametric techniques for analysing data that are generated by the berkson model our approach permits both random and regularly spaced values of the target doses in the absence of data on dosage error it is necessary to propose a distribution for the latter but we show numerically that our method is robust against that assumption the case of dosage error data is also discussed a practical method for smoothing parameter choice is suggested our techniques for errors in variables regression are shown to achieve theoretically optimal convergence rates

a bias corrected estimator for nonlinear systems with output error type model structures parametric identification of linear time invariant lti systems with output error oe type of noise model structures has a well established theoretical framework different algorithms like instrumental variables based approaches or prediction error methods pems have been proposed in the literature to compute a consistent parameter estimate for linear oe systems although the prediction error method provides a consistent parameter estimate also for nonlinear output error noe systems it requires to compute the solution of a nonconvex optimization problem therefore an accurate initialization of the numerical optimization algorithms is required otherwise they may get stuck in a local minimum and as a consequence the computed estimate of the system might not be accurate in this paper we propose an approach to obtain in a computationally efficient fashion a consistent parameter estimate for output error systems with polynomial nonlinearities the performance of the method is demonstrated through a simulation example

stochastic equations in hilbert space with application to navier stokes equations in any dimension abstract we give an existence theorem for an abstract nonlinear stochastic evolution equation in a hilbert space the result is applicable to the stochastic navier stokes equation in any dimension with a nonlinear noise term

backlund transformation lax pairs and explicit exact solutions for the shallow water waves equation in this paper we consider the hirota satsuma equation for shallow water waves we first obtain the backlund transformation and lax pairs by using the extended homogeneous balance method then we find some explicit exact solutions by means of backlund transformation and the extended hyperbolic function method these solutions include the solitary wave solution of rational function soliton solutions double soliton solutions n soliton solutions the multiple solitary wave solutions singular solutions and the periodic wave solutions of triangle function type

a family of completely integrable multi hamiltonian systems explicitly related to some celebrated equations by introducing a spectral problem with an arbitrary parameter we derive a kaup newell type hierarchy of nonlinear evolution equations which is explicitly related to many important equations such as the kundu equation the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the burgers equation the modified korteweg devries mkdv equation and the sharma tasso olver equation it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure under the bargann constraint between the potentials and the eigenfunctions the spectral problem is nonlinearized as a finite dimensional completely integrable hamiltonian system the involutive representation of the solutions for the kaup newell type hierarchy is also presented in addition an n fold darboux transformation of the kundu equation is constructed with the help of its lax pairs and a reduction technique according to the darboux transformation the solutions of the ku

absolute continuity of the invariant measures for some stochastic pdes we consider a free system and an interacting systems having invariant measures and respectively under suitable assumptions we prove an explicit formula relating with and implying the absolute continuity of with respect to we apply our result to a reaction diffusion equation and to the burgers equation

rotating navier stokes equations in mathbb r 3 _ with initial data nondecreasing at infinity the ekman boundary layer problem we prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called the ekman spiral we choose initial data in the vector valued homogeneous besov space dot mathcal b infty 1 sigma 0 mathbb r 2 l p mathbb r for 2 p here the l p integrability is imposed in the normal direction while we may have no decay in tangential components since the besov space dot mathcal b infty 1 0 contains nondecaying functions such as almost periodic functions a crucial ingredient is theory for vector valued homogeneous besov spaces for instance we provide and apply an operator valued bounded h calculus for the laplacian in dot mathcal b infty 1 0 mathbb r n mathsf e for a general banach space mathsf e

markov selections for the 3d stochastic navier stokes equations we investigate the markov property and the continuity with respect to the initial conditions strong feller property for the solutions to the navier stokes equations forced by an additive noise first we prove by means of an abstract selection principle that there are markov solutions to the navier stokes equations due to the lack of continuity of solutions in the space of finite energy the markov property holds almost everywhere in time then depending on the regularity of the noise we prove that any markov solution has the strong feller property for regular initial conditions we give also a few consequences of these facts together with a new sufficient condition for well posedness

corrected score estimation via complex variable simulation extrapolation a monte carlo method of computing unbiased estimating equations for the analysis of data measured with error is described asymptotic distribution results are obtained for estimators derived from the monte carlo estimating equations the method is illustrated with examples applications and simulation studies the monte carlo estimating equations are corrected scores in the sense of nakamura and the proposed methods are closely related to the simulation method described by cook and stefanski

nonlinear mode decoupling for classes of evolution equations the method of third order mode coupling is applied to a general evolution equation which includes as special cases many of the modified and higher order koreteweg de vries equations which have recently appeared in the literature the equations for the slow changes in the amplitudes and phases are derived and specialised to two different classes of evolution equations the first class exhibits the property of nonresonant mode decoupling the evolution of each wave being governed only by its own parameters included in this class are the kdv equation some of the mkdv equations and the sharma tasso olver equation equations of the second class leave the amplitudes and hence the energetics of the waves constant as long as the mode coupling is non resonant here one finds the fifth order kdv equations besides the kdv and sto equations