consistent kdv expansion method and its applications to the kp equation abstract this paper proposed a novel method named as the consistent kdv equation expansion ckdve method for solving nonlinear differential equations with the help of the classical nonlinear kdv equation if a system satisfies the ckdve then it can be defined as ckdve solvability especially the kadomtsev petviashvili kp equation is also verified as a typical case of the ckdve solvability moreover the detailed discussion illustrates the effectiveness and convenience of the proposed method and presents the possibility of constructing relationships among many different partial differential equation models in the related field

direct adaptive control of a class of mimo nonlinear systems a direct adaptive control is presented in this paper for the control of a class of discrete time nonlinear systems which include many useful models well known in the literature the asymptotic stability and global convergence of the algorithm proposed in this paper have been established under mild regularity assumptions a concept of the so called stronger left coprime is first introduced in this paper it is shown that the concept plays a crucial role in the problems of stabilizing a system and realizing the adaptive control algorithm

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variable is measured with error when this happens conventional parametric and nonparametric regression techniques are no longer valid we consider two diverent approaches to nonparametric regression the first uses the simex simulation extrapolation method and makes no assumption about the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

indirect adaptive suboptimal control for linear dynamic systems having polynomial nonlinearities an indirect adaptation algorithm to adaptively implement a control weighted one step ahead suboptimal control law previously derived for the control of stochastic linear dynamic systems having polynomial nonlinearities is presented since identification is separated from the calculation of controller design and a single adaptation algorithm is used the indirect scheme provides more flexibility and has the advantage that few estimated parameters and less memory space are required in the case when the system time delay d and or degree p of the polynomial are large it has been shown that the proposed indirect scheme has the same global convergence property as the direct scheme given by zhang and lang see ibid vol ac 32 no 8 1987

semiparametric regression modeling with mixtures of berkson and classical error with application to fallout from the nevada test site nous construisons des methodes bayesiennes pour une modelisation semi parametrique d une fonction de regression monotone quand les predicteurs sont mesures avec une erreur classique une erreur de berkson ou les deux de telles methodes demandent une distribution pour le predicteur non observe variable latente distribution que nous modelisons aussi de facon semi parametrique de telles combinaisons de methodes semi parametriques pour la reponse a des doses aussi bien que pour la distribution de la variable latente n ont pas ete etudiees dans la litterature sur les erreurs de mesure quelle que soit la forme de l erreur de mesure de plus nos methodes proposent une nouvelle approche des problemes ou l erreur de mesure combine une composante de berkson et une composante classique ces methodes sont generales mais nous les developpons autour d une application particuliere qui est l etude des maladies de la thyroide en relation avec les radiations venant du site de test du nevada nous utilisons ces donnees pour illustrer nos methodes lesquelles suggerent une estimation ponctuelle moyenne a posteriori du risque relatif a des doses pres de deux fois plus elevee que celle obtenue par les analyses precedentes mais suggere aussi une bien plus grande incertitude sur le risque relatif

semi parametric estimation in the nonlinear structural errors in variables model in the nonlinear structural errors in variables model we propose a consistent estimator of the unknown parameter using a modified least squares criterion we give an upper bound of its rate of convergence which is strongly related to the regularity of the regression function and is generally slower than the parametric rate of convergence n 1 2 nevertheless the rate is of order n 1 2 for some particular analytic regression functions for instance when the regression function is either a polynomial function or an exponential function we prove that our estimator achieves the parametric rate of convergence

a nonconfocal generator of involutive systems and three associated soliton hierarchies quite a few new finite dimensional integrable systems have been obtained by the nonlinearization procedure of eigenvalue problems suggested by the author almost all of their associated involutive systems are generated from a confocal generator k nj 1 k j 1 b2kj bkj pkqj pjqk in the present paper a nonconfocal generator k nj 1 2k 2j 1 k j 2a2kj e k j 2 b2kj akj pkpj eqkqj is found from which some new integrable systems and soliton hierarchies are obtained

adaptive output feedback design for a class of nonlinear discrete time systems we present adaptive output feedback schemes for a class of discrete time systems whose continuous time counterparts are the output feedback canonical form we first develop a systematic design procedure for the deterministic case global boundedness and convergence are achieved with no restriction imposed on the nonlinearities then we proceed to develop an analogous design procedure for the adaptive case depending on the characteristics of the nonlinearities global boundedness and convergence can be achieved with various update laws a rank condition is required to ensure such properties for nonlinearities which are not globally lipschitz

comments on a paper by t amemiya on estimation in a dichotomous logit regression model amemiya 1980 derived expressions for the n 2 order mean squared errors of the maximum likelihood and the minimum logit chi squared estimators in the dichotomous logit regression model he numerically evaluated these expressions for a number of specific examples and in all examples found that the minimum chi squared estimator has smaller n 2 order mean squared error in this paper we demonstrate examples in which the maximum likelihood estimator has smaller n 2 order mean squared error

fundamental limitations of discrete time adaptive nonlinear control a particular polynomial is introduced which can be used to determine under what conditions a typical class of discrete time nonlinear systems with uncertainties in both parameters and noises is not stabilizable by feedback thus demonstrating the fundamental limitations of discrete time adaptive nonlinear control as a consequence it is shown that for nonlinear systems with unknown parameters and noises the systems may indeed be nonstabilizable in general whenever the usual linear growth condition is relaxed and the number of unknown parameters is large even though the corresponding noise free systems are globally stabilizable

segmented regression with errors in predictors semi parametric and parametric methods we consider the estimation of parameters in a particular segmented generalized linear model with additive measurement error in predictors with a focus on linear and logistic regression in epidemiologic studies segmented regression models often occur as threshold models where it is assumed that the exposure has no influence on the response up to a possibly unknown threshold furthermore in occupational and environmental studies the exposure typically cannot be measured exactly ignoring this measurement error leads to asymptotically biased estimators of the threshold it is shown that this asymptotic bias is different from that observed for estimating standard generalized linear model parameters in the presence of measurement error being both larger and in different directions than expected in most cases considered the threshold is asymptotically underestimated two standard general methods for correcting for this bias are considered regression calibration and simulation extrapolation simex in ordinary logistic and linear regression these procedures behave similarly but in the threshold segmented regression model they operate quite differently the regression calibration estimator usually has more bias but less variance than the simex estimator regression calibration and simex are typically thought of as functional methods also known as semi parametric methods because they make no assumptions about the distribution of the unobservable covariate x the contrasting structural parametric maximum likelihood estimate assumes a parametric distributional form for x in ordinary linear regression there is typically little difference between structural and functional methods one of the major surprising findings of our study is that in threshold regression the functional and structural methods differ substantially in their performance in one of our simulations approximately consistent functional estimates can be as much as 25 times more variable than the maximum likelihood estimate for a properly specified parametric model structural parametric modelling ought not be a neglected tool in measurement error models an example involving dust concentration and bronchitis in a mechanical engineering plant in munich is used to illustrate the results 1997 by john wiley sons ltd

brief robust adaptive control of uncertain discrete time systems in this paper a robust adaptive controller for a class of nonlinear uncertain discrete time systems is developed by combining the backstepping procedures with a simple parameter estimator subject to parameter projection it is shown that the proposed controller can ensure boundedness of all signals in the overall adaptive systems in the presence of unmodelled dynamics and disturbances it can also guarantee that the tracking error is bounded by a function of the size of the unmodelled dynamics in the ideal case when there are no unmodelled dynamics and disturbances perfect tracking is ensured

self tuning minimum variance control of nonlinear systems of the hammerstein model self tuning is applied to the control of nonlinear systems represented by the hammerstein model wherein the nonlinearity is any odd order polynomial but control costing is not feasible in general initial relay control is employed to contain the deviations

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

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

some aspects of measurement error in explanatory variables for continuous and binary regression models a simple form of measurement error model for explanatory variables is studied incorporating classical and berkson cases as particular forms and allowing for either additive or multiplicative errors the work is motivated by epidemiological problems and therefore consideration is given not only to continuous response variables but also to logistic regression models the possibility that different individuals in a study have errors of different types is also considered the relatively simple estimation procedures proposed for use with cohort data and case control data are checked by simulation under the assumption of various error structures the results show that even in situations where conventional analysis yields slope estimates that are on average attenuated by a factor of approximately 50 per cent estimates obtained using the proposed amended likelihood functions are within 5 per cent of their true values the work was carried out to provide a method for the analysis of lung cancer risk following residential radon exposure but it should be applicable to a wide variety of situations

applications of hta and ehta to ytsf equation new approaches homoclinic test approach hta and extended homoclinic test approach ehta are proposed to seek solitary wave solution of high dimensional nonlinear wave system exact periodic solitary wave periodic soliton cross solitary wave and doubly periodic wave solutions for ytsf equation are obtained using hta and ehta respectively

a measurement error model for binary and ordinal regression exposure assessment poses special problems in air pollution epidemiology this paper proposes a probit regression model for binary and ordinal outcomes that uses exposure validation information to develop estimates for the coefficient of the true exposure when only the inaccurate surrogate measure of exposure is available for the individuals in the health study this method is closely related to recently developed measurement error methods and is based on the assumption that the outcome and the surrogate exposure are conditionally independent given the true exposure a test statistic is proposed for checking this conditional independence assumption when more than one surrogate is available and an interpretation of the coefficient estimate is provided in the event that the assumption is violated the methods are applied to an example involving nitrogen dioxide exposure and wheeze in children

non lie symmetry groups of 2 1 dimensional nonlinear systems obtained from a simple direct method a new direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems using the direct method for the well known 2 1 dimensional kadomtsev petviashvili equation and the ablowitz kaup newell segur system both the lie point symmetry groups and the non lie symmetry groups are obtained the lie symmetry groups obtained via traditional lie approaches are only special cases furthermore the expressions of the exact finite transformations of the lie groups are much simpler than those obtained via the standard approaches

approximations for regression with covariate measurement error abstract the effect of covariate measurement error on maximum likelihood and maximum quasilikelihood estimates mle s or mqle s of regression parameters is considered the naive estimates obtained by ignoring error are modified to account for it the modified estimates can be computed explicitly from the naive ones and have less bias for small error they are particularly useful for berkson error models examples illustrate their application to linear and nonlinear regression errors in continuous covariates and misclassification of discrete covariates the estimates are applied to data relating air pollution to respiratory disease in children analytic methods and simulations are used to compare the estimates to others that have been proposed for dealing with covariate measurement errors the basic idea is that the mle or mqle of the parameter is a function of the size of the error when 0 and there is no error is the usual mle or mqle for small an improvement over is in many cases of

random effect models in nonlinear regression with applications to bioassay summary transformation and weighting techniques are applied to dose response curve models in particular weighting methods derived from a controlled variable random effect model and a closely related random coefficient model are studied these two models correspond to additive and multiplicative effects of variations in the dose and both lead to variance components proportional to the square of the derivative of the response function with respect to dose when the dose response curve is nonlinear in dose the variance components are typically identifiable even without replicate measurements of dose in a bioassay example the fit of a logistic model is studied the transform both sides technique with a power transformation is shown to give a vast improvement in fit compared to the analysis with no transformation and no weighting and it also gives considerably better estimates of the parameters in the logistic function for the data set studied a significant further improvement in the fit is possible by use of the random effect models

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

wavelet shrinkage asymptopia much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects curves densities spectral densities images from noisy data a now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems unfortunately the results have rarely moved into practice for a variety of reasons among them being similarity to known methods computational intractability and lack of spatial adaptivity we discuss a method for curve estimation based on n noisy data translate the empirical wavelet coefficients towards the origin by an amount 2 log n n the proposal differs from those in current use is computationally practical and is spatially adaptive it thus avoids several of the previous objections further the method is nearly minimax both for a wide variety of loss functions pointwise error global error measured in l p norms pointwise and global error in estimation of derivatives and for a wide range of smoothness classes including standard holder and sobolev classes and bounded variation this is a much broader near optimality than anything previously proposed we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves finally the theory underlying the method is interesting as it exploits a correspondence between statistical questions and questions of optimal recovery and information based complexity

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

density estimation in the presence of heteroscedastic measurement error we consider density estimation when the variable of interest is subject to heteroscedastic measurement error the density is assumed to have a smooth but unknown functional form that we model with a penalized mixture of b splines we treat the situation in which multiple mismeasured observations of each variable of interest are observed for at least some of the subjects and the measurement error is assumed to be additive and normal the measurement error variance function is modeled with a second penalized mixture of b splines the article s main contributions are to address the effects of heteroscedastic measurement error effectively explain the biases caused by ignoring heteroscedasticity and present an equivalent kernel for a spline based density estimator derivation of the equivalent kernel may be of independent interest we use small sigma asymptotics to approximate the biases incurred by assuming that the measurement error is homoscedastic when it actually is heteroscedastic the biases incurred

is the minimum chi square estimator the winner in logit regression abstract amemiya 1980 showed that the bias corrected maximum likelihood estimator has a smaller n 2 order mse matrix than minimum chi square in a general logit model in this paper the exact mse is calculated for both estimators for berkson s 1995 examples the bias corrected maximum likelihood has a smaller exact mse provided that berkson s 2n rule is used in the calculation of the exact results the margin by which the exact mse of minimum chi square exceeds that of bias corrected maximum likelihood is small and hence there may be no practical advantage in using the latter estimator

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

adaptive weighted suboptimal control for linear dynamic systems having a polynomial input introducing a cost term on the highest power of the nonlinear polynomial we derive a simple direct adaptive control weighted suboptimal control algorithm which is very useful for the control of all stable nonminimum phase and some unstable nonminimum phase linear systems having a polynomial input both stochastic and deterministic situations are considered and the global convergence of the proposed algorithm has been established

nonparametric regression with errors in variables the effect of errors in variables in nonparametric regression estimation is examined to account for errors in covariates deconvolution is involved in the construction of a new class of kernel estimators it is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution in fact there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth it is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate which is rich enough for many practical applications furthermore to achieve optimality we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators

bayesian smoothing and regression splines for measurement error problems in the presence of covariate measurement error estimating a regression function nonparametrically is extremely difficult the problem being related to deconvolution various frequentist approaches exist for this problem but to date there has been no bayesian treatment in this article we describe bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error the regression function is modeled with smoothing splines and regression p splines two methods are described for exploration of the posterior the first called the iterative conditional modes icm is only partially bayesian icm uses a componentwise maximization routine to find the mode of the posterior it also serves to create starting values for the second method which is fully bayesian and uses markov chain monte carlo mcmc techniques to generate observations from the joint posterior distribution use of the mcmc approach has the advantage that interval estimates that directly model and

on errors in variables in binary regression berkson case abstract in binary regression the predictor variables may be measured with error the berkson case of the errors in variables problem is considered under which the values of the predictor variables are set by the experimenter but not achieved exactly a particular model for this case is considered with probit regression and normally distributed errors of observation the regression parameters for intercept and slope are to be estimated two estimators are studied the maximum likelihood estimator mle and a modification of it in a simulation study the modified mle is shown to improve on the mle in a situation with substantial measurement error quantal bioassay is an important field of application of the berkson case of the binary regression model in quantal bioassay there is a stimulus perhaps a carcinogen or poison with doses x to be determined by the experimenter to address questions on carcinogenicity or toxicity of the stimulus each experimental animal is assigned a dose of the stimulus

new solutions of the 3 1 dimensional jimbo miwa equation we find new exact solutions of the 3 1 dimensional jimbo miwa equation by applying the extended homogeneous balance method we also get an iterative formula of finding exact solutions this paper shows that there exist a lot of solutions for the 3 1 dimensional jimbo miwa equation

simulation extrapolation deconvolution of finite population cumulative distribution function estimators summary we study estimation of a finite population cumulative distribution function when sample units are measured with error we propose a simple bias adjusted estimator that eliminates much of the bias induced by measurement error a variance estimator for the proposed cumulative distribution function estimator is also obtained

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation

adomian decomposition method with chebyshev polynomials in this paper an efficient modification of the adomian decomposition method is presented by using chebyshev polynomials the proposed method can be applied to linear and non linear models the scheme is tested for some examples and the obtained results demonstrate reliability and efficiency of the proposed method