local linear regression smoothers and their minimax efficiencies in this paper we introduce a smooth version of local linear regression estimators and address their advantages the mse and mise of the estimators are computed explicitly it turns out that the local linear regression smoothers have nice sampling properties and high minimax efficiency they are not only efficient in rates but also nearly efficient in constant factors in the nonparametric regression context the asymptotic minimax lower bound is developed via the heuristic of the hardest onedimensional subproblem of donoho and liu connections of the minimax risk with the modulus of continuity are made the lower bound is also applicable for estimating conditional mean regression and conditional quantiles for both fixed and random design regression problems

local asymptotics for polynomial spline regression in this paper we develop a general theory of local asymptotics for least squares estimates over polynomial spline spaces in a regression problem the polynomial spline spaces we consider include univariate splines tensor product splines and bivariate or multivariate splines on triangulations we establish asymptotic normality of the estimate and study the magnitude of the bias due to spline approximation the asymptotic normality holds uniformly over the points where the regression function is to be estimated and uniformly over a broad class of design densities error distributions and regression functions the bias is controlled by the minimum l norm of the error when the target regression function is approximated by a function in the polynomial spline space that is used to define the estimate the control of bias relies on the stability in l norm of l 2 projections onto polynomial spline spaces asymptotic normality of least squares estimates over polynomial or trigonometric polynomial spaces is also treated by the general theory in addition a preliminary analysis of additive models is provided

local polynomial variance function estimation the conditional variance function in a heteroscedastic nonparametric regression model is estimated by linear smoothing of squared residuals attention is focused on local polynomial smoothers both the mean and variance functions are assumed to be smooth but neither is assumed to be in a parametric family the biasing effect of preliminary estimation of the mean is studied and a degrees of freedom correction of bias is proposed the corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known a proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions the proposal is illustrated with data from the lidar method of measuring atmospheric pollutants and from turbulence model computations

reducing variance in univariate smoothing a variance reduction technique in nonparametric smoothing is proposed at each point of estimation form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged the nearby points are chosen to maximize the variance reduction we study in detail the case of univariate local linear regression while the new estimator retains many advantages of the local linear estimator it has appealing asymptotic relative efficiencies bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation a simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes this technique is very general and has a wide range of applications

discontinuous systems and the henstock kurzweil integral abstract by using the henstock kurzweil integral and the inequalities of this integral the existence and uniqueness theorems for the solution of the discontinuous caratheodory system are established the results are generalizations of earlier investigations j he and po chen adv in math 16 1987 17 32 in chinese a f filippov math ussr sb 51 1960 in russian o hajek j differential equations32 1979 149 185 of this discontinuous system

efficient estimation and inferences for varying coefficient models abstract this article deals with statistical inferences based on the varying coefficient models proposed by hastie and tibshirani local polynomial regression techniques are used to estimate coefficient functions and the asymptotic normality of the resulting estimators is established the standard error formulas for estimated coefficients are derived and are empirically tested a goodness of fit test technique based on a nonparametric maximum likelihood ratio type of test is also proposed to detect whether certain coefficient functions in a varying coefficient model are constant or whether any covariates are statistically significant in the model the null distribution of the test is estimated by a conditional bootstrap method our estimation techniques involve solving hundreds of local likelihood equations to reduce the computational burden a one step newton raphson estimator is proposed and implemented the resulting one step procedure is shown to save computational cost on an order of tens with no

multivariate locally weighted least squares regression nonparametric regression using locally weighted least squares was first discussed by stone and by cleveland recently it was shown by fan and by fan and gijbels that the local linear kernel weighted least squares regression estimator has asymptotic properties making it superior in certain senses to the nadaraya watson and gasser muller kernel estimators in this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables we are able to derive the leading bias and variance terms for general multivariate kernel weights using weighted least squares matrix theory this approach is especially convenient when analysing the asymptotic conditional bias and variance of the estimator at points near the boundary of the support of the predictors we also investigate the asymptotic properties of the multivariate local quadratic least squares regression estimator discussed by cleveland and devlin and in the univariate case higher order polynomial fits and derivative estimation

the local piecewisely linear kernel smoothing procedure for fitting jump regression surfaces it is known that a surface fitted by conventional local smoothing procedures is not statistically consistent at the jump locations of the true regression surface this article suggests a procedure for modifying conventional local smoothing procedures such that the modified procedures fit the surface with jumps preserved automatically taking the local linear kernel smoothing procedure as an example in a neighborhood of a given point a bivariate piecewisely linear function is fitted with possible jumps along the boundaries of four quadrants the fitted function provides four estimators of the surface at the given point which are constructed from observations in the four quadrants when the difference among the four estimators is smaller than a threshold value the given point is most likely a continuous point and the surface at that point is then estimated by the average of the four estimators when the difference is larger than the threshold value the given point is likely a jump point and at least

bootstrap choice of bandwidth for density estimation abstract a bootstrap based choice of bandwidth for kernel density estimation is introduced the method works by estimating the integrated mean squared error imse for any given bandwidth and then minimizing over all bandwidths a straightforward application of the bootstrap method to estimate the imse fails because it does not capture the bias component a smoothed bootstrap method based on an initial density estimate is described that solves this problem it is possible to construct pointwise and simultaneous confidence intervals for the density the simulation study compares cross validation and the bootstrap method over a wide range of densities a long tailed a short tailed an asymmetric and a bimodal among others the bootstrap method uniformly outperforms cross validation the accuracy of the constructed confidence bands improves as the sample size increases

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

a nonparametric circular linear multivariate regression model with a rule of thumb bandwidth selector the purpose of this paper is to propose a nonparametric circular linear multivariate regression model using a kernel weighted local linear method the case of several linear regressors and one circular regressor is considered we extend results on the asymptotic bias and variance of the linear multivariate variable to the case of circular linear multivariate variable the rule of thumb selector is used to establish the optimal bandwidths for the nonparametric model the suitability of the model is judged from the coefficient of determination one simulation experiment and one real problem concerning wind energy are used to study the power performance of the nonparametric model

finite sample variance of local polynomials analysis and solutions abstract fitting local polynomials in nonparametric regression has a number of advantages the attractive theoretical features are in a partial contradiction to variance properties for random design and to practical experience over a broad range of situations no upper bound can be given for the conditional variance the unconditional variance is infinite when using optimal weights with compact support properties are better for gaussian weights we analyze local polynomials for finite sample size both theoretically and numerically it turns out that difficulties arise in sparse regions in the realization of the design when the realization has locally a small variance and or a skew empirical distribution two small sample modifications of local polynomials are presented local increase of bandwidth in sparse regions of the design and local polynomial ridge regression both modifications combine a good finite sample behavior with the asymptotic advantages of local polynomials

stability and evolution of the quiescent and travelling solitonic bubbles abstract we simulate numerically the dynamics of the bubble like solitons of the cubic quintic nonlinear schrodinger equation in agreement with earlier predictions slow moving bubbles have been observed to be unstable in contrast to rapid bubbles which stabilize above a certain critical velocity the empirical formula for the critical velocity has been confirmed to a high degree of accuracy based on the choice of some critical perturbation we derive an integral criterion for stability of kinks and bubbles of the general nonlinear schrodinger equation which provides an explanation of the appearance of the critical velocity finally we follow numerically the nonlinear evolution of the unstable bubbles in one two and three dimensions

semiparametric regression analysis for recurrent event interval counts this paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation we consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow up at each visit the patient reports the number of events that occurred since the previous visit or an examination reveals the number of accumulated events such as skin cancers the exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow up times each patient s record thus consists of a sequence of clinic visit dates event counts corresponding to the successive time intervals between clinic visits and baseline covariates we propose a semiparametric regression model extending the fully parametric model of thall 1988 biometrics 44 197 209 to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time varying nature of the underlying event rate covariate effects enter the model parametrically while the underlying time varying event rate is modelled nonparametrically the method of severini and wong 1992 annals of statistics 20 1768 1802 is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution a simulation study and application to a data set are provided

fitting a bivariate additive model by local polynomial regression while the additive model is a popular nonparametric regression method many of its theoretical properties are not well understood especially when the backfitting algorithm is used for computation of the estimators this article explores those properties when the additive model is fitted by local polynomial regression sufficient conditions guaranteeing the asymptotic existence of unique estimators for the bivariate additive model are given asymptotic approximations to the bias and the variance of a homoscedastic bivariate additive model with local polynomial terms of odd and even degree are computed this model is shown to have the same rate of convergence as that of univariate local polynomial regression

monitoring profiles based on nonparametric regression methods the use statistical process control spc in monitoring and diagnosis of process and product quality profiles remains an important problem in various manufacturing industries the spc problem with a nonlinear profile is particularly challenging this article proposes a novel scheme to monitor changes in both the regression relationship and the variation of the profile online it integrates the multivariate exponentially weighted moving average procedure with the generalized likelihood ratio test based on nonparametric regression the proposed scheme not only provides an effective spc solution to handle nonlinear profiles which are common in industrial practice but it also resolves the latent problem in popular parametric monitoring methods of being unable to detect certain types of changes due to a misspecified out of control model our simulation results demonstrate the effectiveness and efficiency of the proposed monitoring scheme in addition a systematic diagnostic approach is provided to locate t

estimation of a nonparametric censored regression model with an application to unemployment insurance spells in this paper we consider identification and estimation of a censored nonparametric location scale model we first show that in the case where the location function is strictly less than the fixed censoring point for all values in the support of the explanatory variables then the location function is not identified anywhere in contrast if the location function is greater or equal to the censoring point with positive probability then the location function is identified on the entire support including the region where the location function is below the censoring point in the latter case we propose a simple estimation procedure based on combining conditional quantile estimators for three distinct quantiles the new estimator is shown to converge at the optimal nonparametric rate with a limiting normal distribution a small scale simulation study indicates that the proposed estimation procedure performs well in finite samples we also present an empirical application to unemployment insurance duration using administrative level data from new jersey jel classification c14 c24 j64 j65

local linear regression on manifolds and its geometric interpretation high dimensional data analysis has been an active area and the main focus areas have been variable selection and dimension reduction in practice it occurs often that the variables are located on an unknown lower dimensional nonlinear manifold under this manifold assumption one purpose of this article is regression and gradient estimation on the manifold and another is developing a new tool for manifold learning as regards the first aim we suggest directly reducing the dimensionality to the intrinsic dimension d of the manifold and performing the popular local linear regression llr on a tangent plane estimate an immediate consequence is a dramatic reduction in the computational time when the ambient space dimension p d we provide rigorous theoretical justification of the convergence of the proposed regression and gradient estimators by carefully analyzing the curvature boundary and nonuniform sampling effects we propose a bandwidth selector that can handle heteroscedastic errors with re

comparison of smoothing parameterizations in bivariate kernel density estimation abstract the basic kernel density estimator in one dimension has a single smoothing parameter usually referred to as the bandwidth for higher dimensions however there are several options for smoothing parameterization of the kernel estimator for the bivariate case there can be between one and three independent smoothing parameters in the estimator which leads to a flexibility versus complexity trade off when using this estimator in practice in this article the performances of the different possible smoothing parameterizations are compared using both the asymptotic and exact mean integrated squared error our results show that it is important to have independent smoothing parameters for each of the coordinate directions although this is enough for many situations for densities with high amounts of curvature in directions different to those of the coordinate axes substantial gains can be made by allowing the kernel mass to have arbitrary orientations the sphering approaches to choosing this o

impulsive retarded differential equations in banach spaces via bochner lebesgue and henstock integrals t f t xt xt0 1 1 where is a given continuous function from r 0 r 0 to a banach space x and f is a continuous map from an open set r c r 0 x to x given a continuous function x t0 r t0 a x a 0 t0 r we follow 11 to deane xt r 0 x by xt x t r 0 t t0 t0 a the initial value problem 1 1 is equivalent to the integral equation

application of nonparametric quantile regression to body mass index percentile curves from survey data increasing rates of overweight among children in the u s stimulated interest in obtaining national percentile curves of body size to serve as a benchmark in assessing growth development in clinical and population settings in 2000 the u s centers for disease control and prevention cdc developed conditional percentile curves for body mass index bmi for ages 2 20 years the 2000 cdc bmi for age curves are partially parametric and only partially incorporated the survey sample weights in the curve estimation as a result they may not fully reflect the underlying pattern of bmi for age in the population this motivated us to develop a nonparametric double kernel based method and automatic bandwidth selection procedure we include sample weights in the bandwidth selection conduct median correction to reduce small sample smoothing bias and rescale the bandwidth to make it scale invariant using this procedure we re estimate the national percentile bmi for age curves and the prevalence of high bmi children in the u s

local polynomial regresssion estimators in survey sampling estimation of finite population totals in the presence of auxiliary information is considered a class of estimators based on local polynomial regression is proposed like generalized regression estimators these estimators are weighted linear combinations of study variables in which the weights are calibrated to known control totals but the assumptions on the superpopulation model are considerably weaker the estimators are shown to be asymptotically design unbiased and consistent under mild assumptions a variance approximation based on taylor linearization is suggested and shown to be consistent for the design mean squared error of the estimators the estimators are robust in the sense of asymptotically attaining the godambe joshi lower bound to the anticipated variance simulation experiments indicate that the estimators are more efficient than regression estimators when the model regression function is incorrectly specified while being approximately as efficient when the parametric specification is correct

on kurzweil generalized ordinary differential equations on etudie sous quelles conditions une equation differentielle generalisee de kurzweil est equivalente a une equation differentielle

nonparametric rotations for sphere sphere regression regression of data represented as points on a hypersphere has traditionally been treated using parametric families of transformations that include the simple rigid rotation as an important special

weighted local regression and kernel methods for nonparametric curve fitting abstract weighted local regression a popular technique for smoothing scatterplots is shown to be asymptotically equivalent to certain kernel smoothers since both methods are local weighted averages of the data it is proved that in the fixed design regression model given a weighted local regression procedure with any weight function there is a corresponding kernel method such that the quotients of weights distributed by both methods tend uniformly to 1 as the number of observations increases to infinity it is demonstrated by examples that in some instances the weights are nearly the same for both methods even for small samples the asymptotic equivalence allows the derivation of the leading terms of the mean squared error and of the local limit distribution for weighted local regression further a close correspondence is found between the orders of the polynomial to be locally fitted in weighted local regression and the order number of vanishing moments of the kernel employed in the kernel smoot

design adaptive nonparametric regression abstract in this article we study the method of nonparametric regression based on a weighted local linear regression this method has advantages over other popular kernel methods moreover such a regression procedure has the ability of design adaptation it adapts to both random and fixed designs to both highly clustered and nearly uniform designs and even to both interior and boundary points it is shown that the local linear regression smoothers have high asymptotic efficiency i e can be 100 with a suitable choice of kernel and bandwidth among all possible linear smoothers including those produced by kernel orthogonal series and spline methods the finite sample property of the local linear regression smoother is illustrated via simulation studies nonparametric regression is frequently used to explore the association between covariates and responses there are many versions of kernel regression smoothers some estimators are not good for random designs such as in observational studies and

variable bandwidth and local linear regression smoothers in this paper we introduce an appealing nonparametric method for estimating the mean regression function the proposed method combines the ideas of local linear smoothers and variable bandwidth hence it also inherits the advantages of both approaches we give expressions for the conditional mse and mise of the estimator minimization of the mise leads to an explicit formula for an optimal choice of the variable bandwidth moreover the merits of considering a variable bandwidth are discussed in addition we show that the estimator does not have boundary effects and hence does not require modifications at the boundary the performance of a corresponding plug in estimator is investigated simulations illustrate the proposed estimation method

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

interpolation methods for adapting to sparse design in nonparametric regression abstract we suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing these methods are based on simple rules determined by the kernel and bandwidth for deciding when and where pseudo design points should be added to augment the original design sequence new ordinates for the added design points are computed by simple interpolation then local linear smoothing is applied directly to the expanded dataset the method is competitive with alternatives e g those involving ridge regression in terms of both simplicity and performance

high order data sharpening for density estimation it is shown that data sharpening can be used to produce density estimators that enjoy arbitrarily high orders of bias reduction practical advantages of this approach relative to competing methods are demonstrated they include the sheer simplicity of the estimators which makes code for computing them particularly easy to write very good mean squared error performance reduced wiggliness of estimates and greater robustness against undersmoothing

eigenvalue cutoff in the cubic quintic nonlinear schrodinger equation using theoretical arguments we prove the numerically well known fact that the eigenvalues of all localized stationary solutions of the cubic quintic 2 1 dimensional nonlinear schr odinger equation exhibit an upper cutoff value the existence of the cutoff is inferred using gagliardo nirenberg and h older inequalities together with pohozaev identities we also show that in the limit of eigenvalues close to zero the eigenstates of the cubic quintic nonlinear schr odinger equation behave similarly to those of the cubic nonlinear schr odinger equation

testing for smooth structural changes in time series models via nonparametric regression checking parameter stability of econometric models is a long standing problem almost all existing structural change tests in econometrics are designed to detect abrupt breaks little attention has been paid to smooth structural changes which may be more realistic in economics we propose a consistent test for smooth structural changes as well as abrupt structural breaks with known or unknown change points the idea is to estimate smooth time varying parameters by local smoothing and compare the fitted values of the restricted constant parameter model and the unrestricted time varying parameter model the test is asymptotically pivotal and does not require prior information about the alternative a simulation study highlights the merits of the proposed test relative to a variety of popular tests for structural changes in an application we strongly reject the stability of univariate and multivariate stock return prediction models in the postwar and post oil shocks periods

on bias reduction in local linear smoothing summary the standard approach to local linear regression involves fitting a straight line segment to a curve in a symmetrical way in that the segment is fitted directly above a small region whose midpoint is the abscissa x at which we wish to estimate the curve in this paper we show that if the segment is fitted in a skew manner with its centre a little to the left or right of x then bias can be reduced by an order of magnitude without affecting the order of magnitude of variance the amount by which the centre should be shifted depends only on the kernel function and not at all on the unknown regression mean or on the design density the average of two similarly but oppositely shifted estimators has two orders of magnitude less bias again at the expense of a slight increase in variance this particular estimator may be viewed as a limiting form of a convex combination of three local linear estimators the two oppositely shifted estimators and the symmetric one which has two orders of magnitude less bias and depending on the kernel function less variance as well

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

stability of traveling waves of nonlinear schrodinger equation with nonzero condition at infinity we study the stability of traveling waves of the nonlinear schrodinger equation with nonzero condition at infinity obtained via a constrained variational approach two important physical models for this are the gross pitaevskii gp equation and the cubic quintic equation first under a non degeneracy condition we prove a sharp instability criterion for 3d traveling waves of gp which had been conjectured in the physical literature this result is also extended for general nonlinearity and higher dimensions including 4d gp and 3d cubic quintic equations second for cubic quintic type nonlinearity we construct slow traveling waves and prove their nonlinear instability in any dimension for dimension two the non degeneracy condition is also proved for these slow traveling waves for general traveling waves without vortices that is nonvanishing and with general nonlinearity in any dimension we find a sharp condition for linear instability third we prove that any 2d traveling wave of gp is transversally unstable and we find the sharp interval of unstable transversal wave numbers near unstable traveling waves of all of the above cases we construct unstable and stable invariant manifolds

peter hall s contributions to nonparametric function estimation and modeling peter hall made wide ranging and far reaching contributions to nonparametric modeling he was one of the leading figures in the developments of nonparametric techniques with over 300 published papers in the field alone this article gives a selective overview on the contributions of peter hall to nonparametric function estimation and modeling the focuses are on density estimation nonparametric regression bandwidth selection boundary corrections inference under shape constraints estimation of residual variances analysis of wavelet estimators multivariate regression and applications of nonparametric methods

the mean shift algorithm and its relation to kernel regression we investigate the connection between the asymptotic bias of the well known nadaraya watson kernel regression and the mean shift ms vector with the gaussian kernel we first show that the asymptotic bias for the univariate nadaraya watson kernel regression can be estimated using the ms scalar then we investigate the general d dimensional case d 1 and derive a formula for the asymptotic bias as a function of the ms vector we show that when the regression function is a linear function of its entries then the asymptotic bias can be represented as a linear function of the ms vector the ms algorithm for the univariate and the linear cases can be used to find points where the nadaraya watson kernel regression gives an unbiased estimate furthermore this connection suggests that exploiting the theoretical properties of the asymptotic bias of the nadaraya watson kernel regression may be helpful to show the convergence of the ms algorithm through the simulations we show that how the given theoretical results can be used to estimate the bias of the estimated clean signal by just observing the noisy signal having access to the bias of the estimator enables us to evaluate the accuracy of the estimated clean data which later will be used to design a quantizer

on the solution of dydx ap f x y abstract we prove a substantial extension of picard s theorem on the solvability of the ordinary differential equation dy dx f x y and also obtain a generalization of the result in terms of approximate derivative dy dx ap the results are illustrated by suitable examples

the correct traveling wave solutions for the high order dispersive nonlinear schrodinger equation the high order dispersive nonlinear schrodinger equation is considered the exact solutions were obtained by zhang et al j l zhang m l wang x z li phys lett a 357 2006 188 195 are analyzed we can demonstrate that some solutions do not satisfy this equation to obtain the correct solutions the f expansion method is applied to solve it

jacobian elliptic function solutions of the discrete cubic quintic nonlinear schrodinger equation the study of solitary wave solutions is of prime significance for the nonlinear schrodinger equation with higher order dispersion and or higher degree nonlinearities in nonlinear physical systems we derive the discrete cubic quintic nonlinear schrodinger equation from a hamiltonian using different poisson brackets by using the extended jacobian elliptic function approach we investigate the abundant exact stationary solitons and periodic waves solution of this equation these solutions include jacobian periodic solutions alternating phase jacobi periodic solution kink and bubble soliton solutions alternating phase kink soliton solution and alternating phase bubble soliton solution provided that coefficients are bound by special relation and then with the aid of symbolic computation we present in explicit form these solutions the stability of bubble and kink soliton as well as alternating kink and alternating bubble soliton are also investigated

weak solutions for the dynamic cauchy problem in banach spaces abstract this paper is devoted to unify and extend the results of the existence of the weak solutions of continuous and discrete cauchy problem in banach spaces we offer the existence of the weak solution of dynamic cauchy problem on an infinite time scale the measure of weak noncompactness and the fixed point theorem of kubiaczyk are used to prove the main result

an improved estimator of the density function at the boundary abstract we propose a new method of boundary correction for kernel density estimation the technique is a kind of generalized reflection method involving reflecting a transformation of the data the transformation depends on a pilot estimate of the logarithmic derivative of the density at the boundary in simulations the new method is seen to clearly outperform an earlier generalized reflection idea it also has overall advantages over boundary kernel methods and a nonnegative adaptation thereof although the latter are competitive in some situations we also present the theory underlying the new methodology

on solutions of differential equations in banach spaces abstract we prove some existence theorems for the cauchy problem x t f t x t x 0 x 0 t i 0 using different types of integrals and its properties the requirements on the function f are depended on types of solutions and as possible as close to necessary conditions we present a brief survey of classes of solutions and we give some comparison results for them

semiparametric estimation of animal abundance using capture recapture data from open populations a semiparametric partially linear model for the size of an open population is proposed and inference is conducted using weighted martingale estimating equations this extends a previous nonparametric approach to modeling capture recapture data for open populations with frequent capture occasions analytic expressions for the large sample variances are derived and these are confirmed in a simulation study the method is illustrated on monthly penguin banding data collected over 6 years

methods for estimating a conditional distribution function abstract motivated by the problem of setting prediction intervals in time series analysis we suggest two new methods for conditional distribution estimation the first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation it produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1 the second method involves an adjusted form of the nadaraya watson estimator it preserves the bias and variance properties of a class of second order estimators introduced by yu and jones but has the added advantage of always being a distribution itself our methods also have application outside the time series setting for example to quantile estimation for independent data this problem motivated the work of yu and jones

multivariate functional coefficient regression models for nonlinear vector time series data summary vector time series data are widely found in practice in this paper we propose a multivariate functional coefficient regression model with heteroscedasticity for modeling such data the local linear smoother is employed to estimate the unknown coefficient matrices asymptotic normality 10 of the proposed estimators is established and bandwidth selection is considered to deal with cointegration widely observed in financial markets we propose an error corrected multivariate functional coefficient model simulations show that the proposed estimation procedures capture nonlinear structures of coefficients well analysis of united states interest rates illustrates the proposed methodology 15

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

rarefaction pulses for the nonlinear schrodinger equation in the transonic limit we investigate the properties of finite energy travelling waves to the nonlinear schrodinger equation with nonzero conditions at infinity for a wide class of nonlinearities in space dimension two and three we prove that travelling waves converge in the transonic limit up to rescaling to ground states of the kadomtsev petviashvili equation our results generalize an earlier result of f bethuel p gravejat and j c saut for the two dimensional gross pitaevskii equation and provide a rigorous proof to a conjecture by c jones and p h roberts about the existence of an upper branch of travelling waves in dimension three