caristi s fixed point theorem and selections of set valued contractions we show without the axiom of choice that the zermelo theorem implies directly a restriction of the caristi fixed point theorem to continuous functions under the axiom of choice this restriction is proved to be equivalent to caristi s theorem we also discuss kirk s problem on an extension of the caristi theorem and we establish two selection theorems for set valued contractions

a simple smooth backfitting method for additive models in this paper a new smooth backfitting estimate is proposed for additive regression models the estimate has the simple structure of nadaraya watson smooth backfitting but at the same time achieves the oracle property of local linear smooth backfitting each component is estimated with the same asymptotic accuracy as if the other components were known

the existence and asymptotic properties of a backfitting projection algorithm under weak conditions we derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function the procedure employs a recent projection interpretation of popular kernel estimators provided by mammen marron turlach and wand 1997 and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in bickel klaassen ritov and wellner 1993 our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components and in this sense improves on the method analysed in opsomer and ruppert 1997 we provide high level conditions independent of the sampling scheme we then verify that these conditions are satisfied in a regression and a time series autoregression under weak conditions

identification and nonparametric estimation of a transformed additively separable model let r x z be a function that along with its derivatives can be consistently estimated nonparametrically this paper discusses the identification and consistent estimation of the unknown functions h m g and f where r x z h m x z m x z g x f z and h is strictly monotonic an estimation algorithm is proposed for each of the model s unknown components when r x z represents a conditional mean function the resulting estimators use marginal integration to separate the components g and f our estimators are shown to have a limiting normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives their small sample performance is studied in a monte carlo experiment we apply our results to estimate generalized homothetic production functions for four industries in the chinese economy

one step local quasi likelihood estimation summary local quasi likelihood estimation is a useful extension of local least squares methods but its computational cost and algorithmic convergence problems make the procedure less appealing particularly when it is iteratively used in methods such as the back fitting algorithm cross validation and bootstrapping a one step local quasi likelihood estimator is introduced to overcome the computational drawbacks of the local quasi likelihood method we demonstrate that as long as the initial estimators are reasonably good the one step estimator has the same asymptotic behaviour as the local quasi likelihood method our simulation shows that the one step estimator performs at least as well as the local quasi likelihood method for a wide range of choices of bandwidths a data driven bandwidth selector is proposed for the one step estimator based on the pre asymptotic substitution method of fan and gijbels it is then demonstrated that the datadriven one step local quasi likelihood estimator performs as well as the maximum local quasilikelihood estimator by using the ideal optimal bandwidth

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

fixed point theorems for set valued contractions in complete metric spaces abstract the fixed point theory of set valued contractions which was initiated by nadler s b nadler jr multi valued contraction mappings pacific j math 30 1969 475 488 was developed in different directions by many authors in particular by s reich fixed points of contractive functions boll unione mat ital 5 1972 26 42 n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188 y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 in the present paper the concept of contraction for set valued maps in metric spaces is introduced and the conditions guaranteeing the existence of a fixed point for such a contraction are established one of our results essentially generalizes the nadler and feng liu theorems and is different from the mizoguchi takahashi result the second result is different from the reich and mizoguchi takahashi results the method used in the proofs of our results is inspired by mizoguchi takahashi and feng liu s ideas comparisons and examples are given

similarity analysis of inelastic contact analysis of mechanical contact of solids is of interest not only regarding a variety of mechanical assemblies but also on a smaller scale such as roughness properties of surfaces and compaction of powder particles indentation testing is another prominent problem in the context to analyse the phenomena involved is inherently difficult at application essentially due to the presence of large strains nonlinear material behaviour time dependence and moving contact boundaries recently progress has been made however to explicitly solve basic boundary value problems especially due to advances in computational techniques a substantial ingredient which facilitates solution procedures is self similarity and it is the present purpose to explore in detail the advantages in a general setting when this feature prevails a viscoplastic framework is laid down for a wide class of constitutive properties where strain hardening plasticity creep and also nonlinear elasticity arise as special cases it is then shown that when surface shapes and material properties are modelled by homogeneous functions associated boundary value problems posed may be reduced to stationary ones as a consequence within hertzian kinematics relations between contact impression and regions become independent of loading and time and the connection to loading characteristics does not usually require a full solution of the problem in particular it is shown that for general head shapes it proves efficient to use an approach where an intermediate flat die solution serves as a basic tool also for hereditary materials an invariant computational procedure based on the intermediate problem is arrived at and decisive results shown to be found by simple cumulative superposition illustrations are given analytically for ellipsoidal contact of newtonian fluids and by detailed computations for spherical indentation of viscoplastic solids for which also universal hardness formulae are proposed for several bodies in contact it is shown how general results may be extracted from fundamental solutions for a half space

elastic analysis of some punch problems for a layered medium abstract the problems of flat ended cylindrical quadrilateral and triangular punches indenting a layered isotropic elastic half space are considered the former two are analyzed using a basis function technique while the latter problem is analyzed via a singular integral equation solutions are obtained numerically load deflection relations are obtained for a series of values of the ratio of young s modulus in the layer and substrate and for a variety of punch sizes these solutions provide an accurate basis for the estimation of young s modulus of thin films from the initial unloading compliance observed in indentation tests and are specifically relevant to axisymmetric vicker s and triangular indenters the results should also be of interest in foundation engineering

estimation of additive regression models with known links summary we consider estimation of an additive nonparametric regression model with known link function the asymptotic distribution of this regression estimate is given the practical performance is investigated via an application to the study of migration between east and west germany

some new fixed point theorems of generalized nonlinear contractive multivalued maps in complete metric spaces in this paper we present some new fixed point theorems for generalized nonlinear contractive multivalued maps and these results generalize or improve the corresponding recent fixed point results in the literature

common fixed point properties for a family of set valued mappings abstract in this paper we study common fixed point properties for a family of mappings we present the extensions of caristi s fixed point theorem and markov kakutani fixed point theorem for a family of set valued mappings

on the development of variable separable asymptotic elastoplastic solutions for interfacial cracks abstract the problem of a plane strain crack lying along the interface between an elasticplastic power law hardening material and a rigid substrate is analysed in detail the possibility of elastoplastic asymptotic crack tip solutions that are separable in r and is explored where r are polar coordinates at the crack tip it is found that such variable separable solutions do exist and the first two terms in the asymptotic expansion of the stress and displacement fields in the neartip region are obtained it is shown that both the first and the second terms in the stress expansion are singular in r as r 0 the asymptotic solution is studied in detail for values of the hardening exponent n near n 1 via a small perturbation of the governing equations about the linear problem it is shown that the leading and second order singular terms in the stress expansion branch from the mode i and mode ii linear elastic solutions respectively the predictions of the asymptotic solution are compared with the results of detailed finite element calculations the region of dominance of the asymptotic solution is found to depend strongly on the geometry of the structure considered and the type of the applied loading

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

direct estimation of low dimensional components in additive models additive regression models have turned out to be a useful statistical tool in analyses of high dimensional data sets recently an estimator of additive components has been introduced by linton and nielsen which is based on marginal integration the explicit definition of this estimator makes possible a fast computation and allows an asymptotic distribution theory in this paper an asymptotic treatment of this estimate is offered for several models a modification of this procedure is introduced we consider weighted marginal integration for local linear fits and we show that this estimate has the following advantages i with an appropriate choice of the weight function the additive components can be efficiently estimated an additive component can be estimated with the same asymptotic bias and variance as if the other components were known ii application of local linear fits reduces the design related bias

linear smoothers and additive models we study linear smoothers and their use in building nonparametric regression models in the first part of this paper we examine certain aspects of linear smoothers for scatterplots examples of these are the running mean and running line kernel and cubic spline smoothers the eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother and several other topics such as the number of degrees of freedom of a smoother are discussed in the second part of the paper we describe how linear smoothers can be used to estimate the additive model a powerful nonparametric regression model using the backfitting algorithm we show that backfitting is the gauss seidel iterative method for solving a set of normal equations associated with the additive model we provide conditions for consistency and nondegeneracy and prove convergence for the backfitting and related algorithms for a class of smoothers that includes cubic spline smoothers

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

spline backfitted kernel smoothing of nonlinear additive autoregression model application of nonparametric and semiparametric regression techniques to high dimensional time series data has been hampered due to the lack of effective tools to address the curse of dimensionality under rather weak conditions we propose spline backfitted kernel estimators of the component functions for the nonlinear additive time series data that are both computationally expedient so they are usable for analyzing very high dimensional time series and theoretically reliable so inference can be made on the component functions with confidence simulation experiments have provided strong evidence that corroborates the asymptotic theory

varying index coefficient models it has been a long history of using interactions in regression analysis to investigate alterations in covariate effects on response variables in this article we aim to address two kinds of new challenges arising from the inclusion of such high order effects in the regression model for complex data the first kind concerns a situation where interaction effects of individual covariates are weak but those of combined covariates are strong and the other kind pertains to the presence of nonlinear interactive effects directed by low effect covariates we propose a new class of semiparametric models with varying index coefficients which enables us to model and assess nonlinear interaction effects between grouped covariates on the response variable as a result most of the existing semiparametric regression models are special cases of our proposed models we develop a numerically stable and computationally fast estimation procedure using both profile least squares method and local fitting we establish both

a theoretical study of the brinell hardness test brinell tests have long been the preferred method of assaying the hardness of metals during forming operations the general significance of the test has been codified in empirical laws especially those of meyer o neill and tabor on the other hand the indentation of elastoplastic media by a ball has never been thoroughly analysed in the context of modern mechanics of continua this is the objective here the actual boundary value problem is non steady but can be made steady in terms of reduced variables when the material response is suitably modelled namely the strain should be infinitesimal and expressible as the tensor gradient of a potential function of the stress deviator the function must be homogeneous of degree n 1 2 but is otherwise arbitrary meyer s law is then derivable rigorously ahead of a detailed solution moreover the predicted index is 2n 1 n substantiating o neill s rule for materials whose strain under uniaxial tension varies as some nth power of the stress it is predicted also that the piling up or sinking in around the indenter is correlated with n in the manner observed these immediate implications of the model amount to a priori evidence of its overall ability to simulate elastoplastic response of the kind induced in brinell tests evidence a posteriori was supplied by finite element computations for a standard potential whose level surfaces are of mises type mixed nine node quadrilateral elements were adopted these are known to promote optimal convergence and are well suited to handling incompressibility a carefully graded mesh provided about 24000 degrees of freedom computations were performed for n 1 2 4 and 10 covering the practical range the results include i distributions of the contact pressure and the radial and circumferential in surface stresses ii profiles of the deformed surface and iii contours of representative strain in the main body of material excellent agreement was obtained with tabor s experimental findings that the representative strain at the contact perimeter is y0 4 a d for any n a is the contact radius and d the ball diameter while the average pressure is 2 8 times the flow stress at strain y in a tension test finally strain paths at fixed stations were sampled to check the simulation of elastoplastic response locally as well as overall

multi valued nonlinear contraction mappings abstract two concepts of nonlinear contractions for multi valued mappings in complete metric spaces are introduced and three fixed point theorems are proved presented theorems are generalizations of very recent fixed point theorems due to klim and wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 and feng and liu y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 as well as a fixed point theorem of mizoguchi and takahashi n mizoguchi w takahash fixed point theorems for multi valued mappings on complete metric spaces j math anal appl 141 1989 177 188 and several others an example is given to show that presented results are genuine generalizations our results are also some contribution to an open problem raised by reich s reich fixed points of contractive functions boll unione mat ital 5 1972 26 42 s reich some fixed point problems atti acad naz lincei 57 1974 194 198 s reich some problems and results in fixed point theory contemp math 21 1983 179 187

oracally efficient two step estimation of generalized additive model the generalized additive model gam is a multivariate nonparametric regression tool for non gaussian responses including binary and count data we propose a spline backfitted kernel sbk estimator for the component functions and the constant which are oracally efficient under weak dependence the sbk technique is both computationally expedient and theoretically reliable thus usable for analyzing high dimensional time series inference can be made on component functions based on asymptotic normality simulation evidence strongly corroborates the asymptotic theory the method is applied to estimate insolvent probability and to obtain higher accuracy ratio than a previous study supplementary materials for this article are available online

a generalization of the banach contraction principle one of the most fundamental fixed point theorems is banach s contraction principle of which the following conjecture is a generalization generalized banach contraction conjecture gbcc let t be a self map of a complete metric space x d and let 0 m 1 let j be a positive integer assume that for each pair x y x min d tkx tky 1 k j md x y then t has a fixed point unlike banach s original theorem the case j 1 the above hypothesis does not compel t to be continuous in this paper we use a density argument coupled with ramsey s theorem from combinatorics to establish the gbcc for arbitrary j without the assumption of continuity it is known that the case j 3 includes instances where t is not continuous at any nonisolated point of x the arguments are constructive and may be useful in establishing other fixed point theorems without appealing to the axiom of choice

fixed point results for set valued contractions by altering distances in complete metric spaces nadler s contraction principle has led to fixed point theory of set valued contraction in non linear analysis inspired by the results of nadler the fixed point theory of set valued contraction has been further developed in different directions by many authors in particular by reich mizoguchi takahashi feng liu and many others in the present paper the concept of generalized contractions for set valued maps in metric spaces is introduced and the existence of fixed point for such a contraction are guaranteed by certain conditions our first result extends and generalizes the nadler feng liu and klim wardowski theorems and the second result is different from the reich and mizoguchi takahashi results as a consequence we derive some results related to fixed point of set valued maps satisfying certain conditions of integral type

the weak ekeland variational principle and fixed points abstract we use the weak ekeland variational principle to obtain a new proof of an improved version of the nadler fixed point theorem for set valued mappings given by dontchev and hager 1994 separately we apply the fixed point theorem to obtain an unconventional existence result for differential inclusions

indentation of a power law creeping solid the aim of this paper is to establish a rigorous theoretical basis for interpreting the results of hardness tests on creeping specimens we investigate the deformation of a creeping half space with uniaxial stress strain behaviour 0 0 m which is indented by a rigid punch both axisymmetric and plane indenters are considered the shape of the punch is described by a general expression which includes most indenter profiles of practical importance two methods are used to solve the problem the main results are found using a transformation method suggested by r hill it is shown that the creep indentation problem may be reduced to a form which is independent of the geometry of the punch and depends only on the material properties through m the reduced problem consists of a nonlinear elastic half space which is indented to a unit depth by a rigid flat punch of unit radius in the axisymmetric case or unit semi width in the plane case exact solutions are given for m 1 and m for m between these two limits the reduced problem has been solved using the finite element method the results enable the load on the indenter and the contact radius to be calculated in terms of the indentation depth and rate of penetration the stress strain and displacement fields in the half space may also be deduced the accuracy of the solution is demonstrated by comparing the results with full field finite element calculations the predictions of the theory are shown to be consistent with experimental observations of hardness tests on creeping materials reported in the literature

estimation in semiparametric spatial regression nonparametric methods have been very popular in the last couple of decades in time series and regression but no such development has taken place for spatial models a rather obvious reason for this is the curse of dimensionality for spatial data on a grid evaluating the conditional mean given its closest neighbors requires a four dimensional nonparametric regression in this paper a semiparametric spatial regression approach is proposed to avoid this problem an estimation procedure based on combining the so called marginal integration technique with local linear kernel estimation is developed in the semiparametric spatial regression setting asymptotic distributions are established under some mild conditions the same convergence rates as in the one dimensional regression case are established an application of the methodology to the classical mercer and hall wheat data set is given and indicates that one directional component appears to be nonlinear which has gone unnoticed in earlier analyses

fixed point theorems for multi valued contractions in complete metric spaces abstract in this paper the concept of a contraction for multi valued mappings in a metric space is introduced and the existence theorems for fixed points of such contractions in a complete metric space are proved presented results generalize and improve the recent results of y feng s liu y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 d klim d wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 and several others the method used in the proofs of our results is new and is simpler than methods used in the corresponding papers two examples are given to show that our results are genuine generalization of the results of feng and liu and klim and wardowski

fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings abstract in this paper the famous banach contraction principle and caristi s fixed point theorem are generalized to the case of multi valued mappings our results are extensions of the well known nadler s fixed point theorem s b nadler jr multi valued contraction mappings pacific j math 30 1969 475 487 as well as of some caristi type theorems for multi valued operators see n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188 j p aubin optima and equilibria an introduction to nonlinear analysis grad texts in math springer verlag berlin 1998 p 17 s s zhang q luo set valued caristi fixed point theorem and ekeland s variational principle appl math mech 10 2 1989 111 113 in chinese english translation appl math mech english ed 10 2 1989 119 121 etc

smooth backfitting in generalized additive models generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non gaussian responses including binary and count data in this paper a new likelihood approach for fitting generalized additive models is proposed it aims to maximize a smoothed likelihood the additive functions are estimated by solving a system of nonlinear integral equations an iterative algorithm based on smooth backfitting is developed from the newton kantorovich theorem asymptotic properties of the estimator and convergence of the algorithm are discussed it is shown that our proposal based on local linear fit achieves the same bias and variance as the oracle estimator that uses knowledge of the other components numerical comparison with the recently proposed two stage estimator ann statist 32 2004 2412 2443 is also made

the contraction principle for set valued mappings on a metric space with a graph let x d be a metric space and f x x be a set valued mapping we obtain sufficient conditions for the existence of a fixed point of the mapping f in the metric space x endowed with a graph g such that the set v g of vertices of g coincides with x and the set of edges of g is e g x y x y xxx

large sample properties of matching estimators for average treatment effects matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases the absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data in this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results we focus on matching with replacement with a fixed number of matches first we show that matching estimators are not n 1 2 consistent in general and describe conditions under which matching estimators do attain n 1 2 consistency second we show that even in settings where matching estimators are n 1 2 consistent simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound third we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions software for implementing these methods is available in matlab stata and r

extension of caristi s fixed point theorem to vector valued metric spaces abstract the paper deals with the classical caristi fixed point theorem in vector valued metric spaces the results obtained seem to be new in this setting

some results on set valued contractions in abstract metric spaces abstract in this paper the concept of contractive set valued maps in the frame of abstract metric spaces is studied and the existence of fixed points for such maps is guaranteed under certain conditions consequently several known fixed point results are either generalized or extended including the corresponding recent fixed point results of wardowski d wardowski endpoints and fixed points of set valued contractions in cone metric spaces nonlinear anal 71 2009 512 516 as well as klim and wardowski d klim d wardowski dynamic process and fixed points of set valued nonlinear contractions in cone metric spaces nonlinear anal 71 2009 5170 5175 examples are given to show that our results are distinct from the existing ones

variable selection and identification of high dimensional nonparametric additive nonlinear systems this paper considers variable selection and identification of dynamic additive nonlinear systems via kernel based nonparametric approaches where the number of variables and additive functions may be large variable selection aims to find which additive functions contribute and which do not the proposed variable selection consists of two successive steps at the first step one estimates each additive function by kernel based nonparametric identification approaches without suffering from the curse of dimensionality at the second step a nonnegative garrote estimator is applied to identify which additive functions are nonzero by utilizing the obtained nonparametric estimates of each function under weak conditions the nonparametric estimates of each additive function can achieve the same asymptotic properties as for 1d nonparametric identification based on kernel functions it is also established that the nonnegative garrote estimator turns a consistent estimate for each additive function into a consistent variable selection with probability one as the number of samples tends to infinity two simulation examples are presented to verify the effectiveness of the variable selection and identification approaches proposed in the paper

intersection bounds estimation and inference we develop a practical and novel method for inference on intersection bounds namely bounds defined by either the infimum or supremum of a parametric or nonparametric function or equivalently the value of a linear programming problem with a potentially infinite constraint set we show that many bounds characterizations in econometrics for instance bounds on parameters under conditional moment inequalities can be formulated as intersection bounds our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters and also applies to models with inequalities that are nonseparable in parameters since analog estimators for intersection bounds can be severely biased in finite samples routinely underestimating the size of the identified set we also offer a median bias corrected estimator of such bounds as a by product of our inferential procedures we develop theory for large sample inference based on the strong approximation of a sequence of series or kernel based empirical processes by a sequence of penultimate gaussian processes these penultimate processes are generally not weakly convergent and thus are non donsker our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes our construction also provides new adaptive inequality moment selection methods we provide conditions for the use of nonparametric kernel and series estimators including a novel result that establishes strong approximation for any general series estimator admitting linearization which may be of independent interest

converses to fixed point theorems of zermelo and caristi let x be an abstract nonempty set and t be a self map of x let per t and fix t denote the sets of all periodic points and all fixed points of t respectively our main theorem says that if pert fixt then there exists a partial ordering such that every chain in x has a supremum and for all x x x tx this result is a converse to zermelo s fixed point theorem we also show that from a purely set theoretical point of view fixed point theorems of zermelo and caristi are equivalent finally we discuss relations between caristi s theorem and its restriction to mappings satisfying caristi s condition with a continuous real function

fixed point theorems for multivalued mappings on complete metric spaces on obtient une version multivaluee du theoreme de point fixe de caristi qui est equivalent au principe e variationnel du a ekeland on utilise ce resultat pour obtenir un theoreme qui deduit le theoreme de nadler et un theoreme de point fixe commun pour une application a 1 valeur et une application multivaluee

fixed point theorems for multi valued contractions with w distance some fixed point theorems for a few nonlinear multi valued contraction mappings in complete metric spaces with w distance are proved the results presented in this paper generalize the recent results due to ciric 2009 3 feng and liu 2006 4 klim and wardowski 2007 8 latif and abdou 2011 12 and liu et al 2010 14 seven examples are given to explain our results

nonparametric estimation of homothetic and homothetically separable functions for vectors x and w let r x w be a function that can be nonparametrically estimated consistently and asymptotically normally we provide consistent asymptotically normal estimators for the functions g and h where r x w h g x w g is linearly homogeneous and h is monotonic in g this framework encompasses homothetic and homothetically separable functions such models reduce the curse of dimensionality provide a natural generalization of linear index models and are widely used in utility production and cost function applications extensions to related functional forms include a generalized partly linear model with unknown link function we provide simulation evidence on the small sample performance of our estimator and we apply our method to a chinese production dataset

remarks on caristi s fixed point theorem and kirk s problem abstract without assumptions on the continuity and the subadditivity of by means of caristi s fixed point theorem we investigated the existence of fixed points for a caristi type mapping which partially answered kirk s problem and improved caristi s fixed point theorem jachymski s fixed point theorem and khamsi s fixed point theorem since is not necessarily assumed to be bounded below on x

miscellanea efficient estimation of additive nonparametric regression models summary we define a new procedure for estimating additive nonparametric regression models we use the integration method of linton nielsen 1995 to provide starting values that are then used in a one step backfitting procedure we show that our new method is efficient in a certain sense and dominates the straight integration method according to mean squared error

some generalizations of caristi s fixed point theorem with applications to the fixed point theory of weakly contractive set valued maps and the minimization problem abstract in this paper we first prove some generalizations of caristi s fixed point theorem then we give some applications to the fixed point theory of weakly contractive set valued maps and the minimization problem

multivalued generalized nonlinear contractive maps and fixed points abstract we introduce some notions of generalized nonlinear contractive maps and prove some fixed point results for such maps consequently several known fixed point results are either improved or generalized including the corresponding recent fixed point results of ciric l b ciric multivalued nonlinear contraction mappings nonlinear anal 71 2009 2716 2723 klim and wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 feng and liu y feng s liu fixed point theorems for multivalued contractive mappings and multivalued caristi type mappings j math anal appl 317 2006 103 112 and mizoguchi and takahashi n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188

nonparametric estimation of an additive quantile regression model this article is concerned with estimating the additive components of a nonparametric additive quantile regression model we develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of n r 2r 1 when the additive components are r times continuously differentiable for some r 2 this result holds regardless of the dimension of the covariates and thus the new estimator has no curse of dimensionality in addition the estimator has an oracle property and is easily extended to a generalized additive quantile regression model with a link function the numerical performance and usefulness of the estimator are illustrated by monte carlo experiments and an empirical example

similarity analysis of creep indentation tests the general theory of axisymmetric hardness tests on nonlinear media is approached from the standpoint of similarity transformations it is shown how an entire process of indentation can be made to depend on the solution of just one boundary value problem in scaled variables and with a fixed geometry once this single auxiliary solution has been obtained the values of all physical quantities in the original problem can be generated readily at any stage without further numerical error even by themselves the similarity relations provide valuable information about for example an invariant connection between the depth of penetration and the radius of contact or about the variation of penetration with time in a creep test under dead load two kinds of material behaviour are considered a nonlinear elastic modelling strain hardening plasticity and b nonlinear viscous modelling secondary creep in either category the constitutive specification is sufficiently flexible to represent a wide range of actual responses in the context of hardness testing the analysis for case a extends a theory of ball indentation by hill et al to a class of indenters with shapes varying from flat to conical it also prepares the ground for case b which is more difficult and calls for a quite different auxiliary problem

endpoints and fixed points of set valued contractions in cone metric spaces abstract in this paper we introduce the concept of set valued contractions in cone metric spaces and establish new endpoint and fixed point theorems for such contractions the paper includes examples

a flexible semiparametric forecasting model for time series in this paper we propose a semiparametric procedure called the model averaging marginal regression mamar that is flexible for forecasting of time series this procedure considers approximating a multivariate regression function by an affine combination of one dimensional marginal regression functions the weight parameters involved in the approximation are estimated by least squares on the basis of the first stage nonparametric kernel estimates of the marginal regressions under some mild conditions we have established asymptotic normality for the estimated weights and the regression function in two cases case i considers that the number of the covariates is fixed while case ii allows the number of the covariates depending on the sample size and diverging as the observations are assumed to be stationary and near epoch dependent the approach developed is applicable to both the estimation and forecasting issues in time series analysis furthermore the method and result are augmented by a simulation study and illustrated by an application in forecasting the high frequency volatility of the ftse100 index

partially linear hazard regression for multivariate survival data this article studies estimation of partially linear hazard regression models for multivariate survival data a profile pseudo partial likelihood estimation method is proposed under the marginal hazard model framework the estimation on the parameters for the linear part is accomplished by maximization of a pseudo partial likelihood profiled over the nonparametric part this enables us to obtain consistent estimators of the parametric component asymptotic normality is obtained for the estimates of both the linear and nonlinear parts the new technical challenge is that the nonparametric component is indirectly estimated through its integrated derivative function from a local polynomial fit an algorithm of fast implementation of our proposed method is presented consistent standard error estimates using sandwich type ideas are also developed which facilitates inferences for the model it is shown that the nonparametric component can be estimated as well as if the parametric components were known and the

nonparametric matching and efficient estimators of homothetically separable functions for vectors z and w and scalar v let r v z w be a function that can be non parametrically estimated consistently and asymptotically normally such as a distribution density or conditional mean regression function we provide consistent asymptotically normal nonparametric estimators for the functions g and h where r v z w h vg z w and some related models this framework encompasses homothetic and homothetically separable functions and transformed partly additive models r v z w h v g z w for unknown functions g and h such models reduce the curse of dimensionality provide a natural generalization of linear index models and are widely used in utility production and cost function applications we also provide an estimator of g that is oracle efficient achieving the same performance as an estimator based on local least squares when h is known

the drop theorem the petal theorem and ekeland s variational principle on montre que le principe variationnel d ekeland ou plus precisement une forme legerement modifiee est une consequence d un resultat geometrique connu sous le terme de theoreme de la goutte

estimating semiparametric arch models by kernel smoothing methods we investigate a class of semiparametric arch models that includes as a special case the partially nonparametric pnp model introduced by engle and ng 1993 and which allows for both flexible dynamics and flexible function form with regard to the news impact function we show that the functional part of the model satisfies a type ii linear integral equation and give simple conditions under which there is a unique solution we propose an estimation method that is based on kernel smoothing and profiled likelihood we establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model we also discuss efficiency of both the parametric part and the nonparametric part we investigate the performance of our procedures on simulated data and on a sample of s p500 index returns we find evidence of asymmetric news impact functions consistent with the parametric analysis

generalized distance and existence theorems in complete metric spaces abstract in this paper we first introduce the concept of distance on a metric space which is a generalized concept of both w distance and tataru s distance we also improve the generalizations of the banach contraction principle caristi s fixed point theorem ekeland s variational principle and the nonconvex minimization theorem according to takahashi further we discuss the relation between w distance and tataru s distance

nonparametric identification of nonlinear time series projections abstract we study the possibility of identifying general linear and nonlinear time series models using nonparametric methods the kernel estimators of the conditional mean and variance are used as a basis and the properties of these quantities as model indicators are briefly discussed some drawbacks are pointed out and motivated by these we introduce projections as tools of identification the projections are especially useful for additive modeling expressions for the asymptotic bias and variance are obtained the projection of the conditional variance is suggested as a tool for identifying heteroscedastic time series the results are illustrated by simulations for both the estimators of the projections and the estimators of the conditional mean and variance

estimation and inference in generalized additive coefficient models for nonlinear interactions with high dimensional covariates in the low dimensional case the generalized additive coefficient model gacm proposed by xue and yang statist sinica16 2006 1423 1446 has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables in this paper we propose estimation and inference procedures for the gacm when the dimension of the variables is high specifically we propose a groupwise penalization based procedure to distinguish significant covariates for the large p small n setting the procedure is shown to be consistent for model structure identification further we construct simultaneous confidence bands for the coefficient functions in the selected model based on a refined two step spline estimator we also discuss how to choose the tuning parameters to estimate the standard deviation of the functional estimator we adopt the smoothed bootstrap method we conduct simulation experiments to evaluate the numerical performance of the proposed methods and analyze an obesity data set from a genome wide association study as an illustration

fixed point theorems for a broad class of multimaps abstract multimaps from a metric space into the collection of all its nonempty closed subsets are considered and fixed point theorems for such maps have been obtained under new contractive conditions not involving the extended hausdorff metric

consistent specification tests for semiparametric nonparametric models based on series estimation methods abstract this paper considers the problem of consistent model specification tests using series estimation methods the null models we consider in this paper all contain some nonparametric components a leading case we consider is to test for an additive partially linear model the null distribution of the test statistic is derived using a central limit theorem for hilbert valued random arrays the test statistic is shown to be able to detect local alternatives that approach the null models at the order of op n 1 2 we show that the wild bootstrap method can be used to approximate the null distribution of the test statistic a small monte carlo simulation is reported to examine the finite sample performance of the proposed test we also show that the proposed test can be easily modified to obtain series based consistent tests for other semiparametric nonparametric models

vectorial form of ekeland type variational principle with applications to vector equilibrium problems and fixed point theory abstract this paper introduces a vectorial form of equilibrium version of ekeland type variational principle some equivalent results to our variational principle are given as applications we derive the existence of solutions of a vector equilibrium problem in the setting of complete quasi metric spaces with a w distance caristi kirk fixed point theorem for multivalued maps is also established in a more general setting

rate optimal estimation for a general class of nonparametric regression models with unknown link functions this paper discusses a nonparametric regression model that naturally generalizes neural network models the model is based on a finite number of one dimensional transformations and can be estimated with a one dimensional rate of convergence the model contains the generalized additive model with unknown link function as a special case for this case it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion

model checking in regression via dimension reduction lack of fit checking for parametric and semiparametric models is essential in reducing misspecification the efficiency of most existing model checking methods drops rapidly as the dimension of the covariates increases we propose to check a model by projecting the fitted residuals along a direction that adapts to the systematic departure of the residuals from the desired pattern consistency of the method is proved for parametric and semiparametric regression models a bootstrap implementation is also discussed simulation comparisons with several existing methods are made suggesting that the proposed methods are more efficient than the existing methods when the dimension increases air pollution data from chicago are used to illustrate the procedure

some generalizations of ekeland type variational principle with applications to equilibrium problems and fixed point theory abstract in this paper we introduce the concept of a q function defined on a quasi metric space which generalizes the notion of a function and a w distance we establish ekeland type variational principles in the setting of quasi metric spaces with a q function we also present an equilibrium version of the ekeland type variational principle in the setting of quasi metric spaces with a q function we prove some equivalences of our variational principles with caristi kirk type fixed point theorems for multivalued maps the takahashi minimization theorem and some other related results as applications of our results we derive existence results for solutions of equilibrium problems and fixed point theorems for multivalued maps we also extend the nadler s fixed point theorem for multivalued maps to a q function and in the setting of complete quasi metric spaces as a consequence we prove the banach contraction theorem for a q function and in the setting of complete quasi metric spaces the results of this paper extend and generalize many results appearing recently in the literature

nonparametric estimation of an additive model with a link function this paper describes an estimator of the additive components of a nonparametric additive model with a known link function when the additive components are twice continuously differentiable the estimator is asymptotically normally distributed with a rate of convergence in probability of 2 5 n this is true regardless of the finite dimension of the explanatory variable thus in contrast to the existing asymptotically normal estimator the new estimator has no curse of dimensionality moreover the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

smooth backfitting of proportional hazards with multiplicative components smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression by projecting the data down onto the structured space of interest smooth backfitting

remarks on caristi s fixed point theorem abstract in this work we give a characterization of the existence of minimal elements in partially ordered sets in terms of fixed points of multivalued maps this characterization shows that the assumptions in caristi s fixed point theorem can a priori be weakened finally we discuss kirk s problem on an extension of caristi s theorem and prove a new positive result which illustrates the weakening mentioned before

the dimensionality reduction principle for generalized additive models soit x y une paire de variables aleatoires telles que x x 1 x j s etende sur c 0 1 j la distribution conditionnelle de y etant donne x x est supposee appartenir a une famille exponentielle appropriee ayant pour parametre r f x denote la dependance de vis a vis de x et f l approximation additive de f ayant la log vraisemblance esperee maximum possible