on the borel summability of planar perturbation series transition to minkowski space in recent years t hooft and rivasseau proved the borel summability of planar asymptotically free massive theories in euclidean space the corresponding borel sums in minkowski space are shown to exist as linear functionals if the euclidean counterparts are bounded polynomially in momentum space and fulfill certain analyticity conditions both can be verified in massive planar wrong sign 44 using rivasseau s approach the functionals alternatively are densely defined and unbounded on anlp space or bounded on the whole of a banach space with a more restrictive norm

a hybrid iterative scheme for mixed equilibrium problems and fixed point problems the purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a mixed equilibrium problem mep and the set of common fixed points of finitely many nonexpansive mappings in a real hilbert space first by using the well known kkm technique we derive the existence and uniqueness of solutions of the auxiliary problems for the mep second by virtue of this result we introduce a hybrid iterative scheme for finding a common element of the set of solutions of mep and the set of common fixed points of finitely many nonexpansive mappings furthermore we prove that the sequences generated by the hybrid iterative scheme converge strongly to a common element of the set of solutions of mep and the set of common fixed points of finitely many nonexpansive mappings

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

an iterative algorithm for solving fixed point problems variational inequality problems and mixed equilibrium problems abstract in this paper we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of some variational inequality furthermore we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets our results extend and improve the corresponding results of zeng and yao l c zeng and j c yao a hybrid iterative scheme for mixed equilibrium problems and fixed point problems j comput appl math 214 2008 186 201 takahashi and takahashi s takahashi and w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2007 506 515 and many others

local existence of the borel transform in euclidean φ 4 4 we bound rigorously the large order behaviour of 44 euclidean perturbative quantum field theory as the simplest example of renormalizable but non super renormalizable theory the needed methods are developed to take into account the structure of renormalization which plays a crucial role in the estimates as a main thorem it is shown that the schwinger functions at ordern are bounded byknn which implies a finite radius of convergence for the borel transform of the perturbation series

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

rigorous construction of planar diagram field theories in four dimensional euclidean space asymptotically free quantum field theories with planar feynman diagrams such as su gauge theory are considered in 4 dimensional euclidean space it is shown that if all particles involved have non vanishing masses and if the coupling constant s org2 are small enough crit then an absolutely convergent procedure exists to obtain green functions that uniquely solve the dyson schwinger equations

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

approximation methods for common fixed points for a countable family of nonexpansive mappings abstract let e l p or l p space 1 p let k be a closed convex and nonempty subset of e let t i i 1 be a family of nonexpansive self mappings of k for arbitrary fixed 0 1 define a family of nonexpansive maps s i i 1 by s i 1 i t i where i is the identity map of k let f i 1 f t i 0 it is proved that the iterative sequence x n defined by x 0 k x n 1 n u i 1 i t n s i x n n 0 converges strongly to a common fixed point of the family t i i 1 where n and i t n are sequences in 0 1 satisfying appropriate conditions in each of the following cases a e l p 1 p and b e l p 1 p and at least one of the maps t i s is demicompact our theorems extend the results of p mainge approximation methods for common fixed points of nonexpansive mappings in hilbert space j math anal appl 325 2007 469 479 from hilbert spaces to l p spaces 1 p

on coverage and local radial rates of credible sets in the mildly ill posed inverse signal in white noise model we construct confidence sets as credible balls with respect to the empirical bayes posterior resulting from a certain two level hierarchical prior the quality of the posterior is characterized by the contraction rate which we allow to be local that is depending on the parameter the issue of optimality of the constructed confidence sets is addressed via a trade off between its size the local radial rate and its coverage probability we introduce excessive bias restriction ebr more general than self similarity and polished tail condition recently studied in the literature under ebr we establish the confidence optimality of our credible set with some local oracle radial rate we also derive the oracle estimation inequality and the oracle posterior contraction rate the obtained local results are more powerful than global adaptive minimax results for a number of smoothness scales follow as consequence in particular the ones considered by szabo et al ann statist 43 2015 1391 1428

sharp adaptation for inverse problems with random noise we consider a heteroscedastic sequence space setup with polynomially increasing variances of observations that allows to treat a number of inverse problems in particular multivariate ones we propose an adaptive estimator that attains simultaneously exact asymptotic minimax constants on every ellipsoid of functions within a wide scale that includes ellipoids with polynomially and exponentially decreasing axes and at the same time satisfies asymptotically exact oracle inequalities within any class of linear estimates having monotone non increasing weights the construction of the estimator is based on a properly penalized blockwise stein s rule with weakly geometically increasing blocks as an application we construct sharp adaptive estimators in the problems of deconvolution and tomography

modulation of estimators and confidence sets an unknown signal plus white noise is observed at n discretetime points within a large convex class of linear estimators of the signal we choose the one which minimizes estimated quadratic risk by construction the resulting estimator is nonlinear this estimation is done after orthogonal transformation of the data to a reasonable coordinate system the procedure adaptively tapers the coefficients of the transformed data if the class of candidate estimators satisfies a uniform entropy condition then our estimator is asymptotically minimax in pinsker s sense over certain ellipsoids in the parameter space and dominates the james stein estimatorasymptotically we describe computational algorithms for the modulation estimator and construct confidence sets for the unknown signal these confidence sets are centered at the estimator have correctasymptotic coverage probability and have relatively small risk asset valued estimators of the signal

react scatterplot smoothers superefficiency through basis economy abstract react estimators for the mean of a linear model involve three steps transforming the model to a canonical form that provides an economical representation of the unknown mean vector estimating the risks of a class of candidate linear shrinkage estimators and adaptively selecting the candidate estimator that minimizes estimated risk applied to one or higher way layouts the react method generates automatic scatterplot smoothers that compete well on standard datasets with the best fits obtained by alternative techniques historical precursors to react include nested model selection ridge regression and nested principal component selection for the linear model however react s insistence on working with an economical basis greatly increases its superefficiency relative to the least squares fit this reduction in risk and the possible economy of the discrete cosine basis of the orthogonal polynomial basis or of a smooth basis that generalizes the discrete cosine basis are illustrated by fitt

a hybrid algorithm for pseudo contractive mappings abstract in this paper we suggest and analyze a hybrid algorithm for pseudo contractive mappings in hilbert spaces further we prove the strong convergence of the proposed iterative algorithm for lipschitz pseudo contractive mappings in hilbert spaces

a general iterative method for nonexpansive mappings in hilbert spaces let h be a real hilbert space consider on h a nonexpansive mapping t with a fixed point a contraction f with coefficient 0 0 let 0

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0

a general iterative method for addressing mixed equilibrium problems and optimization problems abstract in this paper we introduce a new general iterative method for finding a common element of the set of solutions of a mixed equilibrium problem mep the set of fixed points of an infinite family of nonexpansive mappings t n n 1 and the set of solutions of variational inequalities for a inverse strongly monotone mapping in hilbert spaces furthermore we establish the strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems our results extend and improve the recent results of yao et al y yao m a noor s zainab y c liou mixed equilibrium problems and optimization problems j math anal appl 354 2009 319 329 y yao m a noor y c liou on iterative methods for equilibrium problems nonlinear anal 70 1 2009 479 509 and many others

iterative convergence to cesaro means for continuous pseudocontractive mappings abstract let f be a fixed strongly pseudocontractive mapping and t be a continuous pseudocontractive mapping with f t 0 the sequence z m is iteratively defined as follows z m t m f z m 1 t m 1 m 1 j 0 m t j z m m 0 where t m 0 1 satisfies the condition lim m t m 0 we prove that z m converges strongly to the unique solution p to some variational inequality in f t our results develop and complement the corresponding ones by matsushita daishi kuroiwa j math anal appl 294 2004 206 214 and shioji takahashi arch math 72 1999 354 359 and moore nnoli j math anal appl 260 2001 269 278 and su li appl math comput 181 2006 332 341 and song chen appl math comput 186 2007 1120 1128 and wangkeeree appl math comput 201 2008 239 249

on relaxed viscosity iterative methods for variational inequalities in banach spaces in this paper we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self mappings defined on a nonempty closed convex subset of a reflexive banach space we prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method the results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature

common fixed points of strict pseudocontractions by iterative algorithms in this paper we present iteration schemes to weakly and strongly approximate common fixed points of a finite family of a class of strict pseudocontractions

viscosity approximation methods for nonexpansive mappings abstract viscosity approximation methods for nonexpansive mappings are studied consider a nonexpansive self mapping t of a closed convex subset c of a banach space x suppose that the set fix t of fixed points of t is nonempty for a contraction f on c and t 0 1 let x t c be the unique fixed point of the contraction x tf x 1 t tx consider also the iteration process x n where x 0 c is arbitrary and x n 1 n f x n 1 n tx n for n 1 where n 0 1 if x is either hilbert or uniformly smooth then it is shown that x t and under certain appropriate conditions on n x n converge strongly to a fixed point of t which solves some variational inequality

an adaptation theory for nonparametric confidence intervals a nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals a between class modulus of continuity captures the expected length of adaptive confidence intervals sharp lower bounds are given for the expected length and an ordered modulus of continuity is used to construct adaptive confidence procedures which are within a constant factor of the lower bounds in addition minimax theory over nonconvex parameter spaces is developed

adaptive inference for the mean of a gaussian process in functional data summary we propose and analyse fully data driven methods for inference about the mean function of a gaussian process from a sample of independent trajectories of the process observed at random time points and corrupted by additive random error our methods are based on thresholded least squares estimators relative to an approximating function basis the variable threshold levels are determined from the data and the resulting estimates adapt to the unknown sparsity of the mean function relative to the approximating basis these results are obtained via novel oracle inequalities which are further used to derive the rates of convergence of our mean estimates in addition we construct confidence balls that adapt to the unknown regularity of the mean and covariance function of the stochastic process they are easy to compute since they do not require explicit estimation of the covariance operator of the process a simulation study shows that the new method performs very well in practice and is robust against large variations that may be introduced by the random error terms

strong convergence of an iterative method for nonexpansive mappings with new control conditions abstract the purpose of this paper is to study the convergence problem of an iterative method for nonexpansive mappings in banach spaces under some new control conditions on parameters

an iterative method for finding common solutions of equilibrium and fixed point problems we introduce an iterative method for finding a common element of the set of solutions of an equilibrium problem and of the set of fixed points of a finite family of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem

iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings abstract we introduce iterative algorithms for finding a common element of the set of solutions of a system of equilibrium problems and of the set of fixed points of a finite family and a left amenable semigroup of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem our results extend for example the recent result of v colao g marino h k xu an iterative method for finding common solutions of equilibrium and fixed point problems j math anal appl 344 2008 340 352 to systems of equilibrium problems

strong convergence theorems for a new iterative method of k strictly pseudo contractive mappings in hilbert spaces in this paper we introduce a new iterative method of a k strictly pseudo contractive mapping for some email protected k 1 and prove that the sequence x n converges strongly to a fixed point of t which solves a variational inequality related to the linear operator a our results have extended and improved the corresponding results of y j cho s m kang and x qin some results on k strictly pseudo contractive mappings in hilbert spaces nonlinear anal 70 2008 1956 1964 and many others

residual variance and residual pattern in nonlinear regression summary a nonparametric estimator of residual variance in nonlinear regression is proposed it is based on local linear fitting asymptotically the estimator has a small bias but a larger variance compared with the parametric estimator in linear regression finite sample properties are investigated in a simulation study including a comparison with other nonparametric estimators the method is also useful for spotting heteroscedasticity and outliers in the residuals at an early stage of the data analysis a further application is checking the fit of parametric models this is illustrated for longitudinal growth data

approximating fixed points of holomorphic mappings in the hilbert ball abstract we approximate fixed points of holomorphic and nonexpansive self mappings of the hilbert ball using both continuous and discrete schemes

viscosity approximation methods for pseudo contractive semigroups in banach spaces abstract we study the strong convergence of two viscosity iteration processes for pseudo contractive semigroup and for strongly pseudo contractive mapping in uniformly convex banach spaces with uniformly g teaux differentiable norm as special cases we get strong convergence of two viscosity iteration processes for approximating common fixed points of nonexpansive semigroups in certain banach spaces the results presented in this paper extend and generalize previous results

construction and borel summability of planar 4 dimensional euclidean field theory we use the methods of 1 to show that the planar part of the renormalized perturbation theory for 4 4 euclidean field theory is borel summable on the asymptotically free side of the theory the borel sum can therefore be taken as a rigorous definition of then limit of a massiven n matrix model with a trg 4 interaction hence with wrong sign ofg our construction is relevant for a solution of the ultra violet problem for planar qcd we also propose a program for studying the structure of the renormalons singularities within the planar world

some nonasymptotic results on resampling in high dimension i confidence regions we study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure the random vector is supposed to be either gaussian or to have a symmetric and bounded distribution the dimensionality of the vector can possibly be much larger than the number of observations and we focus on a non asymptotic control of the confidence level following ideas inspired by recent results in learning theory we consider two approaches the first based on a concentration principle valid for a large class of resampling weights and the second on a direct resampled quantile specifically using rademacher weights several intermediate results established in the approach based on concentration principles are of self interest we also discuss the question of accuracy when using monte carlo approximations of the resampled quantities we present an application of these results to the one sided and two sided multiple testing problem in which we derive several resampling based step down procedures providing a non asymptotic fwer control we compare our different procedures in a simulation study and we show that they can outperform bonferroni s or holm s procedures as soon as the observed vector has sufficiently correlated coordinates

bandwidth choice for nonparametric regression this paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression we analyze a tapered fourier series estimate and discuss the relationship of this estimate to a kernel estimate we first consider a method based on an unbiased estimate of mean square error and show that the bandwidth thus chosen is asymptotically optimal other methods are examined as well and are shown to be asymptotically equivalent a small simulation shows however that for small or moderate sample size the methods perform quite differently

strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings let c be a nonempty closed convex subset of a real strictly convex and reflexive banach space e which has a uniformly g teaux differentiable norm let f c c be a given contractive mapping and tn n 1 c c be an infinite family of nonexpansive mappings such that the common fixed point sets f n 1 f tn let n and n be two real sequences in 0 1 for given x0 c arbitrarily let the sequence xn be generated iteratively by xn 1 nf xn nxn 1 n n wnxn wherewn is the w mapping generated by the mappings tn tn 1 t1 and n n 1 1 suppose the iterative parameters n and n satisfy the following control conditions c1 limn n 0 c2 n 0 n b5 limsupn n 1 then the sequence xn converges strongly to p f where p is the unique solution in f to the following variational inequality i f p j p x 0for allx f

viscosity methods for common solutions of equilibrium and variational inequality problems via multi step iterative algorithms and common fixed points abstract in this paper we present a new multi step iterative method we prove the strong convergence of the method to a common fixed point of a finite number of nonexpansive mappings that also solves a suitable equilibrium problem

universal donsker classes and metric entropy when mathfrak f is a universal donsker class then for independent indetically distributed i i d observation mathbf x 1 ldots mathbf x n with an unknown law p for any mathfrak f i in mathfrak f i 1 ldots m quad n 1 2 left mathfrak f 1 left mathbf x 1 right ldots mathfrak f i left mathbf x n right right 1 leq i leq m is asymptotically normal with mean vector n 1 2 left int mathfrak f i left mathbf x n right d mathbf p left x right right 1 leq i leq m and covariance matrix int mathfrak f i mathfrak f j d mathbf p int mathfrak f id mathbf p int mathfrak f jd mathbf p uniformly for mathfrak f i in mathfrak f then for certain statistics formed frome the mathfrak f i left mathbf x k right even where mathfrak f i may be chosen depending on the mathbf x k there will be asymptotic distribution as n rightarrow infty for example for mathbf x 2 statistics where f i are indicators of disjoint intervals depending suitably on mathbf x 1 ldots mathbf x n whose union is the real line mathbf x 2 quadratic forms have limiting distributions roy 1956 and watson 1958 which may however not be mathbf x 2 distributions and may depend on p chernoff and lehmann 1954 universal donsker classes of sets are up to mild measurability conditions just classes satisfying the vapnik cervonenkis comdinatorial conditions defined later in this section donsker the vapnik cervonenkis combinatorial conditions defined later in this section durst and dudley 1981 and dudley 1984 chapter 11 the use of such classes allows a variety of extensions of the roy watson results to general multidimensional sample spaces pollard 1979 and moore and subblebine 1981 vapnik and cervonenkis 1974 indicated application of their families of sets to classification pattern recognition problems more recently the classes have been applied to tree structured classifiacation breiman friedman olshen and stone 1984 chapter 12

confidence balls in gaussian regression starting from the observation of an r n gaussian vector of mean f and covariance matrix sigma 2 i n i n is the identity matrix we propose a method for building a euclidean confidence ball around f with prescribed probability of coverage for each n we describe its nonasymptotic property and show its optimality with respect to some criteria

strong convergence theorems of a general iterative process for a finite family of λi strict pseudo contractions in q uniformly smooth banach spaces in this paper we study a general iterative process to have strong convergence for a finite family of l i strict pseudo contractive non self mappings in the framework of q uniformly smooth banach spaces our results improve and extend the corresponding results announced by many others

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

on the large sample minimal coverage probability of confidence intervals after model selection we give a large sample analysis of the minimal coverage probability of the usual confidence intervals for regression parameters when the underlying model is chosen by a conservative or overconsistent model selection procedure we derive an upper bound for the large sample limit minimal coverage probability of such intervals that applies to a large class of model selection procedures including the akaike information criterion as well as various pretesting procedures this upper bound can be used as a safeguard to identify situations where the actual coverage probability can be far below the nominal level we illustrate that the asymptotic upper bound can be statistically meaningful even in rather small samples

minimax estimation with thresholding and its application to wavelet analysis many statistical practices involve choosing between a full model and reduced models where some coefficients are reduced to zero data were used to select a model with estimated coefficients is it possible to do so and still come up with an estimator always better than the traditional estimator based on the full model the james stein estimator is such an estimator having a property called minimaxity however the estimator considers only one reduced model namely the origin hence it reduces no coefficient estimator to zero or every coefficient estimator to zero in many applications including wavelet analysis what should be more desirable is to reduce to zero only the estimators smaller than a threshold called thresholding in this paper is it possible to construct this kind of estimators which are minimax in this paper we construct such minimax estimators which perform thresholding we apply our recommended estimator to the wavelet analysis and show that it performs the best among the well known estimators aiming simultaneously at estimation and model selection some of our estimators are also shown to be asymptotically optimal

statistical inference for the optimal approximating model in the setting of high dimensional linear models with gaussian noise we investigate the possibility of confidence statements connected to model selection although there exist numerous procedures for adaptive point estimation the construction of adaptive confidence regions is severely limited cf li in ann stat 17 1001 1008 1989 the present paper sheds new light on this gap we develop exact and adaptive confidence regions for the best approximating model in terms of risk one of our constructions is based on a multiscale procedure and a particular coupling argument utilizing exponential inequalities for noncentral 2 distributions we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one

wavelet shrinkage for natural exponential families with quadratic variance functions we propose a wavelet shrinkage methodology for univariate natural exponential families with quadratic variance functions covering the gaussian poisson gamma binomial negative binomial and generalised hyperbolic secant distributions simulation studies for poisson and binomial data are used to illustrate the usefulness of the proposed methodology and comparisons are made with other methods available in the literature we also present applications to datasets arising from high energy astrophysics and from epidemiology

strong convergence for a minimization problem on solutions of systems of equilibrium problems and common fixed points of an infinite family and semigroup of nonexpansive mappings in this paper we introduce a suitable mann type algorithm for finding a common element of the set of solutions of systems of equilibrium problems and the set of common fixed points of an infinite family and left amenable semigroup of nonexpansive mappings in hilbert spaces then we prove the strong convergence of the proposed iterative scheme to the unique solution of the minimization problem on the solution of systems of equilibrium problems and the common fixed points of an infinite family and left amenable semigroup of nonexpansive mappings our results extend and improve the recent result of colao and marino v colao and g marino strong convergence for a minimization problem on points of equilibrium and common fixed points of an infinite family of nonexpansive mappings nonlinear anal 73 2010 3513 3524 and many others

analysis of long period variable stars with nonparametric tests for trend detection in astronomy the study of variable stars that is stars characterized by showing significant variation in their brightness over time has made crucial contributions to our understanding of many phenomena from stellar birth and evolution to the calibration of the extragalactic distance scale in this article we develop a method for analyzing multiple pseudo periodic time series with the goal of detecting temporal trends in their periods we allow for nonstationary noise and for clustering among the various time series we apply this method to the long standing astronomical problem of identifying variable stars whose regular brightness fluctuations have periods that change over time the results of our analysis show that such changes can be substantial raising the possibility that astronomers estimates of galactic distances can be refined two significant contributions of our approach relative to existing methods for this problem are as follows 1 the method is nonparametric making minimal assumpt

on the convergence of planar diagram expansions renormalizable quantum field theories whose perturbation expansions are described by planar feynman diagrams only such as su gauge theory are considered in 4 dimensional euclidean space for studying asymptotic properties of the perturbation series one might wish to isolate first all those planar diagrams that do not contain any ultraviolet divergent subgraphs in this paper it is proved that this infinite set of diagrams when summed converges within a finite radius of convergence for the coupling constant

confidence bands in density estimation given a sample from some unknown continuous density f we construct adaptive confidence bands that are honest for all densities in a generic subset of the union of t holder balls 0 t r where r is a fixed but arbitrary integer the exceptional nongeneric set of densities for which our results do not hold is shown to be nowhere dense in the relevant holder norm topologies in the course of the proofs we also obtain limit theorems for maxima of linear wavelet and kernel density estimators which are of independent interest

central limit theorems for stochastic processes under random entropy conditions necessary and sufficient conditions are found for the weak convergence of the row sums of an infinitesimal row independent triangular array nj of stochastic processes indexed by a set s to a sample continuous gaussian process when the array satisfies a random entropy condition analogous to one used by gine and zinn 1984 for empirical processes this entropy condition is satisfied when s is a class of sets or functions with the vapnik ervonenkis property and each nj f fd nj is of the form njc for some reasonable random finite signed measure vnj as a result we obtain necessary and sufficient conditions for the weak convergence of possibly non i i d partial sum processes and new sufficient conditions for empirical processes indexed by vapnik ervonenkis classes special cases include prokhorov s 1956 central limit theorem for empirical processes and shorack s 1979 theorems on weighted empirical processes

adaptive nonparametric confidence sets we construct honest confidence regions for a hilbert space valued parameter in various statistical models the confidence sets can be centered at arbitrary adaptive estimators and have diameter which adapts optimally to a given selection of models the latter adaptation is necessarily limited in scope we review the notion of adaptive confidence regions and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation applications include the finite normal mean model the white noise model density estimation and regression with random design institute of mathematical statistics 2006

viscosity approximative methods to cesaro mean iterations for nonexpansive nonself mappings in banach spaces let e be a real uniformly convex banach space which admits a weakly sequentially continuous duality mapping from e to e e c a closed convex subset of e which is also a sunny nonexpansive retract of e let t c et c e be a nonexpansive nonself mapping with f t f t and f c cf c c be a fixed contractive mapping the implicit viscosity iterative sequence zm zm is defined by tm 0 1 tm 0 1 zm 1m 1 j 0mp tmf zm 1 tm tp jzm for m 0m 0 and two explicit viscosity iterative sequences xn xn and yn yn are given by x0 c xn 1 nf xn 1 n 1n 1 j 0n pt jxn and y0 c yn 1 1n 1 j 0np nf yn 1 n tp jyn for n 0n 0 where n n is a sequence in 0 1 0 1 and p is a sunny nonexpansive retraction of e onto c we prove that under appropriate conditions imposed on tm tm and n n the sequences zm zm xn xn and yn yn converge strongly to some fixed point of t which solves some variational inequalities the results presented extend and improve the corresponding results of matsushita and kuroiwa s matsushita d kuroiwa strong convergence of averaging iterations of nonexpansive nonself mappings j math anal appl 294 2004 206 214 song and chen y song r chen viscosity approximation methods to cesaro means for nonexpansive mappings appl math comput 186 2007 1120 1128 and many authors

a general iterative method for a finite family of nonexpansive mappings abstract we study the approximation of common fixed points of a finite family of nonexpansive mappings and suggest a modification of the iterative algorithm without the assumption of any type of commutativity also we show that the convergence of the proposed algorithm can be proved under some types of control conditions

viscosity approximation methods for fixed points problems the aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed point of a given nonexpansive self mapping

some iterative methods for finding fixed points and for solving constrained convex minimization problems the present paper is divided into two parts in the first part we introduce implicit and explicit iterative schemes for finding the fixed point of a nonexpansive mapping defined on the closed convex subset of a real hilbert space we establish results on the strong convergence of the sequences generated by the proposed schemes to a fixed point of a nonexpansive mapping such a fixed point is also a solution of a variational inequality defined on the set of fixed points in the second part we propose implicit and explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem such a solution is also a solution of a variational inequality defined over the set of fixed points of a nonexpansive mapping the results of this paper extend and improve several results presented in the literature in the recent past

adaptive confidence balls adaptive confidence balls are constructed for individual resolution levels as well as the entire mean vector in a multiresolution framework finite sample lower bounds are given for the minimum expected squared radius for confidence balls with a prespecified confidence level the confidence balls are centered on adaptive estimators based on special local block thresholding rules the radius is derived from an analysis of the loss of this adaptive estimator in addition adaptive honest confidence balls are constructed which have guaranteed coverage probability over all of r n and expected squared radius adapting over a maximum range of besov bodies

cats clustering after transformation and smoothing cats clustering after transformation and smoothing is a technique for nonparametrically estimating and clustering a large number of curves our motivating example is a genetic microarray experiment but the method is very general the method includes transformation and smoothing multiple curves multiple nonparametric testing for screening out flat curves clustering curves with similar shape and nonparametrically inferring the clustering estimation error rate

iterative methods for common fixed points for a countable family of nonexpansive mappings in uniformly convex spaces abstract let e be a uniformly convex real banach space with a uniformly g teaux differentiable norm let k be a closed convex and nonempty subset of e let t i i 1 be a family of nonexpansive self mappings of k for arbitrary fixed 0 1 define a family of nonexpansive maps s i n 1 by s i 1 i t i where i is the identity map of k let f i 1 f t i 0 it is proved that an iterative sequence x n defined by x 0 k x n 1 n u i 1 i t n s i x n n 0 converges strongly to a common fixed point of the family t i i 1 where n and i t n are sequences in 0 1 satisfying appropriate conditions in each of the following cases a e l p 1 p and b at least one of the t i s is demicompact

adaptive confidence bands we show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions we propose instead to construct adaptive bands that cover a surrogate function f which is close to but simpler than f the surrogate captures the significant features in f we establish lower bounds on the width for any confidence band for f and construct a procedure that comes within a small constant factor of attaining the lower bound for finite samples

strong convergence for a minimization problem on points of equilibrium and common fixed points of an infinite family of nonexpansive mappings abstract let h be a hilbert space consider on h a sequence of nonexpansive mappings t n with common fixed points an equilibrium function g a contraction f with coefficient 0 1 and a strongly positive linear bounded operator a with coefficient 0 let 0 we define a suitable mann type algorithm which strongly converges to the unique solution of the minimization problem min x c 1 2 a x x h x where h is a potential function for f and c is the intersection of the equilibrium points and the common fixed points of the sequence t n

convergence theorems of shrinking projection methods for equilibrium problem variational inequality problem and a finite family of relatively quasi nonexpansive mappings we introduce a w mapping for a finite family of relatively quasi nonexpansive mappings and construct an iterative scheme for finding a common element of the solution set of equilibrium problem the solution set of the variational inequality problem for an inverse strongly monotone operator and set of common fixed points of a finite family of relatively quasi nonexpansive mappings strong convergence theorems are presented in a 2 uniformly convex and uniformly smooth banach space our results generalize and extend relative results

information theory and mixing least squares regressions for gaussian regression we develop and analyze methods for combining estimators from various models for squared error loss an unbiased estimator of the risk of the mixture of general estimators is developed special attention is given to the case that the component estimators are least squares projections into arbitrary linear subspaces such as those spanned by subsets of explanatory variables in a given design we relate the unbiased estimate of the risk of the mixture estimator to estimates of the risks achieved by the components this results in simple and accurate bounds on the risk and its estimate in the form of sharp and exact oracle inequalities that is without advance knowledge of which model is best the resulting performance is comparable to or perhaps even superior to what is achieved by the best of the individual models furthermore in the case that the unknown parameter has a sparse representation our mixture estimator adapts to the underlying sparsity simulations show that the performance of these mixture estimators is better than that of a related model selection estimator which picks a model with the highest weight also the connection between our mixtures with bayes procedures is discussed

an extragradient like approximation method for variational inequality problems and fixed point problems the purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone lipschitz continuous mapping we introduce an extragradient like approximation method which is based on so called extragradient method and viscosity approximation method we establish a strong convergence theorem for two iterative sequences generated by this method

strong convergence theorems on an iterative method for a family of finite nonexpansive mappings in reflexive banach spaces in this paper by using some new analysis techniques we study the approximation problems of common fixed points of halpern s iterative sequence for a class of finite nonexpansive mappings in strictly convex and reflexive banach spaces by using banach s limit the main results presented in this paper generalize extend and improve the corresponding results of bauschke the approximation of fixed points of compositions of nonexpansive mappings in hilbert spaces j math anal appl 202 1996 150 159 halpern fixed points of nonexpansive maps bull am math soc 73 1967 957 961 shioji and takahashi strong convergence of approximated sequences for nonexpansive mappings in banach spaces proc am math soc 125 1997 3641 3645 takahashi et al approximation of common fixed points of a family of finite nonexpansive mappings in banach spaces sci math jpn 56 2002 475 480 wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 xu another control condition in an iterative method for nonexpansive mappings bull austral math soc 65 2002 109 113 remarks on an iterative method for nonexpansive mappings commun appl nonlinear anal 10 2003 67 75 and others

ordered linear smoothers this paper deals with the following approach for estimating the mean mu of an n dimensional random vector y first a family s of n x n matrices is specified then an element s is an element of s is selected by mallows c l and mu s y the case is considered that s is an ordered linear smoother according to some easily interpretable qualitative conditions examples include linear smoothing procedures in nonparametric regression as e g smoothing splines minimax spline smoothers and kernel estimators stochastic probability bounds are given for the difference 1 n parallel to mu s y parallel to 2 2 1 n parallel to mu s mu y parallel to 2 2 where s mu denotes the minimizer of 1 n parallel to mu s y parallel to 2 2 for s is an element of s these probability bounds are generalized to the situation that s is the union of a moderate number of ordered linear smoothers the results complement work by li on the asymptotic optimality of c l implications for nonparametric regression are studied in detail it is shown that there exists a direct connection between james stein estimation and the use of smoothing procedures leading to a decision theoretic justification of the latter further conclusions concern the choice of the order of a smoothing spline or a minimax spline smoother and the rates of convergence of smoothing parameters

strong convergence of viscosity approximation methods for finding zeros of accretive operators in banach spaces abstract in this paper we introduce a composite iterative scheme by viscosity approximation method for finding a zero of an accretive operator in banach spaces then we establish strong convergence theorems for the composite iterative scheme the main theorems improve and generalize the recent corresponding results of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 qin and su x qin y su approximation of a zero point of accretive operator in banach spaces j math anal appl 329 2007 415 424 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 as well as aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 benavides et al t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 chen and zhu r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory and appl 2006 2006 1 10 and kamimura and takahashi s kamimura w takahashi approximation solutions of maximal monotone operators in hilberts spaces j approx theory 106 2000 226 240

hybrid shrinkage estimators using penalty bases for the ordinal one way layout this paper constructs improved estimators of the means in the gaussian saturated one way layout with an ordinal factor the least squares estimator for the mean vector in this saturated model is usually inadmissible the hybrid shrinkage estimators of this paper exploit the possibility of slow variation in the dependence of the means on the ordered factor levels but do not assume it and respond well to faster variation if present to motivate the development candidate penalized least squares pls estimators for the mean vector of a one way layout are represented as shrinkage estimators relative to the penalty basis for the regression space this canonical representation suggests further classes of candidate estimators for the unknown means monotone shrinkage ms estimators or soft thresholding st estimators or most generally hybrid shrinkage hs estimators that combine the preceding two strategies adaptation selects the estimator within a candidate class that minimizes estimated risk under the gaussian saturated one way layout model such adaptive estimators minimize risk asymptotically over the class of candidate estimators as the number of factor levels tends to infinity thereby adaptive hs estimators asymptotically dominate adaptive ms and adaptive st estimators as well as the least squares estimator local annihilators of polynomials among them difference operators generate penalty bases suitable for a range of numerical examples in case studies adaptive hs estimators recover high frequency details in the mean vector more reliably than pls or ms estimators and low frequency details more reliably than st estimators

on the convergence of han s method for convex programming with quadratic objective we present an iterative method for minimizing strictly convex quadratic functions over the intersection of a finite number of convex sets the method consists in computing projections onto the individual sets simultaneously and the new iterate is a convex combination of those projections we give convergence proofs even for the inconsistent case i e when the intersection of the sets is empty

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail

the approximation of fixed points of compositions of nonexpansive mappings in hilbert space determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences an algorithm for finding common fixed points of nonexpansive mappings in hilbert space essentially due to halpern is analyzed the main theorem extends wittmann s recent work and partially generalizes a result by lions algorithms of this kind have been applied to the convex feasibility problem

an implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings abstract let h be a hilbert space consider on h a sequence of nonexpansive mappings t n with common fixed points a finite family of equilibrium functions g i i 1 k a contraction f with coefficient 0 1 and a strongly positive linear bounded operator a with coefficient 0 let 0 assuming there are common equilibrium points of the family g i i 1 k which are also fixed points for t n we define a suitable sequence which strongly converges to the unique such point which also satisfies the variational inequality a f x x x 0 for all the x in the intersection of the equilibrium points and the common fixed points of the sequence t n

on general systems of variational inequalities in this paper we present a new relaxed viscosity approximation method and prove the strong convergence of the method to a common fixed point of finitely many nonexpansive mappings and a strict pseudocontraction that also solves a suitable equilibrium problem and a general system of variational inequalities