testing for cointegration using partially linear models abstract a partially linear model of cointegration is developed where stationary covariates enter nonparametrically we propose tests for cointegration using singular values of the estimated autoregressive matrix the tests are based on eigenvalues of standardized matrices and are relatively simple to compute asymptotic theory of the proposed test is developed it is shown that the limiting distribution of the proposed test is similar to that of several tests in the recent literature a gamma approximation of the distribution is discussed to facilitate inference finite sample properties of the proposed procedure are illustrated in some limited monte carlo experiments an empirical application to us macroeconomic time series is conducted to highlight the approach

generalized partially linear single index models abstract the typical generalized linear model for a regression of a response y on predictors x z has conditional mean function based on a linear combination of x z we generalize these models to have a nonparametric component replacing the linear combination t 0x t 0z by 0 t 0x t 0z where 0 is an unknown function we call these generalized partially linear single index models gplsim the models include the single index models which have 0 0 using local linear methods we propose estimates of the unknown parameters 0 0 and the unknown function 0 and obtain their asymptotic distributions examples illustrate the models and the proposed estimation methodology

boundary susceptibility in the open xxz chain in the first part we calculate the boundary susceptibility b in the open xxz chain at zero temperature and arbitrary magnetic field h by the bethe ansatz we present analytical results for the leading terms when h where is a known scale and a numerical solution for the entire range of fields in the second part we calculate susceptibility profiles near the boundary at finite temperature t numerically by using the density matrix renormalization group for transfer matrices and analytically for t 1 by field theoretical methods finally we compare b at finite temperature with a low temperature asymptotics which we obtain by combining our bethe ansatz result with recent predictions from bosonization

efficient estimates in semiparametric additive regression models with unknown error distribution several authors have shown how to efficiently estimate beta in the semiparametric additive model y x beta g t text error g t smooth but unknown when the error distribution is normal however the general theory suggests that efficient estimation should be possible for general error distributions with finite fisher information even when the error distribution is unknown in this note we construct a sequence of estimators which achieves this goal under technical assumptions

steepest descent method with a generalized armijo search for quasiconvex functions on riemannian manifolds this paper extends the full convergence of the steepest descent method with a generalized armijo search and a proximal regularization to solve minimization problems with quasiconvex objective functions on complete riemannian manifolds previous convergence results are obtained as particular cases and some examples in non euclidian spaces are given in particular our approach can be used to solve constrained minimization problems with nonconvex objective functions in euclidian spaces if the set of constraints is a riemannian manifold and the objective function is quasiconvex in this manifold

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

conformal anomaly and critical exponents of the spin 1 takhtajan babujian model the authors consider the critical behaviour of the spin 1 hamiltonian of the takhtajan babujian model the bethe ansatz equations for this antiferromagnet in a finite chain are investigated analytically and numerically the conformal anomaly and critical exponents are obtained by exploiting their relations with the eigenspectrum of the finite system the results strongly support the conjecture that the wess zumino witten non linear sigma model with topological charge k 2 is the underlying field theory for this statistical mechanics model

quenched annealed and functional large deviations for one dimensional random walk in random environment suppose that the integers are assigned random variables i taking values in the unit interval which serve as an environment this environment defines a random walk x n called a rwre which when at i moves one step to the right with probability i and one step to the left with probability 1 i when the i sequence is i i d greven and den hollander 1994 proved a large deviation principle for x n n conditional upon the environment with deterministic rate function we consider in this paper large deviations both conditioned on the environment quenched and averaged on the environment annealed for the rwre in the ergodic environment case the annealed rate function is the solution of a variational problem involving the quenched rate function and specific relative entropy we also give a detailed qualitative description of the resulting rate functions our techniques differ from those of greven and den hollander and allow us to present also a trajectorial quenched large deviation principle

the relative efficiency of liu type estimator in a partially linear model in this paper we study the partially linear model y x b f e we introduce a new liu type estimator in a partially linear model then we compared the new estimator with the two step estimator in the mean squared error sense finally we give a simulation study to explain the validity and feasibility of the approach

efficient statistical inference procedures for partially nonlinear models and their applications motivated by an analysis of a real data set in ecology we consider a class of partially nonlinear models where both a nonparametric component and a parametric component are present we develop two new estimation procedures to estimate the parameters in the parametric component consistency and asymptotic normality of the resulting estimators are established we further propose an estimation procedure and a generalized f test procedure for the nonparametric component in the partially nonlinear models asymptotic properties of the newly proposed estimation procedure and the test statistic are derived finite sample performance of the proposed inference procedures are assessed by monte carlo simulation studies an application in ecology is used to illustrate the proposed methods

component identification and estimation in nonlinear high dimensional regression models by structural adaptation this article proposes a new method of analysis of a partially linear model whose nonlinear component is completely unknown the target of analysis is identification of the set of regressors that enter in a nonlinear way in the model function and complete estimation of the model including slope coefficients of the linear component and the link function of the nonlinear component the procedure also allows selection of the significant regression variables we also develop a test of linear hypothesis against a partially linear alternative or more generally a test that the nonlinear component is m dimensional for m 0 1 2 the approach proposed in this article is fully adaptive to the unknown model structure and applies under mild conditions on the model the only important assumption is that the dimensionality of nonlinear component is relatively small the theoretical results indicate that the procedure provides a prescribed level of the identification error and estimates the linear component with

semiparametric regression analysis with missing response at random we develop inference tools in a semiparametric partially linear regression model with missing response data a class of estimators is defined that includes as special cases a semiparametric regression imputation estimator a marginal average estimator and a marginal propensity score weighted estimator we show that any of our class of estimators is asymptotically normal the three special estimators have the same asymptotic variance they achieve the semiparametric efficiency bound in the homoscedastic gaussian case we show that the jackknife method can be used to consistently estimate the asymptotic variance our model and estimators are defined with a view to avoid the curse of dimensionality which severely limits the applicability of existing methods the empirical likelihood method is developed it is shown that when missing responses are imputed using the semiparametric regression method the empirical log likelihood is asymptotically a scaled chi squared variable an adjusted empirical log likel

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

estimation for a partial linear single index model in this paper we study the estimation for a partial linear single index model a two stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index as well as the parameters in the linear component of the model asymptotic normality is established for both parametric components for the index a constrained estimating equation leads to an asymptotically more efficient estimator than existing estimators in the sense that it is of a smaller limiting variance the estimator of the nonparametric link function achieves optimal convergence rates and the structural error variance is obtained in addition the results facilitate the construction of confidence regions and hypothesis testing for the unknown parameters a simulation study is performed and an application to a real dataset is illustrated the extension to multiple indices is briefly sketched

non abelian gauge theory for quantum heisenberg antiferromagnetic chain a continuum su 2s u 1 gauge theory for a heisenberg antiferromagnet with arbitrary spin s is obtained we show that the level 1 su 2 wzw model with a certain marginally irrelevant perturbation describes the low energy phenomena of the heisenberg model with spin 1 2 the model with spins other than 1 2 can be described in the level 2s su 2 wzw model with a certain relevant perturbation we give a qualitative explanation of the haldane conjecture for heisenberg antiferromagnets

the operator content of the exactly integrable su n magnets the operator content of the exactly integrable models associated with the su n lie algebras with periodic boundaries are studied the authors results were obtained from a numerical and analytical analysis of the associated bethe ansatz equations the resulting spectra indicate that the ferromagnetic and antiferromagnetic models have different operator content for n 2 being realizations of distinct modular invariant solutions

semiparametric inference in a partial linear model in a partial linear model the dependence of a response variate y on covariates w x is given by y w x e where e is independent of w x with densities g and f respectively in this paper an asymptotically efficient estimator of is constructed solely under mild smoothness assumptions on the unknown f and g thereby removing the assumption of finite residual variance on which all least squares type estimators available in the literature are based

operator dimensions and surface exponents for the non linear schrodinger model at t 0 using the euler maclaurin formula the authors compute finite size corrections to the ground and excited state energies and momenta this enables them to obtain all possible operator scaling dimensions at the critical point t 0 and surface exponents for a variety of boundary conditions they extend the predictions of conformal invariance to include green functions with oscillating terms

penalized quasi likelihood estimation in partial linear models consider a partial linear model where the expectation of a random variable y depends on covariates x z through f theta 0 x m 0 z with theta 0 an unknown parameter and m 0 an unknown function we apply the theory of empirical processes to derive the asymptotic properties of the penalized quasi likelihood estimator

positive shrinkage improved pretest and absolute penalty estimators in partially linear models shrinkage estimators of a partially linear regression parameter vector are constructed by shrinking estimators in the direction of the estimate which is appropriate when the regression parameters are restricted to a linear subspace we investigate the asymptotic properties of positive stein type and improved pretest semiparametric estimators under quadratic loss under an asymptotic distributional quadratic risk criterion their relative dominance picture is explored analytically it is shown that positive stein type semiparametric estimators perform better than the usual stein type and least square semiparametric estimators and that an improved pretest semiparametric estimator is superior to the usual pretest semiparametric estimator we also consider an absolute penalty type estimator for partially linear models and give a monte carlo simulation comparisons of positive shrinkage improved pretest and the absolute penalty type estimators the comparison shows that the shrinkage method performs better than the absolute penalty type estimation method when the dimension of the parameter space is much larger than that of the linear subspace

relaxation to equilibrium for two dimensional disordered ising systems in the griffiths phase we consider glauber type dynamics for two dimensional disordered magnets of ising type we prove that if the disorder averaged influence of the boundary condition is sufficiently small in the equilibrium system then the corresponding glauber dynamics is ergodic with probability one and the disorder average c t of time autocorrelation function satisfies for large t for the standard two dimensional dilute ising ferromagnet with i i d random nearest neighbor couplings taking the values 0 or j 0 0 our results apply even if the active bonds percolate and j 0 is larger than the critical value j c of the corresponding pure ising model for the same model we also prove that in the whole griffiths phase the previous upper bound is optimal this implies the existence of a dynamical phase transition which occurs when j crosses j c

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

invaded cluster algorithm for potts models the invaded cluster algorithm a method for simulating phase transitions is described in detail theoretical albeit nonrigorous justification of the method is presented and the algorithm is applied to potts models in two and three dimensions the algorithm is shown to be useful for both first order and continuous transitions and evidently provides an efficient way to distinguish between these possibilities the dynamic properties of the invaded cluster algorithm are studied numerical evidence suggests that the algorithm has no critical slowing for ising models s1063 651x 96 09208 2

conformal theory of spin correlations in the semi infinite 3 state potts and self dual zn models in the conformal theory the magnetization operator of the critical 3 state potts or self dual z3 model is degenerate at level 6 solving a sixth order differential equation the authors calculate the bulk 4 spin correlation function and the spin spin correlation function in the half space the spin spin correlation function of the semi infinite self dual zn model is also obtained for arbitrary n both free and fixed spin boundary conditions are considered

second order approximation in the partially linear regression model we examine the second order properties of various quantities of interest in the partially linear regression model we obtain a stochastic expansion with remainder op n 2 4 where u 1 2 for the standardized semiparametric least squares estimator a standard error estimator and a studentized statistic we use the second order expansions to correct the standard error estimates for second order effects and to define a method of bandwidth choice a monte carlo experiment provides favorable evidence on our method of bandwidth choice

semiparametric additive regression a simple estimator for is proposed for the model y x g 1 error g smooth but unknown the approach is to approximate the estimating equation obtained from a semiparametric likelihood and in the simplest case reduces to minimizing the distance between the pseudoresiduals y x and a local linear cross validated estimate of them when the errors are independent with finite variance the bias and variance of the estimate are computed and compared against the least squares estimate with g known

the effect of attractive monomer monomer interactions on adsorption of a polymer chain the authors have used transfer matrix techniques to study a model of polymer adsorption and collapse they consider the conventional model of a self avoiding walk with attractive nearest neighbour interactions on the square lattice and introduce adsorbing boundaries the numerical results are consistent with the existence of a multicritical point where the adsorption and collapse transitions coincide and suggest that the adsorption transition of a collapsed polymer chain in first order there is also clear evidence that the collapse transition lowers the adsorption temperature estimates of the surface scaling dimensions at the ordinary theta transition support the conjecture of seno and stella 1988 that the surface critical behaviour at the theta and theta points belong to different universality classes

discontinuity of the percolation density in one dimensional 1 x y 2 percolation models we consider one dimensional percolation models for which the occupation probability of a bond kx y has a slow power decay as a function of the bond s length for independent models and with suitable reformulations also for more general classes of models it is shown that i no percolation is possible if for short bondskx y p 1 this dichotomy resembles one for the magnetization in 1 x y 2 ising models which was first proposed by thouless and further supported by the renormalization group flow equations of anderson yuval and hamann the proofs of the above percolation phenomena involve rigorous renormalization type arguments of a different sort

marginal extended perturbations in two dimensions and gap exponent relations the most general form of a marginal extended perturbation in a two dimensional system is deduced from scaling considerations it includes as particular cases extended perturbations decaying either from a surface a line or a point for which exact results have been previously obtained the first order corrections to the local exponents which are functions of the amplitude of the defect are deduced from a perturbation expansion of the two point correlation functions assuming covariance under conformal transformation the perturbed system is mapped onto a cylinder working in the hamiltonian limit the first order corrections to the lowest gaps are calculated for the ising model the results confirm the validity of the gap exponent relations for the perturbed system

partial linear regression models for clustered data this article considers the analysis of clustered data via partial linear regression models adopting the idea of modeling the within cluster correlation from the method of generalized estimating equations a least squares type estimate of the slope parameter is obtained through piecewise local polynomial approximation of the nonparametric component this slope estimate has several advantages a it attains n1 2 consistency without undersmoothing b it is efficient when correct within cluster correlation is used assuming multivariate normality of the error c the preceding properties hold regardless of whether or not the nonparametric component is of cluster level and d this estimation method naturally extends to deal with generalized partial linear models simulation studies and a real example are presented in support of the theory

penalized partially linear models using sparse representations with an application to fmri time series in this paper we consider modeling the nonparametric component in partially linear models plms using linear sparse representations e g wavelet expansions two types of representations are investigated namely orthogonal bases complete and redundant overcomplete expansions for bases we introduce a regularized estimator of the nonparametric part the important contribution here is that the nonparametric part can be parsimoniously estimated by choosing an appropriate penalty function for which the hard and soft thresholding estimators are special cases this allows us to represent in an effective manner a broad class of signals including stationary and or nonstationary signals and avoids excessive bias in estimating the parametric component we also give a fast estimation algorithm the method is then generalized to handle the case of overcomplete representations a large scale simulation study is conducted to illustrate the finite sample properties of the estimator the estimator is finally applied to real neurophysiological functional magnetic resonance imaging mri data sets that are suspected to contain both smooth and transient drift features

some exact results for moments of 2d directed animals using computer enumerations and the algebraic approximant method of series analysis several new exact results have been found for moments of width perimeter and loops for directed animals on the square and triangular lattices a proof using q series is given for exact solutions for widths on both the square and triangular lattices

gauge symmetries and percolation in j ising spin glasses we consider the j spin glass on a finite graph g v e with i i d couplings our approach considers the z2 local gauge invariance of the system we see the gauge group as a graph theoretic linear code over gf 2 the gauge is fixed by choosing a convenient linear supplement of assuming some relation between the disorder parameter p and the inverse temperature of the thermal bath pb we study percolation in the random interaction random cluster model and extend the results to dilute spin glasses

a general euclidean connection for the so n m lie algebra and the algebraic approach to scattering we obtain a general euclidean connection for the so n m lie algebra this euclidean connection allows an algebraic derivation of the s matrix and it reduces to the known connection in suitable circumstances

inference on the primary parameter of interest with the aid of dimension reduction estimation summary as high dimensional data become routinely available in applied sciences sufficient dimension reduction has been widely employed and its research has received considerable attention however with the majority of sufficient dimension reduction methodology focusing on the dimension reduction step complete analysis and inference after dimension reduction have yet to receive much attention we couple the strategy of sufficient dimension reduction with a flexible semiparametric model we concentrate on inference with respect to the primary variables of interest and we employ sufficient dimension reduction to bring down the dimension of the regression effectively extensive simulations demonstrate the efficacy of the method proposed and a real data analysis is presented for illustration

on asymptotically efficient estimation in semiparametric models on presente une methode generale qui ameliore et modifie la construction de bickel 1982 des estimateurs adaptatifs

semiparametric estimates of the relation between weather and electricity sales abstract a nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data this accommodates introduction of covariates timing adjustments due to the actual billing schedules and serial correlation the procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross validation criterion introduced by craven and wahba 1979 estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines

on the swendsen wang dynamics i exponential convergence to equilibrium we present rigorous results on the exponential convergence to equilibrium for the swendsen wang stochastic dynamics for thed dimensional ising ferromagnet with external magnetic fieldh in the thermodynamic limit we consider various situations mainly in the low temperature regime in which boundary conditions are homogeneous and parallel or opposite to the external field in the latter case we relate directly the tunneling from the metastable phase to the stable one with the exponential convergence to equilibrium

relaxation of disordered magnets in the griffiths regime we study the relaxation to equilibrium of discrete spin systems with random finite range not necessarily ferromagnetic interactions in the griffiths regime we prove that the speed of convergence to the unique reversible gibbs measure is almost surely faster than any stretched exponential at least if the probability distribution of the interaction decays faster than exponential e g gaussian furthermore if the interac tion is uniformly bounded the average over the disorder of the time autocorrelation function goes to equilibrium as exp k log t d d 1 in d 1 in agreement with previous results obtained for the dilute ising model

a two way semilinear model for normalization and analysis of cdna microarray data a basic question in analyzing cdna microarray data is normalization the purpose of which is to remove systematic bias in the observed expression values by establishing a normalization curve across the whole dynamic range a proper normalization procedure ensures that the normalized intensity ratios provide meaningful measures of relative expression levels we propose a two way semilinear model tw slm for normalization and analysis of microarray data this method does not make the usual assumptions underlying some of the existing methods for example it does not assume that the percentage of differentially expressed genes is small or that there is symmetry in the expression levels of up regulated and down regulated genes as required in the lowess normalization method the tw slm also naturally incorporates uncertainty due to normalization into significance analysis of microarrays we use a semiparametric approach based on polynomial splines in the tw slm to estimate the normalization curves and the no

a simple consistent bootstrap test for a parametric regression function abstract a simple consistent test is considered and a bootstrap method is proposed for testing a parametric regression functional form it is shown that the bootstrap method gives a more accurate approximation to the null distribution of the test than the asymptotic normal theory result we also propose a consistent test for testing a parametric partially linear model versus a semiparametric partially linear alternative monte carlo simulations suggest that the bootstrap test performs well based on wild bootstrap critical values

empirical likelihood confidence regions in a partially linear single index model summary empirical likelihood based inference for the parameters in a partially linear singleindex model is investigated unlike existing empirical likelihood procedures for other simpler models if there is no bias correction the limit distribution of the empirical likelihood ratio cannot be asymptotically tractable to attack this difficulty we propose a bias correction to achieve the standard x2 limit the bias corrected empirical likelihood ratio shares some of the desired features of the existing least squares method the estimation of the parameters is not needed when estimating nonparametric functions in the model undersmoothing for ensuring in consistency of the estimator of the parameters is avoided the bias corrected empirical likelihood is self scale invariant and no plug in estimator for the limiting variance is needed furthermore since the index is of norm 1 we use this constraint as information to increase the accuracy of the confidence regions smaller regions at the same nominal level as a by product our approach of using bias correction may also shed light on nonparametric estimation in model checking for other semiparametric regression models a simulation study is carried out to assess the performance of the bias corrected empirical likelihood an application to a real data set is illustrated

the number of metastable states in the projection rule neural network we calculate the direct average n of the number of metastable states in the projection rule neural network by means of the saddle point method n is obtained as a function of the hamming distance g to a given pattern stability gamma and energy e the critical storage capacity of the model is calculated the examination of the energy dependence of n leads to lower bounds for the energies of the spin glass states

non analytic finite size corrections for the heisenberg chain in a magnetic field with free and twisted boundary conditions the finite size energy spectrum of the anisotropic heisenberg chain in an external magnetic field is calculated for free and twisted boundary conditions as with periodic boundary conditions it is found that the spectra exhibit non analytical terms which do not fit into the form predicted on the basis of conformal invariance unless extra commensurability conditions between the size of the system and the external field are introduced taking these conditions into account some scaling dimensions for associated models are derived

linear or nonlinear automatic structure discovery for partially linear models partially linear models provide a useful class of tools for modeling complex data by naturally incorporating a combination of linear and nonlinear effects within one framework one key question in partially linear models is the choice of model structure that is how to decide which covariates are linear and which are nonlinear this is a fundamental yet largely unsolved problem for partially linear models in practice one often assumes that the model structure is given or known and then makes estimation and inference based on that structure alternatively there are two methods in common use for tackling the problem hypotheses testing and visual screening based on the marginal fits both methods are quite useful in practice but have their drawbacks first it is difficult to construct a powerful procedure for testing multiple hypotheses of linear against nonlinear fits second the screening procedure based on the scatterplots of individual covariate fits may provide an educated guess on the regressio

minimax estimates in a semiparametric model abstract the statistical analysis of multidimensional data has been greatly influenced by the widespread use of computer intensive smoothing techniques these techniques allow one to look at the dependency of a response on several covariates without actually specifying the exact form of that dependency nevertheless when the response s dependency on some subset of the covariates can be assumed to be say linear common sense dictates incorporating this assumption into the estimation technique in the semiparametric model with covariates x and t the response y is modeled as the sum of three components g t with g unknown lying in an infinite dimensional space a linear component x and random error if were the parameter of interest with the function g treated as a nuisance parameter the conservative statistician would be led to a minimax approach with the estimate of minimizing the worst that could happen over a specified class of functions of course the class of functions should be one

excited states in the twisted xxz spin chain we compute the finite size spectrum for the spin chain with twisted boundary conditions for anisotropy in the regime and arbitrary twist the string hypothesis is employed for treating complex excitations the bethe ansatz equtions are solved within a coupled nonlinear integral equation approach with one equation for each type of string the root of unity quantum group invariant periodic chain reduces to the chain with a set of twist boundary conditions an integer multiple of for this model the restricted hilbert space corresponds to a unitary conformal field theory and we recover all primary states in the kac table in terms of states with specific twist and strings

a steepest descent method for vector optimization in this work we propose a cauchy like method for solving smooth unconstrained vector optimization problems when the partial order under consideration is the one induced by the nonnegative orthant we regain the steepest descent method for multicriteria optimization recently proposed by fliege and svaiter we prove that every accumulation point of the generated sequence satisfies a certain first order necessary condition for optimality which extends to the vector case the well known gradient equal zero condition for real valued minimization finally under some reasonable additional hypotheses we prove global convergence to a weak unconstrained minimizer as a by product we show that the problem of finding a weak constrained minimizer can be viewed as a particular case of the so called abstract equilibrium problem

inhomogeneous percolation problems and incipient infinite clusters the authors consider inhomogeneous percolation models with density pc f x and examine the forms of f x which produce incipient structures taking f x approximately mod x mod lambda and assuming the existence of a correlation length exponent v for the homogeneous percolation model they prove that in d 2 the borderline value of lambda is lambda b 1 v if lambda 1 v then with probability one there is no infinite cluster while if lambda 2 the models studied suggest what sort of incipient objects should be examined in random surface models

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

the phase boundary in dilute and random ising and potts ferromagnets the authors present an approach to dilute ising and potts models based on the fortuin kasteleyn random cluster representation which is simultaneously rigorous intuitive and surprisingly simple their analysis yields with no dimensional restrictions or other caveats the following asymptotic form of the phase boundary for the regular dilute model in which bonds have constant ferromagnetic coupling j with probability p and are vacant with probability 1 p the critical temperature scales as exp j ktc p approximately mod p pc mod implying that the crossover exponent is phi 1 if the constant couplings are replaced by a distribution f j with mass near j 0 quite different crossover behaviour is observed for example if f j approximately jalpha then for p near pc tc p approximately mod p pc mod 1 alpha

convergence rates for parametric components in a partly linear model consider the regression model y i x i beta g t i e i for i 1 cdots n here g is an unknown holder continuous function of known order p in r beta is a k times 1 parameter vector to be estimated and e i is an unobserved disturbance such a model is often encountered in situations in which there is little real knowledge about the nature of g a piecewise polynomial g n is proposed to approximate g the least squares estimator hat beta is obtained based on the model y i x i beta g n t i e i it is shown that hat beta can achieve the usual parametric rates n 1 2 with the smallest possible asymptotic variance for the case that x and t are correlated

local convergence of the proximal point method for a special class of nonconvex functions on hadamard manifolds abstract local convergence analysis of the proximal point method for a special class of nonconvex functions on hadamard manifold is presented in this paper the well definedness of the sequence generated by the proximal point method is guaranteed moreover it is proved that each cluster point of this sequence satisfies the necessary optimality conditions and under additional assumptions its convergence for a minimizer is obtained

gaussian process based bayesian semiparametric quantitative trait loci interval mapping in linkage analysis it is often necessary to include covariates such as age or weight to increase power or avoid spurious false positive findings however if a covariate term in the model is specified incorrectly e g a quadratic term misspecified as a linear term then the inclusion of the covariate may adversely affect power and accuracy of the identification of quantitative trait loci qtl furthermore some covariates may interact with each other in a complicated fashion we implement semiparametric models for single and multiple qtl mapping both mapping methods include an unspecified function of any covariate found or suspected to have a more complex than linear but unknown relationship with the response variable they also allow for interactions among different covariates this analysis is performed in a bayesian inference framework using markov chain monte carlo the advantages of our methods are demonstrated via extensive simulations and real data analysis

tests of specification for parametric and semiparametric models abstract this paper provides a general framework for constructing specification tests for parametric and semiparametric models the paper develops new specification tests using the general framework in particular specification tests for semiparametric partially linear regression and sample selection models are introduced the results apply in time series and cross sectional contexts the method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes

the gradient and heavy ball with friction dynamical systems the quasiconvex case we consider the gradient system dot x t nabla phi x t 0 and the so called heavy ball with friction dynamical system ddot x t lambda dot x t nabla phi x t 0 as well as an implicit discrete proximal version of it and study the asymptotic behavior of their solutions in the case of a smooth and quasiconvex objective function minimization properties of trajectories are obtained under various additional assumptions we finally show a minimizing property of the heavy ball method which is not shared by the gradient method the genericity of the convergence of each trajectory at least when is a morse function towards local minimum of

kernel smoothing in partial linear models on considere deux methodes d estimation l une reliee aux splines de lissage partiels l autre motivee par une analyse de residus partielle

consistent covariate selection and post model selection inference in semiparametric regression this paper presents a model selection technique of estimation in semiparametric regression models of the type y i x i f t i w i i 1 n the parametric and nonparametric components are estimated simultaneously by this procedure estimation is based on a collection of finite dimensional models using a penalized least squares criterion for selection we show that by tailoring the penalty terms developed for nonparametric regression to semiparametric models we can consistently estimate the subset of nonzero coefficients of the linear part moreover the selected estimator of the linear component is asymptotically normal

sieve maximum likelihood estimator for semiparametric regression models with current status data in a randomized controlled clinical trial study where the response variable of interest is the time to occurrence of a certain event it is often too expensive or even impossible to observe the exact time however the current status of the subject at a random time of inspection is much more natural feasible and practical in terms of cost effectiveness this article considers a semiparametric regression model that consists of parametric and nonparametric regression components a sieve maximum likelihood estimator mle is proposed to estimate the regression parameter allowing exploration of the nonlinear relationship between a certain covariate and the response function asymptotic properties of the proposed sieve mles are discussed under some mild conditions the estimators are shown to be strongly consistent moreover the estimators of the unknown parameters are asymptotically efficient and normally distributed and the estimator of the nonparametric function has an optimal convergence rate simula

convergence to equilibrium of random ising models in the griffiths phase we consider glauber type dynamics for disordered ising spin systems with nearest neighbor pair interactions in the griffiths phase we prove that in a nontrivial portion of the griffiths phase the system has exponentially decaying correlations of distant functions with probability exponentially close to 1 this condition has in turn been shown elsewhere to imply that the convergence to equilibrium is faster than any stretched exponential and that the average over the disorder of the time autocorrelation function goes to equilibrium faster than exp k log t d d 1 we then show that for the diluted ising model these upper bounds are optimal

ridge estimation of a semiparametric regression model considered the semiparametric regression model li aitx s ti i i 1 2 n firstly ridge estimators of both parameters and nonparameters are attained without a restrained design matrix secondly the ridge estimator will be compared with two steps estimation under a mean square error and some conditions in which the former excels the latter are given finally the validity and feasibility of the method are illustrated by a simulating example

estimation in a semiparametric partially linear errors in variables model we consider the partially linear model relating a response y to predictors x t with mean function x t g t when the x s are measured with additive error the semiparametric likelihood estimate of severini and staniswalis leads to biased estimates of both the parameter and the function g when measurement error is ignored we derive a simple modification of their estimator which is a semiparametric version of the usual parametric correction for attenuation the resulting estimator of is shown to be consistent and its asymptotic distribution theory is derived consistent standard error estimates using sandwich type ideas are also developed

efficiency of a liu type estimator in semiparametric regression models in this paper we consider the semiparametric regression model y x b f e recently hu 11 proposed ridge regression estimator in a semiparametric regression model we introduce a liu type combined ridge stein estimator lte in a semiparametric regression model firstly liu type estimators of both b and f are attained without a restrained design matrix secondly the lte estimator of b is compared with the two step estimator in terms of the mean square error we describe the almost unbiased liu type estimator in semiparametric regression models the almost unbiased liu type estimator is compared with the liu type estimator in terms of the mean squared error matrix a numerical example is provided to show the performance of the estimators

semiparametric regression in likelihood based models abstract a weighted likelihood is used to estimate the parameters in a semiparametric model involving two covariates and allowing an association between the covariates the development is for arbitrary but specified densities of the observations the estimators are consistent and asymptotically normal hypothesis testing of the parametric component can be performed using a wald test simulations and analysis of data with bernoulli observations demonstrate the estimators application speckman developed kernel estimators where the conditional density of the observations is normal with p parametric covariates speckman s estimators and the new estimators are asymptotically equivalent with the bias of speckman s estimators being smaller as an example we study the relationship between a binary response indicating the occurrence of an intraoperative cardiac complication icc in vascular surgery patients and two risk factors duration of the operation or and asa score which is an evaluation of the patien

conformal invariance and the operator content of the xxz model with arbitrary spin the authors are concerned with the critical properties of the anisotropic heisenberg chain or xxz model with arbitrary integer or half integer spin the eigenspectra of these hamiltonians with periodic boundaries are calculated for finite chains by solving numerically their associated bethe ansatz equations the resulting spectra are found to be in accord with the predictions of conformal invariance and the operator content is identified for lattices with an even and odd number of sites the results for spin 1 and spin 3 2 indicate that the conformal anomaly c for these models in the gapless regime has the value c 3s 1 s independent of the anisotropy and the exponents vary continuously with the anisotropy as in the eight vertex model the operator content of these models indicate that the underlying field theory governing these critical spin s models is described by composite fields formed by the product of gaussian and z n fields with n 2s finally some of the irrelevant operators which produce the leading finite size corrections of the eigenenergies are identified

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

variable selection in semiparametric regression modeling in this paper we are concerned with how to select significant variables in semiparametric modeling variable selection for semiparametric regression models consists of two components model selection for nonparametric components and select significant variables for parametric portion thus it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel this leads to very heavy computational burden in this paper we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood the newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously this allows us to establish the sampling properties of the resulting estimate we first establish the rate of convergence of the resulting estimate with proper choices of penalty functions and regularization parameters we then establish the asymptotic normality of the resulting estimate and further demonstrate that the proposed procedures perform as well as an oracle procedure semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component we investigate the asymptotic behavior of the proposed test and demonstrate its limiting null distribution follows a chi squared distribution which is independent of the nuisance parameters extensive monte carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures