strong convergence theorem for nonexpansive mappings on star shaped sets in hilbert spaces abstract in this paper using the concept of attractive points of a nonlinear mapping we obtain a strong convergence theorem of halpern s type 7 for nonexpansive mappings in a star shaped subset of a hilbert space using this result we obtain a new fixed point theorem and a strong convergence theorem which generalizes wittmann s theorem 26

exact large deviation bounds up to t c for the ising model in two dimensions we prove an upper large deviation bound for the block spin magnetization in the 2d ising model in the phase coexistence region the precise rate given by the wulff construction is shown to hold true for all c combined with the lower bounds derived in i those results yield an exact second order large deviation theory up to the critical temperature

seminonparametric bayesian estimation of the asymptotically ideal production model abstract recently it has been shown that seminonparametric methods can be used to produced high quality approximations to a firm s technology unlike the local approximations provided by the conventional class of flexible functional forms seminonparametric methods generate global spans within large classes of functions however that approach usually spans a much larger space than the neoclassical function space relevant to most production modeling an exception is the asymptotically ideal model aim generated from the muntz szatz series expansion since every basis function in that expansion is within the neoclassical function space a straightforward method exists for imposing neoclassical regularity when all factors are substitutes since the relevant constraints are inequality restrictions we implement the approach using bayesian methods to avoid the problems of sampling distribution truncation that would occur from sampling theoretic methods we further discuss the relevant extensions that would permit complementary factors nonconstant returns to scale and technological change

likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

hybrid mann halpern iteration methods for nonexpansive mappings and semigroups abstract in this paper we introduce some new iteration methods based on the hybrid method in mathematical programming the mann s iterative method and the halpern s method for finding a fixed point of a nonexpansive mapping and a common fixed point of a nonexpansive semigroup hilbert spaces

monte carlo results on several new and existing tests for the error component model abstract the breusch pagan test is a popular test for testing zero variances in a random error component model realizing the one sided nature of this problem honda 1985 derived the one sided lm test for the one way error component model and suggested a handy one sided candidate for the two way error component model in this paper we derive a new one sided test for testing the two way error component model based upon the results of gourieroux holly and monfort 1982 next we derive a lm test for testing zero individual time specific effects assuming that the other time period individual effects are present this is in contrast to the usual lm test which assumes that under the null hypothesis both effects are absent exact power comparisons whenever possible as well as monte carlo experiments are employed to compare the performance of these tests with the corresponding likelihood ratio and anova f tests

large deviations for the 2d ising model a lower bound without cluster expansions we show that a lower large deviation bound for the block spin magnetization in the 2d ising model can be pushed all the way forward toward its correct wulff value for all c

a new sufficient condition for the strong convergence of halpern type iterations abstract the aim of this work is to give a new sufficient condition of the strong convergence of the halpern type iteration for a non expansive self mapping defined on a banach space with a uniformly g teaux differentiable norm several examples satisfying our condition are presented our results not only remove the restriction of the space with the fixed point property for non expansive self mappings but also get rid of the dependence on the convergence of the implicit anchor like continuous path z t in the proof

weak and strong convergence theorems for strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the mann s algorithm generates a sequence x n by the formula x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then x n converges weakly to a fixed point of t however this convergence is in general not strong we then modify mann s algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence this result extends a recent result of nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 from nonexpansive mappings to strict pseudo contractions

equivalences of the large deviation principle for gibbs measures and critical balance in the ising model in this paper we obtain the equivalence of the large deviation principle for gibbs measures with and without an external field for the ising model the equivalence allows us to study the result of competing influences of a positive external fieldh and a negative boundary condition in the cube b h ash 0 for variousb we find a critical balance at a valueb0 ofb

joint tests for zero restrictions on nonnegative regression coefficients summary three tests for zero restrictions on regression coefficients that are known to be nonnegative are considered the classical f test the likelihood ratio test and a one sided t test in a particular direction critical values for the likelihood ratio test are given for the cases of two and three restrictions and the power function is calculated for the case of two restrictions the analysis is conducted in terms of a characterization of the clas all similar tests for the problem of which each of the above tests is a member the likelihood ratio test emerges as the preferred test

constrained variational problem with applications to the ising model we continue our study of the behavior of the two dimensional nearest neighbor ferromagnetic ising model under an external magnetic fieldh initiated in our earlier work we strengthen further a result previously proven by martirosyan at low enough temperature which roughly states that for finite systems with boundary conditions under a positive external field the boundary effect dominates in the system if the linear size of the system is of orderb h withb small enough while ifb is large enough then the external field dominates in the system in our earlier work this result was extended to every subcritical value of the temperature here for every subcritical value of the temperature we show the existence of a critical valueb0 t which separates the two regimes specified above we also find the asymptotic shape of the region occupied by the phase in the second regime which turns out to be a squeezed wulff shape the main step in our study is the solution of the variational problem of finding the curve minimizing the wulff functional which curve is constrained to the unit square other tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field extended to all temperatures below the critical one

testing for garch effects a one sided approach arch models often lie at the boundary of the parameter space under conditional homoskedasticity which invalidates the usual s2 distribution of lr and wald tests although lm tests are not a ected the one sided nature of the alternative hypothesis should result in more powerful tests we propose a simple one sided version of the lm test which is closely related to the kuhn tucker multiplier test we also present critical values for lr wald and one sided lm tests the results of a monte carlo comparison suggest that one sided tests are indeed more powerful than their two sided counterparts 1998 elsevier science s a all rights reserved jel classification c22

strong convergence to common fixed points of families of nonexpansive mappings abstract we introduce iteration schemes for families of nonexpansive mappings in hilbert spaces and prove that the iterates converge strongly to common fixed points of the mappings

second order large deviation estimates for ferromagnetic systems in the phase coexistence region we consider thed dimensional ising model with ferromagnetic nearest neighbor interaction at inverse temperature let m lambda lambda 1 sum limits i in lambda sigma i be the magnetization inside ad dimensional hyper cube be the gibbs state andm be the spontaneous magnetization for such thatm 0 we find a sufficient condition easily verified to hold for large for m a b to decay exponentially with d 1 d when m b m 1 a b ford 2 this sufficient condition is the exponential decay of a connectivity function we also prove a partial converse to this result obtain a sharper result for the magnetization ond 1 dimensional cross sections of the model and prove a similar result ford 2 m a b m and large when free boundary conditions are chosen outside

finite size scaling for the 2d ising model with minus boundary conditions we study the magnetization m l h for the ising model on a large but finite lattice square under the minus boundary conditions using known large deviation results evaluating the balance between the competing effects of the minus boundary conditions and the external magnetic field h we describe the details of its dependence on h as exemplified by the finite size rounding of the infinite volume magnetization discontinuity and its shift with respect to the infinite volume transition point

inference for non stationary time series regression with or without inequality constraints summary we consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non stationary behaviours over time meanwhile the regression parameters may be subject to linear inequality constraints a simple and unified procedure for structural stability checks and parameter inference is proposed in the case where the regression parameters are constrained the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones

non standard inference for augmented double autoregressive models with null volatility coefficients abstract this paper considers an augmented double autoregressive dar model which allows null volatility coefficients to circumvent the over parameterization problem in the dar model since the volatility coefficients might be on the boundary the statistical inference methods based on the gaussian quasi maximum likelihood estimation gqmle become non standard and their asymptotics require the data to have a finite sixth moment which narrows the applicable scope in studying heavy tailed data to overcome this deficiency this paper develops a systematic statistical inference procedure based on the self weighted gqmle for the augmented dar model except for the lagrange multiplier test statistic the wald quasi likelihood ratio and portmanteau test statistics are all shown to have non standard asymptotics the entire procedure is valid as long as the data are stationary and its usefulness is illustrated by simulation studies and one real example

slow droplet driven relaxation of stochastic ising models in the vicinity of the phase coexistence region we consider the stochastic ising models glauber dynamics corresponding to the infinite volume basic ising model in arbitrary dimensiond 2 with nearest neighbor interaction and under a positive external magnetic fieldh under minimal assumptions on the rates of flip so that all the common choices are included we obtain results which state that when the system is at low temperaturet the relaxation time when the evolution is started with all the spins down blows up whenh 0 as exp t hd 1 the precise results are lower and upper bounds of this form moreover after a time which does not scale withh and before a time which also grows as an exponential of a multiple of 1 hd 1 ash 0 the law of the state of the process stays whenh is small close to the minus phase of the same ising model without an external field these results may be considered as a partial vindication of a conjecture raised by aizenman and lebowitz in connection to the metastable behavior of these stochastic ising models

strong convergence theorem for nonexpansive semigroups in hilbert space abstract the purpose of this paper is to prove the strong convergence of a method combining the descent method and the hybrid method in mathematical programming for finding a point in the common fixed point set of a semigroup of nonexpansive mappings in hilbert space

complete analyticity for 2d ising completed we study the behavior of the two dimensional nearest neighbor ferromagnetic ising model under an external magnetic fieldh we extend to every subcritical value of the temperature a result previously proven by martirosyan at low enough temperature and which roughly states that for finite systems with boundary conditions under a positive external field the boundary effect dominates in the bulk if the linear size of the system is of orderb h withb small enough while ifb is large enough then the external field dominates in the bulk as a consequence we are able to complete the proof that complete analyticity for nice sets holds for every value of the temperature and external field in the interior of the uniqueness region in the phase diagram of the model the main tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field and recently extended to all temperatures below the critical one by ioffe

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

strong convergence of the cq method for fixed point iteration processes strong convergence theorems are obtained for the cq method for an ishikawa iteration process a contractive type iteration process for nonexpansive mappings and the proximal point algorithm for maximal monotone operators in hilbert spaces

joint one sided tests of linear regression coefficients abstract the main example of the class of problems considered below is that of testing whether a subset of regression coefficients are jointly zero assuming knowledge of the coefficients signs if this knowledge is ignored the likelihood ratio wald and lagrange multiplier tests are each equivalent to the f test we propose a new test which can be applied as a one sided t test and which is umpi in a subspace of the parameter space empirical power comparisons with the power envelope the f test and the exact one sided likelihood ratio test show that the new test can have exceptionally good power over a wide range of the parameter space

a unified approach to likelihood inference on stochastic orderings in a nonparametric context abstract for data in a two way contingency table with ordered margins we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities this leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log likelihood ratio tests the usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases in particular for each of these three orderings we determine the transformation required to apply the estimation algorithm we then consider testing the hypothesis that the rows are identically distributed against the alternative that they are stochastically ordered as well as testing each stochastic order against an u

confidence sets for partially identified parameters that satisfy a finite number of moment inequalities this paper proposes a computationally simple way to construct confidence sets for a parameter of interest in models comprised of moment inequalities building on results from the literature on multivariate one sided tests i show how to test the hypothesis that any particular parameter value is logically consistent with the maintained moment inequalities the associated test statistic has an asymptotic chi bar square distribution and can be inverted to construct an asymptotic confidence set for the parameter of interest even if that parameter is only partially identified critical values for the test are easily computed and a monte carlo study demonstrates implementation and finite sample performance

adaptive critical value for constrained likelihood ratio testing summary we present a new general method for constrained likelihood ratio testing which when few constraints are violated improves upon the existing approach in the literature that compares the likelihood ratio with the quantile of a mixture of chi squared distributions the improvement is in terms of both simplicity and power the proposed method compares the constrained likelihood ratio statistic against the quantile of only one chi squared random variable with data dependent degrees of freedom the new test is shown to have a valid exact significance level alpha it also has more power than the classical approach against alternatives for which the number of violations is not large we provide more details for testing a simple order mu 1 leqslant cdots leqslant mu p against all alternatives using the proposed approach and give clear guidelines as to when the new method would be advantageous a simulation study suggests that for testing a simple order the new approach is more powerful in many scenarios than the existing method that uses a mixture of chi squared variables we illustrate the results of our adaptive procedure using real data on the liquidity preference hypothesis

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

strong convergence theorem of an iterative method for variational inequalities and fixed point problems in hilbert spaces in this paper we introduce a new iteration method based on the hybrid method in mathematical programming and the descent like method for finding a common element of the set of solutions for a variational inequality and the set of fixed points for a nonexpansive mapping in hilbert spaces our method modifies and improves some methods in literature

on the stability of iterative approximations to fixed points of nonexpansive mappings abstract we study iterative retraction approximations to fixed points of the nonexpansive self mapping a g g given on the closed convex set g in a banach space b the conditions which guarantee weak and strong convergence and stability of these approximations with respect to perturbations of both operator a and constraint set g are considered the results of this paper are new even in a hilbert space for the iterative projection approximations

robust tests of inequality constraints and one sided hypotheses in the linear model summary for the linear regression model with independent and identically distributed errors robust tests of various hypotheses on the regression parameter are developed by robust we mean robustness of size and power against long tailed error distributions which may not be symmetric the proposed test statistic denoted by fm resembles the usual f statistic the two main results are i under the null hypothesis the asymptotic distribution of fm and that of the least squares based f statistic are the same and ii the pitman asymptotic efficiency of fm relative to f is equal to the asymptotic efficiency of the corresponding m estimator relative to the least squares estimator an example and simulation results illustrate that fm has desirable robustness properties compared to f

additive multilevel item structure models with random residuals item modeling for explanation and item generation an additive multilevel item structure amis model with random residuals is proposed the model includes multilevel latent regressions of item discrimination and item difficulty parameters on covariates at both item and item category levels with random residuals at both levels the amis model is useful for explanation purposes and also for prediction purposes as in an item generation context the parameters can be estimated with an alternating imputation posterior algorithm that makes use of adaptive quadrature and the performance of this algorithm is evaluated in a simulation study

a normalized quadratic semiflexible functional form estimation of flexible functional forms for large consumer or producer demand systems is often precluded due to computational difficulties or due to a lack of degrees of freedom we propose the concept of a semiflexible form which is a special case of a flexible form but which requires fewer free parameters our proposed method of estimation allows the researcher to choose the degree of flexibility consistent with feasibility of estimation while at the same time maintaining the concavity in prices property required by economic theory in our empirical illustration we estimate a normalized quadratic semiflexible form using canadian per capita time series data for ten consumer expenditure categories

sampling performance of some joint one sided preliminary test estimators under squared error loss in many areas of science when drawing conclusions concerning a set of phenomena individual or linear combinations of parameters are assumed to be nonnegative nonpositive or to lie between upper and lower bounds likewise many functions are assumed to be monotonic convex or quasiconvex consequently questions naturally arise as to the correctness of the assumptions and within the context of statistical inference how to evaluate the evidence against these assumptions and to use the data at hand to seek the appropriate statistical model and the corresponding method of estimation within the context of the general linear statistical model multivariate analogues of one sided inequality hypotheses tests have been explored by bartholomew 1959 kudo 1963 osterhoff 1969 barlow et al 1972 yancey judge and bock 1981 yancey bohrer and judge 1982 gourieroux holly and montfort ghm 1982 judge and yancey 1986 wolak 1987 and shapiro 1988 in general the likelihood ratio framework has been used in developing a test statistic and determining acceptance and rejection regions in order to facilitate the interpretation of these test results in econometric practice in this paper we evaluate under a squared error loss sel measure the risk characteristics of the preliminary test pt estimators that evolve when based on the data at hand an estimation decision is taken as a result of the outcomes of two one sided multivariate hypothesis tests

on criticality for competing influences of boundary and external field in the ising model we continue a study of schonmann 1994 schonmann and shlosman 1996 and greenwood and sun 1997 regarding the competing influences of boundary conditions and external field for the ising model we find a critical point b0 in the competing influences for low temperature in dimension d 2a7e 2

testing inequality constraints in linear econometric models abstract this paper develops three asymptotically equivalent tests for examining the validity of imposing linear inequality restrictions on the parameters of linear econometric models first we consider the model y x e where e is n 0 and the hypothesis test h r r versus k rk later we generalize this testing framework to the linear simultaneous equations model we show that the joint asymptotic distribution of these test statistics and the test statistics from the hypothesis test h r r versus k r r is a weighted sum of two sets of independent 2 distributions we also derive a useful duality relation between the multivariate inequality constraints test developed here and the multivariate one sided hypothesis test in small samples these three test statistics satisfy inequalities similar to those derived by berndt and savin 1977 for the case of equality constraints the paper also contains an illustrative application of this testing technique

modified lagrange multiplier tests for problems with one sided alternatives abstract a modified lagrange multiplier test statistic is proposed which takes explicit account of the one sided nature of the alternative in problems where the null hypothesis specifies that the true value of the parameter vector lies on the boundary of the parameter space computation of this statistic requires only the constrained maximum likelihood estimator conditions for the consistency of tests based on this statistic are examined and it is shown that the distribution of the statistic is not affected of nuisance parameters are allowed to lie on the boundary of the parameter space