a one factor multivariate time series model of metropolitan wage rates abstract the paper formulates and estimates a single factor multivariate time series model the model is a dynamic generalization of the multiple indicator or factor analysis model it is shown to be a special case of the general state space model and can be estimated by maximum likelihood methods using the kalman filter algorithm the model is used to obtain estimates of the unobserved metropolitan wage rate for los angeles based on observations of sectoral wages within the standard metropolitan statistical area hypothesis tests model diagnostics and out of sample forecasts are used to evaluate the model

mixed boundary value problems for elliptic and parabolic differential equations of second order on considere les problemes aux valeurs limites mixtes suivants lu f 1 dans mu f 2 sur u f 3 sur avec l operateur elliptique et pu f 1 dans 0 t mu f 2 sur 0 t u f 3 sur 0 t 0 pour des operateurs p paraboliques pour des operateurs obliques generaux m et pour des domaines ou et se rencontrent a des angles arbitraires on montre l existence de solutions classiques quand les angles sont non nuls et f 3 est continue de holder

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

generalized synchronization in linearly coupled time periodic systems abstract we consider the synchronization of a network of linearly coupled and not necessarily identical oscillators we present an approach to the existence of the synchronization manifold which is based on some results developed by r smith for the study of periodic solutions of odes our framework allows the study of a large class of systems and does not assume that they are small perturbations of linear systems moreover it provides a practical way to compute estimations on the parameters of the system for which generalized synchronization occurs additionally we give a new proof of the main result of r smith on invariant manifolds using wazewski s principle several examples of application are presented

nonlinear oblique boundary value problems for nonlinear elliptic equations on considere le probleme aux valeurs limites a derivee oblique non lineaire pour des equations uniformement elliptiques quasi lineaires et totalement non lineaires d ordre 2 les operateurs elliptiques satisfont des conditions de structure naturelle on donne des theoremes d existence pour les solutions

a free boundary problem for the parabolic poisson kernel abstract we study parabolic chord arc domains introduced by hofmann lewis and nystrom 14 and prove a free boundary regularity result below the continuous threshold more precisely we show that a reifenberg flat parabolic chord arc domain whose poisson kernel has logarithm in vmo must in fact be a vanishing chord arc domain i e satisfies a vanishing carleson measure condition this generalizes to the parabolic setting a result of kenig and toro 26 and answers in the affirmative a question left open in the aforementioned paper of hofmann et al a key step in this proof is a classification of flat blowups for the parabolic problem

intermediate schauder theory for second order parabolic equations i estimates on introduit les normes et les espaces de fonctions a utiliser les estimations a priori pour les problemes a coefficients constants dans des domaines simples sont reduits a des estimations integrales on donne des conditions sous lesquelles on peut passer localement a des coefficients variables on donne des estimations globales

hypothesis testing with a restricted parameter space abstract this paper considers hypothesis tests when the parameter space is restricted under the alternative hypothesis multivariate one sided tests are a leading example optimal tests called directed tests are derived using a weighted average power criterion exact results are established first for gaussian linear regression models with known variance asymptotic analogues are then established for dynamic nonlinear models simulation is used to compare the tests discussed in the paper the d w directed test is found to perform best in an overall sense for multivariate one sided alternatives with the likelihood ratio test being a close second the d w and likelihood ratio tests are found to perform best for mixed one and two sided alternatives

some results on the statistical properties of an inequality constrained least squares estimator in a linear model with two regressors abstract the inequality constrained least squares estimator in this paper is from the regression model y x 1 1 x 2 2 e where both of the regression coefficients are subject to non negative inequality constraints the first and second moments of this estimator are derived the regressors are permitted to be non orthogonal a number of conclusions are drawn from comparisons of the inequality constrained least squares estimator with the ordinary least squares and equality constrained least squares estimators

kalman filtering estimation of unobserved rational expectations with an application to the german hyperinflation abstract the assumption that rational expectations always lie on a convergent path is subject to an empirical test using the german hyperinflation data the estimation technique employs a kalman filtering algorithm after presenting a brief background for the convergent expectations problem and a derivation of the various model specifications a generalized expectations model and its attendant kalman filtering estimation technique are discussed additional estimation details and empirical results are then presented based on an assumption of normally distributed errors the null hypothesis of convergent paths is rejected in all situations involving a deterministic specification of the evolution of the unobserved parameter which characterizes the convergent path the same null hypothesis is rejected in four of the six cases corresponding to a stochastic specification of the evolution of the unobserved parameter which characterizes the convergent path a discussion of these findings their economic significance and suggestions for further research concludes the paper

spatial pattern in an ecosystem of phytoplankton nutrient from remote sensing abstract in this paper we consider an ecosystem of phytoplankton nutrient which comes from pelagic zone of the ocean by using remote sensing we are concerned with the pattern formation of the model we first give the asymptotic behavior of positive solutions of parabolic dynamical system then we discuss the stability of constant positive solution and the boundedness of stationary solutions finally the non existence and existence results of the pattern are investigated by considering some parameters the result shows that under certain range of these parameters the pattern of the model occurs

bounded domains of negative multipliers abstract a natural problem associated with coupling of non autonomous oscillators and synchronization is described it leads to a question about the boundedness of a domain associated with a derived quadratic form properties of real symmetric matrices with bounded domains are developed and unboundedness is translated into satisfiability of a certain lyapunov like matrix form eventually the real symmetric matrices associated with unbounded domains are explicitly characterized in terms of inertia explicit matrices a consequence of the characterization is that large irreducible matrices are likely to have bounded domains

the divergence equation in rough spaces abstract we aim at extending the existence theory for the equation div v f in a bounded or exterior domain with homogeneous dirichlet boundary conditions to a class of solutions which need not have a trace at the boundary typically the weak solutions that we shall consider will belong to some besov space b p q s with s 1 1 p 1 p after generalizing the notion of a solution for this equation we propose an explicit construction by means of the classical bogovski formula this construction enables us to keep track of a marginal information about the trace of solutions in particular it ensures that the trace is zero if f is smooth enough we expect our approach to be of interest for the study of rough solutions to systems of fluid mechanics

bayesian versus frequentist measures of error in small area estimation summary this paper compares analytically and empirically the frequentist and bayesian measures of error in small area estimation the model postulated is the nested error regression model which allows for random small area effects to represent the joint effect of small area characteristics that are not accounted for by the fixed regressor variables when the variance components are known then under a uniform prior for the regression coefficients and normality of the error terms the frequentist and the bayesian approaches yield the same predictors and prediction mean squared errors mses defined accordingly when the variance components are unknown it is common practice to replace the unknown variances by sample estimates in the expressions for the optimal predictors so that the resulting empirical predictors remain the same under the two approaches the use of this paradigm requires however modifications to the expressions of the prediction mse to account for the extra variability induced by the need to estimate the variance components the main focus of this paper is to review and compare the modifications to prediction mses proposed in the literature under the two approaches with special emphasis on the orders of the bias of the resulting approximations to the true mses some new approximations based on monte carlo simulation are also proposed and compared with the existing methods the advantage of these approximations is their simplicity and generality finite sample frequentist properties of the various methods are explored by a simulation study the main conclusions of this study are that the use of second order bias corrections generally yields better results in terms of the bias of the mse approximations and the coverage properties of confidence intervals for the small area means the bayesian methods are found to have good frequentist properties but they can be inferior to the frequentist methods the second order approximations under both approaches have however larger variances than the corresponding first order approximations which in most cases result in higher mses of the mse approximations

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

continuous time state space modeling of panel data by means of sem maximum likelihood parameter estimation of the continuous time linear stochastic state space model is considered on the basis of largen discrete time data using a structural equation modeling sem program random subject effects are allowed to be part of the model the exact discrete model edm is employed which links the discrete time model parameters to the underlying continuous time model parameters by means of nonlinear restrictions the edm is generalized to cover not only time invariant parameters but also the cases of stepwise time varying piecewise time invariant parameters and parameters varying continuously over time according to a general polynomial scheme the identification of the continuous time parameters is discussed and an educational example is presented

a test of the null of integer integration against the alternative of fractional integration abstract this paper proposes a test of the null of integer integration against the alternative of fractional integration the null of integer integration is satisfied if the series is either i 0 or i 1 we reject the null if the kpss test rejects i 0 and a unit root test rejects i 1 we suggest a new unit root test a lower tail kpss test applied to the differenced data to use in this procedure we provide critical values under standard asymptotics and fixed b asymptotics we prove the consistency of this testing procedure against i d alternatives with 0 d 1 and simulation evidence on the size and power of the test in finite samples is provided

area integral estimates for caloric functions we study the relationship between the area integral and the para bolic maximal function of solutions to the heat equation in domains whose boundary satisfies a 5 1 mixed lipschitz condition our main result states that the area integral and the parabolic maximal function are equivalent in lp p 0 p oo the measure p must satisfy muckenhoupt s loo condition with respect to caloric measure we also give a fatou theorem which shows that the existence of parabolic limits is a e with respect to caloric measure equivalent to the finiteness of the area integral

existence of solution to parabolic equations with mixed boundary condition on non cylindrical domains abstract in this paper we study the existence of weak solutions to initial boundary value problems of linear and semi linear parabolic equations with mixed boundary conditions on non cylindrical domains t 0 t t t of spatial temporal space r n r in the case of the linear equation each boundary condition is given on any open subset of the boundary surface t 0 t t t under a condition that the boundary portion for dirichlet condition 0 is nonempty at any time t due to this it is difficult to reduce the problem to the one on a cylindrical domain by diffeomorphism of the spatial domains t by a transformation of the unknown function and the penalty method we connect the problem to a monotone operator equation for functions defined on the non cylindrical domain we are also concerned with a semilinear problem when the boundary portion for dirichlet condition is cylindrical

the perron process applied to oblique derivative problems abstract the perron process has been used with great success to prove the solvability of the dirichlet problem for linear elliptic equations by elementary methods a modification of this process is used to give an elementary proof of the solvability of the regular oblique derivative problem for linear elliptic equations

on an inverse type problem for the heat equation in parabolic regular graph domains in this paper we prove some results concerning inverse free boundary type problems below the continuous threshold for the heat equation in the setting of parabolic regular graph domains

chord arc surfaces with small constant i abstract we introduce a notion for hypersurfaces in r d 1 that is analogous to the chord arc condition with small constant for curves in the plane we give various equivalent operator theoretic function theoretic and geometrical characterizations of these surfaces we not know any nice potential theoretic characterizations in a companion paper we address the issue of finding good parameterizations for these surfaces

harmonic measure on locally flat domains we will review work with tatiana toro yielding a characterizati on of those domains for which the harmonic measure has a density whose logarithm has vanishing mean oscillation

the tricomi problem for a genuinely nonlinear lavrentiev bitsadze equation of mixed type abstract in this paper we consider the tricomi problem for a genuinely nonlinear lavrentiev bitsadze mixed type equation 2 u x 2 sgn y 1 u x 2 2 u y 2 0 whose coefficients depend on the first order derivative of an unknown function we prove the existence of a solution to this problem by a method which can be used to study more difficult problems for nonlinear mixed type equations arising in gas dynamics

systems of seemingly unrelated regression equations with time varying coefficients an interplay of kalman filtering scoring em and minque method abstract this paper gives a detailed description of the implementation of ml estimation using scoring and em for the hyperparameters of a particular econometric state space we also show how the em method can be turned into an on line estimation method and how this procedure relates to an adaptive method of variance component estimation based on minque theory a small simulation study for a single equation model indicates how much can be gained in terms of computer time by using a combination of scoring and em

simple tests of alternative specifications in stochastic frontier models abstract previous work on stochastic production frontiers has generated a family of models of varying degrees of complexity since this family is nested in the sense that the more general models contain the less general we can test the restrictions that distinguish the model in this paper we provide tests of these restrictions based on the results of estimating the simpler restricted models some of our tests are lm tests however in other cases the lm test fails so we provide alternative simple tests

free boundary regularity for harmonic measures and poisson kernels one of the basic aims of this paper is to study the relationship between the geometry of hypersurface like subsets of euclidean space and the properties of the measures they support in this context we show that certain doubling properties of a measure determine the geometry of its support a radon measure is said to be doubling with constant c if c times the measure of the ball of radius r centered on the support is greater than the measure of the ball of radius 2r and the same center we prove that if the doubling constant of a measure on r n 1 is close to the doubling constant of the ndimensional lebesgue measure then its support is well approximated by ndimensional a ne spaces provided that the support is relatively at to start with primarily we consider sets which are boundaries of domains in r n 1 the n dimensional hausdorfi measure may not be deflned on the boundary of a domain in r n 1 thus we turn our attention to the harmonic measure which is well behaved under minor assumptions see section 3 we obtain a new characterization of locally at domains in terms of the doubling properties of their harmonic measure see section 3 along these lines we investigate how the weak regularity of the poisson kernel of a domain determines the geometry of its boundary sections 5 and 6 pursue this goal as in alt and cafiarelli s work see ac c1 c2 and also jerison s j in both cases the goal is to prove that under the appropriate technical conditions at at points of the boundary the oscillation of the poisson kernel controls the oscillation of the unit normal vector the difierence between our work and the work in ac is that we measure the oscillation in an integral sense bmo estimates

rectifiable sets and the traveling salesman problem let k c c be a bounded set in this paper we shall give a simple necessary and sufficient condit ion for k to lie in a rectifiable curve we say that a set is a rectifiable curve if it is the image of a finite interval under a lipschitz mapping recall that for a connected set f c c f is a rectifiable curve not necessarily simple if and only if l f where l denotes one dimensional hausdorff measure this classical result follows from the fact that on any finite graph there is a tour which covers the entire graph and which crosses each edge but not necessarily each vertex at most twice if k is a finite set then we are essentially reduced to the classical traveling salesman problem tsp compute the length of the shortest hami l ton ian cycle which hits all points of k this is the same up to a constant multiple as asking for the inf imum of l f where f is a curve k c f such a f is called a spanning tree in tsp theory for infinite sets k we cannot hope in general to have k be a subset of a jordan curve what we should therefore look at is connected sets which conta in k let fmi n be the shortest minimal spanning tree then we cannot possibly solve our problem for sets k of infinite cardinality if we cannot find f i f c o fmin for any finite set k here and throughout the paper c co c1 c o etc denote various universal constants while there are several algorithms for computing l fml these algorithms work for finite graphs satisfying the triangle inequality and do not use the euclidean properties of k see 13 for an excellent discussion of some of these algorithms therefore these methods cannot solve our problem for general infinite k we present a method which is a minor modification of a well known algorithm farthest insert ion see 13 which yields a f with i f c o l fmi the farthest insert ion algorithm has been extensively studied with large numerical calculations on computers and is experimentally good in the sense that the f produced satisfy i f c o l f i for all examples which have

intermediate schauder theory for second order parabolic equations ii existence uniqueness and regularity on etablit et on demontre des theoremes d existence d unicite et de regularite pour des solutions de problemes aux valeurs limites et initiales paraboliques lineaires dans des espaces de holder ponderes

alternative algorithms for the estimation of dynamic factor mimic and varying coefficient regression models this paper provides a general approach to the formulation and estimation of dynamic unobserved component models after introducing the general model two methods for estimating the unknown parameters are presented both are algorithms for maximizing the likelihood function the first is based on the method of scoring the second is the em algorithm a derivative free method each iteration of em requires a kalman filter and smoother followed by straightforward regression calculations the paper suggests using the em methods to quickly locate a neighborhood of the maximum scoring can then be used to pinpoint the maximum and calculate the information matrix

characterizations and criteria for synchronization of heterogeneous networks to linear subspaces in this paper we investigate synchronization issues in heterogeneous complex networks we start with a necessary condition for the existence of synchronous trajectories by analyzing the vector fie

local estimates for subsolutions and supersolutions of oblique derivative problems for general second order elliptic equations we consider solutions and subsolutions and supersolutions of the boundary value problem au x u du diju u x u du 0 in 2 s x diu y x u g x on3fi for a lipschitz domain s a positive definite matrix valued function u j and a vector field s which points uniformly into q without making any continuity assumptions on the known functions we prove harnack and holder estimates for u near 3i2 in addition we bound the l norm of u near 3i2 in terms of an appropriate lp norm and the known functions our approach is based on that for the corresponding interior estimates of trudinger this paper is concerned with analogs for solutions of oblique boundary value problems of the results in 10 our results will extend previous work of lieberman and trudinger 5 and of nadirashvili 9 specifically we consider second order differential operators q of the form

caloric measure in parabolic flat domains in this paper we define parabolic chord arc domains and show that in a parabolic chord arc domain with vanishing constant the logarithm of the density of caloric measure with respect to a certain projective lebesgue measure is of vanishing mean oscillation we also obtain a partial converse to this result our work generalizes to the heat equation recent work of kenig and toro for the laplacian

a standard error for the estimated state vector of a state space model abstract this paper motivates an estimate of the variance of the estimated state vector x t in a state space model when the vector of parameters characterizing system dynamics must be estimated from the data

kuhn tucker likelihood ratio and wald tests for nonlinear models with inequality constraints on the parameters abstract this paper considers the problem of testing statistical hypothesis in nonlinear regression models with inequality constraints on the parameters first the kuhn tucker test procedure is defined next it is shown that the distribution of the kuhn tucker the likelihood ratio and the wald test statistics converges to the same mixture of chi square distributions under the null hypothesis to illustrate these results two examples are considered 1 the problem of testing that individual effects are missing in an error component model and 2 the problem of testing equilibrium for a model of markets in disequilibrium

global c1 1 regularity for solutions of quasilinear variational inequalities on considere les solutions u des inegalites variationnelles de la forme u k 0 v k ou k v h 1 v v ou au d i a i x u du est un operateur elliptique et ou hu h x u du est un ensemble ouvert borne dans r n n 2

boundary value problem for a nonlinear equation of mixed type abstract in this paper we consider the boundary value problem for a nonlinear lavrentiev bitsadze equation of mixed type 2 u x 2 sgn y 1 u x 2 2 u y 2 0 whose coefficients depend on the first order derivatives of unknown function above y 0 and below y 0 the equation becomes the nonlinear elliptic equation and nonlinear hyperbolic equation respectively this is different from the equation studied in chen 2011 9 we prove the existence of solution to the problem by the method which can be used to study more difficult problems for nonlinear equations of mixed type arising in gas dynamics

locally best invariant tests of the error covariance matrix of the linear regression model summary this paper considers a class of hypothesis testing problems concerning the covariance matrix of the disturbances in the classical linear regression model a test that is locally best invariant against one sided alternative hypotheses is constructed and shown to be identical to a one sided version of the lagrange multiplier test

a score test against one sided alternatives abstract a score type statistic t s is introduced for testing h 0 against k 0 and more general one sided hypotheses when nuisance parameters may be present is a vector parameter the main advantages of t s are that it requires estimation of the model only under the null hypothesis and that it is asymptotically equivalent to the likelihood ratio statistic these are precisely the reasons for the popularity of the score tests for testing against two sided alternatives in this sense t s preserves the main attractive features of the classical two sided score test the theoretical results are presented in a general framework where the likelihood based score function is replaced by an estimating function so that the test is applicable even if the exact population distribution is unknown computation of t s is simplified by the fact that it can be computed easily once the corresponding two sided statistic has been computed the relevance and simplicity of t s are illustrated by discussing

global regularity of solutions of nonlinear second order elliptic and parabolic differential equations on considere des solutions du probleme de dirichlet pour une equation elliptique totalement non lineaire dans un domaine borne lisse et du probleme parabolique analogue

the conormal derivative problem for equations of variational type in nonsmooth domains it is well known that elliptic boundary value problems in smooth domains have smooth solutions but if the domain is say c 1 the solutions need not be lipschitz recently korevaar has identified a class of lipschitz domains in which solutions of the capillary problem are lipschitz assuming the contact angle relates correctly to the geometry of the domain lipschitz bounds for more general boundary value problems in the same class of domains are proved applications to variational inequalities are also considered

testing the nullity of garch coefficients correction of the standard tests and relative efficiency comparisons this article is concerned with testing the nullity of coefficients in generalized autoregressive conditionally heteroscedastic garch models the problem is nonstandard because the quasi maximum likelihood estimator is subject to positivity constraints this article establishes the asymptotic null and local alternative distributions of wald score and quasi likelihood ratio tests efficiency comparisons under fixed alternatives are considered two cases of special interest are tests of the null hypothesis of one coefficient equal to zero and tests of the null hypothesis of no conditional heteroscedasticity finally the proposed approach is used in the analysis of financial data and suggests reconsidering the preeminence of garch 1 1 among garch models

a parabolic free boundary problem with bernoulli type condition on the free boundary consider the parabolic free boundary problem u t u 0 in u 0 u 1 on u 0 for a realistic class of solutions containing for example all limits of the singular perturbation problem ue t ue e ue as e 0 we prove that one sided flatness of the free boundary implies regularity in particular we show that the topological free boundary u 0 can be decomposed into an open regular set relative to u 0 which is locally a surface with holder continuous space normal and a closed singular set our result extends the main theorem in the paper by h w alt l a caffarelli 1981 to more general solutions as well as the time dependent case our proof uses methods developed in h w alt l a caffarelli 1981 however we replace the core of that paper which relies on non positive mean curvature at singular points by an argument based on scaling discrepancies which promises to be applicable to more general free boundary or free discontinuity problems

boundary regularity for linear and quasilinear variational inequalities on montre a l aide d une extension d une methode de jensen que les derivees secondes des solutions de divers problemes d obstacles lineaires sont bornees sous des hypotheses de regularite des donnees plus faibles que celles de jensen