asymptotic distributions of quasi maximum likelihood estimators for spatial autoregressive models this paper investigates asymptotic properties of the maximum likelihood estimator and the quasi maximum likelihood estimator for the spatial autoregressive model the rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model it is important to make the distinction with dif ferent spatial scenarios under the scenario that each unit will be influenced by only a few neighboring units the estimators may have n rate of convergence and be asymp totically normal when each unit can be influenced by many neighbors irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence

on duality of multiobjective fractional measurable subset selection problems in this paper we prove some duality results for the multiobjective fractional measurable subset selection problems under more general assumptions than convexity

central limit theorems and uniform laws of large numbers for arrays of random fields over the last decades spatial interaction models have been increasingly used in economics however the development of a sufficiently general asymptotic theory for nonlinear spatial models has been hampered by a lack of relevant central limit theorems clts uniform laws of large numbers ullns and pointwise laws of large numbers llns these limit theorems form the essential building blocks towards developing the asymptotic theory of m estimators including maximum likelihood and generalized method of moments estimators the paper establishes a clt ulln and lln for spatial processes or random fields that should be applicable to a broad range of data processes

optimality conditions for multiobjective programming with generalized i ρ θ convex set functions abstract necessary conditions for pareto optimality in multiobjective programming with subdifferentiable set functions are established in theorem 12 of h c lai and l j lin j math anal appl 132 1988 558 571 in this paper we establish some sufficient conditions under which a feasible solution of such a problem will be pareto optimal provided that a weaker convexity requirement is satisfied for instance i convexity is assumed for both objective and constraint set functions some duality models are also discussed wolfe type and mond weir type duality theorems are proved

optimization theory for n set functions abstract an optimization theory is developed for functions of n sets optimality conditions are established and a lagrangian duality is obtained

saddle points and lagrangian type duality for discrete minmax fractional subset programming problems with generalized convex functions abstract in this paper we present four sets of saddle point type optimality conditions construct two lagrangian type dual problems and prove weak and strong duality theorems for a discrete minmax fractional subset programming problem we establish these optimality and duality results under appropriate b convexity hypotheses

on the optimality conditions of vector valued n set functions abstract in a finite atomless measure space x the optimization problem of vector valued n set functions defined on a convex subfamily s of n is investigated the necessary and sufficient conditions of pareto optimal solution or proper r p solution of optimization problem with differentiable vector valued n set functions are given

the local isometric embedding in r3 of two dimensional riemannian manifolds with gaussian curvature changing sign cleanly on etudie le plongement isometrique local de surfaces a 2 dimensions dans r 3 on suppose que la premiere forme fondamentale edu 2 2fdudv gdv 2 on cherche trois fonctions c 2 x u v y u v z u v telles que dx 2 dy 2 dz 2 edu 2 2fdudv gdv 2 dans un voisinage de p

panel data methods for fractional response variables with an application to test pass rates we revisit the effects of spending on student performance using data from the state of michigan in addition to exploiting a dramatic change in funding in the mid 1990s and subsequent nonsmooth changes we propose nonlinear panel data models that recognize the bounded nature of the pass rate importantly we show how to estimate average partial effects which can be compared across many different models linear and nonlinear under different assumptions and estimated using many different methods we find that spending has nontrivial and statistically significant effects although the diminishing effect is not especially pronounced

gmm estimation of spatial autoregressive models with unknown heteroskedasticity abstract in the presence of heteroskedastic disturbances the mle for the sar models without taking into account the heteroskedasticity is generally inconsistent the 2sls estimates can have large variances and biases for cases where regressors do not have strong effects in contrast gmm estimators obtained from certain moment conditions can be robust asymptotically valid inferences can be drawn with consistently estimated covariance matrices efficiency can be improved by constructing the optimal weighted estimation the approaches are applied to the study of county teenage pregnancy rates the empirical results show a strong spatial convergence among county teenage pregnancy rates

duality for generalized fractional programs involving n set functions abstract making use of a strong duality theorem for nonlinear programs involving n set functions we first establish a gordan type transposition theorem which is then utilized to construct a dual problem for a class of generalized fractional programming problems with n set functions as special cases of the main result we also obtain dual problems for discrete minmax and fractional programming problems

a spatial autoregressive model with a nonlinear transformation of the dependent variable abstract this paper develops a nonlinear spatial autoregressive model of particular interest is a structural interaction model for share data we consider possible instrumental variable iv and maximum likelihood estimation mle for this model and analyze asymptotic properties of the iv and mle based on the notion of spatial near epoch dependence we also design a statistical test to compare the nonlinear transformation against alternatives monte carlo experiments are designed to investigate finite sample performance of the proposed estimates and the sizes and powers of the test

on spatial processes and asymptotic inference under near epoch dependence abstract the development of a general inferential theory for nonlinear models with cross sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems to facilitate a general asymptotic inference theory relevant to economic applications this paper first extends the notion of near epoch dependent ned processes used in the time series literature to random fields the class of processes that is ned on say an mixing process is shown to be closed under infinite transformations and thus accommodates models with spatial dynamics this would generally not be the case for the smaller class of mixing processes the paper then derives a central limit theorem and law of large numbers for ned random fields these limit theorems allow for fairly general forms of heterogeneity including asymptotically unbounded moments and accommodate arrays of random fields on unevenly spaced lattices the limit theorems are employed to establish consistency and asymptotic normality of gmm estimators these results provide a basis for inference in a wide range of models with spatial dependence

existence of distributional solutions of a closed dirichlet problem for an elliptic hyperbolic equation abstract the closed dirichlet problem for an elliptic hyperbolic equation arising in linearizing the monge ampere type equation is shown to admit a distributional solution by using an a b c integral method

a likelihood ratio test for spatial model selection abstract this paper develops a nondegenerate likelihood ratio test for model selection between two competitive spatial econometrics models it generalizes the test of vuong 1989 to models with spatial near epoch dependent ned data we do not make any structural assumption on the true model specification and allow for the cases where both or one of the two competing models are mis specified the test is valid whether two models are nested or non nested as a prerequisite of the test we first show that quasi maximum likelihood estimators qmle of spatial econometrics models are consistent estimators of their pseudo true values and are asymptotically normal under regularity conditions in particular we study spatial autoregressive models with spatial autoregressive errors sarar and matrix exponential spatial specification mess models we derive the limiting null distribution of the test statistic a spatial heteroskedastic and autoregressive consistent estimator of asymptotic variance of the test statistic under the null which is necessary to implement the test is constructed monte carlo experiments are designed to investigate finite sample performance of qmles for sarar and mess models as well as the size and power of the proposed test

duality for a minimax programming problem containingn set functions abstract parameter necessary and sufficient optimality conditions for the discrete minimax programming problem with differentiable n set functions are established in zalmai optimization 20 1989 377 395 in this paper we establish nonparameter necessary and sufficient optimality conditions the nonparameter necessary optimality conditions suggest the establishment of two parameter free duality models for the discrete minimax programming problem with differentiable n set functions and the weak strong and strict converse duality theorems have been derived

on a dynamic fractional game consider a two person zero sum game constructed by a dynamic fractional form we establish the upper value as well as the lower value of a dynamic fractional game and prove that the dual gap is equal to zero under certain conditions it is also established that the saddle point function exists in the fractional game system under certain conditions so that the equilibrium point exists in this game system

nonparametric spatial regression under near epoch dependence abstract this paper establishes asymptotic normality and uniform consistency with convergence rates of the local linear estimator for spatial near epoch dependent ned processes the class of the ned spatial processes covers important spatial processes including nonlinear autoregressive and infinite moving average random fields which generally do not satisfy mixing conditions apart from accommodating a larger class of dependent processes the proposed asymptotic theory allows for triangular arrays of heterogeneous random fields located on unevenly spaced lattices and sampled over regions of arbitrary configuration all these features make the results applicable in a wide range of empirical settings

moreau rockafellar type theorem for convex set functions abstract let x be an atomless finite measure space and s a convex subfamily it is proved that the moreau rockafellar theorem f 1 f n f 1 f n holds for proper convex set functions f 1 f n and s if all set functions f i except possibly one are w lower semicontinuous on s as applications the kuhn tucker type condition for an optimal solution of convex programming problem with set functions and the fritz john type condition for an optimal solution of vector valued minimization problem for set functions are obtained

duality in mathematical programming of set functions on fenchel duality theorem abstract the optimization problem of a set function defined on a family a of measurable subsets in an atomless finite measure space x a m is investigated the generalized fenchel theorem is formulated and proved in this note

duality for multiobjective fractional programming involving n set functions abstract in the present paper we consider a class of multiobjective fractional programming problems involving differentiable n set functions and establish duality results in terms of properly efficient solutions further we relate the problem to a certain saddle point of a lagrangian

sieve maximum likelihood estimation of the spatial autoregressive tobit model abstract this paper extends the ml estimation of a spatial autoregressive tobit model under normal disturbances in xu and lee 2015b journal of econometrics to distribution free estimation we examine the sieve mle of the model where the disturbances are i i d with an unknown distribution we show that the spatial autoregressive process with tobit censoring and related variables are spatial near epoch dependent ned a related contribution is that we develop some exponential inequalities for spatial ned random fields with these inequalities we establish the consistency of the estimator asymptotic distributions of structural parameters of the model are derived from a functional central limit theorem and projection simulations show that the sieve mle can improve the finite sample performance upon misspecified normal mles as an empirical application we examine the school district income surtax rates in iowa our results show that the spatial spillover effects are significant but they may be overestimated if disturbances are restricted to be normally distributed

on duality theorems for a nondifferentiable minimax fractional programming the optimality conditions of lai et al j math anal appl 230 1999 311 can be used to construct two kinds of parameter free dual models of nondifferentiable minimax fractional programming problems which involve pseudo quasi convex functions in this paper the weak duality strong duality and strict converse duality theorems are established for the two dual models

on minimax fractional programming of generalized convex set functions abstract we derive necessary and sufficient optimality conditions for the discrete minimax programming problem with subdifferentiable i convex set functions then we apply these optimality criteria to construct two models of parameter free dual problems and a third model of another dual problem we also establish weak strong and strictly converse duality theorems

necessary and sufficient conditions for minimax fractional programming we establish the necessary and sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems solving generalized convex functions subsequently we apply the optimality conditions to formulate one parametric dual problem and we prove weak duality strong duality and strict converse duality theorems

gmm and 2sls estimation of mixed regressive spatial autoregressive models the gmm method and the classical 2sls method are considered for the estimation of mixed regressive spatial autoregressive models these methods have computational advantage over the conventional maximum likelihood method the proposed gmm estimators are shown to be consistent and asymptotically normal within certain classes of gmm estimators best ones are derived the proposed gmm estimators improve upon the 2sls estimators and are applicable even if all regressors are irrelevant a best gmm estimator may have the same limiting distribution as the ml estimator with normal disturbances

maximum likelihood estimation of a spatial autoregressive tobit model this paper examines a tobit model with spatial autoregressive interactions we consider the maximum likelihood estimation for this model and analyze asymptotic properties of the estimator based on the spatial near epoch dependence of the dependent variable process generated from the model structure we show that the maximum likelihood estimator is consistent and asymptotically normally distributed monte carlo experiments are performed to verify finite sample properties of the estimator

pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension pseudo maximum likelihood estimates are developed for higher order spatial autoregressive models with increasingly many parameters including models with spatial lags in the dependent variables both with and without a linear or nonlinear regression component and regression models with spatial autoregressive disturbances consistency and asymptotic normality of the estimates are established monte carlo experiments examine finite sample behaviour

the local isometric embedding in mathbb r 3 of two dimensional riemannian manifolds with gaussian curvature changing sign to finite order on a curve we consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of monge ampere type these two problems are the local isometric embedding problem for two dimensional riemannian manifolds and the problem of locally prescribed gaussian curvature for surfaces in r3 we prove a general local existence result for a large class of monge ampere equations in the plane and obtain as corollaries the existence of regular solutions to both problems in the case that the gaussian curvature vanishes to arbitrary finite order on a single smooth curve

on closed boundary value problems for equations of mixed elliptic hyperbolic type for partial differential equations of mixed elliptic hyperbolic type we prove results on existence and existence with uniqueness of weak solutions for closed boundary value problems of dirichlet and mixed dirichlet conormal types such problems are of interest for applications to transonicflow and are overdetermined for solutions with classical regularity the method employed consists in variants of the a b c integral method of friedrichs in sobolev spaces with suitable weights particular attention is paid to the problem of attaining results with a minimum of restrictions on the boundary geometry and the form of the type change function in addition interior regularity results are also given in the important special case of the tricomi equation c

on the asymptotic distribution of the moran i test statistic with applications by far the most popular test for spatial correlation is the one based on moran s 1950 i test statistic despite this the available results in the literature concerning the large sample distribution of this statistic are limited and have been derived under assumptions that do not cover many applications of interest in this paper we 3rst give a general result concerning the large sample distribution of moran i type test statistics we then apply this result to derive the large sample distribution of the moran i test statistic for a variety of important models in order to establishth ese results we also give a new central limit theorem for linear quadratic forms 2001 elsevier science s a all rights reserved jel classi cation c12 c21

three types dual model for minimax fractional programming abstract we establish necessary and sufficient optimality conditions for minimax fractional programming involving nonsmooth generalized t convex functions three types dual model of 1 are considered and certain duality results have been derived in the framework of generalized t convex functions