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

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

hac estimation in a spatial framework abstract we suggest a non parametric heteroscedasticity and autocorrelation consistent hac estimator of the variance covariance vc matrix for a vector of sample moments within a spatial context we demonstrate consistency under a set of assumptions that should be satisfied by a wide class of spatial models we allow for more than one measure of distance each of which may be measured with error monte carlo results suggest that our estimator is reasonable in finite samples we then consider a spatial model containing various complexities and demonstrate that our hac estimator can be applied in the context of that model

large sample properties of the matrix exponential spatial specification with an application to fdi this paper studies large sample properties of the matrix exponential spatial specification mess we find that the quasi maximum likelihood estimator qmle for the mess is consistent under heteroskedasticity a property not shared by the qmle of the sar model for the general model that has mess in both the dependent variable and disturbances labeled mess 1 1 the qmle can be consistent under unknown heteroskedasticity when the spatial weights matrices in the two mess processes are commutative we also consider the generalized method of moments estimator gmme in the homoskedastic case we derive a best gmme that is as efficient as the maximum likelihood estimator under normality and can be asymptotically more efficient than the qmle under non normality in the heteroskedastic case an optimal gmme can be more efficient than the qmle asymptotically the qml approach for the mess model has the computational advantage over that of a sar model the computational simplicity carries over to mess models with any finite order of spatial matrices no parameter range needs to be imposed in order for the model to be stable results of monte carlo experiments for finite sample properties of the estimators are reported finally the mess 1 1 is applied to belgium s outward fdi data and we observe that the dominant motivation of belgium s outward fdi lies in finding cheaper factor inputs

estimation and model selection of semiparametric copula based multivariate dynamic models under copula misspecification we introduce a new class of semiparametric copula based multivariate dynamic scomdy models which specify the conditional mean and the conditional variance of a multivariate time series parametrically but specify the multivariate distribution of the standardized innovation semiparametrically as a parametric copula evaluated at nonparametric marginal distributions we first study large sample properties of the estimators of scomdy model parameters under a misspecified parametric copula then propose pseudo likelihood ratio plr tests for model selection between two scomdy models with possibly misspecified copulas and finally develop plr tests for model selection between more than two scomdy models the limiting null distributions of the plr tests do not depend on the estimation of conditional mean and conditional variance parameters hence are very easy to simulate empirical applications to three and higher dimensional daily exchange rate series indicate that a scomdy model with a tail dependent copula is generally preferred

spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix this paper considers spatial heteroskedasticity and autocorrelation consistent spatial hac estimation of covariance matrices of parameter estimators we generalize the spatial hac estimator introduced by kelejian and prucha 2007 to apply to linear and nonlinear spatial models with moment conditions we establish its consistency rate of convergence and asymptotic truncated mean squared error mse based on the asymptotic truncated mse criterion we derive the optimal bandwidth parameter and suggest its data dependent estimation procedure using a parametric plug in method the finite sample performances of the spatial hac estimator are evaluated via monte carlo simulation

an asymptotic analysis of likelihood based diffusion model selection using high frequency data abstract we provide a new asymptotic analysis of model selection procedure that compares likelihoods of two candidate diffusion models our asymptotic analysis relies on two dimensional asymptotic expansions with shrinking sampling interval and increasing sampling span t and clarifies the different roles of drift and diffusion functions in the selection of diffusion models in particular we show that the model with superior diffusion function specification is always preferred to the competing model regardless of their drift specifications if is sufficiently small relative to t the specifications of drift functions matter only when the models have an identical diffusion specification

nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models we propose a nonparametric likelihood ratio testing procedure for choosing between a parametric likelihood model and a moment condition model when both models could be misspecified our procedure is based on comparing the kullback leibler information criterion klic between the parametric model and moment condition model we construct the klic for the parametric model using the difference between the parametric log likelihood and a sieve nonparametric estimate of population entropy and obtain the klic for the moment model using the empirical likelihood statistic we also consider multiple 2 model comparison tests when all the competing models could be misspecified and some models are parametric while others are moment based we evaluate the performance of our tests in a monte carlo study and apply the tests to an example from industrial organization

general pseudoadditivity of composable entropy prescribed by the existence of equilibrium the concept of composability states that entropy of the total system composed of independent subsystems is a function of entropies of the subsystems here the most general pseudoadditivity rule for composable entropy is derived based only on the existence of equilibrium

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

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

a matrix exponential spatial specification we introduce the matrix exponential as a way of modelling spatially dependent data the matrix exponential spatial specification mess simplifies the log likelihood allowing a closed form solution to the problem of maximum likelihood estimation and greatly simplifies the bayesian estimation of the model the mess can produce estimates and inferences similar to those from conventional spatial autoregressive models but has analytical computational and interpretive advantages we present maximum likelihood and bayesian approaches to the estimation of this spatial model specification along with methods of model comparisons over different explanatory variables and spatial specifications

stability of tsallis entropy and instabilities of renyi and normalized tsallis entropies a basis for q exponential distributions the q exponential distributions which are generalizations of the zipf mandelbrot power law distribution are frequently encountered in complex systems at their stationary states from the viewpoint of the principle of maximum entropy they can apparently be derived from three different generalized entropies the renyi entropy the tsallis entropy and the normalized tsallis entropy accordingly mere fittings of observed data by the q exponential distributions do not lead to identification of the correct physical entropy here stabilities of these entropies i e their behaviors under arbitrary small deformation of a distribution are examined it is shown that among the three the tsallis entropy is stable and can provide an entropic basis for the q exponential distributions whereas the others are unstable and cannot represent any experimentally observable quantities

coprime sensing via chinese remaindering over quadratic fields part ii generalizations and applications the practical application of a new class of coprime arrays based on the chinese remainder theorem crt over quadratic fields is presented in this paper the proposed crt arrays are constructed by ideal lattices embedded from coprime quadratic integers with mathbf b 1 and mathbf b 2 being their matrix representations respectively whereby the degrees of freedom dof surges to o det mathbf b 1 mathbf b 2 with det mathbf b 1 det mathbf b 2 sensors the geometrical constructions and theoretical foundations were discussed in the accompanying paper in great detail while this paper focuses on aspects of the application of the proposed arrays in two dimensional 2 d remote sensing a generalization of crt arrays based on two or more pairwise coprime ideal lattices is proposed with closed form expressions on sensor locations the total number of sensors and the achievable dof the issues pertaining to the coprimality of any two quadratic integers are also addressed to explore all possible ideal lattices exploiting the symmetry of lattices sensor reduction methods are discussed with the coarray remaining intact for economic maximization in order to extend conventional angle estimation techniques based on uniformly distributed arrays to the method that can exploit any coarray configurations based on lattices this paper introduces a hexagon to rectangular transformation to 2 d spatial smoothing providing the possibility of finding more compact sensor arrays examples are provided to verify the feasibility of the proposed methods

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

rates of convergence of non extensive statistical distributions to levy distributions in full and half spaces the levy type distributions are derived using the principle of maximum tsallis non extensive entropy both in the full and half spaces the rates of convergence to the exact levy stable distributions are determined by taking the n fold convolutions of these distributions the marked difference between the problems in the full and half spaces is elucidated analytically it is found that the rates of convergence depend on the ranges of the levy indices an important result emerging from the present analysis is deduced if interpreted in terms of random walks implying the dependence of the asymptotic long time behaviours of the walks on the ranges of the levy indices if n is identified with the total time of the walks

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

asymptotics for semiparametric econometric models via stochastic equicontinuity this paper provides a general framework for proving the square root of t consistency and asymptotic normality of a wide variety of semiparametric estimators the class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator the method of proof exploits results concerning the stochastic equicontinuity of stochastic processes the results are applied to the problem of semiparametric weighted least squares estimation of partially parametric regression models primitive conditions are given for square root of t consistency and asymptotic normality of this estimator copyright 1994 by the econometric society

statistical mechanical foundations of power law distributions abstract the foundations of the boltzmann gibbs bg distributions broadly fall into i probabilistic approaches based on the principle of equal a priori probability the central limit theorem or the state density considerations and ii the gibbs jaynes maximum entropy principle a minimal set of requirements on each of these are the function space the counting algorithm and additivity property of the entropy in the past few decades a class of complex systems which are not necessarily in thermodynamic equilibrium e g glasses have been found to display power law distributions which are not describable by the traditional methods here parallels to all the inquiries underlying the bg theory are given for the power law distributions in particular a different function space is employed and additivity of the entropy is discarded the requirement of stability identifies the entropy proposed by tsallis from this a generalized thermodynamic description of such systems in quasi equilibrium states is developed