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

the universal r matrix for u_q rm sl 3 and beyond ther matrices for the quantised lie algebrasa n are constructed through the quantum double procedure given by drinfel d 6 the case ofu q sl 3 is thoroughly analysed initially to demonstrate the more subtle points of the calculation the ease of the calculation fora n is very dependent on a choice of generators for the borel subalgebrau q b and its dual and a certain ordering imposed on these generators which is related to the length of a certain word in the weyl group

colored solutions of the yang baxter equation from representations of uqgl 2 we study the hopf algebra structure and the highest weight representation of a multiparameter version of uqgl 2 the hopf algebra maps of this algebra are explicitly given we show that the multiparameter universal r matrix can be constructed directly as a quantum double intertwiner without using reshetikhin s twisting transformation we find there are two types highest weight representations for this algebra type a corresponds to the qeneric q and type b corresponds to the case that q is a root of unity when applying the representation theory to the multi parameter universal r matrix both standard and nonstandard colored solutions of the yang baxter equation are obtained

unusual solutions to the yang baxter equation the complete list of non symmetric eight vertex constant solutions to the yang baxter equation is obtained and new solutions dependent on more than one variable are presented the corresponding spin hamiltonians are derived by sutherland s method 1970

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

on the quantum symmetries associated with the two parameter free fermion model the quantum algebras associated with the r matrix obtained from the two parameter free fermion model are examined it is shown that in addition to uq s gl 1 1 there exists another algebra which is isomorphic to uq s gl 1 1 as an algebra but has a different hopf structure it does not have a classical limit and is related to up sl 2 c at a root of unity p i i2 1

duals of colored quantum universal enveloping algebras and colored universal t matrices we extend the notion of dually conjugate hopf super algebras to the colored hopf super algebras hc that we recently introduced we show that if the standard hopf super algebras hq that are the building blocks of hc have hopf duals hq then the latter may be used to construct coloured hopf duals hc endowed with colored algebra and antipode maps but with a standard coalgebraic structure next we review the case where the hq s are quantum universal enveloping algebras of lie super algebras uq g so that the corresponding hq s are quantum super groups gq we extend the fronsdal and galindo universal t matrix formalism to the colored pairs uc g gc by defining colored universal t matrices we then show that together with the colored universal r matrices previously introduced the latter provide an algebraic formulation of the colored rtt relations proposed by basu mallick this establishes a link between the colored extensions of drinfeld jimbo and faddeev reshetikhin takhtajan pictures of quant

incomplete generalized l statistics given data x 1 x n and a kernel h with m arguments serfling introduced the class of generalized l statistics gl statistics which is defined by taking linear combinations of the ordered h x i1 x im where i 1 i m ranges over all n n m distinct m tuples of 1 n in this paper we derive a class of incomplete generalized l statistics igl statistics by taking linear combinations of the ordered elements from a subset of h x i1 x im with size n n a special case is the class of incomplete u statistics introduced by blom under very general conditions the igl statistic is asymptotically equivalent to the gl statistic as soon as n n n as n which makes the igl much more computationally feasible we also discuss various ways of selecting the subset of h x i x im several examples are discussed in particular some new estimates of the scale parameter in nonparametric regression are introduced it is shown that these estimates are asymptotically equivalent to an igl statistic some extensions for example functionals other than l and multivariate kernels are also addressed

on the nonparametric estimation of covariance functions we describe kernel methods for estimating the covariance function of a stationary stochastic process and show how to ensure that the estimator has the positive semidefiniteness property from a practical viewpoint our method is significant because it does not demand a parametric model for covariance from a technical angle our results exhibit a striking departure from those in more familiar cases of kernel estimation for example in the context of covariance estimation kernel estimators can have the same convergence rates as maximum likelihood estimators and can have exceptionally fast convergence rates when employed to estimate variance

parameter estimation for a stationary process on a d dimensional lattice summary we study asymptotic properties of various estimation procedures for a general stationary regular process on a d dimensional lattice differences between d 1 time series and d 2 spatial processes are pointed out we suppose that the process is observed on a set pn with cn points which tends to infinity with the same speed in all directions the relative edge effect is of order cn lid increasing with d this effect is without statistical importance if d 1 but is important if d 2 we give a lcn consistent asymptotically normal estimator of the underlying parameter the procedure being constructed by a modification of whittle s approximation to the log likelihood in the gaussian case this procedure is asymptotically efficient

the universal r matrix and the yang baxter equation with parameters the authors formulate and demonstrate with some examples a method for obtaining solutions of the yang baxter equation with parameters

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

coloured frt algebra and its yang baxterization leading to integrable models with non additive r matrices a colour representation of faddeev reshetikhin takhtajan frt algebra which in contrast to the standard case is related to the coloured braid group representation with generic values of q is presented explicit realizations of l or matrices occurring in this coloured variant of frt algebra are also obtained for the uq gl 2 quantized algebra though these realizations are found to depend manifestly on the colour parameters the underlying quantum group structure and associated co product are interestingly free from such dependence this allows us to perform the yang baxterization of the coloured frt algebra successfully which leads to the construction of an ancestor law operator associated with a new non additive type quantum r matrix through different realizations of this lax operator a new class of quantum integrable models representing colour generalizations of the well known models such as the lattice sine gordon model the ablowitz ladik model lattice and the derivative nonlinear schrodinger model etc is generated

spatial correlation robust inference with errors in location or distance this paper presents results from a monte carlo study concerning inference with spatially dependent data we investigate the impact of location distance measurement errors upon the accuracy of parametric and nonparametric estimators of asymptotic variances nonparametric estimators are quite robust to such errors method of moments estimators perform surprisingly well and mle estimators are very poor we also present and evaluate a specification test based on a parametric bootstrap that has good power properties for the types of measurement error we consider

properties of nonparametric estimators of autocovariance for stationary random fields we introduce nonparametric estimators of the autocovariance of a stationary random field one of our estimators has the property that it is itself an autocovatiance this feature enables the estimator to be used as the basis of simulation studies such as those which are necessary when constructing bootstrap confidence intervals for unknown parameters unlike estimators proposed recently by other authors our own do not require assumptions such as isotropy or monotonicity indeed like nonparametric function estimators considered more widely in the context of curve estimation our approach demands only smoothness and tail conditions on the underlying curve or surface here the autocovariance and moment and mixing conditions on the random field we show that by imposing the condition that the estimator be a covariance function we actually reduce the numerical value of integrated squared error

an optimal time algorithm for slope selection given n points in the plane and an integer k the problem of selecting that pair of points that determines the line with the kth smallest or largest slope is considered in the restricted case where k is o n line sweeping gives an optimal o n log n time algorithm for general k the parametric search technique of megiddo is used to describe an o n log n 2 time algorithm this is modified to produce a new optimal o n log n time selection algorithm by incorporating an approximation idea

testing panel data regression models with spatial error correlation this paper derives several lagrange multiplier lm tests for the panel data regression model with spatial error correlation these tests draw upon two strands of earlier work the first is the lm tests for the spatial error correlation model discussed in anselin spatial econometrics methods and models kluwer academic publishers dordrecht rao s score test in spatial econometrics j statist plann inference 97 2001 113 and anselin et al regional sci urban econom 26 1996 77 and the second is the lm tests for the error component panel data model discussed in breusch and pagan rev econom stud 47 1980 239 and baltagi et al j econometrics 54 1992 95 the idea is to allow for both spatial error correlation as well as random region effects in the panel data regression model and to test for their joint significance additionally this paper derives conditional lm tests which test for random regional effects given the presence of spatial error correlation also spatial error correlation given the presence of random regional effects these conditional lm tests are an alternative to the one directional lm tests that test for random regional effects ignoring the presence of spatial error correlation or the one directional lm tests for spatial error correlation ignoring the presence of random regional effects we argue that these joint and conditional lm tests guard against possible misspecification extensive monte carlo experiments are conducted to study the performance of these lm tests as well as the corresponding likelihood ratio tests

on the rates in the central limit theorem for weakly dependent random fields let xa a zd d 2 be a random field satisfying some weak dependence condition for a finite subset v of zd set s v sum limits a in v x a in this paper under the conditions related to moment and dependence coefficients we show that l and l1 rates in the central limit theorem for s v are of order o v 1 2 log v d strong mixing case o v 1 2 m dependent case here v denotes the number of elements in v the content of this paper is a negative answer to the conjecture of prakasa rao z wahrscheinlichkeitstheorie verw gebiete 58 247 256 1981

new hierarchy of colored braid group representations novel solutions of the yang baxter relation for a series of multistate vertex models are presented in the braid group limit the obtained family of solutions gives a sequence of colored braid group representations possible generalizations of the multivariable alexander polynomial are discussed

approximate geometric pattern matching under rigid motions we present techniques for matching point sets in two and three dimensions under rigid body transformations we prove bounds on the worst case performance of these algorithms to be within a small constant factor of optimal and conduct experiments to show that the average performance of these matching algorithms is often better than that predicted by the worst case bounds

universal r matrix of reductive lie algebras and quantum integrable systems from its colour representation the universal r matrix intertwining between the coproduct structures related to the universal deformations of reductive lie algebras has been found in an explicit form using twisting a possible colour representation of this r matrix and its application to the integrable systems are shown using the example of a deformed gl n algebra

yang baxterization of braid group representations for a given braid group representation bgr a process of the yang baxterization is formulated to generate solutions of the yang baxter equation ybe when a bgr admits the birman wenzl bw algebraic structure this process can be explicitly passed through and two types of trigonometric solutions of ybe are generated from such a bgr these two solutions have the essential difference to each other and both of them preserve the crossing symmetry property if the given bgr has by taking certain reduction on the bw algebra the rational solution is also generated a practical condition to judge whether a bgr satisfies the bw algebra is given from which one finds that not only the familiar bgrs of 5 7 9 but also some new ones obtained recently in 12 have the bw structure thus they can be explicitly yang baxterized to solutions of the ybe

linear time algorithms for parametric minimum spanning tree problems on planar graphs abstract a linear time algorithm for the minimum ratio spanning tree problem on planar graphs is presented the algorithm is based on a new planar minimum spanning tree algorithm the approach extends to other parametric minimum spanning tree problems on planar graphs and to other families of graphs having small separators

gmm estimation with cross sectional dependence this paper presents a spatial model of dependence among agents using a metric of economic distance measurements of this economic distance provide cross sectional data with a structure similar to that provided by the time index in time series data generalized method of moments estimators using such dependent data are shown to be consistent and asymptotically normal this paper presents a class of non parametric positive semi definite covariance matrix estimators that allow for general forms of dependence characterized by economic distance these covariance matrix estimators are shown to remain consistent when economic distances are not precisely observed

autoregressive spatial spectral estimates abstract nonparametric spectral density estimates find many uses in econometrics for stationary random fields on a regular spatial lattice we propose an autoregressive nonparametric spectral density estimate that is guaranteed positive even when suitable edge effect correction is employed and is simple to compute using least squares our estimate is based on truncating a true half plane infinite autoregressive representation while also allowing the truncation length to diverge in all dimensions to avoid the potential bias due to truncation at a fixed lag length uniform consistency of the proposed estimate is established and new criteria for order selection are also suggested and studied in practical settings the asymptotic distribution of the estimate is shown to be zero mean normal and independent at fixed distinct frequencies mirroring the behaviour for time series a small monte carlo experiment examines finite sample performance technically the key to the results is the covariance structure of stationary random fields defined on regularly spaced lattices we show the covariance matrix to satisfy a generalization of the toeplitz property familiar from time series analysis

universal r matrix for a two parametric quantization of gl 2 for the two parametric quantized group glq s 2 the authors calculate the explicit form of the universal r matrix

a nonlinear deformed su 2 algebra with a two color quasitriangular hopf structure nonlinear deformations of the enveloping algebra of su 2 involving two arbitrary functions of j0 and generalizing the witten algebra were introduced some time ago by delbecq and quesne in the present paper the problem of endowing some of them with a hopf algebraic structure is addressed by studying in detail a specific example referred to as aq 1 this algebra is shown to possess two series of n 1 dimensional unitary irreducible representations where n 0 1 2 to allow the coupling of any two such representations a generalization of the standard hopf axioms is proposed by proceeding in two steps in the first one a variant and extension of the deforming functional technique is introduced variant because a map between two deformed algebras suq 2 and aq 1 is considered instead of a map between a lie algebra and a deformed one and extension because use is made of a two valued functional whose inverse is singular as a result the hopf structure of suq 2 is carried over to aq 1 ther

maximum likelihood estimation of models for residual covariance in spatial regression we describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters observations are assumed to be gaussian we give conditions which ensure consistency and asymptotic normality of the estimators our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators we also discuss an application of the spectral approximation to the likelihood for processes on a lattice

on the central limit theorem for stationary mixing random fields a simple proof of a central limit theorem for stationary random fields under mixing conditions is given generalizing some results obtained by more complicated methods e g bernstein s method

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