a nonparametric test for spatial isotropy using subsampling a common requirement for spatial modeling is the development of an appropriate correlation structure although the assumption of isotropy is often made for this structure it is not always appropriate a conventional practice when checking for isotropy is to informally assess plots of direction specific sample semi variograms although a useful diagnostic these graphical techniques are difficult to assess and open to interpretation formal alternatives to graphical diagnostics are valuable but have been applied to a limited class of models in this article we propose a formal approach to test for isotropy that is both objective and valid for a wide class of models this approach which is based on the asymptotic joint normality of the sample variogram can be used to compare sample variograms in multiple directions an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample variogram is derived and used to construct a test statistic a subsampling approach and a limiting

direct and inverse computation of jacobi matrices of infinite iterated function systems we introduce a new set of algorithms to compute the jacobi matrices associated with invariant measures of infinite iterated function systems composed of one dimensional homogeneous affine maps we demonstrate their utility in the study of theoretical problems like the conjectured almost periodicity of such jacobi matrices the singularity of the measures and the logarithmic capacity of their support since our technique is based on a reversible transformation between pairs of jacobi matrices it can also be applied to solve an inverse approximation problem the proposed algorithms are tested in significant highly sensitive cases they perform in a stable fashion and can reliably compute jacobi matrices of large order

edge effects and efficient parameter estimation for stationary random fields summary we consider the estimation of the parameters of a stationary random field on d dimensional lattice by minimizing the classical whittle approximation to the gaussian log likelihood if the usual biased sample covariances are used the estimate is efficient only in one dimension to remove this edge effect we introduce data tapers and show that the resulting modified estimate is efficient also in two and three dimensions this avoids the use of the unbiased sample covariances which are in general not positive definite

infinite finitely generated fields are biinterpretable with mathbb n using the work of several other mathematicians principally the results of poonen refining the work of pop that algebraic independence is definable within the class of finitely generated fields and of rumely that the ring of rational integers is uniformly interpreted in global fields and a theorem on the definability of valuations on function fields of curves we show that each infinite finitely generated field considered in the ring language is parametrically biinterpretable with as a consequence for any finitely generated field there is a first order sentence in the language of rings which is true in that field but false in every other finitely generated field and hence pop s conjecture that elementarily equivalent finitely generated fields are isomorphic is true

the absolutely continuous spectrum of jacobi matrices i explore some consequences of a groundbreaking result of brei messer and pearson on the absolutely continuous spectrum of one dimensional schrodinger operators these include an oracle theorem that predicts the potential and rather general results on the approach to certain limit potentials in particular we prove a denisov rakhmanov type theorem for the general nite gap case the main theme is the following it is extremely dicult to produce abso lutely continuous spectrum in one space dimension and thus its existence has strong implications

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

local linear spatial regression a local linear kernel estimator of the regression function x g x e y i x i x x r d of a stationary d 1 dimensional spatial process y i x i i z n observed over a rectangular domain of the form in i i 1 i n z n 1 i k n k k 1 n n n 1 n n z n is proposed and investigated under mild regularity assumptions asymptotic normality of the estimators of g x and its derivatives is established appropriate choices of the bandwidths are proposed the spatial process is assumed to satisfy some very general mixing conditions generalizing classical time series strong mixing concepts the size of the rectangular domain in is allowed to tend to infinity at different rates depending on the direction in z n

two step estimation for inhomogeneous spatial point processes summary the paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second order properties k function regression parameters are estimated by using a poisson likelihood score estimating function and in the second step minimum contrast estimation is applied for the residual clustering parameters asymptotic normality of parameter estimates is established under certain mixing conditions and we exemplify how the results may be applied in ecological studies of rainforests

a canonical factorization for meromorphic herglotz functions on the unit disk and sum rules for jacobi matrices we prove a general canonical factorization for meromorphic herglotz functions on the unit disk whose notable elements are that there is no restriction other than interlacing on the zeros and poles for their blaschke product to converge and there is no singular inner function we use this result to provide a significant simplification in the proof of killip simon ann math 158 2003 253 of their result characterizing the spectral measures of jacobi matrices j with j j 0 hilbert schmidt we prove a nonlocal version of case and step by step sum rules

szegő s theorem on parreau widom sets in this paper we generalize szeg s theorem for orthogonal polynomials on the real line to infinite gap sets of parreau widom type this notion includes cantor sets of positive measure the szeg condition involves the equilibrium measure which in turn is absolutely continuous our approach builds on a canonical factorization of the m function and the covering space formalism of sodin yuditskii

least squares variogram fitting by spatial subsampling summary least squares methods are popular for fitting valid variogram models to spatial data the paper proposes a new least squares method based on spatial subsampling for variogram model fitting we show that the method proposed is statistically efficient among a class of least squares methods including the generalized least squares method further it is computationally much simpler than the generalized least squares method the method produces valid variogram estimators under very mild regularity conditions on the underlying random field and may be applied with different choices of the generic variogram estimator without analytical calculation an extension of the method proposed to a class of spatial regression models is illustrated with a real data example results from a simulation study on finite sample properties of the method are also reported

the use of subseries values for estimating the variance of a general statistic from a stationary sequence let z i infty i infty be a strictly stationary infty mixing sequence without specifying the dependence model giving rise to z i and without specifying the marginal distribution of z i we address the question of variance estimation for a general statistic t n t n z 1 z n for estimating var t n from just the available data z 1 z n we propose computing subseries values t m z i 1 z i 2 z i m 0 leq i i m leq n these subseries values are used as replicates to model the sampling variability of t n in particular we use adjacent nonoverlapping subseries of length m m n with m rightarrow infty and m n n rigtharrow 0 our variance estimator is just the usual sample variance computed amongst these subseries values after appropriate standardization this estimator is shown to be consistent under mild integrability conditions we present optimal i e minimum m s e choices of m n for the special case where t n overset z n and z i is a normal ar 1 sequence a simulation study is conducted showing that those same choices of m n are effective when t n is a robust estimator of location and z i is subject to contamination

on optimal spatial subsample size for variance estimation we consider the problem of determining the optimal block or subsample size for a spatial subsampling method for spatial processes observed on regular grids we derive expansions for the mean square error of the subsampling variance estimator which yields an expression for the theoretically optimal block size the optimal block size is shown to depend in an intricate way on the geometry of the spatial sampling region as well as characteristics of the underlying random field final expressions for the optimal block size make use of some nontrivial estimates of lattice point counts in shifts of convex sets optimal block sizes are computed for sampling regions of a number of commonly encountered shapes numerical studies are performed to compare subsampling methods as well as procedures for estimating the theoretically best block size

spectral properties of a class of reflectionless schrodinger operators abstract we prove that one dimensional reflectionless schrodinger operators with spectrum a homogeneous set in the sense of carleson belonging to the class introduced by sodin and yuditskii have purely absolutely continuous spectra this class includes all earlier examples of reflectionless almost periodic schrodinger operators in addition we construct examples of reflectionless schrodinger operators with more general types of spectra given by the complement of a denjoy widom type domain in c which exhibit a singular component

limit theorems for monolayer ballistic deposition in the continuum we consider a deposition model in which balls rain down at random towards a 2 dimensional surface roll downwards over existing adsorbed balls are adsorbed if they reach the surface and discarded if not we prove a spatial law of large numbers and central limit theorem for the ultimate number of balls adsorbed onto a large toroidal surface and also for the number of balls adsorbed on the restriction to a large region of an infinite surface

nonparametric estimation of the moments of a general statistic computed from spatial data abstract a statistic s is computed on spatially indexed data x i i d where d is a finite subset of the integer lattice z2 we propose a simple nonparametric method for estimating the moments e g variance skewness of s d using only the observed data at hand the method uses replicates of s computed on smaller subsets of d no explicit knowledge of the underlying spatial dependence mechanism is needed and the marginal distribution of x i may also be unknown the shape of d can be quite irregular and s is allowed to be a general statistic the proposed estimator is shown to be consistent and asymptotically normal under mild conditions on s d and mixing conditions on the strength of spatial dependence as a numerical example the estimator is used in assessing the geographic clumping of cancer deaths in the united states

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

tests for independence between marks and points of a marked point process a convenient assumption while modeling a marked point process is that the observations i e marks and the locations i e points are independent we propose new graphical and formal testing approaches to test for this assumption the proposed graphical procedures are easy to obtain and can be used to diagnose the nature and range of dependence between marks and points the formal testing procedures require only minimal conditions on marks and thus can be applied to a variety of settings we illustrate these procedures through a simulation study and an application to some real data

sum rules and the szegő condition for orthogonal polynomials on the real line we study the case sum rules especially c 0 for general jacobi matrices we establish situations where the sum rule is valid applications include an extension of shohat s theorem to cases with an infinite point spectrum and a proof that if lim n a n 1 and lim nb n exist and 2 then the szeg condition fails

translation invariant pure state on b j zmd j c and its split property in this paper we prove that a real lattice symmetric reflection positive translation invariant pure state of b j zmd j c admits split property if and only if its two point spatial correlation functions decay exponentially we use amalgamated representation of cuntz algebras to represent two point spatial correlation functions on an augmented hilbert space the underling symmetries and reflection positive property of the pure state make it possible to investigate its split and decaying two point correlation functions properties as spectral properties of a contractive self adjoint operator on the augmented hilbert space haag duality property of the pure state is crucially used in the analysis

invariance principles for self similar set indexed random fields for a stationary random field x j j in z d and some measure m on r d we consider the set indexed weighted sum process s n a sum j in z d m na cap r j frac12 x j where r j is the unit cube with lower corner j we establish a general invariance principle under a p stability assumption on the x j s and an entropy condition on the class of sets a the limit processes are self similar set indexed gaussian processes with continuous sample paths using chentsov s type representations to choose appropriate measures m and particular sets a we show that these limits can be levy fractional brownian fields or fractional brownian sheets

diophantine unsolvability for function fields over certain infinite fields of characteristic p abstract we prove that if f is a proper subfield of the algebraic closure of z p diophantine equations over the function field f t are not algorithmically decidable where p is an odd prime

moment estimation for statistics from marked point processes in spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations in other words the data form a realization of a marked point process in this paper we formulate subsampling estimators of the moments of general statistics computed from marked point process data and we establish their l 2 consistency the variance estimator in particular can be used for the construction of confidence intervals for estimated parameters a practical data based method for choosing a subsampling parameter is given and illustrated on a data set finite sample simulation examples are also presented

assessment of texture stationarity using the asymptotic behavior of the empirical mean and variance given textured images considered as realizations of 2 d stochastic processes a framework is proposed to evaluate the stationarity of their mean and variance existing strategies focus on the asymptotic behavior of the empirical mean and variance respectively em and ev known for some types of nondeterministic processes in this paper the theoretical asymptotic behaviors of the em and ev are studied for large classes of second order stationary ergodic processes in the sense of the wold decomposition scheme including harmonic and evanescent processes minimal rates of convergence for the em and the ev are derived for these processes they are used as criteria for assessing the stationarity of textures the experimental estimation of the rate of convergence is achieved using a nonparametric block sub sampling method our framework is evaluated on synthetic processes with stationary or nonstationary mean and variance and on real textures it is shown that anomalies in the asymptotic behavior of the empirical estimators allow detecting nonstationarities of the mean and variance of the processes in an objective way

finite gap jacobi matrices an announcement we consider jacobi matrices whose essential spectrum is a finite union of closed intervals we focus on szego s theorem jost solutions and szego asymptotics for this situation this announcement describes talks the authors gave at opsfa 2007

estimation in semiparametric spatial regression nonparametric methods have been very popular in the last couple of decades in time series and regression but no such development has taken place for spatial models a rather obvious reason for this is the curse of dimensionality for spatial data on a grid evaluating the conditional mean given its closest neighbors requires a four dimensional nonparametric regression in this paper a semiparametric spatial regression approach is proposed to avoid this problem an estimation procedure based on combining the so called marginal integration technique with local linear kernel estimation is developed in the semiparametric spatial regression setting asymptotic distributions are established under some mild conditions the same convergence rates as in the one dimensional regression case are established an application of the methodology to the classical mercer and hall wheat data set is given and indicates that one directional component appears to be nonlinear which has gone unnoticed in earlier analyses

a central limit theorem for stationary random fields we prove a central limit theorem for strictly stationary random fields under a projective assumption our criterion is similar to projective criteria for stationary sequences derived from gordin s theorem about approximating martingales however our approach is completely different for we establish our result by adapting lindeberg s method the criterion that it provides is weaker than martingale type conditions and moreover we obtain as a straightforward consequence central limit theorems for mixing or mixing random fields

inference with dependent data using cluster covariance estimators this paper presents a novel way to conduct inference using dependent data in time series spatial and panel data applications our method involves constructing t and wald statistics utilizing a cluster covariance matrix estimator cce we then use an approximation that takes the number of clusters groups as xed and the number of observations per group to be large and calcu late limiting distributions of the t and wald statistics this approximation is analogous to xed b asymptotics of kiefer and vogelsang 2002 2005 kv for heteroskedasticity and autocorrelation consistent inference but in our case yields standard t and f distributions where the number of groups essentially plays the role of sample size we provide simulation evidence that demonstrates our procedure outperforms conventional inference procedures and performs comparably to kv

the analogue of buchi s problem for function fields abstract buchi s n squares problem asks for an integer m such that any sequence x 0 x m 1 whose second difference of squares is the constant sequence 2 i e x n 2 2 x n 1 2 x n 2 2 2 for all n satisfies x n 2 x n 2 for some integer x hensley s problem for r th powers where r is an integer 2 is a generalization of buchi s problem asking for an integer m such that given integers and a the quantity n r a cannot be an r th power for m or more values of the integer n unless a 0 the analogues of these problems for rings of functions consider only sequences with at least one non constant term let k be a function field of a curve of genus g we prove that hensley s problem for r th powers has a positive answer for any r if k has characteristic zero improving results by pasten and vojta in positive characteristic p we obtain a weaker result but which is enough to prove that buchi s problem has a positive answer if p 312 g 169 improving results by pheidas and the second author

orthogonal polynomials of equilibrium measures supported on cantor sets the equilibrium measure of a compact set is a fundamental object in logarithmic potential theory we compute numerically this measure and its orthogonal polynomials when the compact set is a cantor set defined by an iterated function system we first construct sequences of discrete measures via the solution of large systems of non linear equations that converge weakly to the equilibrium measure successively we compute their jacobi matrices via standard procedures enhanced for the scope numerical estimates of the convergence rate to the limit jacobi matrix are provided which show stability and efficiency of the whole procedure as a companion result we also compute jacobi matrices in two other cases equilibrium measures on finite sets of intervals and balanced measures of iterated function systems these algorithms can reach large polynomial orders therefore we study the asymptotic behavior of the orthogonal polynomials and by a natural extension of the concept of regular root asymptotics we derive an efficient scheme for the computation of complex green s functions and of related conformal mappings

uniform existential interpretation of arithmetic in rings of functions of positive characteristic we show that first order integer arithmetic is uniformly positive existentially interpretable in large classes of subrings of function fields of positive characteristic over some languages that contain the language of rings one of the main intermediate results is a positive existential definition in these classes uniform among all characteristics p of the binary relation y x p s or x y p s for some integer s 0 a natural consequence of our work is that there is no algorithm to decide whether or not a system of polynomial equations over mathbb z z has solutions in all but finitely many polynomial rings mathbb f p z analogous consequences are deduced for the rational function fields mathbb f p z over languages with a predicate for the valuation ring at zero

sum rules for jacobi matrices and their applications to spectral theory we discuss the proof of and systematic application of case s sum rules for jacobi matrices of special interest is a linear combination of two of his sum rules which has strictly positive terms among our results are a complete classification of the spectral measures of all jacobi matrices j for which j j 0 is hilbert schmidt and a proof of nevai s conjecture that the szego condition holds if j j 0 is trace class

recursively enumerable sets of polynomials over a finite field are diophantine we construct a diophantine interpretation of mathbb f q w z over mathbb f q z using this together with a previous result that every recursively enumerable r e relation over mathbb f q z is diophantine over mathbb f q w z we will prove that every r e relation over mathbb f q z is diophantine over mathbb f q z we will also look at recursive infinite base fields mathbb f algebraic over mathbb f p it turns out that the diophantine relations over mathbb f z are exactly the relations which are r e for every recursive presentation

estimating equations for spatially correlated data in multi dimensional space summary we use the quasilikelihood concept to propose an estimating equation for spatial data with correlation across the study region in a multi dimensional space with appropriate mixing con ditions we develop a central limit theorem for a random field under various lp metrics the consistency and asymptotic normality of quasilikelihood estimators can then be derived we also conduct simulations to evaluate the performance of the proposed estimating equation and a dataset from east lansing woods is used to illustrate the method

loss network representation of peierls contours we present a probabilistic approach for the study of systems with exclusions in the regime traditionally studied via cluster expansion methods in this paper we focus on its application for the gases of peierls contours found in the study of the ising model at low temperatures but most of the results are general we realize the equilibrium measure as the invariant measure of a loss network process whose existence is ensured by a subcriticality condition of a dominant branching process in this regime the approach yields besides existence and uniqueness of the measure properties such as exponential space convergence and mixing and a central limit theorem the loss network converges exponentially fast to the equilibrium measure without metastable traps this convergence is faster at low temperatures where it leads to the proof of an asymptotic poisson distribution of contours our results on the mixing properties of the measure are comparable to those obtained with duplicated variables expansion used to treat systems with disorder and coupled map lattices it works in a larger region of validity than usual cluster expansion formalisms and it is not tied to the analyticity of the pressure in fact it does not lead to any kind of expansion for the latter and the properties of the equilibrium measure are obtained without resorting to combinatorial or complexanalysis techniques

resampling methods for spatial regression models under a class of stochastic designs in this paper we consider the problem of bootstrapping a class of spatial regression models when the sampling sites are generated by a possibly nonuniform stochastic design and are irregularly spaced it is shown that the natural extension of the existing block bootstrap methods for grid spatial data does not work for irregularly spaced spatial data under nonuniform stochastic designs a variant of the blocking mechanism is proposed it is shown that the proposed block bootstrap method provides a valid approximation to the distribution of a class of m estimators of the spatial regression parameters finite sample properties of the method are investigated through a moderately large simulation study and a real data example is given to illustrate the methodology

assessing isotropy for spatial point processes summary a common assumption while analyzing spatial point processes is direction invariance i e isotropy in this article we propose a formal nonparametric approach to test for isotropy based on the asymptotic joint normality of the sample second order intensity function we derive an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample second order intensity function and use this to construct a test statistic with a 2 limiting distribution we demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set where our approach confirms suspected directional effects in the spatial distribution of the desert plant species

prediction of spatial cumulative distribution functions using subsampling abstract the spatial cumulative distribution function scdf is a random function that provides a statistical summary of a random field over a spatial domain of interest in this article we develop a spatial subsampling method for predicting an scdf based on observations made on a hexagonal grid similar to the one used in the environmental monitoring and assessment program of the u s environmental protection agency we show that under quite general conditions the proposed subsampling method provides accurate data based approximations to the sampling distributions of various functionals of the scdf predictor in particular it produces estimators of different population characteristics such as the quantiles and weighted mean integrated squared errors of the empirical predictor as an illustration we apply the subsampling method to construct large sample prediction bands for the scdf of an ecological index for foliage condition of red maple trees in the state of maine

reflectionless herglotz functions and jacobi matrices we study several related aspects of reflectionless jacobi matrices first we discuss the singular part of the corresponding spectral measures we then show how to identify sets on which measures are reflectionless by looking at the logarithmic potentials of these measures

limit theory for panel data models with cross sectional dependence and sequential exogeneity abstract the paper derives a general central limit theorem clt and asymptotic distributions for sample moments related to panel data models with large n the results allow for the data to be cross sectionally dependent while at the same time allowing the regressors to be only sequentially rather than strictly exogenous the setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and or from the presence of common factors the latter leads to the need for random norming the limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied we prove such a central limit theorem by first extending results for stable convergence in hall and heyde 1980 to non nested martingale arrays relevant for our applications we illustrate our result by establishing a generalized estimation theory for gmm estimators of a fixed effect panel model without imposing i i d or strict exogeneity conditions we also discuss a class of maximum likelihood ml estimators that can be analyzed using our clt

variance estimation for statistics computed from spatial lattice data summary a statistic s is computed on spatially indexed data x i e d where d is a finite subset of the integer lattice 22 we propose a method for estimating the variance and other moments of s by using only the data the set d may be irregularly shaped the statistic s may be arbitrarily complicated and no distributional assumptions marginal or joint are necessary the method uses the statistic computed on overlapping subshapes of d as replicates of s the estimator is simply the sample variance of the standardized replicates we demonstrate c2 consistency of the estimator under mild conditions on s and the strength of spatial dependence a rate of convergence is also given giving guidance into the appropriate choice of subshape size and the estimator is illustrated in two data examples

on central limit theorems in the random connection model abstract consider a sequence of poisson random connection models x n n g n on r d where n n d 0 and g n x g nx for some non increasing integrable connection function g let i n g be the number of isolated vertices of x n n g n in some bounded borel set k where k has non empty interior and boundary of lebesgue measure zero roy and sarkar physica a 318 2003 1047 claim that i n g e i n g v ar i n g n 0 1 n where denotes convergence in distribution however their proof has errors we correct their proof and extend the result to larger components when the connection function g has bounded support

on subsampling estimators with unknown rate of convergence abstract politis and romano have put forth a general subsampling methodology for the construction of large sample confidence regions for a general unknown parameter associated with the probability distribution generating the stationary sequence x 1 x n the subsampling methodology hinges on approximating the large sample distribution of a statistic t n t n x 1 x n that is consistent for at some known rate n although subsampling has been shown to yield confidence regions for of asymptotically correct coverage under very weak assumptions the applicability of the methodology as it has been presented so far is limited if the rate of convergence n happens to be unknown or intractable in a particular setting in this article we show how it is possible to circumvent this limitation by a using the subsampling methodology to derive a consistent estimator of the rate n and b using the estimated rate to construct asymptotically correct confidence regions for based on subsampling

hilbert s tenth problem for fields of rational functions over finite fields we prove that there is no algorithm to solve arbitrary polynomial equations over a field of rational functions in one letter with constants in a finite field of characteristic other than 2 and hence hilbert s tenth problem for any such field is undecidable

green s functions for multiply connected domains via conformal mapping a method is described for the computation of the green s function in the complex plane corresponding to a set of k symmetrically placed polygons along the real axis an important special case is a set of k real intervals the method is based on a schwarz christoffel conformal map of the part of the upper half plane exterior to the problem domain onto a semi infinite strip whose end contains k 1 slits from the green s function one can obtain a great deal of information about polynomial approximations with applications in digital filters and matrix iterations by making the end of the strip jagged the method can be generalized to weighted green s functions and weighted approximations

efficient pairwise composite likelihood estimation for spatial clustered data spatial clustered data refer to high dimensional correlated measurements collected from units or subjects that are spatially clustered such data arise frequently from studies in social and health sciences we propose a unified modeling framework termed as geocopula to characterize both large scale variation and small scale variation for various data types including continuous data binary data and count data as special cases to overcome challenges in the estimation and inference for the model parameters we propose an efficient composite likelihood approach in that the estimation efficiency is resulted from a construction of over identified joint composite estimating equations consequently the statistical theory for the proposed estimation is developed by extending the classical theory of the generalized method of moments a clear advantage of the proposed estimation method is the computation feasibility we conduct several simulation studies to assess the performance of the proposed models and estimation methods for both gaussian and binary spatial clustered data results show a clear improvement on estimation efficiency over the conventional composite likelihood method an illustrative data example is included to motivate and demonstrate the proposed method

asymptotic distribution of the empirical spatial cumulative distribution function predictor and prediction bands based on a subsampling method a spatial cumulative distribution function f say is a random distribution function that provides a statistical summary of random field over a given region this paper considers the empirical predictor of f based on a finite set of observations from a region in d under a uniform sampling design a functional central limit theorem is proved for the predictor as a random element of the space d a striking feature of the result is that the rate of convergence of the predictor to the predictand f depends on the location of the data sites specified by the sampling design a precise description of the dependence is given furthermore a subsampling method is proposed for integral based functionals of random fields which is then used to construct large sample prediction bands for f

a central limit theorem for endogenous locations and complex spatial interactions we provide a new central limit theorem clt for spatial processes under weak conditions that are plausible for many economic applications in which location is endogenous in particular our clt is designed for problems that have some but not necessarily all of the following features i agents choose the locations of observations to maximize profits welfare or some other objective ii the objects that are chosen e g stores or brands interact with one another for example they can be substitutes or complements iii interaction can be complex in particular interaction between i and j need not depend only on the distance between the locations of i and j but can also depend on distance to or location of other observations k or possibly on the number of other such observations

local spectral properties of reflectionless jacobi cmv and schrodinger operators we prove that jacobi cmv and schrodinger operators which are reflectionless on a homogeneous set e in the sense of carleson under the assumption of a blaschke type condition on their discrete spectra accumulating at e have purely absolutely continuous spectrum on e

sharp lower bounds for the widom factors on the real line abstract we derive lower bounds for the l p norms of monic extremal polynomials with respect to compactly supported probability measures we obtain a sharp universal lower bound for all 0 p and all measures in the szeg class and an improved lower bound on l 2 norm for several classes of orthogonal polynomials including jacobi polynomials isospectral torus of a finite gap set and orthogonal polynomials with respect to the equilibrium measure of an arbitrary non polar compact subset of r

window subsampling of estimating functions with application to regression models abstract we propose a subsampling method for estimating the asymptotic standard error of a statistic n that is the solution to an estimating equation 1 n n j 1 uj y j xj 0 where the data yj may be temporally or spatially correlated and the estimating function may depend on covariates xj a key statistic that we consider in detail is a generalized linear model regression coefficient computed under the assumption of independence the availability of a consistent variance estimator allows semiparametric regression approaches for clustered and longitudinal data to be used with time series and spatial data the methods that we develop extend the subsampling ideas of carlstein sherman and garcia soidan and hall to estimating functions our approach provides an attractive alternative to the jackknife method of lele particularly for large datasets because we do not require parameter reestimation

decay of correlations under dobrushin s uniqueness condition and its applications an estimate on the correlation of functionals of gibbs fields satisfying dobrushin s uniqueness condition is given as a consequence a result of gross saying that the truncated pair correlation function decays in the same weighted summability sense as the potential can be extended to the whole dobrushin uniqueness region applications to the central limit theorem and the second derivative of the pressure are also given

subseries methods in regression abstract we extend subseries methods for stationary sequences to the regression setting to estimate sampling distributions the subseries approach computes the statistic of interest on all possible subseries of a shorter length than the original series and uses the distribution of these replicates to mimic the distribution of the original statistic for proper choice of subseries length the regression parameters can be estimated to order o n 2 3 thus improving on the normal approximation the replicates can also be used to reduce the bias of robust estimators simulation results demonstrate the finite sample effectiveness of the approach for both distribution function estimation and bias reduction applications to spatial data are also discussed

estimation and inference of change points in high dimensional factor models abstract in this paper we consider the estimation of break points in high dimensional factor models where the unobserved factors are estimated by principal component analysis pca the factor loading matrix is assumed to have a structural break at an unknown time we establish the conditions under which the least squares ls estimator is consistent for the break date our consistency result holds for both large and small breaks we also find the ls estimator s asymptotic distribution simulation results confirm that the break date can be accurately estimated by the ls even if the magnitudes of breaks are small in two empirical applications we implement the method to estimate break points in the u s stock market and u s macroeconomy respectively

statistical inference on regression with spatial dependence central limit theorems are developed for instrumental variables estimates of linear and semiparametric partly linear regression models for spatial data general forms of spatial dependence and heterogeneity in explanatory variables and unobservable disturbances are permitted we discuss estimation of the variance matrix including estimates that are robust to disturbance heteroscedasticity and or dependence a monte carlo study of finite sample performance is included in an empirical example the estimates and robust and non robust standard errors are computed from indian regional data following tests for spatial correlation in disturbances and nonparametric regression fitting some final comments discuss modifications and extensions

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

statistical inference for max stable processes in space and time max stable processes have proved to be useful for the statistical modelling of spatial extremes several families of max stable random fields have been proposed in the literature one such representation is based on a limit of normalized and rescaled pointwise maxima of stationary gaussian processes that was first introduced by kabluchko and co workers this paper deals with statistical inference for max stable space time processes that are defined in an analogous fashion we describe pairwise likelihood estimation where the pairwise density of the process is used to estimate the model parameters for regular grid observations we prove strong consistency and asymptotic normality of the parameter estimates as the joint number of spatial locations and time points tends to furthermore we discuss extensions to irregularly spaced locations a simulation study shows that the method proposed works well for these models

analysis of binary spatial data by quasi likelihood estimating equations the goal of this paper is to describe the application of quasi likelihood estimating equations for spatially correlated binary data in this paper a logistic function is used to model the marginal probability of binary responses in terms of parameters of interest with mild assumptions on the correlations the leonov shiryaev formula combined with a comparison of characteristic functions can be used to establish asymptotic normality for linear combinations of the binary responses the consistency and asymptotic normality for quasi likelihood estimates can then be derived by modeling spatial correlation with a variogram we apply these asymptotic results to test independence of two spatially correlated binary outcomes and illustrate the concepts with a well known example based on data from lansing woods the comparison of generalized estimating equations and the proposed approach is also discussed