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

on the behavior of randomization tests without a group invariance assumption abstract fisher s randomization construction of hypothesis tests is a powerful tool to yield tests that are nonparametric in nature in that their level is exactly equal to the nominal level in finite samples over a wide range of distributional assumptions for example the usual permutation t test to test equality of means is valid without a normality assumption of the underlying populations on the other hand fisher s randomization construction is not applicable in this example unless the underlying populations differ only in location in general the basis for the randomization construction is invariance of the probability distribution of the data under a transformation group it is the goal of this article to understand the robustness properties of randomization tests by studying their asymptotic validity in situations where the basis for their construction breaks down here asymptotic validity refers to whether the probability of a type i error tends asymptotically to the nominal level in particula

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

bootstrap and permutation tests of independence for point processes motivated by a neuroscience question about synchrony detection in spike train analysis we deal with the independence testing problem for point processes we introduce non parametric test statistics which are rescaled general u statistics whose corresponding critical values are constructed from bootstrap and randomization permutation approaches making as few assumptions as possible on the underlying distribution of the point processes we derive general consistency results for the bootstrap and for the permutation w r t to wasserstein s metric which induce weak convergence as well as convergence of second order moments the obtained bootstrap or permutation independence tests are thus proved to be asymptotically of the prescribed size and to be consistent against any reasonable alternative a simulation study is performed to illustrate the derived theoretical results and to compare the performance of our new tests with existing ones in the neuroscientific literature

identification and estimation of econometric models with group interactions contextual factors and fixed effects this paper considers identification and estimation of structural interaction effects in a social interaction model the model allows unobservables in the group structure which may be correlated with included regressors we show that both the endogenous and exogenous interaction effects can be identified if there are sufficient variations in group sizes we consider the estimation of the model by the conditional maximum likelihood and instrumental variables methods for the case with large group sizes the possible identification can be weak in the sense that the estimates converge in distribution at low rates

testing continuity of a density via g order statistics in the regression discontinuity design abstract in the regression discontinuity design rdd it is common practice to assess the credibility of the design by testing the continuity of the density of the running variable at the cut off e g mccrary 2008 in this paper we propose an approximate sign test for continuity of a density at a point based on the so called g order statistics and study its properties under two complementary asymptotic frameworks in the first asymptotic framework the number q of observations local to the cut off is fixed as the sample size n diverges to infinity while in the second framework q diverges to infinity slowly as n diverges to infinity under both of these frameworks we show that the test we propose is asymptotically valid in the sense that it has limiting rejection probability under the null hypothesis not exceeding the nominal level more importantly the test is easy to implement asymptotically valid under weaker conditions than those used by competing methods and exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity in a simulation study we find that the approximate sign test provides good control of the rejection probability under the null hypothesis while remaining competitive under the alternative hypothesis we finally apply our test to the design in lee 2008 a well known application of the rdd to study incumbency advantage

upscaling of a parabolic system with a large nonlinear surface reaction term abstract motivated by the study of the dynamics of calcium ions in biological cells the authors derived in 33 via periodic homogenization a macroscopic bidomain model by considering in the corresponding microscopic two component problem a properly scaled nonlinear exchange term we study here at the microscopic scale a similar parabolic system with a large nonlinear interfacial reaction term at the macroscopic scale the nonlinear effect of this reaction term is recovered in the homogenized diffusion matrix which is not anymore constant this nonstandard phenomenon shows the fine interplay between reaction and diffusion in such processes

the method of elimination and substitution in the gmm estimation of mixed regressive spatial autoregressive models this paper proposes a computationally simple gmm for the estimation of mixed regressive spatial autoregressive models the proposed method explores the advantage of the method of elimination and substitution in linear algebra the modified gmm approach reduces the joint nonlinear estimation of a complete vector of parameters into estimation of separate components for the mixed regressive spatial autoregressive model the nonlinear estimation is reduced to the estimation of the single spatial effect parameter we identify situations under which the resulting estimator can be efficient relative to the joint gmm estimator where all the parameters are jointly estimated

modeling complex networks with self similar outerplanar unclustered graphs this paper introduces a family of modular self similar small world graphs with clustering zero relevant properties of this family are comparable to those of some networks associated with technological systems with a low clustering like the power grid or some electronic circuits moreover the graphs are outerplanar and it is know that many algorithms that are np complete for general graphs perform polynomial in outerplanar graphs therefore the graphs constitute a good mathematical model for these systems

homogenization of an alternating robin neumann boundary condition via time periodic unfolding abstract we consider the homogenization of a parabolic problem in a perforated domain with robin neumann boundary conditions oscillating in time such oscillations must compensate the blow up of the boundary measure of the holes we use the technique of time periodic unfolding in order to obtain a macroscopic parabolic problem containing an extra linear term due to the absorption determined by the robin condition

panel data models with spatially correlated error components abstract in this paper we consider a panel data model with error components that are both spatially and time wise correlated the model blends specifications typically considered in the spatial literature with those considered in the error components literature we introduce generalizations of the generalized moments estimators suggested in kelejian and prucha 1999 a generalized moments estimator for the autoregressive parameter in a spatial model international economic review 40 509 533 for estimating the spatial autoregressive parameter and the variance components of the disturbance process we then use those estimators to define a feasible generalized least squares procedure for the regression parameters we give formal large sample results for the proposed estimators we emphasize that our estimators remain computationally feasible even in large samples

tests for a change point summary the problem considered is that of testing a sequence of independent normal random variables with constant known or unknown variance for no change in mean versus alternatives with a single change point various tests such as those based on the likelihood ratio and recursive residuals are studied power approximations are developed by integrating approximations for conditional boundary crossing probabilities a comparison of several tests is made

random fields on a network modeling statistics and applications the theory of spatial models over lattices or random fields as they are known has developed significantly over recent years this book provides a graduate level introduction to the subject which assumes only a basic knowledge of probability and statistics finite markov chains and the spectral theory of second order processes a particular strength of this book is its emphasis on examples both to motivate the theory which is being developed and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms

combining estimators to improve structural model estimation and inference under quadratic loss asymptotically semi parametric estimators of the parameters in linear structural models have the same sampling properties in finite samples the sampling properties of these estimators vary and large biases may result for sample sizes often found in practice with a goal of improving asymptotic risk performance and finite sample efficiency properties we investigate the idea of combining correlated structural equation estimators with different finite and asymptotic sampling characteristics based on a quadratic loss measure we present evidence that the finite sample performance of the resulting combination estimator can be notably superior to that of a leading traditional moment based estimator

permutation tests for least absolute deviation regression a permutation test based on proportionate reduction in sums of absolute deviations when passing from reduced to full parameter models is developed for testing hypotheses about least absolute deviation lad estimates of conditional medians in linear regression models sampling simulations demonstrated that the permutation test on full model lad estimates had greater relative power 1 06 1 43 than normal theory tests on least squares estimates for asymmetric chi square error distributions and symmetric double exponential error distributions for models with one n 35 and n 63 and three n 63 independent variables relative power was 77 84 for normal error distributions power simulations demonstrated the low sensitivity of lad estimates and permutation tests to outlier contamination and heteroscedasticity that was a linear function of x and increased sensitivity to heteroscedasticity that was a function of x2 for simple regression models three permutation procedures for testing partial models in multiple regression were compared permuting residuals from the reduced model permuting residuals from the full model and permuting the dependent variable permuting residuals from the reduced model maintained nominal error rates best under the null hypothesis for all error distributions and for correlated and uncorrelated independent variables power under the alternative hypotheses for this partial testing procedure was similar to full lad regression model tests four example applications of lad regression are provided

a uniform law of large numbers for dependent and heterogeneous data processes uniform laws of large numbers ullns consider sums of the form n 1 t n 1 q t z t eq t z t where z t denotes a stochastic data generating process that takes its values in a space z is an element of the parameter space and q t z r ullns provide conditions under which the above sum converges to zero uniformly over the parameter space the purpose of the present note is to introduce a new generic ulln it maintains a set of assumptions that is relatively easy to verify and allows at the same time the analysis of a wide variety of estimators and models of interest in economics

homogenization results for a coupled system of reaction diffusion equations abstract the macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction diffusion processes in periodic porous media is analyzed our mathematical model can be used for studying several metabolic processes taking place in living cells in which biochemical species can diffuse in the cytosol and react both in the cytosol and also on the organellar membranes the coupling of the concentrations of the biochemical species is realized via various properly scaled nonlinear reaction terms these nonlinearities which model at the microscopic scale various volume or surface reaction processes give rise in the macroscopic model to different effects such as the appearance of additional source or sink terms or of a non standard diffusion matrix

bias reduction in nonlinear and dynamic panels in the presence of cross section dependence abstract fixed effects estimation of nonlinear dynamic panel models is subject to the incidental parameter issue leading to a biased asymptotic distribution while this problem has been studied extensively in the literature a general analysis allowing for both serial and cross sectional dependence is missing in this paper we investigate the large n t theory of the profile and integrated likelihood estimators allowing for dependence across both dimensions we show that under stronger dependence types the asymptotic bias disappears but a o p 1 t small sample bias remains we provide bias correction and inference methods and also obtain primitive conditions for asymptotic normality under various dependence settings

generic uniform convergence and equicontinuity concepts for random functions abstract equicontinuity type concepts for random functions which are important for establishing convergence results for such functions have increasingly been used in the econometrics literature in this paper we define and discuss various equicontinuity type concepts for random functions and employ those concepts to provide sufficient conditions for uniform convergence and in particular for uniform laws of large numbers furthermore we clarify the differences and similarities between uniform laws of large numbers based on pointwise and local laws of large numbers given in the recent literature as they relate to differences in the employed equicontinuity type concepts

a bootstrap revival of some nonparametric distance tests abstract several tests based on the empirical measure have been proposed to test independence of variables goodness of fit equality of distributions rotational invariance and so forth these tests have excellent power properties but critical values are difficult if not impossible to obtain furthermore these tests usually assume that the data are real valued with continuous distributions here critical values are determined by bootstrapping and the resulting tests are shown to have the correct asymptotic level under minimal assumptions for example given data xi x i 1 xi d i 1 n it may be desired to test independence of the d components the proposed test compares the empirical measure and the product of its marginals by taking a supremum over an appropriate vapnik cervonenkis class of sets no assumptions are made on the probability distribution of the data or on the space in which it lives indeed some components may be discrete some continuous and others categorical simil

placebo inference on treatment effects when the number of clusters is small abstract i introduce a general fisher style randomization testing framework to conduct nearly exact inference about the lack of effect of a binary treatment in the presence of very few large clusters when the treatment effect is identified across clusters the proposed randomization test formalizes and extends the intuitive notion of generating null distributions by assigning placebo treatments to untreated clusters i show that under simple and easily verifiable conditions the placebo test leads to asymptotically valid inference in a very large class of empirically relevant models examples discussed explicitly are i least squares regression with cluster level treatment ii difference in differences estimation and iii binary choice models with cluster level treatment a simulation study and an empirical example are provided the proposed inference procedure is easy to implement and performs well with as few as three treated and three untreated clusters

a multiscale galerkin approach for a class of nonlinear coupled reaction diffusion systems in complex media abstract a galerkin approach for a class of multiscale reaction diffusion systems with nonlinear coupling between the microscopic and macroscopic variables is presented this type of models are obtained e g by upscaling of processes in chemical engineering particularly in catalysis biochemistry or geochemistry exploiting the special structure of the models the functions spaces used for the approximation of the solution are chosen as tensor products of spaces on the macroscopic domain and on the standard cell associated to the microstructure uniform estimates for the finite dimensional approximations are proven based on these estimates the convergence of the approximating sequence is shown this approach can be used as a basis for the numerical computation of the solution

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

exact and asymptotically robust permutation tests given independent samples from p and q two sample permutation tests allow one to construct exact level tests when the null hypothesis is p q on the other hand when comparing or testing particular parameters of p and q such as their means or medians permutation tests need not be level or even approximately level in large samples under very weak assumptions for comparing estimators we provide a general test procedure whereby the asymptotic validity of the permutation test holds while retaining the exact rejection probability in finite samples when the underlying distributions are identical a quite general theory is possible based on a coupling construction as well as a key contiguity argument for the binomial and hypergeometric distributions the ideas are broadly applicable and special attention is given to a nonparametric k sample behrens fisher problem whereby a permutation test is constructed which is exact level under the hypothesis of identical distributions but has asymptotic rejection probability under the more general null hypothesis of equality of means a monte carlo simulation study is performed 2010 msc subject classifications primary 62e20 secondary 62g10

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

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

estimation of simultaneous systems of spatially interrelated cross sectional equations in this paper we consider a simultaneous system of spatially interrelated cross sectional equations our speci cation incorporates spatial lags in the endogenous and exogenous variables in modelling the disturbance process we allow for both spatial correlation as well as correlation across equations the data set is taken to be a single cross section of observations the model may be viewed as an extension of the widely used single equation cli3 ord model we suggest computationally simple limited and full information instrumental variable estimators for the parameters of the system and give formal large sample results

multivariate and multiple permutation tests abstract in this article we consider the use of permutation tests for comparing multivariate parameters from two populations first the underlying properties of permutation tests when comparing parameter vectors from two distributions p and q are developed although an exact level test can be constructed by a permutation test when the fundamental assumption of identical underlying distributions holds permutation tests have often been misused indeed permutation tests have frequently been applied in cases where the underlying distributions need not be identical under the null hypothesis in such cases permutation tests fail to control the type 1 error even asymptotically however we provide valid procedures in the sense that even when the assumption of identical distributions fails one can establish the asymptotic validity of permutation tests in general while retaining the exactness property when all the observations are i i d in the multivariate testing problem for testing the global null hypothesis of equality of parameter vectors a modified hotelling s t 2 statistic as well as tests based on the maximum of studentized absolute differences are considered in the latter case a bootstrap prepivoting test statistic is constructed which leads to a bootstrapping after permuting algorithm then these tests are applied as a basis for testing multiple hypotheses simultaneously by invoking the closure method to control the familywise error rate lastly monte carlo simulation studies and an empirical example are presented

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

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

some nonasymptotic results on resampling in high dimension i confidence regions we study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure the random vector is supposed to be either gaussian or to have a symmetric and bounded distribution the dimensionality of the vector can possibly be much larger than the number of observations and we focus on a non asymptotic control of the confidence level following ideas inspired by recent results in learning theory we consider two approaches the first based on a concentration principle valid for a large class of resampling weights and the second on a direct resampled quantile specifically using rademacher weights several intermediate results established in the approach based on concentration principles are of self interest we also discuss the question of accuracy when using monte carlo approximations of the resampled quantities we present an application of these results to the one sided and two sided multiple testing problem in which we derive several resampling based step down procedures providing a non asymptotic fwer control we compare our different procedures in a simulation study and we show that they can outperform bonferroni s or holm s procedures as soon as the observed vector has sufficiently correlated coordinates

how do bootstrap and permutation tests work resampling methods are frequently used in practice to adjust critical values of nonparametric tests in the present paper a comprehensive and unified approach for the conditional and unconditional analysis of linear resampling statistics is presented under fairly mild assumptions we prove tightness and an asymptotic series representation for their weak accumulation points from this series it becomes clear which part of the resampling statistic is responsible for asymptotic normality the results leads to a discussion of the asymptotic correctness of resampling methods as well as their applications in testing hypotheses they are conditionally correct iff a central limit theorem holds for the original test statistic we prove unconditional correctness iff the central limit theorem holds or when symmetric random variables are resampled by a scheme of asymptotically random signs special cases are the m n out of k n bootstrap the weighted bootstrap the wild bootstrap and all kinds of permutation statistics the program is carried out for convergent partial sums of rowwise independent infinitesimal triangular arrays in detail these results are used to compare power functions of conditional resampling tests and their unconditional counterparts the proof uses the method of random scores for permutation type statistics

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

randomization tests under an approximate symmetry assumption this paper develops a theory of randomization tests under an approximate symmetry assumption randomization tests provide a general means of constructing tests that control size in nite samples whenever the distribution of the observed data exhibits symmetry under the null hypothesis here by exhibits symmetry we mean that the distribution remains invariant under a group of transformations in this paper we provide conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis an important application of this idea is in settings where the data may be grouped into a xed number of clusters with a large number of observations within each cluster in such settings we show that the distribution of the observed data satises our approximate symmetry requirement under weak assumptions in particular our results allow for the clusters to be heterogeneous and also have dependence not only within each cluster but also across clusters this approach enjoys several advantages over other approaches in these settings among other things it leads to a test that is asymptotically similar which as shown in a simulation study translates into improved power at many alternatives finally we use our results to revisit the analysis of angrist and lavy 2009 who examine the impact of a cash award on exam performance for low achievement students in israel

an assumption free exact test for fixed design linear models with exchangeable errors we propose the cyclic permutation test cpt to test general linear hypotheses for linear models this test is non randomized and valid in finite samples with exact type i error alpha for an arbitrary fixed design matrix and arbitrary exchangeable errors whenever 1 alpha is an integer and n p ge 1 alpha 1 the test involves applying the marginal rank test to 1 alpha linear statistics of the outcome vector where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a non standard cyclic permutation group under the null hypothesis the power can be further enhanced by solving a secondary non linear travelling salesman problem for which the genetic algorithm can find a reasonably good solution extensive simulation studies show that the cpt has comparable power to existing tests when testing for a single contrast of coefficients an exact confidence interval can be obtained by inverting the test furthermore we provide a selective yet extensive literature review of the century long efforts on this problem highlighting the novelty of our test

permutation tests for joinpoint regression with applications to cancer rates the identification of changes in the recent trend is an important issue in the analysis of cancer mortality and incidence data we apply a joinpoint regression model to describe such continuous changes and use the grid search method to fit the regression function with unknown joinpoints assuming constant variance and uncorrelated errors we find the number of significant joinpoints by performing several permutation tests each of which has a correct significance level asymptotically each p value is found using monte carlo methods and the overall asymptotic significance level is maintained through a bonferroni correction these tests are extended to the situation with non constant variance to handle rates with poisson variation and possibly autocorrelated errors the performance of these tests are studied via simulations and the tests are applied to u s prostate cancer incidence and mortality rates

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

nonparametric hypothesis tests for statistical dependency determining the structure of dependencies among a set of variables is a common task in many signal and image processing applications including multitarget tracking and computer vision in this paper we present an information theoretic machine learning approach to problems of this type we cast this problem as a hypothesis test between factorizations of variables into mutually independent subsets we show that the likelihood ratio can be written as sums of two sets of kullback leibler kl divergence terms the first set captures the structure of the statistical dependencies within each hypothesis whereas the second set measures the details of model differences between hypotheses we then consider the case when the signal prior models are unknown so that the distributions of interest must be estimated directly from data showing that the second set of terms is asymptotically negligible and quantifying the loss in hypothesis separability when the models are completely unknown we demonstrate the utility of nonparametric estimation methods for such problems providing a general framework for determining and distinguishing between dependency structures in highly uncertain environments additionally we develop a machine learning approach for estimating lower bounds on kl divergence and mutual information from samples of high dimensional random variables for which direct density estimation is infeasible we present empirical results in the context of three prototypical applications association of signals generated by sources possessing harmonic behavior scene correspondence using video imagery and detection of coherent behavior among sets of moving objects

randomization inference for difference in differences with few treated clusters abstract inference using difference in differences with clustered data requires care previous research has shown that when there are few treated clusters t tests based on cluster robust variance estimators crves severely overreject and different variants of the wild cluster bootstrap can either overreject or underreject dramatically we study two randomization inference ri procedures a procedure based on estimated coefficients may be unreliable when clusters are heterogeneous a procedure based on t statistics typically performs better although by no means perfectly under the null but at the cost of some power loss an empirical example demonstrates that ri procedures can yield inferences that differ dramatically from those of other methods

contracting in space an application of spatial statistics to discrete choice models abstract we develop tests for spatial error correlation and methods of estimation in the presence of such correlation for discrete choice models the tests which are based on the notion of a generalized residual are a set of orthogonality conditions that should be satisfied under the null when the restrictions are rejected the full model can be estimated by generalized method of moments these techniques are used to evaluate spatial patterns in retail gasoline contracts we examine whether the spatial configuration is random or whether there is a tendency towards clustering or dispersion of contract types the data consist of all contracts between integrated oil companies and their branded service stations in the city of vancouver six metrics or measures of closeness are examined euclidean distance competition along streets a combination of the first two nearest neighbors along streets nearest neighbors in euclidean distance and neighbors that share a common marked boundary

vertex degree sequences in complex networks new characteristics and applications abstract many complex networks exhibit a scale free vertex degree distribution in a power law form c k where k is the vertex degree variable and c and are constants to better understand the mechanism of power law formation in real world networks it is effective to explore and analyze their vertex degree sequences we had shown before that for a scale free network of size n if its vertex degree sequence is k 1 k 2 k l where k 1 k 2 k l is the set of all unequal vertex degrees in the network and if its power exponent satisfies 1 then the length l of the vertex degree sequence is of order log n in the present paper we further study complex networks with an exponential vertex degree distribution and prove that the same conclusion also holds in addition we verify our claim by showing many real world examples we finally discuss some applications of the new finding in various fields of science and technology

a functional central limit theorem for strongly mixing sequences of random variables we prove a functional central limit theorem for a class of strongly mixing sequences of random variables stationarity is not assumed but the variances of the partial sums must grow linearly our theorem extends previous results by supplying sufficient conditions for the weak convergence of the partial sum process to the wiener process under less restrictive moment assumptions for instance if mathop sup limits n text ex n 2 log x n parallel 1 varepsilon 0 and the mixing rate is exponential then this functional c l t holds under the weaker assumption with e 0 the c l t may fail to hold and it is possible that the c l t is satisfied but the sequence of partial sum processes is not tight

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

bootstrap technology and applications bootstrap resampling methods have emerged as powerful tools for constructing inferential procedures in modern statistical data analysis although these methods depend on the availability of fast inexpensive computing they offer the potential for highly accurate methods of inference moreover they can even eliminate the need to impose a convenient statistical model that does not have a strong scientific basis in this article we review some bootstrap methods emphasizing applications through illustrations with some real data special attention is given to regression problems with dependent data and choosing tuning parameters for optimal performance

specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances this study develops a methodology of inference for a widely used cliff ord type spatial model containing spatial lags in the dependent variable exogenous variables and the disturbance terms while allowing for unknown heteroskedasticity in the innovations we first generalize the gmm estimator suggested in kelejian and prucha 1998 1999 for the spatial autoregressive parameter in the disturbance process we also define iv estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the gmm estimator much of the theory is kept general to cover a wide range of settings

the two sample problem for poisson processes adaptive tests with a non asymptotic wild bootstrap approach considering two independent poisson processes we address the question of testing equality of their respective intensities we first propose single tests whose test statistics are u statistics based on general kernel functions the corresponding critical values are constructed from a non asymptotic wild bootstrap approach leading to level alpha tests various choices for the kernel functions are possible including projection approximation or reproducing kernels in this last case we obtain a parametric rate of testing for a weak metric defined in the rkhs associated with the considered reproducing kernel then we introduce in the other cases an aggregation procedure which allows us to import ideas coming from model selection thresholding and or approximation kernels adaptive estimation the resulting multiple tests are proved to be of level alpha and to satisfy non asymptotic oracle type conditions for the classical l2 norm from these conditions we deduce that they are adaptive in the minimax sense over a large variety of classes of alternatives based on classical and weak besov bodies in the univariate case but also sobolev and anisotropic nikol skii besov balls in the multivariate case

surrogate data methods based on a shuffling of the trials for synchrony detection the centering issue we investigate several distribution free dependence detection procedures all based on a shuffling of the trials from a statistical point of view the mathematical justification of such procedures lies in the bootstrap principle and its approximation properties in particular we show that such a shuffling has mainly to be done on centered quantities that is quantities with zero mean under independence to construct correct p values meaning that the corresponding tests control their false positive fp rate thanks to this study we introduce a method named permutation ue which consists of a multiple testing procedure based on permutation of experimental trials and delayed coincidence count each involved single test of this procedure achieves the prescribed level so that the corresponding multiple testing procedure controls the false discovery rate fdr and this with as few assumptions as possible on the underneath distribution except independence and identical distribution across trials the mathematical meaning of this assumption is discussed and it is in particular argued that it does not mean what is commonly referred in neuroscience to as cross trials stationarity some simulations show moreover that permutation ue outperforms the trial shuffling of pipa and grun 2003 and the mtgaue method of tuleau malot eti al 2014 in terms of single levels and fdr for a comparable amount of false negatives application to real data is also provided

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

econometric analysis of production networks with dominant units abstract this paper introduces the notions of strongly and weakly dominant units for networks and shows that pervasiveness of shocks to a network is measured by the degree of dominance of its most pervasive unit shown to be equivalent to the inverse of the shape parameter of the power law fitted to the network outdegrees new cross section and panel extremum estimators of the degree of dominance in networks are proposed and their asymptotic properties investigated the small sample properties of the proposed estimators are examined by monte carlo experiments and their use is illustrated by an empirical application to us input output tables

testing for serial correlation spatial autocorrelation and random effects using panel data abstract this paper considers a spatial panel data regression model with serial correlation on each spatial unit over time as well as spatial dependence between the spatial units at each point in time in addition the model allows for heterogeneity across the spatial units using random effects the paper then derives several lagrange multiplier tests for this panel data regression model including a joint test for serial correlation spatial autocorrelation and random effects these tests draw upon two strands of earlier work the first is the lm tests for the spatial error correlation model discussed in anselin and bera 1998 spatial dependence in linear regression models with an introduction to spatial econometrics in ullah a giles d e a eds handbook of applied economic statistics marcel dekker new york and in the panel data context by baltagi et al 2003 testing panel data regression models with spatial error correlation journal of econometrics 117 123 150 the second is the lm tests for the error component panel data model with serial correlation derived by baltagi and li 1995 testing ar 1 against ma 1 disturbances in an error component model journal of econometrics 68 133 151 hence the joint lm test derived in this paper encompasses those derived in both strands of earlier works in fact in the context of our general model the earlier lm tests become marginal lm tests that ignore either serial correlation over time or spatial error correlation the paper then derives conditional lm and lr tests that do not ignore these correlations and contrast them with their marginal lm and lr counterparts the small sample performance of these tests is investigated using monte carlo experiments as expected ignoring any correlation when it is significant can lead to misleading inference

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

simulated power functions on etudie par simulation la puissance de huit tests contre des alternatives comportant le meme parametre de puissance inconnu

bootstrap and randomization tests of some nonparametric hypotheses in this paper the asymptotic behavior of some nonparametric tests is studied in situations where both bootstrap tests and randomization tests are applicable under fairly general conditions the tests are asymptotically equivalent in the sense that the resulting critical values and power functions are appropriately close this implies among other things that the difference in the critical functions of the tests evaluated at the observed data tends to 0 in probability randomization tests may be preferable since an exact desired level of the test may be obtained for finite samples examples considered are testing independence testing for spherical symmetry testing for exchangeability testing for homogeneity and testing for a change point

qml estimation of dynamic panel data models with spatial errors abstract we propose quasi maximum likelihood qml estimation of dynamic panel models with spatial errors when the cross sectional dimension n is large and the time dimension t is fixed we consider both the random effects and fixed effects models and prove consistency and derive the limiting distributions of the qml estimators under different assumptions on the initial observations we propose a residual based bootstrap method for estimating the standard errors of the qml estimators monte carlo simulation shows that both the qml estimators and the bootstrap standard errors perform well in finite samples under a correct assumption on initial observations but may perform poorly when this assumption is not met

homogenization of a nonlinear multiscale model of calcium dynamics in biological cells abstract calcium is one of the most important intracellular messengers which occurs in the cytosol and the endoplasmic reticulum of animal cells while most calcium dynamics models either do not account properly for the fact that the endoplasmic reticulum constitutes a microstructure of the cell or are infeasible by resolving the fine structure very explicitly goel et al 15 derived an effective macroscopic model by formal homogenization in this paper this approach is made rigorous using periodic homogenization techniques to upscale the nonlinear coupled system of reaction diffusion equations and moreover the appropriate scaling of the interfacial exchange term is taken into consideration

some nonasymptotic results on resampling in high dimension ii multiple tests in the context of correlated multiple tests we aim to nonasymptotically control the family wise error rate fwer using resampling type procedures we observe repeated realizations of a gaussian random vector in possibly high dimension and with an unknown covariance matrix and consider the one and two sided multiple testing problem for the mean values of its coordinates we address this problem by using the confidence regions developed in the companion paper ann statist 2009 to appear which lead directly to single step procedures these can then be improved using step down algorithms following an established general methodology laid down by romano and wolf j amer statist assoc 100 2005 94 108 this gives rise to several different procedures whose performances are compared using simulated data

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

a permutation test for inference in logistic regression with small and moderate sized data sets inference based on large sample results can be highly inaccurate if applied to logistic regression with small data sets furthermore maximum likelihood estimates for the regression parameters will on occasion not exist and large sample results will be invalid exact conditional logistic regression is an alternative that can be used whether or not maximum likelihood estimates exist but can be overly conservative this approach also requires grouping the values of continuous variables corresponding to nuisance parameters and inference can depend on how this is done a simple permutation test of the hypothesis that a regression parameter is zero can overcome these limitations the variable of interest is replaced by the residuals from a linear regression of it on all other independent variables logistic regressions are then done for permutations of these residuals and a p value is computed by comparing the resulting likelihood ratio statistics to the original observed value simulations of binary outcome data with two independent variables that have binary or lognormal distributions yield the following results a in small data sets consisting of 20 observations type i error is well controlled by the permutation test but poorly controlled by the asymptotic likelihood ratio test b in large data sets consisting of 1000 observations performance of the permutation test appears equivalent to that of the asymptotic test and c in small data sets the p value for the permutation test is usually similar to the mid p value for exact conditional logistic regression

pseudofractal scale free web we find that scale free random networks are excellently modeled by simple deterministic graphs our graph has a discrete degree distribution degree is the number of connections of a vertex which is characterized by a power law with exponent gamma 1 ln 3 ln 2 properties of this compact structure are surprisingly close to those of growing random scale free networks with gamma in the most interesting region between 2 and 3 we succeed to find exactly and numerically with high precision all main characteristics of the graph in particular we obtain the exact shortest path length distribution for a large network ln n 1 the distribution tends to a gaussian of width approximately sqrt ln n centered at l approximately ln n we show that the eigenvalue spectrum of the adjacency matrix of the graph has a power law tail with exponent 2 gamma

quasi maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and t are large this paper investigates the asymptotic properties of quasi maximum likelihood estimators for spatial dynamic panel data with xed eects when both the number of individuals n and the number of time periods t are large we consider the case where t is asymptotically large relative to n the case where t is asymptotically proportional to n and the case where n is asymptotically large relative to t in the case where t is asymptotically large relative to n the estimators are p nt consistent and asymptotically normal with the limit distribution centered around 0 when n is asymptotically proportional to t the estimators are p nt consistent and asymptotically normal but the limit distribution is not centered around 0 and when n is large relative to t the estimators are consistent with rate t and have a degenerate limit distribution the estimators of the xed eects are p t consistent and asymptotically normal we also propose a bias correction for our estimators we show that when t grows faster than n 1 3 the correction will asymptotically eliminate the bias and yield a centered con dence interval

tests for order restrictions in binary data in this article a general procedure is presented for testing for equality of k independent binary response probabilities against any given ordered alternative the proposed methodology is based on an estimation procedure developed in hwang and peddada 1994 annals of statistics 22 67 93 and can be used for a very broad class of order restrictions the procedure is illustrated through application to two data sets that correspond to three commonly encountered order restrictions simple tree order simple order and down turn order

simple and trustworthy cluster robust gmm inference abstract this paper develops a new asymptotic theory for gmm estimation and inference in the presence of clustered dependence the key feature of our alternative asymptotics is that the number of clusters g is regarded as fixed as the sample size increases under the fixed g asymptotics we show that the wald and t tests in two step gmm are asymptotically pivotal only if we recenter the estimated moment process in the clustered covariance estimator cce also the j statistic the trinity of two step gmm statistics qlr lm and wald and the t statistic can be modified to have an asymptotic standard f distribution or t distribution we suggest a finite sample variance correction to further improve the accuracy of the f and t approximations the proposed tests are very appealing to practitioners because the test statistics are simple modifications of conventional gmm test statistics and critical values are readily available from f and t tables no further simulations or resampling methods are needed a monte carlo study shows that our proposed tests are more accurate than the conventional large g asymptotic inferences

heteroskedasticity autocorrelation robust standard errors using the bartlett kernel without truncation in this paper we analyze heteroskedasticity autocorrelation hac robust tests constructed using the bartlett kernel without truncation we show that while such an hac estimator is not consistent asymptotically valid testing is still possible we show that tests using the bartlett kernel without truncation are exactly equivalent to recent hac robust tests proposed by kiefer vogelsang and bunzel 2000 econometrica 68 pp 695 714

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

existence for reaction diffusion systems a compactness method approach the authors study the existence of weak solutions for the following system ut u f u v vt v g u v in 0 t u v 0 on 0 t u 0 x u0 x v 0 x v0 x in the region rn with smooth boundary the functions r r are assumed to be continuous and nondecreasing with 0 0 0 u0 v0 l f g r2 2r with f an upper semicontinuous mapping u s c the following local existence results are shown 1 for the diffusive case i e when both and are strictly increasing with u s c g 2 for the semi diffusive case only one function is strictly increasing with g being either with separated variables i e having the form of the product or of the sum of two functions g u and h v or globally lipschitz with respect to its second variable i e g u v g u v l v v for each u b r v v r and some l l b additional conditions of linear form on the growth of f and g are indicated to guarantee global existence results

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

kernel based tests for joint independence summary we investigate the problem of testing whether d possibly multivariate random variables which may or may not be continuous are jointly or mutually independent our method builds on ideas of the two variable hilbert schmidt independence criterion but allows for an arbitrary number of variables we embed the joint distribution and the product of the marginals in a reproducing kernel hilbert space and define the d variable hilbert schmidt independence criterion dhsic as the squared distance between the embeddings in the population case the value of dhsic is 0 if and only if the d variables are jointly independent as long as the kernel is characteristic on the basis of an empirical estimate of dhsic we investigate three non parametric hypothesis tests a permutation test a bootstrap analogue and a procedure based on a gamma approximation we apply non parametric independence testing to a problem in causal discovery and illustrate the new methods on simulated and real data sets

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

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

asymptotic theory for clustered samples abstract we provide a complete asymptotic distribution theory for clustered data with a large number of independent groups generalizing the classic laws of large numbers uniform laws central limit theory and clustered covariance matrix estimation our theory allows for clustered observations with heterogeneous and unbounded cluster sizes our conditions cleanly nest the classical results for i n i d observations in the sense that our conditions specialize to the classical conditions under independent sampling we use this theory to develop a full asymptotic distribution theory for estimation based on linear least squares 2sls nonlinear mle and nonlinear gmm