series estimation under cross sectional dependence an asymptotic theory is developed for series estimation of nonparametric and semiparametric regression models for cross sectional data under conditions on disturbances that allow for forms of cross sectional dependence and hetero geneity including conditional and unconditional heteroskedascity along with conditions on regressors that allow dependence and do not require existence of a density the conditions aim to accommodate various settings plausible in economic applications and can apply also to panel spatial and time series data a mean square rate of convergence of nonparametric regression estimates is established followed by asymptotic normality of a quite general statistic data driven studentizations that rely on single or double indices to order the data are justified in a partially linear model setting monte carlo investigation of finite sample properties and two empirical applications are carried out

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

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

topological properties of self similar fractals with one parameter abstract in this paper we study two classes of planar self similar fractals t e with a shifting parameter e the first one is a class of self similar tiles by shifting x coordinates of some digits we give a detailed discussion on the disk likeness i e the property of being a topological disk in terms of e we also prove that t e determines a quasi periodic tiling if and only if e is rational the second one is a class of self similar sets by shifting diagonal digits we give a necessary and sufficient condition for t e to be connected

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

disklikeness of planar self affine tiles we consider the disklikeness of the planar self affine tile t generated by an integral expanding matrix a and a consecutive collinear digit set v 0 v 2v q 1 v z 2 let f x x 2 px q be the characteristic polynomial of a we show that the tile t is disklike if and only if 2 p g 2 moreover t is a hexagonal tile for all the cases except when p 0 in which case t is a square tile the proof depends on certain special devices to count the numbers of nodal points and neighbors of t and a criterion of bandt and wang 2001 on disklikeness

cross section regression with common shocks this paper considers regression models for cross section data that exhibit cross section dependence due to common shocks such as macroeconomic shocks the paper analyzes the properties of least squares ls estimators in this context the results of the paper allow for any form of cross section dependence and heterogeneity across population units the probability limits of the ls estimators are determined and necessary and sufficient conditions are given for consistency the asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling the t wald and f statistics are found to have asymptotic standard normal x 2 and scaled x 2 distributions respectively under the null hypothesis when the conditions required for consistency of the parameter under test hold however the absolute values of t wald and f statistics are found to diverge to infinity under the null hypothesis when these conditions fail confidence intervals exhibit similarly dichotomous behavior hence common shocks are found to be innocuous in some circumstances but quite problematic in others models with factor structures for errors and regressors are considered using the general results conditions are determined under which consistency of the ls estimators holds and fails in models with factor structures the results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units

estimation and inference in semiparametric quantile factor models we propose an estimation methodology for a semiparametric quantile factor panel model we provide tools for inference that are robust to the existence of moments and to the form of weak cross sectional dependence in the idiosyncratic error term we apply our method to crsp daily data

a varying coefficient panel data model with fixed effects theory and an application to us commercial banks in this paper we propose a semiparametric varying coefficient categorical panel data model in which covariates variables affecting the coefficients are purely categorical this model has two features first fixed effects are included to allow for correlation between individual unobserved heterogeneity and the regressors second it allows for cross sectional dependence through a general spatial error dependence structure we derive a semiparametric estimator for our model by using a modified within transformation and then show the asymptotic and finite properties for this estimator under large n and t the monte carlo study shows that our methodology works well for both large n and t and large n and small t cases finally we illustrate our model by analyzing the effects of state level banking regulations on the returns to scale of commercial banks in the us our empirical results suggest that returns to scale is higher in more regulated states than in less regulated states

functional limit theorems for weighted sums of i i d random variables on etudie des theoremes limites fonctionnels pour des sommes ponderees specialement pour des poids concernant les methodes de sommabilite classiques telles que celles de cesaro abel borel et euler

rational self affine tiles an integral self affine tile is the solution of a set equation mathbf a mathcal t bigcup d in mathcal d mathcal t d where mathbf a is an n times n integer matrix and mathcal d is a finite subset of mathbb z n in the recent decades these objects and the induced tilings have been studied systematically we extend this theory to matrices mathbf a in mathbb q n times n we define rational self affine tiles as compact subsets of the open subring mathbb r n times prod mathfrak p k mathfrak p of the adele ring mathbb a k where the factors of the finite product are certain mathfrak p adic completions of a number field k that is defined in terms of the characteristic polynomial of mathbf a employing methods from classical algebraic number theory fourier analysis in number fields and results on zero sets of transfer operators we establish a general tiling theorem for these tiles we also associate a second kind of tiles with a rational matrix these tiles are defined as the intersection of a translation of a rational self affine tile with mathbb r n times prod mathfrak p 0 simeq mathbb r n although these intersection tiles have a complicated structure and are no longer self affine we are able to prove a tiling theorem for these tiles as well for particular choices of digit sets intersection tiles are instances of tiles defined in terms of shift radix systems and canonical number systems therefore we gain new results for tilings associated with numeration systems

the topological structure of fractal tilings generated by quadratic number systems let a be a root of an irreducible quadratic polynomial x 2 ax b with integer coefficients a b and assume that a forms a canonical number system i e each x a admits a representation of the shape x a 0 a 1 a a h a h with a i 0 1 b 1 it is possible to associate a tiling to such a number system in a natural way if 2a b 3 then the topological structure of the tiles is quite involved in this case we prove that the interior of a tile is disconnected furthermore we are able to construct finite labelled directed graphs which allow to determine the set of neighbours of a given tile t i e the set of all tiles which have nonempty intersection with t in a next step we give the structure of the set of points in which t coincides with l other tiles in this paper we use two different approaches geometry of numbers and finite automata theory each of these approaches has its advantages and emphasizes different properities of the tiling in particular the conjecture in 1 that for a 0 and 2a b 3 there exist exactly six points where t coincides with two other tiles is solved in these two ways in theorems 6 6 and 10 1

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

nonparametric specification testing via the trinity of tests tests are developed for inference on a parameter vector whose dimension grows slowly with sample size the statistics are based on the lagrange multiplier wald and pseudo likelihood ratio principles admit standard normal asymptotic distributions under the null and are straightforward to compute they are shown to be consistent and possessing non trivial power against local alternatives the settings considered include multiple linear regression panel data models with fixed effects and spatial autoregressions when a nonparametric regression function is estimated by series we use our statistics to propose specification tests and in semiparametric adaptive estimation we provide a test for correct error distribution specification these tests are nonparametric but handled in practice with parametric techniques a monte carlo study suggests that our tests perform well in finite samples two empirical examples use them to test for correct shape of an electricity distribution cost function and linearity and equality of engel curves

self affine tiles in ℝn abstract a self affine tile in r n is a set t of positive measure with a t d d t d where a is an expanding n n real matrix with det a m an integer and d d d 2 d m r n is a set of m digits it is known that self affine tiles always give tilings of r n by translation this paper extends known characterizations of digit sets d yielding self affine tiles it proves several results about the structure of tilings of r n possible using such tiles and gives examples showing the possible relations between self replicating tilings and general tilings which clarify results of kenyon on self replicating tilings

asymptotic normality of series estimators for nonparametric and semiparametric regression models this paper establishes the asymptotic normality of series estimators for nonparametric regression models gallant s fourier flexible form estimators trigonometric series estimators and polynomial series estimators are prime examples of the estimators covered by the results the results apply to a wide variety of estimates in the regression model under consideration including derivatives and integrals of the regression function the errors in the model may be homoskedastic or heteroskedastic the paper also considers series estimators for additive interactive regression semiparametric regression and semiparametric index regression models and shows them to be consistent and asymptotically normal copyright 1991 by the econometric society

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

a note on convergence rates and asymptotic normality for series estimators uniform convergence rates this paper establishes improved uniform convergence rates for series estimators series estimators are least squares fits of a regression function where the number of regressors depends on sample size i will specialize my results to the cases of polynomials and regression splines these results improves upon results obtained earlier by newey yet fail to attain the optimal rates of convergence

simple robust testing of regression hypotheses in this paper we consider the problem of hypothesis testing in models with errors that have serial correlation or heteroskedasticity of unknown form this situation is often encountered in regression models applied to economic time series data it is a classic textbook result that while ordinary least squares ols estimates of regression parameters remain consistent and asymptotically normal when errors are heteroskedastic or autocorrelated provided usual regularity conditions hold and no lagged dependent variables are in the model standard tests are no longer valid if the true form of serial correlation heteroskedasticity were known then generalized least squares gls provides efficient estimates and standard inference can be conducted on the gls transformed model but in practice the form of serial correlation heteroskedasticity is often unknown and this has led to the development of techniques that permit valid asymptotic inference without having to specify a model of the serial correlation or heteroskedasticity the most common approach is to estimate the variance covariance matrix of the ols estimates nonparametrically using spectral methods heteroskedasticity and autocorrelation consistent hac estimators and construct standard tests using the asymptotic normality of the ols estimates hac estimators have been extensively analyzed in the econometrics literature and important contributions are given by andrews 1991 andrews and monahan 1992 gallant 1987 hansen 1992 newey and west 1987 robinson 1991 1998 and white 1984 among others the benefit of hac estimator tests is asymptotically valid inference that is robust to general forms of serial correlation heteroskedasticity in the errors we propose an alternative method of constructing robust test statistics we apply a nonsingular data dependent stochastic transformation to the ols estimates the asymptotic distribution of the transformed estimates does not depend on nuisance parameters then test statistics that are asymptotically invariant to nuisance parameters asymptotic pivotal statistics are constructed the resulting test statistics have nonstandard asymptotic distributions that only depend on the number of restrictions being tested and critical values are easy to simulate using standard techniques the main advantage of our approach compared to standard approaches is that estimates of the variance covariance matrix are not explicitly required to construct the tests this is potentially important for two reasons first with the exception of the estimator proposed by robinson 1998 2 consistent nonparametric estimates of variance covariance matrices in models with serial

estimation and inference in large heterogeneous panels with a multifactor error structure this paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure the unobserved factors and the individual specific errors are allowed to follow arbitrary stationary processes and the number of unobserved factors need not be estimated the basic idea is to filter the individual specific regressors by means of cross section averages such that asymptotically as the cross section dimension n tends to infinity the differential effects of unobserved common factors are eliminated the estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross sectional averages of the dependent variable and the individual specific regressors a number of estimators referred to as common correlated effects cce estimators are proposed and their asymptotic distributions are derived the small sample properties of mean group and pooled cce estimators are investigated by monte carlo experiments showing that the cce estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics and for relatively small values of n and t

heterogeneous panel data models with cross sectional dependence abstract this paper considers a semiparametric panel data model with heterogeneous coefficients and individual specific trending functions where the random errors are assumed to be serially correlated and cross sectionally dependent we propose mean group estimators for the coefficients and trending functions involved in the model it can be shown that the proposed estimators can achieve an asymptotic consistency with rates of root n t and root n t h respectively as n t where n is allowed to increase faster than t furthermore a statistic for testing homogeneous coefficients is constructed based on the difference between the mean group estimator and a pooled estimator its asymptotic distributions are established under both the null and a sequence of local alternatives even if the difference between these estimators vanishes considerably fast can achieve root n t 2 rate at most under the null and no consistent estimator for the covariance matrix is required the finite sample performance of the proposed estimators together with the size and local power properties of the test are demonstrated by simulated data examples and an empirical application with the oecd health care expenditure dataset is also provided

self affine manifolds abstract this paper studies closed 3 manifolds which are the attractors of a system of finitely many affine contractions that tile r 3 such attractors are called self affine tiles effective characterization and recognition theorems for these 3 manifolds as well as theoretical generalizations of these results to higher dimensions are established the methods developed build a bridge linking geometric topology with iterated function systems and their attractors a method to model self affine tiles by simple iterative systems is developed in order to study their topology the model is functorial in the sense that there is an easily computable map that induces isomorphisms between the natural subdivisions of the attractor of the model and the self affine tile it has many beneficial qualities including ease of computation allowing one to determine topological properties of the attractor of the model such as connectedness and whether it is a manifold the induced map between the attractor of the model and the self affine tile is a quotient map and can be checked in certain cases to be monotone or cell like deep theorems from geometric topology are applied to characterize and develop algorithms to recognize when a self affine tile is a topological or generalized manifold in all dimensions these new tools are used to check that several self affine tiles in the literature are 3 balls an example of a wild 3 dimensional self affine tile is given whose boundary is a topological 2 sphere but which is not itself a 3 ball the paper describes how any 3 dimensional handlebody can be given the structure of a self affine 3 manifold it is conjectured that every self affine tile which is a manifold is a handlebody

a reduced complexity online state sequence and parameter estimator for superimposed convolutional coded signals this paper develops a reduced complexity online state sequence and parameter estimator for superimposed convolutional coded signals joint state sequence and parameter estimation is achieved by iteratively estimating the state sequence via a variable reduced complexity viterbi algorithm vrcva and the model parameters via a recursive expectation maximization em approach the vrcva is developed from a fixed reduced complexity viterbi algorithm frcva the frcva is a special case of the delayed decision feedback sequence estimation ddfse algorithm the performance of online versions of the frcva vrcva and the standard viterbi algorithm va are compared when they are used to estimate the state sequence as part of the reduced complexity online state sequence and parameter estimator

certain discrete dynamical systems number systems and related integral self affine sets we consider certain discrete dynamical systems conventional number systems and redundant number systems for z 2 which are associated with certain 2x2 integral expansive matrices and collinear digit sets for them using integral self affine sets in r n we also give a geometric characterization to attractors of certain discrete dynamical systems and associated redundant number systems for z n

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

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

panel data models with interactive fixed effects this paper considers large n and large t panel data models with unobservable multiple interactive eects these models are useful for both micro and macro econometric modelings in earnings studies for example workers motivation persistence and diligence combined to influence the earnings in addition to the usual argument of innate ability in macroeconomics the interactive eects represent unobservable common shocks and their heterogeneous responses over cross sections since the interactive eects are allowed to be correlated with the regressors they are treated as fixed eects parameters to be estimated along with the common slope coecients the model is estimated by the least squares method which provides the interactive eect s counterpart of the within estimator we first consider model identification and then derive the rate of convergence and the limiting distribution of the interactive eect s estimator of the common slope coecients the estimator is shown to be p nt consistent this rate is valid even in the presence of correlations and heteroskedasticities in both dimensions a striking contrast with fixed t framework in which serial correlation and heteroskedasticity imply unidentification the asymptotic distribution is not necessarily centered at zero biased corrected estimators are derived we also derive the constrained estimator and its limiting distribution imposing additivity coupled with interactive eects the problem of testing additive versus interactive eects is also studied we also derive identification conditions for models with grand mean time invariant regressors and common regressors it is shown that there exists a set of necessary and sucient identification conditions for those models given identification the rate of convergence and limiting results continue to hold

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

asymptotic theory for nonparametric regression with spatial data nonparametric regression with spatial or spatio temporal data is considered the conditional mean of a dependent variable given explanatory ones is a nonparametric function while the conditional covariance reflects spatial correlation conditional heteroscedasticity is also allowed as well as non identically distributed observations instead of mixing conditions a possibly non stationary linear process is assumed for disturbances allowing for long range as well as short range dependence while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities a basic triangular array setting is employed with the aim of covering various patterns of spatial observation sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates when the cross sectional dependence is sufficiently mild the asymptotic variance in the central limit theorem is the same as when observations are independent otherwise the rate of convergence is slower we discuss the application of our conditions to spatial autoregressive models and models defined on a regular lattice