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

separation of unistochastic matrices from the double stochastic ones recovery of a 3 3 unitary matrix from experimental data the aim of the paper is to provide a constructive method for recovering a unitary matrix from experimental data since there is a natural immersion of unitary matrices within the set of double stochastic ones the problem to solve is to find necessary and sufficient criteria that separate the two sets a complete solution is provided for the three dimensional case accompanied by a 2 test necessary for the reconstruction of a unitary matrix from error affected data

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 biunimodular vectors for unitary matrices abstract a biunimodular vector of a unitary matrix a u n is a vector v t n c n such that av t n as well over the last 30 years the sets of biunimodular vectors for fourier matrices have been the object of extensive research in various areas of mathematics and applied sciences here we broaden this basic harmonic analysis perspective and extend the search for biunimodular vectors to arbitrary unitary matrices this search can be motivated in various ways the main motivation is provided by the fact that the existence of biunimodular vectors for an arbitrary unitary matrix allows for a natural understanding of the structure of all unitary matrices

some formulas for invariant phases of unitary matrices by jarlskog we describe a calculation of jarlskog s determinant in the case of n 4 in detail next we investigate some formulas for invariant phases of unitary matrices and derive some explicit relations for them

panel data methods for fractional response variables with an application to test pass rates we revisit the effects of spending on student performance using data from the state of michigan in addition to exploiting a dramatic change in funding in the mid 1990s and subsequent nonsmooth changes we propose nonlinear panel data models that recognize the bounded nature of the pass rate importantly we show how to estimate average partial effects which can be compared across many different models linear and nonlinear under different assumptions and estimated using many different methods we find that spending has nontrivial and statistically significant effects although the diminishing effect is not especially pronounced

gmm estimation of spatial autoregressive models with unknown heteroskedasticity abstract in the presence of heteroskedastic disturbances the mle for the sar models without taking into account the heteroskedasticity is generally inconsistent the 2sls estimates can have large variances and biases for cases where regressors do not have strong effects in contrast gmm estimators obtained from certain moment conditions can be robust asymptotically valid inferences can be drawn with consistently estimated covariance matrices efficiency can be improved by constructing the optimal weighted estimation the approaches are applied to the study of county teenage pregnancy rates the empirical results show a strong spatial convergence among county teenage pregnancy rates

correlated random effects models with unbalanced panels abstract i propose some strategies for allowing unobserved heterogeneity to be correlated withobserved covariates and sample selection for unbalanced panels the methods are extensions of the chamberlain mundlak approach for balanced panels when explanatory variables are strictly exogenous conditional on unobserved effects a byproduct is fully robust hausman tests for unbalanced panels even for nonlinear models in many cases the estimators can be implemented using standard software the framework suggests straightforward tests for sample selection that is correlated with unobserved shocks while allowing selection to be correlated with the observed covariates and unobserved heterogeneity

limited information estimators and exogeneity tests for simultaneous probit models a two step maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators conditions under which each estimator attains the cramer rao lower bound are obtained simple tests for exogeneity based on the new two step estimator are proposed and are shown to be asymptotically equivalent to one another and to have the same local asymptotic power as classical tests based on the limited information maximum likelihood estimator finite sample comparisons between the new and alternative estimators are presented based on some monte carlo evidence the performance of the proposed tests for exogeneity is also assessed

sound wave propagation from a point source over a homogeneous surface and over a surface with an impedance discontinuity the sound field from a point source above an infinite plane with an impedance discontinuity is studied by considering the helmholtz equation with boundary conditions the helmholtz equation is transformed into a singular integral equation and an exact solution formula is given the formula is evaluated for the case when the source and the receiver are close to the boundary many wavelengths from the discontinuity the evaluation gives among other things information on the dependence of the surface wave structure on the impedances and in the case of no surface waves information on the farfield solution if one of the impedances gives a surface wave in the case of a homogeneous boundary then a surface wave appears also in the nonhomogeneous case and is modified depending on the other impedance in the case of no surface waves the rapid decay of the sound field in the homogeneous case does not appear in the nonhomogeneous case since the discontinuity acts as a weak source of slowly decaying waves a numb

aspects of ground effect modeling a recently published one parameter ground model based on darcy s law is here generalized into a two parameter model which depends on an effective flow resistivity and an effective layer depth extensive field measurements of the acoustic impedance of various ground types have been carried out for frequencies in the range from 200 hz to 2 5 khz the model based on darcy s law gives an improved fit to the measurements compared to the delany bazley model it is in addition argued on purely theoretical grounds that the suggested model is preferable in contrast to the delany bazley model it corresponds to a proper causal time domain model this is particularly relevant for extrapolation of the models to lower frequencies and for the recently developed harmonized methods intended for use in the implementation of the european union directive on the assessment and management of environmental noise the harmonized methods include frequencies down to the 25 hz third octave band and have the delany bazley ground

a spatial autoregressive model with a nonlinear transformation of the dependent variable abstract this paper develops a nonlinear spatial autoregressive model of particular interest is a structural interaction model for share data we consider possible instrumental variable iv and maximum likelihood estimation mle for this model and analyze asymptotic properties of the iv and mle based on the notion of spatial near epoch dependence we also design a statistical test to compare the nonlinear transformation against alternatives monte carlo experiments are designed to investigate finite sample performance of the proposed estimates and the sizes and powers of the test

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

note on a result of morse and bolt abstract a result given without derivation by morse and bolt 1 pertaining to the reflection of a spherical sound wave from an absorbent surface is investigated it is shown that the result as given is not quite accurate

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

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

on a generalized entropic uncertainty relation in the case of the qubit we revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two dimensional hilbert space r nyi entropy is used as an uncertainty measure associated with the distribution probabilities corresponding to the outcomes of the observables we derive a general expression for the tight lower bound of the sum of r nyi entropies for any couple of positive entropic indices thus we have overcome the h lder conjugacy constraint imposed on the entropic indices by riesz thorin theorem in addition we present an analytical expression for the tight bound inside the square 0 1 2 2 in the plane and a semi analytical expression on the line it is seen that previous results are included as particular cases moreover we present a semi analytical suboptimal bound for any couple of indices in all cases we provide the minimizing states

sound propagation above an inhomogeneous plane boundary integral equation methods abstract a boundary integral equation method is used to compute the sound pressure emitted by a harmonic source above an inhomogeneous plane first the theoretical aspects of the problem behaviour of the pressure around the discontinuities are studied then a comparison between theoretical levels and experimental levels obtained in an anechoic room is presented it shows that the boundary integral equation bie method is quite convenient for solving this kind of problem two interesting results are pointed out i if only a prediction of maximum sound levels is needed the attenuation is the same for a cylindrical source a spherical source and n spherical sources and so it is possible to transform some three dimensional problems into two dimensional ones ii a numerical method of computation of the sound field above an inhomogeneous plane does not provide a correct prediction if each part of the plane is not accurately described by the boundary condition chosen

a note on factoring unitary matrices abstract the note concerns three factorizations of unitary matrices a recent factorization allowing to obtain any unitary matrix of dimension 2n from four unitary matrices of dimension n the cosine sine decomposition and a new factorization decomposing a given unitary matrix into a product of two orthogonal matrices and a diagonal unitary matrix

a note on reflection of spherical waves in 1909 sommerfeld gave an exact solution for the reflection of a spherical wave from a plane surface in terms of an oscillatory integral and also presented an asymptotic solution for the case where both source and receiver are at the boundary weyl 1919 presented an alternative solution and also an asymptotic solution for the case where the source is at the boundary it is known that the general case is solved if a general solution for the case where the source is at the boundary is known here it is demonstrated that it is sufficient to have the general solution for the case where both source and receiver are at the boundary this is mainly of theoretical interest but may have practical applications as an example it is demonstrated that sommerfeld s approximate solution gives ingard s 1951 approximate solution which is valid for arbitrary source and receiver heights

a recursive parametrization of unitary matrices a simple recursive scheme for parametrization of n by n unitary matrices is presented the n by n matrix is expressed as a product containing the n 1 by n 1 matrix and a unitary matrix that contains the additional parameters needed to go from n 1 to n the procedure is repeated to obtain recursion formulas for n by n unitary matrices

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 composite parameterization of unitary groups density matrices and subspaces unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form in this paper we present a parameterization of the unitary group of arbitrary dimension d which is constructed in a composite way we show explicitly how any element of can be composed of matrix exponential functions of generalized anti symmetric matrices and one dimensional projectors the specific form makes it considerably easy to identify and discard redundant parameters in several cases in this way redundancy free density matrices of arbitrary rank k can be formulated our construction can also be used to derive an orthonormal basis of any k dimensional subspaces of with the minimal number of parameters as an example it is shown that this feature leads to a significant reduction of parameters in the case of investigating distillability of quantum states via lower bounds of an entanglement measure the m concurrence

sound propagation above an inhomogeneous impedance plane abstract boundary integral equation bie methods are described for the prediction of sound propagation in particular from a line source over a flat plane of inhomogeneous impedance approximate methods which satisfy reciprocity for the calculation of the wave field over a two impedance plane are proposed these approximations applied to propagation from a line source give results agreeing well with those of the bie method when they are applied to propagation from a point source agreement with experiment is shown

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

composite parameterization and haar measure for all unitary and special unitary groups we adopt the concept of the composite parameterization of the unitary group u d to the special unitary group su d furthermore we also consider the haar measure in terms of the introduced parameters we show that the well defined structure of the parameterization leads to a concise formula for the normalized haar measure on u d and su d with regard to possible applications of our results we consider the computation of high order integrals over unitary groups

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

long distance sound propagation over an impedance discontinuity abstract a calculation method is presented for sound propagation over an impedance discontinuity which is an improvement over previous methods being particularly efficient for long distances a homogeneous still atmosphere and flat ground are assumed the starting point is to make an approximation in a two dimensional boundary integral equation formulation of the problem this leads to an expression of the solution as the solution for homogeneous ground plus an integral over part of the boundary this integral is recognized as a generalized fourier integral to which standard techniques of asymptotic analysis can be applied an asymptotic approximation is found which can replace the part of the integral which is most expensive to evaluate by numerical quadrature the remaining integral is evaluated by numerical quadrature monofrequency excess attenuation results for propagation from a point source above rigid ground to a receiver above absorbing ground are discussed when the source and receiver are low enough very orderly trends are observed the results are applied with air attenuation and a weighting to a notional jet engine noise source simple trends are noted

the canonical coset decomposition of unitary matrices through householder transformations this paper reveals the relation between the canonical coset decomposition of unitary matrices and the corresponding decomposition via householder reflections these results can be used to parametrize unitary matrices via householder reflections

identification and estimation of local average treatment effects we investigate conditions sufficient for identification of average treatment effects using instrumental variables first we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect we then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument finally we derive the probability limit of the standard iv estimator under these conditions it is seen to be a weighted average of local average treatment effects this abstract was borrowed from another version of this item

maximum likelihood estimation of a spatial autoregressive tobit model this paper examines a tobit model with spatial autoregressive interactions we consider the maximum likelihood estimation for this model and analyze asymptotic properties of the estimator based on the spatial near epoch dependence of the dependent variable process generated from the model structure we show that the maximum likelihood estimator is consistent and asymptotically normally distributed monte carlo experiments are performed to verify finite sample properties of the estimator

pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension pseudo maximum likelihood estimates are developed for higher order spatial autoregressive models with increasingly many parameters including models with spatial lags in the dependent variables both with and without a linear or nonlinear regression component and regression models with spatial autoregressive disturbances consistency and asymptotic normality of the estimates are established monte carlo experiments examine finite sample behaviour

ground effect analysis surface wave and layer potential representations abstract this paper presents two kinds of analytical exact expressions of the sound field reflected by a plane boundary as obtained by using either surface wave or layer potentials representations both solutions are first expressed as a sum of integrals which have a form suitable for numerical computation then these integrals are expanded into convergent series which provide analytical approximations of the solution numerical techniques are proposed for computing a the surface wave representation and b the approximation deduced from the layer potentials representation this approximation and the classical one sum of the surface wave and the first two terms of the asymptotic series are compared with the exact solution several examples show that the approximate formulas established here are valid on a range much wider than the validity domain of the classical ones

an exact laplace transform formulation for a point source above a ground surface an exact analysis is given for a point source in air above a ground surface by representing the plane wave reflection coefficient as the laplace transform of an image source distribution a well behaved image integral instead of the usual sommerfeld integral is obtained the approach is valid for both locally and extended reacting surfaces for a locally reacting ground surface the image integral is an especially simple rapidly convergent integral the integral for local reaction is investigated analytically for a number of limiting cases the resulting analytic solutions are compared with analytic solutions obtained from more standard approaches finally the image integral for local reaction is analyzed numerically and an upper limit on the numerical integration is given it is shown that with realistic values of ground impedance the prescribed integration limit allows the image integral to be easily and accurately computed numerically

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

near field computation for sound propagation above ground using complex image theory in this paper a very simple method is introduced for the efficient computation of the sound field in the near region above an impedance ground or an extended reaction ground the procedure is based on complex image theory using prony s method the slowly varying factor in the integrand of the sommerfeld integral is approximated by a short series in terms of complex exponential functions the result can be exactly evaluated by the sommerfeld identity a new closed form approximate expression of the sound field is obtained which is represented as the original source its quasistatic image and several images with complex amplitudes and positions avoiding numerical evaluation of the sommerfeld integral makes these closed form expressions computationally very efficient the representation of the field with complex images makes the formula useful in measurement of ground impedance or in other cases requiring repeated mapping of the sound field numerical results show that these closed form green s functions are very accurate for the computation of the near field