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

2d finite rate of innovation reconstruction method for step edge and polygon signals in the presence of noise the finite rate of innovation fri principle is developed for sampling a class of non bandlimited signals that have a finite number of degrees of freedom per unit of time i e signals with fri this sampling scheme is later extended to three classes of sampling kernels with compact support and applied to the step edge reconstruction problem by treating the image row by row in this paper we regard step edges as 2d fri signals and reconstruct them block by block the step edge parameters are obtained from the 2d moments of a given image block experimentally our technique can reconstruct the edge more precisely and track the cramer rao bounds crbs closely with a signal to noise ratio snr larger than 4 db on synthetic step edge images experiments on real images show that our proposed method can reconstruct the step edges under practical conditions i e in the presence of various types of noise and using a real sampling kernel the results on locating the corners of data matrix barcodes using our method also outperform some state of the art barcode decoders

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

on the bootstrap for moran s i test for spatial dependence this paper is concerned with the use of the bootstrap for statistics in spatial econometric models with a focus on the test statistic for moran s i test for spatial dependence we show that for many statistics in spatial econometric models the bootstrap can be studied based on linear quadratic lq forms of disturbances by proving the uniform convergence of the cumulative distribution function for lq forms to that of a normal distribution we show that the bootstrap is generally consistent for test statistics that can be approximated by lq forms including moran s i possible asymptotic refinements of the bootstrap are most commonly studied using edgeworth expansions for spatial econometric models we may establish asymptotic refinements of the bootstrap based on asymptotic expansions of lq forms when the disturbances are normal we prove the existence of the usual edgeworth expansions for lq forms when the disturbances are not normal we establish an asymptotic expansion of lq forms based on martingales these results are applied to show the second order correctness of the bootstrap for moran s i test

negativity as an estimator of entanglement dimension among all entanglement measures negativity arguably is the best known and most popular tool to quantify bipartite quantum correlations it is easily computed for arbitrary states of a composite system and can therefore be applied to discuss entanglement in an ample variety of situations however as opposed to logarithmic negativity its direct physical meaning has not been pointed out yet we show that the negativity can be viewed as an estimator of how many degrees of freedom of two subsystems are entangled as it is possible to give lower bounds for the negativity even in a device independent setting it is the appropriate quantity to certify quantumness of both parties in a bipartite system and to determine the minimum number of dimensions that contribute to the quantum correlations

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

quantifying entanglement resources we present an overview of the quantitative theory of single copy entanglement in finite dimensional quantum systems in particular we emphasize the point of view that different entanglement measures quantify different types of resources which leads to a natural interdependence of entanglement classification and quantification apart from the theoretical basis we outline various methods for obtaining quantitative results on arbitrary mixed states this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

large sample properties of the matrix exponential spatial specification with an application to fdi this paper studies large sample properties of the matrix exponential spatial specification mess we find that the quasi maximum likelihood estimator qmle for the mess is consistent under heteroskedasticity a property not shared by the qmle of the sar model for the general model that has mess in both the dependent variable and disturbances labeled mess 1 1 the qmle can be consistent under unknown heteroskedasticity when the spatial weights matrices in the two mess processes are commutative we also consider the generalized method of moments estimator gmme in the homoskedastic case we derive a best gmme that is as efficient as the maximum likelihood estimator under normality and can be asymptotically more efficient than the qmle under non normality in the heteroskedastic case an optimal gmme can be more efficient than the qmle asymptotically the qml approach for the mess model has the computational advantage over that of a sar model the computational simplicity carries over to mess models with any finite order of spatial matrices no parameter range needs to be imposed in order for the model to be stable results of monte carlo experiments for finite sample properties of the estimators are reported finally the mess 1 1 is applied to belgium s outward fdi data and we observe that the dominant motivation of belgium s outward fdi lies in finding cheaper factor inputs

asymptotic optimality of empirical likelihood for testing moment restrictions we show by example that empirical likelihood and other commonly used tests for moment restrictions are unable to control the exponential rate at which the probability of a type i error tends to zero unless the possible distributions for the observed data are restricted appropriately from this it follows that for the optimality claim for empirical likelihood in kitamura 2001 to hold additional assumptions and qualifications are required under stronger assumptions than those in kitamura 2001 we establish the following optimality result i empirical likelihood controls the rate at which the probability of a type i error tends to zero and ii among all procedures for which the probability of a type i error tends to zero at least as fast empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for most alternatives this result further implies that empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their type i error probabilities

multidimensional esprit for damped and undamped signals algorithm computations and perturbation analysis in this paper we present and analyze the performance of multidimensional esprit n d esprit method for estimating parameters of n d superimposed damped and or undamped exponentials n d esprit algorithm is based on low rank decomposition of multilevel hankel matrices formed by the n d data in order to reduce the computational complexity for large signals we propose a fast n d esprit using truncated singular value decomposition svd then through a first order perturbation analysis we derive simple expressions of the variance of the estimates in n d multiple tones case these expressions do not involve the factors of the svd we also derive closed form expressions of the variances of the complex modes frequencies and damping factors estimates in the n d single tone case computer results are presented to show effectiveness of the fast version of n d esprit and verify theoretical expressions

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

sampling sparse signals on the sphere algorithms and applications we propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass filtered observations central to our algorithm is a generalization of the annihilating filter method a tool widely used in array signal processing and finite rate of innovation fri sampling the proposed algorithm can reconstruct k spikes from k sqrt k 2 spatial samples for large k this sampling requirement improves over previously known fri sampling schemes on the sphere by a factor of four we showcase the versatility of the proposed algorithm by applying it to three problems 1 sampling diffusion processes induced by localized sources on the sphere 2 shot noise removal and 3 sound source localization ssl by a spherical microphone array in particular we show how ssl can be reformulated as a spherical sparse sampling problem

the second order bias and mean squared error of nonlinear estimators abstract despite the now widespread use of nonlinear estimators their finite sample properties have received very little attention in either the statistics or econometrics literature we partially redress this problem by deriving and examining the second order bias and mean squared error of a fairly wide class of nonlinear estimators which includes nonlinear least squares maximum likelihood and many generalized method of moments estimators as special cases a number of examples are provided the results from a monte carlo exercise demonstrate how the results can be applied for improved inferences

sampling signals with a finite rate of innovation on the sphere the state of the art in sampling theory now contains several theorems for signals that are non bandlimited for signals on the sphere however most theorems still require the assumptions of bandlimitedness in this work we show that a particular class of non bandlimited signals which have a finite rate of innovation can be exactly recovered using a finite number of samples we consider a sampling scheme where k weighted diracs are convolved with a kernel on the rotation group we prove that if the sampling kernel has a bandlimit l 2k then 2k 1 4k 1 1 equiangular samples are sufficient for exact reconstruction if the samples are uniformly distributed on the sphere we argue that the signal can be accurately reconstructed using 4k2 samples and validate our claim through numerical simulations to further reduce the number of samples required we design an optimal sampling kernel that achieves accurate reconstruction of the signal using only 3k samples the number of parameters of the weighted diracs in addition to weighted diracs we show that our results can be extended to sample diracs integrated along the azimuth finally we consider kernels with antipodal symmetry which are common in applications such as diffusion magnetic resonance imaging

a multivariate generalization of prony s method abstract prony s method is a prototypical eigenvalue analysis based method for the reconstruction of a finitely supported complex measure on the unit circle from its moments up to a certain degree in this note we give a generalization of this method to the multivariate case and prove simple conditions under which the problem admits a unique solution provided the order of the moments is bounded from below by the number of points on which the measure is supported as well as by a small constant divided by the separation distance of these points stable reconstruction is guaranteed in its simplest form the reconstruction method consists of setting up a certain multilevel toeplitz matrix of the moments compute a basis of its kernel and compute by some method of choice the set of common roots of the multivariate polynomials whose coefficients are given in the second step all theoretical results are illustrated by numerical experiments

bartlett adjustment of empirical discrepancy statistics summary we introduce two classes of empirical discrepancy statistics that extend empirical likelihood and establish simple conditions under which they admit bartlett adjustment

empirical likelihood in the presence of nuisance parameters summary empirical likelihood was introduced as a nonparametric analogue of ordinary parametric likelihood it is well known that the empirical likelihood ratio statistic inherits a number of properties of the parametric likelihood ratio statistic such as the asymptotic chi squared distribution and bartlett correctability this raises the question of whether or not the same is true in the presence of nuisance parameters recent work by qin lawless 1994 indicates that the chi squared distribution is still valid to first order we show that when nuisance parameters are present as introduced via a system of estimating equations the asymptotic expansion for the signed square root of the empirical likelihood ratio statistic has a nonstandard form this implies that the empirical likelihood ratio statistic itself does not permit a bartlett correction

efficient multidimensional diracs estimation with linear sample complexity estimating diracs in continuous two or higher dimensions is a fundamental problem in imaging previous approaches extended one dimensional 1 d methods like the ones based on finite rate of innovation fri sampling in a separable manner e g along the horizontal and vertical dimensions separately in 2 d the separate estimation leads to a sample complexity of mathcal o left k d right for k diracs in d dimensions despite that the total degrees of freedom only increase linearly with respect to d we propose a new method that enforces the continuous domain sparsity constraints simultaneously along all dimensions leading to a reconstruction algorithm with linear sample complexity mathcal o k or a gain of mathcal o left k d 1 right over previous fri based methods the multi dimensional dirac locations are subsequently determined by the intersections of hypersurfaces e g curves in 2 d which can be computed algebraically from the common roots of polynomials we first demonstrate the performance of the new multidimensional algorithm on simulated data multidimensional dirac location retrieval under noisy measurements then we show results on real data radio astronomy point source reconstruction from lofar telescope measurements and the direction of arrival estimation of acoustic signals using pyramic microphone arrays

constructive entanglement test from triangle inequality we derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system the main ingredient of the presented derivation is the triangle inequality applied to the root infidelity distance in the space of density matrices the obtained bound leads to entanglement criteria with a straightforward interpretation the proposed criteria provide an experimentally accessible powerful entanglement test

empirical likelihood estimation and consistent tests with conditional moment restrictions this paper is about efficient estimation and consistent tests of conditional moment restrictions we use unconditional moment restrictions based on splines or other approximating functions for this purpose empirical likelihood estimation is particularly appropriate for this setting because of its relatively low bias with many moment conditions we give conditions so that efficiency of estimators and consistency of tests is achieved as the number of restrictions grows with the sample size we also give results for generalized empirical likelihood generalized method of moments and nonlinear instrumental variable estimators

estimation of frequencies and damping factors by two dimensional esprit type methods in this paper we consider two dimensional 2 d signals modeled by the sum of damped cisoids we propose two high resolution approaches to estimate their frequencies and damping factors both high resolution methods are based on the shift invariance structure of the signal subspace related to each dimension the first one estimates the frequency components in both dimensions as in the matrix enhancement and matrix pencil memp method before pairing them with a new algorithm the second one consists of the direct estimation of the signal frequency pairs without an additional step to pair the frequencies related to each dimension we show how these methods can estimate the scattering points of radar images

sampling signals with finite rate of innovation the authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation examples of signals with a finite rate of innovation include streams of diracs e g the poisson process nonuniform splines and piecewise polynomials even though these signals are not bandlimited we show that they can be sampled uniformly at or above the rate of innovation using an appropriate kernel and then be perfectly reconstructed thus we prove sampling theorems for classes of signals and kernels that generalize the classic bandlimited and sinc kernel case in particular we show how to sample and reconstruct periodic and finite length streams of diracs nonuniform splines and piecewise polynomials using sinc and gaussian kernels for infinite length signals with finite local rate of innovation we show local sampling and reconstruction based on spline kernels the key in all constructions is to identify the innovative part of a signal e g time instants and weights of diracs using an annihilating or locator filter a device well known in spectral analysis and error correction coding this leads to standard computational procedures for solving the sampling problem which we show through experimental results applications of these new sampling results can be found in signal processing communications systems and biological systems

empirical likelihood for linear models empirical likelihood is a nonparametric method of inference it has sampling properties similar to the bootstrap but where the bootstrap uses resampling it profiles a multinomial likelihood supported on the sample its properties in i i d settings have been investigated in works by owen by hall and by diciccio hall and romano this article extends the method to regression problems fixed and random regressors are considered as are robust and heteroscedastic regressions to make the extension three variations on the original idea are considered it is shown that when some functionals of the distribution of the data are known one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization the result is first order equivalent to conditioning on a sample value of the known functional the use of a euclidean alternative to the likelihood function is investigated a triangular array version of the empirical likelihood theorem is given the one way anova and heteroscedastic regression models are considered in detail an example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

exact sampling results for some classes of parametric nonbandlimited 2 d signals we present sampling results for certain classes of two dimensional 2 d signals that are not bandlimited but have a parametric representation with a finite number of degrees of freedom while there are many such parametric signals it is often difficult to propose practical sampling schemes therefore we will concentrate on those classes for which we are able to give exact sampling algorithms and reconstruction formulas we analyze in detail a set of 2 d diracs and extend the results to more complex objects such as lines and polygons unlike most multidimensional sampling schemes the methods we propose perfectly reconstruct such signals from a finite number of samples in the noiseless case some of the techniques we use are already encountered in the context of harmonic retrieval and error correction coding in particular singular value decomposition svd based methods and the annihilating filter approach are both explored as inherent parts of the developed algorithms potentials and limitations of the algorithms in the noisy case are also pointed out applications of our results can be found in astronomical signal processing image processing and in some classes of identification problems

non nested testing of spatial correlation we develop non nested tests in a general spatial spatio temporal or panel data context the spatial aspect can be interpreted quite generally in either a geographical sense or employing notions of economic distance or when parametric modelling arises in part from a common factor or other structure in the former case observations may be regularly spaced across one or more dimensions as is typical with much spatio temporal data or irregularly spaced across all dimensions both isotropic models and non isotropic models can be considered and a wide variety of correlation structures in the second case models involving spatial weight matrices are covered such as spatial autoregressive models the setting is sufficiently general to potentially cover other parametric structures such as certain factor models and vector valued observations and here our preliminary asymptotic theory for parameter estimates is of some independent value the test statistic is based on a gaussian pseudo likelihood ratio and is shown to have an asymptotic standard normal distribution under the null hypothesis that one of the two models is correct this limit theory rests strongly on a central limit theorem for the gaussian pseudo maximum likelihood parameter estimates a small monte carlo study of finite sample performance is included

sampling schemes for multidimensional signals with finite rate of innovation in this paper we consider the problem of sampling signals that are nonband limited but have finite number of degrees of freedom per unit of time and call this number the rate of innovation streams of diracs and piecewise polynomials are the examples of such signals and thus are known as signals with finite rate of innovation fri we know that the classical band limited sine sampling theory does not enable perfect reconstruction of such signals from their samples since they are not band limited however the recent results on fri sampling suggest that it is possible to sample and perfectly reconstruct such nonband limited signals using a rich class of kernels in this paper we extend those results in higher dimensions using compactly supported kernels that reproduce polynomials satisfy strang fix conditions in fact the polynomial reproduction property of the kernel makes it possible to obtain the continuous moments of the signal from its samples using these moments and the annihilating filter method prony s method the innovative part of the signal and therefore the signal itself is perfectly reconstructed in particular we present local directional derivatives based and global complex moments based radon transform based sampling schemes for classes of fri signals such as sets of diracs bilevel and planar polygons quadrature domains e g circles ellipses and cardioids 2d polynomials with polygonal boundaries and n dimensional diracs and convex polytopes this work has been explored in a promising way in super resolution algorithms and distributed compression and might find its applications in photogrammetry computer graphics and machine vision

sampling curves with finite rate of innovation in this paper we extend the theory of sampling signals with finite rate of innovation fri to a specific class of two dimensional curves which are defined implicitly as the zeros of a mask function here the mask function has a parametric representation as a weighted summation of a finite number of complex exponentials and therefore has finite rate of innovation an associated edge image which is discontinuous on the predefined parametric curve is proved to satisfy a set of linear annihilation equations we show that it is possible to reconstruct the parameters of the curve i e to detect the exact edge positions in the continuous domain based on the annihilation equations robust reconstruction algorithms are also developed to cope with scenarios with model mismatch moreover the annihilation equations that characterize the curve are linear constraints that can be easily exploited in optimization problems for further image processing e g image up sampling we demonstrate one potential application of the annihilation algorithm with examples in edge preserving interpolation experimental results with both synthetic curves as well as edges of natural images clearly show the effectiveness of the annihilation constraint in preserving sharp edges and improving snrs

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

sampling and reconstruction of shapes with algebraic boundaries we present a sampling theory for a class of binary images with finite rate of innovation fri every image in our model is the restriction of mathbb 1 p leq 0 to the image plane where mathbb 1 denotes the indicator function and p is some real bivariate polynomial this particularly means that the boundaries in the image form a subset of an algebraic curve with the implicit polynomial p we show that the image parameters i e the polynomial coefficients satisfy a set of linear annihilation equations with the coefficients being the image moments the inherent sensitivity of the moments to noise makes the reconstruction process numerically unstable and narrows the choice of the sampling kernels to polynomial reproducing kernels as a remedy to these problems we replace conventional moments with more stable generalized moments that are adjusted to the given sampling kernel the benefits are threefold 1 it relaxes the requirements on the sampling kernels 2 produces annihilation equations that are robust at numerical precision and 3 extends the results to images with unbounded boundaries we further reduce the sensitivity of the reconstruction process to noise by taking into account the sign of the polynomial at certain points and sequentially enforcing measurement consistency we consider various numerical experiments to demonstrate the performance of our algorithm in reconstructing binary images including low to moderate noise levels and a range of realistic sampling kernels

an efficient gmm estimator of spatial autoregressive models in this paper we consider gmm estimation of the regression and mrsar models with sar disturbances we derive the best gmm estimator within the class of gmm estimators based on linear and quadratic moment conditions the best gmm estimator has the merit of computational simplicity and asymptotic efficiency it is asymptotically as efficient as the ml estimator under normality and asymptotically more efficient than the gaussian qml estimator otherwise monte carlo studies show that with moderate sized samples the best gmm estimator has its biggest advantage when the disturbances are asymmetrically distributed when the diagonal elements of the spatial weights matrix have enough variation incorporating kurtosis of the disturbances in the moment functions will also be helpful

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

gel estimation and tests of spatial autoregressive models abstract this paper considers the generalized empirical likelihood gel estimation and tests of high order spatial autoregressive sar models by exploring an inherent martingale structure the gel estimator has the same asymptotic distribution as the generalized method of moments estimator explored with same moment conditions for estimation but circumvents a first step estimation of the optimal weighting matrix with a preliminary estimator and thus can be robust to unknown heteroskedasticity and non normality while the gel removes the asymptotic bias from the preliminary estimator and partially removes the bias due to the correlation between the moment conditions and their jacobian the empirical likelihood as a special member of gels further partially removes the bias from estimating the second moment matrix we also formulate the gel overidentification test moran s i test and gel ratio tests for parameter restrictions and non nested hypotheses while some of the conventional tests might not be robust to non normality and or unknown heteroskedasticity the corresponding gel tests can be robust

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

on bahadur efficiency of empirical likelihood this paper studies the bahadur efficiency of empirical likelihood for testing moment condition models it is shown that under mild regularity conditions the empirical likelihood overidentifying restriction test is bahadur efficient i e its p value attains the fastest convergence rate under each fixed alternative hypothesis analogous results are derived for parameter hypothesis testing and set inference problems

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

ellipse fitting using the finite rate of innovation sampling principle standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse when the data are noisy and come from a partial ellipse the state of the art methods tend to produce biased ellipses we rely on the sampling structure of the underlying signal and show that the x and y coordinate functions of an ellipse are finite rate of innovation fri signals and that their parameters are estimable from partial data we consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude modulated complex exponentials a low pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials the annihilating filter used in fri approaches is applied to estimate the sampling interval in the closed form we perform experiments on simulated and real data and assess both objective and subjective performances in comparison with the state of the art ellipse fitting methods the proposed method produces ellipses with lesser bias furthermore the mean squared error is lesser by about 2 to 10 db we show the applications of ellipse fitting in iris images starting from partial edge contours and to free hand ellipses drawn on a touch screen tablet

computing the common zeros of two bivariate functions via bezout resultants the common zeros of two bivariate functions can be computed by finding the common zeros of their polynomial interpolants expressed in a tensor chebyshev basis from here we develop a bivariate rootfinding algorithm based on the hidden variable resultant method and bezout matrices with polynomial entries using techniques including domain subdivision bezoutian regularization and local refinement we are able to reliably and accurately compute the simple common zeros of two smooth functions with polynomial interpolants of very high degree ge 1 000 1 000 we analyze the resultant method and its conditioning by noting that the bezout matrices are matrix polynomials two implementations are available one on the matlab central file exchange and another in the roots command in chebfun2 that is adapted to suit chebfun s methodology

a frequency domain empirical likelihood method for irregularly spaced spatial data this paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain unlike the frequency domain empirical likelihood fdel methodology for time series on a regular grid the formulation of the spatial fdel needs special care due to lack of the usual orthogonality properties of the discrete fourier transform for irregularly spaced data and due to presence of nontrivial bias in the periodogram under different spatial asymptotic structures a spatial fdel is formulated in the paper taking into account the effects of these factors the main results of the paper show that wilks phenomenon holds for a scaled version of the logarithm of the proposed empirical likelihood ratio statistic in the sense that it is asymptotically distribution free and has a chi squared limit as a result the proposed spatial fdel method can be used to build nonparametric asymptotically correct confidence regions and tests for covariance parameters that are defined through spectral estimating equations for irregularly spaced spatial data in comparison to the more common studentization approach a major advantage of our method is that it does not require explicit estimation of the standard error of an estimator which is itself a very difficult problem as the asymptotic variances of many common estimators depend on intricate interactions among several population quantities including the spectral density of the spatial process the spatial sampling density and the spatial asymptotic structure results from a numerical study are also reported to illustrate the methodology and its finite sample properties

empirical likelihood methods with weakly dependent processes this paper studies the method of empirical likelihood in models with weakly dependent processes in such cases if the likelihood function is formulated as if the data process were independent obviously empirical likelihood fails we propose to use empirical likelihood of blocks of observations to solve this problem in a nonparametric manner this method of blockwise empirical likelihood preserves the dependence of data and the resulting likelihood ratios can be used to construct asymptotically valid confidence intervals we consider general estimating equations for which an efficient estimator is derived by maximizing blockwise empirical likelihood we also introduce blocks of blocks empirical likelihood to conduct inference for parameters of the infinite dimensional joint distribution of data the smooth function model is used for such cases we show that blockwise empirical likelihood of the smooth function model with weakly dependent processes is bartlett correctable a wide variety of problems such as time series regressions and spectral densities can be treated using our methodology

towards generalized fri sampling with an application to source resolution in radioastronomy it is a classic problem to estimate continuous time sparse signals like point sources in a direction of arrival problem or pulses in a time of flight measurement the earliest occurrence is the estimation of sinusoids in time series using prony s method this is at the root of a substantial line of work on high resolution spectral estimation the estimation of continuous time sparse signals from discrete time samples is the goal of the sampling theory for finite rate of innovation fri signals both spectral estimation and fri sampling usually assume uniform sampling but not all measurements are obtained uniformly as exemplified by a concrete radioastronomy problem we set out to solve thus we develop the theory and algorithm to reconstruct sparse signals typically sum of sinusoids from nonuniform samples we achieve this by identifying a linear transformation that relates the unknown uniform samples of sinusoids to the given measurements these uniform samples are known to satisfy the annihilation equations a valid solution is then obtained by solving a constrained minimization such that the reconstructed signal is consistent with the given measurements and satisfies the annihilation constraint thanks to this new approach we unify a variety of fri based methods we demonstrate the versatility and robustness of the proposed approach with five fri reconstruction problems namely dirac reconstructions with irregular time or fourier domain samples fri curve reconstructions dirac reconstructions on the sphere and point source reconstructions in radioastronomy the proposed algorithm improves substantially over state of the art methods and is able to reconstruct point sources accurately from irregularly sampled fourier measurements under severe noise conditions

almost sure identifiability of multidimensional harmonic retrieval two dimensional 2 d and more generally multidimensional harmonic retrieval is of interest in a variety of applications including transmitter localization and joint time and frequency offset estimation in wireless communications the associated identifiability problem is key in understanding the fundamental limitations of parametric methods in terms of the number of harmonics that can be resolved for a given sample size consider a mixture of 2 d exponentials each parameterized by amplitude phase and decay rate plus frequency in each dimension suppose that i equispaced samples are taken along one dimension and likewise j along the other dimension we prove that if the number of exponentials is less than or equal to roughly ij 4 then assuming sampling at the nyquist rate or above the parameterization is almost surely identifiable this is significant because the best previously known achievable bound was roughly i j 2 for example consider i j 32 our result yields 256 versus 32 identifiable exponentials we also generalize the result to n dimensions proving that the number of exponentials that can be resolved is proportional to total sample size

gmm gel serial correlation and asymptotic bias for stationary time series models with serial correlation we consider generalized method of moments gmm estimators that use heteroskedasticity and autocorrelation consistent hac positive definite weight matrices and generalized empirical likelihood gel estimators based on smoothed moment conditions following the analysis of newey and smith 2004 for independent observations we derive second order asymptotic biases of these estimators the inspection of bias expressions reveals that the use of smoothed gel in contrast to gmm removes the bias component associated with the correlation between the moment function and its derivative while the bias component associated with third moments depends on the employed kernel function we also analyze the case of no serial correlation and find that the seemingly unnecessary smoothing and hac estimation can reduce the bias for some of the estimators

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

analytical performance assessment of multi dimensional matrix and tensor based esprit type algorithms in this paper we present a generic framework for the asymptotic performance analysis of subspace based parameter estimation schemes it is based on earlier results on an explicit first order expansion of the estimation error in the signal subspace obtained via an svd of the noisy observation matrix we extend these results in a number of aspects firstly we demonstrate that an explicit first order expansion of the higher order svd hosvd based subspace estimate can be derived secondly we show how to obtain explicit first order expansions of the estimation error of arbitrary esprit type algorithms and provide the expressions for r d standard esprit r d unitary esprit r d standard tensor esprit as well as r d unitary tensor esprit thirdly we derive closed form expressions for the mean square error mse and show that they only depend on the second order moments of the noise hence to apply this framework we only need the noise to be zero mean and possess finite second order moments additional assumptions such as gaussianity or circular symmetry are not needed