distortions of asymptotic confidence size in locally misspecified moment inequality models this paper studies the behavior under local misspecification of several confidence sets css commonly used in the literature on inference in moment in equality models we propose the amount of asymptotic confidence size distortion as a criterion to choose among competing inference methods this criterion is then applied to compare across test statistics and critical values employed in the construction of css we find two important results under weak assumptions first we show that css based on subsampling and generalized moment selection andrews and soares 2010 suffer from the same degree of asymptotic confidence size distortion despite the fact that asymptotically the latter can lead to css with strictly smaller expected volume under correct model specification second we show that the asymptotic confidence size of css based on the quasi likelihood ratio test statistic can be an arbitrary small fraction of the asymptotic confidence size of css based on the modified method of moments test statistic

coherent multiscale image processing using dual tree quaternion wavelets the dual tree quaternion wavelet transform qwt is a new multiscale analysis tool for geometric image features the qwt is a near shift invariant tight frame representation whose coefficients sport a magnitude and three phases two phases encode local image shifts while the third contains image texture information the qwt is based on an alternative theory for the 2d hilbert transform and can be computed using a dual tree filter bank with linear computational complexity to demonstrate the properties of the qwt s coherent magnitude phase representation we develop an efficient and accurate procedure for estimating the local geometrical structure of an image we also develop a new multiscale algorithm for estimating the disparity between a pair of images that is promising for image registration and flow estimation applications the algorithm features multiscale phase unwrapping linear complexity and sub pixel estimation accuracy

moment invariants under similarity transformation this paper presents a method of deriving moment invariants under similarity transformation the invariants sets are algebraically independent and complete the method can be adopted for arbitrary dimension and order this paper also presents some explicit formulas for computing invariant sets dimension which reveals how the number of invariants increases with moments order and dimension elevating we present a method for constructing moment invariant under similarity transformation our method can be used for deriving moment invariants of arbitrary dimension and order our invariants are algebraically independent and complete we present some explicit formulas for computing invariant sets dimensions

two stage least squares estimation of average causal effects in models with variable treatment intensity abstract two stage least squares tsls is widely used in econometrics to estimate parameters in systems of linear simultaneous equations and to solve problems of omitted variables bias in single equation estimation we show here that tsls can also be used to estimate the average causal effect of variable treatments such as drug dosage hours of exam preparation cigarette smoking and years of schooling the average causal effect in which we are interested is a conditional expectation of the difference between the outcomes of the treated and what these outcomes would have been in the absence of treatment given mild regularity assumptions the probability limit of tsls is a weighted average of per unit average causal effects along the length of an appropriately defined causal response function the weighting function is illustrated in an empirical example based on the relationship between schooling and earnings

testing single index restrictions with a focus on average derivatives abstract this paper considers a situation where the violation of a single index restriction is a concern only to the extent that it causes bias to the estimates of the average derivatives we propose a method to construct tests that concentrate their asymptotic powers upon only such interesting alternatives the test has a 1 2 limiting distribution under the null hypothesis and even accommodates the case where the parameter estimates have a convergence rate slower than n as in the case of maximum score estimation the testing procedure can be easily modified when the main interest lies in average increment effects of binary covariates multivariate average derivatives or linear restrictions other than those of average derivatives results from monte carlo experiments show that the asymptotic theory is a reasonable approximation of the finite sample distributions and an application of our methods to female labor market participation illustrates the importance of this non omnibus approach

parameters of interest nuisance parameters and orthogonality conditions an application to autoregressive error component models abstract in general when one considers a set of orthogonality conditions the parameters can be divided into parameters of interest that the econometrician wants to estimate the coefficient of the lagged endogenous variable in the case of an autoregressive error component arec model for instance and nuisance parameters most of the second order terms in an arec model we demonstrate that the elimination of such nuisance parameters using their empirical counterpart does not entail an efficiency loss when only the parameters of interest are estimated applications of our results to both autoregressive error component models and time varying individual fixed effects models are discussed at length they show the nature of the efficiency losses when some orthogonality conditions are left aside

image analysis by bessel fourier moments in this paper we proposed a new set of moments based on the bessel function of the first kind named bessel fourier moments bfms which are more suitable than orthogonal fourier mellin and zernike moments for image analysis and rotation invariant pattern recognition compared with orthogonal fourier mellin and zernike polynomials of the same degree the new orthogonal radial polynomials have more zeros and these zeros are more evenly distributed the bessel fourier moments can be thought of as generalized orthogonalized complex moments theoretical and experimental results show that the bessel fourier moments perform better than the orthogonal fourier mellin and zernike moments ofmms and zms in terms of image reconstruction capability and invariant recognition accuracy in noise free noisy and smooth distortion conditions

two step two stage least squares estimation in models with rational expectations abstract the paper develops a two step estimator for use in rational expectations models with autocorrelated residuals and predetermined but not strictly exogenous instruments the estimator extends the applicability of mccallum s 1976 error in variablesapproach to estimating such models and is asymptotically efficient in a class of intrumental variables estimators as an application we use instrumental variables techniques to estimate taylor s 1979 rational expectations macroeconomic model of the united states

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

image analysis by circularly semi orthogonal moments various types of circularly orthogonal moments have been widely used for image reconstruction and rotation invariant classification however they suffer from two errors namely numerical integration error and geometric error which affect their reconstruction capability and pattern recognition accuracy in this paper a novel category of circular moments named circularly semi orthogonal moments is proposed in the proposed moment a set of orthogonal basis functions modulated by a negative power exponential envelope is utilized as the radial basis function for a given degree n the radial basis function possesses more compact bandwidth less cutoff frequency and more zeros compared with the frequently used circularly orthogonal moments including zernike and orthogonal fourier mellin moments and so the circularly semi orthogonal moment calculated with the zeroth order approximation is more robust to numerical error than the frequently used circularly orthogonal moments furthermore the capability of the semi orthogonal moment to describe high spatial frequency components of images is relatively higher than that of the frequently used circularly orthogonal moments experimental results demonstrate that the semi orthogonal moments calculated with the zeroth order approximation perform better than the frequently used circularly orthogonal moments in terms of image reconstruction capability and invariant recognition accuracy in noise free noisy and smooth distortion conditions it is also shown that the proposed high order moments are more numerically stable than the circularly orthogonal moments a kind of circular moments named circularly semi orthogonal moment is proposed it outperforms in image reconstruction over the circularly orthogonal moments it performs better in invariant image recognition under noisy and smooth distortions

improving zernike moments comparison for optimal similarity and rotation angle retrieval zernike moments constitute a powerful shape descriptor in terms of robustness and description capability however the classical way of comparing two zernike descriptors only takes into account the magnitude of the moments and loses the phase information the novelty of our approach is to take advantage of the phase information in the comparison process while still preserving the invariance to rotation this new zernike comparator provides a more accurate similarity measure together with the optimal rotation angle between the patterns while keeping the same complexity as the classical approach this angle information is particularly of interest for many applications including 3d scene understanding through images experiments demonstrate that our comparator outperforms the classical one in terms of similarity measure in particular the robustness of the retrieval against noise and geometric deformation is greatly improved moreover the rotation angle estimation is also more accurate than state of the art algorithms

quaternion fourier mellin moments for color images the quaternion fourier mellin moments for describing color images are introduced which can be seen as the generalization of traditional fourier mellin moments for gray level images then the quaternion fourier mellin moment invariants are derived which could be a useful tool in color object recognition tasks that require the similarity invariance in addition the problem of color image registration using quaternion fourier mellin moments is discussed the registration method can match color images differing in rotation and scaling the advantage of our method is that it can process color image directly without losing color information experimental results validate the effectiveness of the method we proposed

quaternion generic fourier descriptor for color object recognition by introducing quaternions fourier transforms the fundamental tool in signal and image processing were extended to treat a color image in a holistic manner on the other hand color image description has long been a major topic of pattern recognition in this work inspired by the quaternion fourier transforms we propose a quaternion generic fourier descriptor to describe color images holistically and effectively without losing any color information the theoretical framework to construct a set of invariants with respect to geometric transformation is also provided moreover several experiments are conducted on color image databases to illustrate the effectiveness of the proposed invariants the results provide supports for that the quaternion generic fourier descriptor invariants have striking robustness to geometric transformation and noise remarkable progress in accuracy robustness and efficiency of color object recognition has been made by the proposed descriptor in addition it presents superior performances on real recognition scenarios highlightswe propose an image descriptor with the quaternion algebra to describe color images a framework to develop robust invariants to geometric transformation is provided experiments are conducted to validate the performance of the proposed descriptor the proposed descriptor performs robustly to geometric transformation and noise a progress in accuracy of recognition has been made by the proposed descriptor on real recognition scenarios the proposed descriptor also performs superiorly

efficient estimation of dynamic panel data models alternative assumptions and simplified estimation abstract this paper considers the estimation of dynamic models for panel data it shows how to count and express the moment conditions implied by a variety of covariance restrictions these conditions can be imposed in a gmm framework many of the moment conditions are nonlinear in the parameters we derive a simple linearized estimator that is asymptotically as efficient as the nonlinear gmm estimator and convenient tests of the validity of the nonlinear restrictions

a zernike moment phase based descriptor for local image representation and matching a local image descriptor robust to the common photometric transformations blur illumination noise and jpeg compression and geometric transformations rotation scaling translation and viewpoint is crucial to many image understanding and computer vision applications in this paper the representation and matching power of region descriptors are to be evaluated a common set of elliptical interest regions is used to evaluate the performance the elliptical regions are further normalized to be circular with a fixed size the normalized circular regions will become affine invariant up to a rotational ambiguity here a new distinctive image descriptor to represent the normalized region is proposed which primarily comprises the zernike moment zm phase information an accurate and robust estimation of the rotation angle between a pair of normalized regions is then described and used to measure the similarity between two matching regions the discriminative power of the new zm phase descriptor is compared with five major existing region descriptors sift gloh pca sift complex moments and steerable filters based on the precision recall criterion the experimental results involving more than 15 million region pairs indicate the proposed zm phase descriptor has generally speaking the best performance under the common photometric and geometric transformations both quantitative and qualitative analyses on the descriptor performances are given to account for the performance discrepancy first the key factor for its striking performance is due to the fact that the zm phase has accurate estimation accuracy of the rotation angle between two matching regions second the feature dimensionality and feature orthogonality also affect the descriptor performance third the zm phase is more robust under the nonuniform image intensity fluctuation finally a time complexity analysis is provided

multilevel modeling with correlated effects when there exist omitted effects measurement error and or simultaneity in multilevel models explanatory variables may be correlated with random components and standard estimation methods do not provide consistent estimates of model parameters this paper introduces estimators that are consistent under such conditions by employing generalized method of moments gmm estimation techniques in multilevel modeling the authors present a series of estimators along a robust to efficient continuum this continuum depends on the assumptions that the analyst makes regarding the extent of the correlated effects it is shown that the gmm approach provides an overarching framework that encompasses well known estimators such as fixed and random effects estimators and also provides more options these gmm estimators can be expressed as instrumental variable iv estimators which enhances their interpretability moreover by exploiting the hierarchical structure of the data the current technique does not require additional variables unlike traditional iv methods further statistical tests are developed to compare the different estimators a simulation study examines the finite sample properties of the estimators and tests and confirms the theoretical order of the estimators with respect to their robustness and efficiency it further shows that not only are regression coefficients biased but variance components may be severely underestimated in the presence of correlated effects empirical standard errors are employed as they are less sensitive to correlated effects when compared to model based standard errors an example using student achievement data shows that gmm estimators can be effectively used in a search for the most efficient among unbiased estimators

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

quaternion polar harmonic fourier moments for color images abstract this paper proposes quaternion polar harmonic fourier moments qphfm for color image processing and analyzes the properties of qphfm after extending chebyshev fourier moments chfm to quaternion chebyshev fourier moments qchfm comparison experiments including image reconstruction and color image object recognition on the performance of qphfm and quaternion zernike moments qzm quaternion pseudo zernike moments qpzm quaternion orthogonal fourier mellin moments qofmm qchfm and quaternion radial harmonic fourier moments qrhfm are carried out experimental results show qphfm can achieve an ideal performance in image reconstruction and invariant object recognition in noise free and noisy conditions in addition this paper discusses the importance of phase information of quaternion orthogonal moments in image reconstruction

specification testing in panel data with instrumental variables i show that specification tests for correlated fixed effects developed by hausman and taylor extend in an analogous way to panel data sets with endogenous regressors given panel data different sets of instrumental variables can be used to construct the test for a simple class of models the test in many cases is asymptotically more efficient if an incomplete set of instruments is used however in small samples one may do better using the complete set of instruments monte carlo results demonstrate the likely gains for different assumptions about the degree of between and within variance in the data

robust inference with gmm estimators the local robustness properties of generalized method of moments gmm estimators and of a broad class of gmm based tests are investigated in a unified framework gmm statistics are shown to have bounded influence if and only if the function defining the orthogonality restrictions imposed on the underlying model is bounded since in many applications this function is unbounded it is useful to have procedures that modify the starting orthogonality conditions in order to obtain a robust version of a gmm estimator or test we show how this can be obtained when a reference model for the data distribution can be assumed we develop a flexible algorithm for constructing a robust gmm rgmm estimator leading to stable gmm test statistics the amount of robustness can be controlled by an appropriate tuning constant we relate by an explicit formula the choice of this constant to the maximal admissible bias on the level or and the power of a gmm test and the amount of contamination that one can reasonably assume given some information on the data finally we illustrate the rgmm methodology with some simulations of an application to rgmm testing for conditional heteroscedasticity in a simple linear autoregressive model in this example we find a significant instability of the size and the power of a classical gmm testing procedure under a non normal conditional error distribution on the other side the rgmm testing procedures can control the size and the power of the test under non standard conditions while maintaining a satisfactory power under an approximatively normal conditional error distribution

testing instrument admissibility some refined asymptotic results this paper is concerned with the refined asymptotic properties of several tests for the admissibility of a subset of overidentifying instrumental variables it derives maximum likelihood and linearized maximum likelihood tests and calculates size corrections to the order 1 t the local power function of the size corrected tests is the same to the order 1 t irrespectively of the form of the test statistic or the limited information estimator used in its computation futher it compares these tests with two previously proposed tests the size and the power of the original and the size corrected tests are compared by monte carlo experiments copyright 1994 by the econometric society

shape descriptors and mapping methods for full field comparison of experimental to simulation data validation of computational solid mechanics simulations requires full field comparison methodologies between numerical and experimental results the continuous zernike and chebyshev moment descriptors are applied to decompose data obtained from numerical simulations and experimental measurements in order to reduce the high amount of raw data to a fairly modest number of features and facilitate their comparisons as zernike moments are defined over a unit disk space a geometric transformation mapping of rectangular to circular domain is necessary before zernike decomposition is applied to non circular geometry four different mapping techniques are examined and their decomposition reconstruction efficiency is assessed a deep mathematical investigation to the reasons of the different performance of the four methods has been performed comprising the effects of image mapping distortion and the numerical integration accuracy special attention is given to the schwarz christoffel conformal mapping which in most cases is proven to be highly efficient in image description when combined to zernike moment descriptors in cases of rectangular structures it is demonstrated that despite the fact that zernike moments are defined on a circular domain they can be more effective even from chebyshev moments which are defined on rectangular domains provided that appropriate mapping techniques have been applied

estimation of motions in color image sequences using hypercomplex fourier transforms although the motion estimation problem has been extensively studied most of the proposed estimation approaches deal mainly with monochrome videos the most usual way to apply them also in color image sequences is to process each color channel separately a different more sophisticated approach is to process the color channels in a ldquoholisticrdquo manner using quaternions as proposed by ell and sangwine in this paper we extend standard spatiotemporal fourier based approaches to handle color image sequences using the hypercomplex fourier transform we show that translational motions are manifested as energy concentration along planes in the hypercomplex 3d fourier domain and we describe a methodology to estimate the motions based on this property furthermore we compare the three channels separately approach with our approach and we show that the computational effort can be reduced by a factor of 1 3 using the hypercomplex fourier transform also we propose a simple accompanying method to extract the moving objects in the hypercomplex fourier domain our experimental results on synthetic and natural images verify our arguments throughout the paper

near exogeneity and weak identification in generalized empirical likelihood estimators many moment asymptotics abstract this paper investigates the generalized empirical likelihood gel estimators when there are local violations of the exogeneity condition near exogeneity in the case of many weak moments we also examine the tradeoff between the degree of violation of the exogeneity and the number of nearly exogenous instruments in this respect this paper extends many weak moment asymptotics of newey and windmeijer 2009a the overidentifying restrictions test can detect both mild and large violations of exogeneity in the case of minor violations the anderson rubin 1949 and wald tests are not size distorted

specification testing and quasi maximum likelihood estimation abstract this paper develops robust regression based conditional moment tests for models estimated by quasi maximum likelihood using a density in the linear exponential family the tests are relatively simple to compute while being robust to distributional assumptions other than those being explicitly tested the conditional mean tests assume only that the conditional mean is correctly specified under the null hypothesis but are asymptotically equivalent to standard forms of the tests if the conditional variance is correctly specified tests for conditional variance misspecification assume only that the first two moments are correctly specified under the null hypothesis an empirical application to individual arrest data is included

quaternion polar complex exponential transform for invariant color image description moments and moment invariants have been widely used as a basic feature descriptors in image analysis pattern recognition and image retrieval however they are mainly used to deal with the binary or gray scale images which lose some significant color information recently quaternion techniques were introduced to conventional image moments including fourier mellin moments zernike pseudo zernike moments and bessel fourier moments etc for describing color images and some quaternion moment and moment invariants were developed but the conventional image moments usually cannot effectively capture the image information especially the edges besides the kernel computation of them involves computation of a number of factorial terms which inevitably cause the numerical stability of these moments based on effective polar complex exponential transform pcet and algebra of quaternions we introduced the quaternion polar complex exponential transform qpcet for describing color images in this paper which can be seen as the generalization of pcet for gray level images it is shown that the qpcets can be obtained from the pcet of each color channel we derived and analyzed the rotation scaling and translation rst invariant property of qpcet we also discussed the problem of color image retrieval using qpcet experimental results are provided to illustrate the efficiency of the proposed color image descriptors

simulated method of moments estimation for copula based multivariate models this article considers the estimation of the parameters of a copula via a simulated method of moments mm type approach this approach is attractive when the likelihood of the copula model is not known in closed form or when the researcher has a set of dependence measures or other functionals of the copula that are of particular interest the proposed approach naturally also nests mm and generalized method of moments estimators drawing on results for simulation based estimation and on recent work in empirical copula process theory we show the consistency and asymptotic normality of the proposed estimator and obtain a simple test of overidentifying restrictions as a specification test the results apply to both iid and time series data we analyze the finite sample behavior of these estimators in an extensive simulation study we apply the model to a group of seven financial stock returns and find evidence of statistically significant tail dependence and mild evidence that the dependence between thes

a unified approach to estimation and orthogonality tests in linear single equation econometric models abstract maximum likelihood estimation is considered for a generalisation of the model of anderson and rubin 1949 in which the exogenous variables in the structural equation may not be included in the reduced form equations classical and specification tests are derived for orthogonality hypotheses a necessary and sufficient condition for their equivalence is presented the classical tests are compared using bahadur s asymptotic relative efficiency criterion it is shown that a generalisation of the durbin wu hausman t 2 statistics is asymptotically bahadur efficient

robust rotation angle estimator the conventional method of estimating the rotation angle of a pattern using the principal axes is not suitable for circular symmetric patterns since their eigenvalues are similar in both directions in the paper a robust method of estimating a rotation angle using the phase information of zernike moments is presented the experimental results show that the proposed method estimates the rotation angle of the circular symmetric patterns more accurately than the principal axes method even in the presence of noise

efficient estimation and identification of simultaneous equation models with covariance restrictions this paper is a revision of an earlier version presented at the european econometric meetings 1982

neglected heterogeneity in moment condition models abstract the central concern of this paper is parameter heterogeneity in models specified by a number of unconditional or conditional moment conditions and thereby the provision of a framework for the development of apposite optimal m tests against its potential presence we initially consider the unconditional moment restrictions framework optimal m tests against moment condition parameter heterogeneity are derived with the relevant jacobian matrix obtained in terms of the second order own derivatives of the moment indicator in a leading case gmm and gel tests of specification based on generalized information matrix equalities appropriate for moment based models are described and their relation to optimal m tests against moment condition parameter heterogeneity examined a fundamental and important difference is noted between gmm and gel constructions the paper is concluded by a generalization of these tests to the conditional moment context and the provision of a limited set of simulation experiments to illustrate the efficacy of the proposed tests

specification test on mixed logit models abstract this paper proposes a specification test of the mixed logit models by generalizing hausman and mcfadden 1984 test we generalize the test even further by considering a model developed by berry et al 1995

tests of additional conditional moment restrictions abstract the primary focus of this article is the provision of tests for the validity of a set of conditional moment constraints additional to those defining the maintained hypothesis that are relevant for independent cross sectional data contexts the point of departure and principal contribution of the paper is the explicit and full incorporation of the conditional moment information defining the maintained hypothesis in the design of the test statistics thus the approach mirrors that of the classical parametric likelihood setting by defining restricted tests in contradistinction to unrestricted tests that partially or completely fail to incorporate the maintained information in their formulation the framework is quite general allowing the parameters defining the additional and maintained conditional moment restrictions to differ and permitting the conditioning variates to differ likewise gmm and generalised empirical likelihood test statistics are suggested the asymptotic properties of the statistics are described under both null hypothesis and a suitable sequence of local alternatives an extensive set of simulation experiments explores the practical efficacy of the various test statistics in terms of empirical size and size adjusted power confirming the superiority of restricted over unrestricted tests a number of restricted tests possess both sufficiently satisfactory empirical size and power characteristics to allow their recommendation for econometric practice

convergence of semi lagrangian approximations to convex hamilton jacobi equations under very large courant numbers we consider a class of semi lagrangian high order approximation schemes for convex hamilton jacobi equations in this framework we prove that under certain restrictions on the relationship between delta x and delta t the sequence of approximate solutions is uniformly lipschitz continuous and hence by consistency that it converges to the exact solution the argument is suitable for most reconstructions of interest including high order polynomials and eno reconstructions

generalized method of moments specification testing abstract this paper analyzes the asymptotic power properties of specification tests which are based on a finite set of moment conditions it shows that any such test may fail against general misspecification that causes estimator inconsistency the mutual asymptotic equivalence of maximal degree of freedom tests is shown and the form of optimal tests against specific forms of misspecification is derived applications to testing for exogeneity of a set of instrumental variables are presented

hypercomplex fourier transforms of color images fourier transforms are a fundamental tool in signal and image processing yet until recently there was no definition of a fourier transform applicable to color images in a holistic manner in this paper hypercomplex numbers specifically quaternions are used to define a fourier transform applicable to color images the properties of the transform are developed and it is shown that the transform may be computed using two standard complex fast fourier transforms the resulting spectrum is explained in terms of familiar phase and modulus concepts and a new concept of hypercomplex axis a method for visualizing the spectrum using color graphics is also presented finally a convolution operational formula in the spectral domain is discussed

translation invariants of zernike moments moment functions defined using a polar coordinate representation of the image space such as radial moments and zernike moments are used in several recognition tasks requiring rotation invariance however this coordinate representation does not easily yield translation invariant functions which are also widely sought after in pattern recognition applications this paper presents a mathematical framework for the derivation of translation invariants of radial moments defined in polar form using a direct application of this framework translation invariant functions of zernike moments are derived algebraically from the corresponding central moments both derived functions are developed for non symmetrical as well as symmetrical images they mitigate the zero value obtained for odd order moments of the symmetrical images vision applications generally resort to image normalization to achieve translation invariance the proposed method eliminates this requirement by providing a translation invariance property in a zernike feature set the performance of the derived invariant sets is experimentally confirmed using a set of binary latin and english characters

exogeneity tests incomplete models weak identification and non gaussian distributions invariance and finite sample distributional theory abstract we study the distribution of durbin wu hausman dwh and revankar hartley rh tests for exogeneity from a finite sample viewpoint under the null and alternative hypotheses we consider linear structural models with possibly non gaussian errors where structural parameters may not be identified and where reduced forms can be incompletely specified or nonparametric on level control we characterize the null distributions of all the test statistics through conditioning and invariance arguments we show that these distributions do not involve nuisance parameters in particular this applies to several test statistics for which no finite sample distributional theory is yet available such as the standard statistic proposed by hausman 1978 the distributions of the test statistics may be non standard so corrections to usual asymptotic critical values are needed but the characterizations are sufficiently explicit to yield finite sample monte carlo tests of the exogeneity hypothesis the procedures so obtained are robust to weak identification missing instruments or misspecified reduced forms and can easily be adapted to allow for parametric non gaussian error distributions we give a general invariance result block triangular invariance for exogeneity test statistics this property yields a convenient exogeneity canonical form and a parsimonious reduction of the parameters on which power depends in the extreme case where no structural parameter is identified the distributions under the alternative hypothesis and the null hypothesis are identical so the power function is flat for all the exogeneity statistics however as soon as identification does not fail completely this phenomenon typically disappears we present simulation experiments which confirm the finite sample theory the theoretical results are illustrated with an empirical example the relation between trade and economic growth

tests of overidentification and predeterminedness in simultaneous equation models abstract a set of simultaneous equations that is a part of a larger complete system is considered one hypothesis concerning this set of equations is that it is overidentified as a block by a block of zero restrictions another hypothesis is that a subset of the current endogenous variables is uncorrelated with the disturbances in the set of simultaneous equations econometric predeterminedness likelihood ratio lagrange multiplier and wald tests are derived for the overidentification hypothesis against unrestricted alternatives for the predeterminedness hypothesis against unrestricted alternatives and for the predeterminedness hypothesis against overidentified alternatives the tests are derived on the basis of normality but are asymptotically valid under very general conditions this study generalizes and unifies many test procedures proposed previously some new tests are developed

a consistent test of functional form via nonparametric estimation techniques abstract this paper presents a consistent test of functional form of nonlinear regression models the test combines the methodology of the conditional moment test and nonparametric estimation techniques using degenerate and nondegenerate u statistic theories the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct while diverging to infinity at a rate arbitrarily close to n the sample size if the parametric model is misspecified therefore the test is consistent against all deviations from the parametric model the test is robust to heteroskedasticity a version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1 n a simulation study reveals that the test has good finite sample properties

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

sensitivity analysis for instrumental variables regression with overidentifying restrictions instrumental variables regression iv regression is a method for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables the method requires one or more valid instrumental variables ivs a valid iv is a variable that is associated with the treatment is independent of unmeasured confounding variables and has no direct effect on the outcome often there is uncertainty about the validity of the proposed ivs when a researcher proposes more than one iv the validity of these ivs can be tested through the overidentifying restrictions test although the overidentifying restrictions test does provide some information the test has no power versus certain alternatives and can have low power versus many alternatives due to its omnibus nature to fully address uncertainty about the validity of the proposed ivs we argue that a sensitivity analysis is needed a sensitivity analysis examines the impact of plausible amounts of

quaternion bessel fourier moments and their invariant descriptors for object reconstruction and recognition in this paper the quaternion bessel fourier moments are introduced the significance of phase information in quaternion bessel fourier moments is investigated and an accurate estimation method for rotation angle is described furthermore a new set of invariant descriptors based on the magnitude and the phase information of quaternion bessel fourier moments is derived experimental results show that quaternion bessel fourier moments lead to better performance for color image reconstruction than the other quaternion orthogonal moments such as quaternion zernike moments quaternion pseudo zernike moments and quaternion orthogonal fourier mellin moments in addition the angles estimated by the proposed moments are more accurate than those obtained by using other quaternion orthogonal moments the proposed invariant descriptors show also better robustness to geometric and photometric transformations quaternion bessel fourier moments for color image reconstruction and recognition an accurate estimation method for rotation angle throughout quaternion moments the invariant descriptor using the moment magnitudes and phase coefficients

the validity of instruments revisited valid instrumental variables must be relevant and exogenous however in practice it is difficult to find instruments that are exogenous in that they satisfy the knifeedged orthogonality condition and at the same time are strongly correlated with the endogenous regressors in this paper we show how a mild violation of the exogeneity assumption affects the limit of the anderson rubin test 1949 this test statistic is frequently used in economics due to the fact that it is robust to identification problems however when there is mild violation of exogeneity the test is oversized and with larger samples the problem gets worse in order to correct this problem we introduce the fractionally resampled anderson rubin test far that is derived by modifying the resampling technique introduced by wu 1990 our main result is that in large samples the far test does not overreject the null hypothesis when we use half of the sample without replacement as the block size from the original sample we also show that subsampling will not achieve this simulations show that in finite samples the far is conservative thus we suggest a block size choice that has very good size and power when there are possible violations of the exogeneity assumption thus we show that we can conduct inference and get good size and power when instruments mildly violate the exogeneity assumption