diagnostics for nonlinearity and heteroscedasticity in errors in variables regression we suggest new plotting methods for residual analysis in errors in variables regression the standard residuals analyses are based on the methods of miller and fuller and are appropriate when the errors in the regression and the measurement error are symmetrically distributed by appropriate we mean that in large samples the plots will not falsely identify a nonexistent pattern of heteroscedasticity or nonlinearity the standard methods are not appropriate in this sense for skewed error distributions our methods require replication of the error prone predictors but they are appropriate for both symmetric and skewed error distributions besides residual plots we also construct hypothesis tests for heteroscedasticity in terms of power for detecting heteroscedasticity we show that the standard plot is more efficient when the residuals are normally distributed although it does not achieve its nominal level for skewed error distributions simulations are used to illustrate the results we also conside

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

new tight frames of curvelets and optimal representations of objects with piecewise c2 singularities this paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along piecewise c 2 edges conceptually the curvelet transform is a multiscale pyramid with many directions and positions at each length scale and needle shaped elements at fine scales these elements have many useful geometric multiscale features that set them apart from classical multiscale representations such as wavelets for instance curvelets obey a parabolic scaling relation which says that at scale 2 j each element has an envelope that is aligned along a ridge of length 2 j 2 and width 2 j we prove that curvelets provide an essentially optimal representation of typical objects f that are c 2 except for discontinuities along piecewise c 2 curves such representations are nearly as sparse as if f were not singular and turn out to be far more sparse than the wavelet decomposition of the object for instance the n term partial reconstruction f c n obtained by selecting the n largest terms in the curvelet series obeys f f c n 2 l2 c n 2 log n 3 n this rate of convergence holds uniformly over a class of functions that are c 2 except for discontinuities along piecewise c 2 curves and is essentially optimal in comparison the squared error of n term wavelet approximations only converges as n 1 as n which is considerably worse than the optimal behavior

a simple fuzzy method to remove mixed gaussian impulsive noise from color images mixed impulsive and gaussian noise reduction from digital color images is a challenging task because it is necessary to appropriately process both types of noise that in turn need to be distinguished from the original image structures such as edges and details fuzzy theory is useful to build simple efficient and effective solutions for this problem in this paper we propose a fuzzy method to reduce gaussian and impulsive noise from color images our method uses one only filtering operation a weighted averaging a fuzzy rule system is used to assign the weights in the averaging so that both noise types are reduced and image structures are preserved we provide experimental results to show that the performance of the method is competitive with respect to state of the art filters

image denoising and segmentation via nonlinear diffusion abstract image denoising and segmentation are fundamental problems in the field of image processing and computer vision with numerous applications in this paper we present a nonlinear pde based model for image denoising and segmentation which unifies the popular model of alvarez lions and morel alm for image denoising and the caselles kimmel and sapiro model of geodesic snakes our model includes nonlinear diffusive as well as reactive terms and leads to quality denoising and segmentation results as depicted in the experiments presented here we present a proof for the existence uniqueness and stability of the viscosity solution of this pde based model the proof is in spirit similar to the proof of the alm model however there are several differences which arise due to the presence of the reactive terms that require careful treatment consideration a fast implementation of our model is realized by embedding the model in a scale space and then achieving the solution via a dynamic system governed by a coupled system of first order differential equations the dynamic system finds the solution at a coarse scale and tracks it continuously to a desired fine scale we demonstrate the smoothing and segmentation results on several real images

fuzzy peer groups for reducing mixed gaussian impulse noise from color images the peer group of an image pixel is a pixel similarity based concept which has been successfully used to devise image denoising methods however since it is difficult to define the pixel similarity in a crisp way we propose to represent this similarity in fuzzy terms in this paper we introduce the fuzzy peer group concept which extends the peer group concept in the fuzzy setting a fuzzy peer group will be defined as a fuzzy set that takes a peer group as support set and where the membership degree of each peer group member will be given by its fuzzy similarity with respect to the pixel under processing the fuzzy peer group of each image pixel will be determined by means of a novel fuzzy logic based procedure we use the fuzzy peer group concept to design a two step color image filter cascading a fuzzy rule based switching impulse noise filter by a fuzzy average filtering over the fuzzy peer group both steps use the same fuzzy peer group which leads to computational savings the proposed filter is able to efficiently suppress both gaussian noise and impulse noise as well as mixed gaussian impulse noise experimental results are provided to show that the proposed filter achieves a promising performance

oriented texture completion by am fm reaction diffusion we provide an automated method to repair broken occluded oriented image textures our approach is based on partial differential equations pdes and am fm image modeling reconstruction of the texture occurs via simultaneous pde generated diffusion and reaction in the diffusion process the image is adaptively smoothed preserving important boundaries and features the reaction process produces the reconstructed textural information in the occluded image regions gabor 1946 filters are designed and used in the reaction process using an am fm dominant component analysis an am fm model of the texture image is constructed making it possible to localize the reaction filters spatio spectrally in contrast to previous disocclusion techniques that depend on interpolation on continuity of the connected components within the image level sets or on texture estimation the reaction diffusion process proposed here yields a seamless transition between the recreated region and the unoccluded image regions using am fm dominant component analysis we avoid the ad hoc parameter selection typified with other reaction diffusion approaches as a useful example we focus on the repair of broken occluded fingerprints we also treat several exemplary natural textures to demonstrate the technique s generality

robustifying glejser test of heteroskedasticity verifying that the glejser test for heteroskedasticity is asymptotically invalid unless the error density is symmetric this paper proposes a simple modification to make the test robust to asymmetric disturbances simulation results demonstrate that the size of the modified test is correct for both symmetric and skewed errors

prior learning and gibbs reaction diffusion this article addresses two important themes in early visual computation it presents a novel theory for learning the universal statistics of natural images and it proposes a general framework of designing reaction diffusion equations for image processing we studied the statistics of natural images including the scale invariant properties then generic prior models were learned to duplicate the observed statistics based on minimax entropy theory the resulting gibbs distributions have potentials of the form u i spl lambda s spl sigma sub spl alpha 1 sup k spl sigma sub x y spl lambda sup spl alpha f sup spl alpha i x y with s f sup 1 f sup 2 f sup k being a set of filters and spl lambda spl lambda sup 1 spl lambda sup 2 spl lambda sup k the potential functions the learned gibbs distributions confirm and improve the form of existing prior models such as line process but in contrast to all previous models inverted potentials were found to be necessary we find that the partial differential equations given by gradient descent on u i spl lambda s are essentially reaction diffusion equations where the usual energy terms produce anisotropic diffusion while the inverted energy terms produce reaction associated with pattern formation enhancing preferred image features we illustrate how these models can be used for texture pattern rendering denoising image enhancement and clutter removal by careful choice of both prior and data models of this type incorporating the appropriate features

diffusion tensors for processing sheared and rotated rectangles image restoration and simplification methods that respect important features such as edges play a fundamental role in digital image processing however known edge preserving methods like common nonlinear diffusion methods tend to round vertices for large diffusion times in this paper we adapt the diffusion tensor for anisotropic diffusion to avoid this effects in images containing rotated and sheared rectangles respectively in this context we propose a new method for estimating rotation angles and shear parameters based on the so called structure tensor further we show how the knowledge of appropriate diffusion tensors can be used in variational models numerical examples including orientation estimation denoising and segmentation demonstrate the good performance of our methods

image quantization using reaction diffusion equations in this paper we present an image quantization model based on a reaction diffusion partial differential equation the quantized image is given by the asymptotic state of this equation existence and uniqueness of the solution are proved in the framework of viscosity solutions we introduce an l infty stable algorithm in order to compute numerically the solution of the equation and some experimental results are shown a new energy functional based on the classical lloyd method is used to compute the quantizer codewords

some heteroskedasticity consistent covariance matrix estimators with improved finite sample properties abstract we examine several modified versions of the heteroskedasticity consistent covariance matrix estimator of hinkley 1977 and white 1980 on the basis of sampling experiments which compare the performance of quasi t statistics we find that one estimator based on the jackknife performs better in small samples than the rest we also examine the finite sample properties of using modified critical values based on edgeworth approximations as proposed by rothenberg 1984 in addition we compare the power of several tests for heteroskedasticity and find that it may be wise to employ the jackknife heteroskedasticity consistent covariance matrix even in the absence of detected heteroskedasticity

local strong homogeneity of a regularized estimator this paper deals with regularized pointwise estimation of discrete signals which contain large strongly homogeneous zones where typically they are constant or linear or more generally satisfy a linear equation the estimate is defined as the minimizer of an objective function combining a quadratic data fidelity term and a regularization prior term the latter term is the sum of the values obtained by applying a potential function pf to each component called a difference of a linear transform of the signal minimizers of functions of this form arise in various settings in statistics and optimization the features exhibited by such an estimate are closely related to the shape of the pf our goal is to determine estimators providing solutions which involve large strongly homogeneous zones where more precisely the differences are null in spite of the noise corrupting the data to this end we require that the strongly homogeneous zones recovered by the estimator be insensitive to any variation of th

the curvelet transform for image denoising we describe approximate digital implementations of two new mathematical transforms namely the ridgelet transform and the curvelet transform our implementations offer exact reconstruction stability against perturbations ease of implementation and low computational complexity a central tool is fourier domain computation of an approximate digital radon transform we introduce a very simple interpolation in the fourier space which takes cartesian samples and yields samples on a rectopolar grid which is a pseudo polar sampling set based on a concentric squares geometry despite the crudeness of our interpolation the visual performance is surprisingly good our ridgelet transform applies to the radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain our curvelet transform uses our ridgelet transform as a component step and implements curvelet subbands using a filter bank of a spl grave trous wavelet filters our philosophy throughout is that transforms should be overcomplete rather than critically sampled we apply these digital transforms to the denoising of some standard images embedded in white noise in the tests reported here simple thresholding of the curvelet coefficients is very competitive with state of the art techniques based on wavelets including thresholding of decimated or undecimated wavelet transforms and also including tree based bayesian posterior mean methods moreover the curvelet reconstructions exhibit higher perceptual quality than wavelet based reconstructions offering visually sharper images and in particular higher quality recovery of edges and of faint linear and curvilinear features existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems the empirical results reported here are in encouraging agreement

nonlinear wavelet image processing variational problems compression and noise removal through wavelet shrinkage this paper examines the relationship between wavelet based image processing algorithms and variational problems algorithms are derived as exact or approximate minimizers of variational problems in particular we show that wavelet shrinkage can be considered the exact minimizer of the following problem given an image f defined on a square i minimize over all g in the besov space b11 l1 i the functional f g l2 i 2 g b11 l1 i we use the theory of nonlinear wavelet image compression in l2 i to derive accurate error bounds for noise removal through wavelet shrinkage applied to images corrupted with i i d mean zero gaussian noise a new signal to noise ratio snr which we claim more accurately reflects the visual perception of noise in images arises in this derivation we present extensive computations that support the hypothesis that near optimal shrinkage parameters can be derived if one knows or can estimate only two parameters about an image f the largest for which f bq lq i 1 q 2 1 2 and the norm f bq lq i both theoretical and experimental results indicate that our choice of shrinkage parameters yields uniformly better results than donoho and johnstone s visushrink procedure an example suggests however that donoho and johnstone s 1994 1995 1996 sureshrink method which uses a different shrinkage parameter for each dyadic level achieves a lower error than our procedure

shearlet based total variation diffusion for denoising we propose a shearlet formulation of the total variation tv method for denoising images shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization common approaches in combining wavelet like representations such as curvelets with tv or diffusion methods aim at reducing gibbs type artifacts after obtaining a nearly optimal estimate we show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain we also analyze the performance of a shearlet based diffusion method numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform furthermore the shearlet tv scheme requires far fewer iterations than similar competitors

the perona malik paradox the perona malik equation is a formally ill posed parabolic equation for which simple discretizations are nevertheless numerically found to be stable after discussing the background of this parad

asymptotic relative efficiency of the classical test statistics under misspecification abstract asymptotic properties of the three classical test statistics the likelihood ratio lagrange multiplier efficient score and wald statistics are studied in the case of two types of misspecification the first misspecification is that the alternative used to construct the test is different from the true nonnull model in the second case the alternative hypothesis is correct but some of the nuisance parameters satisfy restrictions which are not taken into account in the test pitman s local alternatives and the concept of asymptotic relative efficiency are used to derive the asymptotic distributions of the test statistics and to examine the effects of the misspecifications the general results of the paper are illustrated by an example on the dynamic specification of a regression model

image recovery using the anisotropic diffusion equation a new approach for image recovery using the anisotropic diffusion equation is developed which is based on the first derivative of the signal in time embedded in family of images with different scales the diffusion coefficient is determined as a function of the gradient of the signal convolved with a symmetric exponential filter a new discrete realization is developed for the simultaneous removal of noise and preservation of edges

a heteroscedasticity consistent covariance matrix estimator for time series regressions abstract this paper provides a covariance matrix estimator for the ordinary least squares coefficients of a linear time series model which is consistent even when the disturbances are heteroscedastic this estimator does not require a formal model of the heteroscedasticity one can also obtain a direct test of heteroscedasticity although monte carlo experiments show that it may have low power

image denoising using svm classification in nonsubsampled contourlet transform domain for image denoising the main challenge is how to preserve the information bearing structures such as edges and textures to get satisfactory visual quality when improving the signal to noise ratio snr edge preserving image denoising has become a very intensive research topic in this paper we propose an image denoising using support vector machine svm classification in nonsubsampled contourlet transform nsct domain firstly the noisy image is decomposed into different subbands of frequency and orientation responses using the nsct secondly the feature vector for a pixel in a noisy image is formed by the spatial regularity in nsct domain and the least squares support vector machine ls m model is obtained by training then the nsct detail coefficients are divided into two classes edge related coefficients and noise related ones by ls svm training model finally the detail subbands of nsct coefficients are denoised by using shrink method in which the adaptive bayesian threshold is utilized extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state of the art denoising techniques especially the proposed method can preserve edges very well while removing noise

an analysis of the perona malik scheme the perona malik scheme is a numerical procedure for de noising digital pictures in this work we investigate how it evolves piecewise smooth initial data in one space dimension by scaling a natural parameter that appears in the scheme in an appropriate way with respect to the grid size we obtain a meaningful continuum limit the resulting evolution is unusual it involves solving a system of heat equations coupled to each other through nonlinear boundary conditions that become singular at special times leading to gradient blow up for the solutions however the scheme suggests a natural continuation beyond each of the singular times that involves a change in the p d e system we give a convergence proof that applies under some technical restrictions on any bounded interval of time which might include singular times furthermore the proposed continuum limit has some of the essential features observed in applications of the numerical scheme

time displaced interactions classical dynamics and path integral quantization the path integral was created to quantize systems whose dynamics are nonlocal in time and for which a hamiltonian formulation could not be found in this article we quantize a linear oscillator with an interaction that depends on the oscillator s position at past and future times the central issue is the classical boundary value problem for such an oscillator because two time functional boundary conditions are used to implement the quantization we take up related questions such as causality in this context and the general issue of stability for forward and inward data specifications

a note on studentizing a test for heteroscedasticity abstract breusch and pagan 1979 have recently proposed a convenient test for heteroscedasticity in general linear models this note derives the asymptotic distribution of their test under sequences of contiguous alternatives to the null hypothesis of homoscedasticity the test is shown to possess asymptotically incorrect size nominal significance level except in the case of strictly gaussian disturbances a slight modification of the test is proposed which corrects this defect

a segmentation based regularization term for image deconvolution this paper proposes a new and original inhomogeneous restoration deconvolution model under the bayesian framework for observed images degraded by space invariant blur and additive gaussian noise in this model regularization is achieved during the iterative restoration process with a segmentation based a priori term this adaptive edge preserving regularization term applies a local smoothness constraint to pre estimated constant valued regions of the target image these constant valued regions the segmentation map of the target image are obtained from a preliminary wiener deconvolution estimate in order to estimate reliable segmentation maps we have also adopted a bayesian markovian framework in which the regularized segmentations are estimated in the maximum a posteriori map sense with the joint use of local potts prior and appropriate gaussian conditional luminance distributions in order to make these segmentations unsupervised these likelihood distributions are estimated in the maximum likelihood sense to compute the map estimate associated to the restoration we use a simple steepest descent procedure resulting in an efficient iterative process converging to a globally optimal restoration the experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state of the art methods in benchmark tests

explicit evaluation of a path integral with memory kernel an explicit expression is presented for the path integral of an harmonic oscillator interacting with itself in the past the time dependence of the memory kernel is assumed to be exponential the relation with the feynman trial action for the variational calculation of the polaron ground state energy is discussed

accuracy of the semiclassical approximation for the time dependent propagator for chaotic systems the semiclassical approximation to the time dependent propagator consists of a large number of terms some of which may involve classical trajectories near focal points caustics despite this the approximation has been found to remain accurate for relatively long times in this article that accuracy and potential reasons for its breakdown are studied the principal tool is the jacobi morse equation the eigenvalue equation associated with the second variational derivative of the classical action our explanation for the accuracy lies partly in the following considerations 1 verification of the efficacy of phase space smearing 2 given an explicit form of the near caustic propagator it is seen that the arguments concerning loops in phase space may be less relevant than the determination of the amount of separation in path space 3 and finally the caustics in the chaotic examples studied may not be placed for maximum mischief

robustness of size of tests of autocorrelation and heteroscedasticity to nonnormality abstract a comprehensive empirical examination is made of the sensitivity of tests of disturbance covariance in the linear regression model to nonnormal disturbance behaviour tests of autocorrelation appear to be quite robust except for extreme nonnormality but tests for heteroscedasticity are highly susceptible to kurtosis

anisotropic second and fourth order diffusion models based on convolutional virtual electric field for image denoising this paper proposes novel second order and fourth order anisotropic diffusion models for image denoising these two models are based on convolutional virtual electric field convef the proposed second order anisotropic diffusion model was introduced by introducing the convef into the perona malik p m equation and the fourth order one is coined by combining convef and the you kaveh y k equation the employment of the convef model allows to improve the estimation of high order derivatives and makes the proposed methods more robust to noise in addition the proposed convef based y k model is an anisotropic diffusion equation which can avoid the over smoothness of edges and provide better edge protection capability except for better denoising some experiments are conducted to demonstrate the efficiency of the proposed methods

dual norms and image decomposition models following a recent work by y meyer decomposition models into a geometrical component and a textured component have recently been proposed in image processing in such approaches negative sobolev norms have seemed to be useful to modelize oscillating patterns in this paper we compare the properties of various norms that are dual of sobolev or besov norms we then propose a decomposition model which splits an image into three components a first one containing the structure of the image a second one the texture of the image and a third one the noise our decomposition model relies on the use of three different semi norms the total variation for the geometrical component a negative sobolev norm for the texture and a negative besov norm for the noise we illustrate our study with numerical examples

stability properties of the perona malik scheme the perona malik scheme is a numerical technique for denoising digital images without blurring object boundaries edges in general solutions generated by this scheme do not satisfy a comparison principle we identify conditions under which two solutions initially ordered remain ordered and we state restricted comparison principles these allow us to study stability properties of the scheme we also explore what these results say in the limit as the discretization size goes to 0

a model based on local graphs for colour images and its application for gaussian noise smoothing in this paper a new model for processing colour images is presented a graph is built for each image pixel taking into account some constraints on links each pixel is characterized depending on the features of its related graph which allows to process it appropriately as an example we provide a characterization of each pixel based on the link cardinality of its connected component this feature enables us to properly distinguish flat image regions respect to edge and detail regions according to this we have designed a hybrid filter for colour image smoothing it combines a filter able to properly process flat image regions with another one that is more appropriate for details and texture experimental results show that our model performs appropriately we also see that our proposed filter is competitive with respect to state of the art methods it is close closer to the corresponding optimal switching filter respect to other analogous hybrid method

some results on the glejser and koenker tests for heteroskedasticity abstract the glejser and koenker studentized lagrange multiplier tests for heteroskedasticity are considered asymptotic theory and monte carlo experiments are used to investigate the effects of nonnormality under null and alternative hypotheses and also the consequences of using an incorrect alternative a method for using test outcomes to select models of heteroskedasticity is critically examined glejser s test is not in general asymptotically valid under asymmetric disturbances koenker s test is asymptotically valid under asymmetric and other nonnormal disturbances but has estimated finite sample significance levels that are sometimes sensitive to skewness an adjusted version of koenker s statistic is discussed

adaptive regularized constrained least squares image restoration in noisy environments a constrained least squares cls approach is presented to restore images blurred by a gaussian impulse response where instead of choosing a global regularization parameter each point in the signal has its own associated regularization parameter these parameters are found by constraining the weighted standard deviation of the wavelet transform coefficients on the finest scale of the inverse signal by a function r which is a local measure of the intensity variations around each point of the blurred and noisy observed signal border ringing in the inverse solution is proposed decreased by manipulating its wavelet transform coefficients on the finest scales close to the borders if the noise in the inverse solution is significant wavelet transform techniques are also applied to denoise the solution examples are given for images and the results are shown to outperform the optimum constrained least squares solution using a global regularization parameter both visually and in the mean squared error sense

an extension of a standard test for heteroskedasticity to a systems framework the glejser 1969 test for heteroskedasticity concerning the disturbance terms of a regression model is widely referenced see e g goldfeld and quandt 1972 johnston 1972 theil 1971 and maddala 1978 among others as originally proposed glejser suggested estimating the model s disturbance terms via least squares and then regressing their absolute values on certain known functions of the regressors the suggested test for heteroskedasticity then relates to the significance of the slope coefficients obvious modifications of this procedure such as using squared estimated disturbance terms have been suggested see goldfeld and quandt 1972 and kelejian and oates 1974 still others have suggested modifications of the procedure which involve iterations see maddala 1978 glejser noted that there may be shortcomings in the procedure which arise due to the use of the estimated disturbances in the second stage regression goldfeld and quandt 1972 among others also noted shortcomings in the procedure but recognized that conditions may exist under which these shortcomings are of no consequence in the relevant asymptotic distribution they went on to note however that at the time a demonstration of such conditions was not available in recent papers amemiya 1977 and white 1980 gave results which justify the large sample version of the glejser test based on squared estimated disturbances however their results assumed the absence of lagged dependent variables and were given in the single equation context the purpose of this paper is to extend the amemiya 1977 and white 1980 results to the case of a simultaneous equation framework which may or may not contain lagged endogenous variables we consider two cases the first is the one in which the researcher suspects that heteroskedasticity may exist in only one of the system s equations this extension is not trivial due to among other things feedbacks involving the endogenous regressors nevertheless it turns out that if the least squares procedure in the first stage is replaced by virtually any consistent procedure such as two stage least squares henceforth 2sls no additional complexities arise the importance of this result is that under typical modelling specifications a computationally simple large sample test for heteroskedasticity which is associated with one equation of a system can be carried out in the context of that system this test should be especially useful in those cases in which the exact specification of the suspected heteroskedasticity is not known1 the second case we consider is the one in which the researcher suspects that heteroskedasticity may be associated with more than one equation of the system as expected the resulting test is computationally more demanding the model is specified in section 2 and the basic results are given in section 3 suggestions for further work are given in section 4 technical details are relegated to the appendix

nonlinear regularized reaction diffusion filters for denoising of images with textures denoising is always a challenging problem in natural imaging and geophysical data processing in this paper we consider the denoising of texture images using a nonlinear reaction diffusion equation and directional wavelet frames in our model a curvelet shrinkage is used for regularization of the diffusion process to preserve important features in the diffusion smoothing and a wave atom shrinkage is used as the reaction in order to preserve and enhance interesting oriented textures we derive a digital reaction diffusion filter that lives on graphs and show convergence of the corresponding iteration process experimental results and comparisons show very good performance of the proposed model for texture preserving denoising

the approximate slopes of econometric tests in this paper the concept of approximate slope introduced by r r bahadur is used to make asymptotic global power comparisons of econometric tests the approximate slope of a test is the rate at which the logarithm of the asymptotic marginal significance level of the test decreases as sample size increases under a given alternative a test with greater approximate slope may therefore be expected to reject the null hypothesis more frequently under that alternative than one with smaller approximate slope two theorems which facilitate the computation and interpretation of the approximate slopes of most econometric tests are established these results are used to undertake some illustrative comparisons sampling experiments and an empirical illustration suggest that the comparison of approximate slopes may provide an adequate basis for evaluating the actual performance of alternative tests of the same hypothesis

a new perspective on functional integration the core of this article is a general theorem with a large number of specializations given a manifold n and a finite number of one parameter groups of point transformations on n with generators y x 1 x d we obtain via functional integration over spaces of pointed paths on n paths with one fixed point a one parameter group of functional operators acting on tensor or spinor fields on n the generator of this group is a quadratic form in the lie derivatives lx in the x direction plus a term linear in ly the basic functional integral is over l2 1 paths x t n continuous paths with square integrable first derivative although the integrator is invariant under time translation the integral is powerful enough to be used for systems which are not time translation invariant seven nontrivial applications of the basic formula are given and the semiclassical expansion is computed the methods of proof are rigorous and combine albeverio ho egh krohn oscillatory integrals with elworthy s parametr

the finite sample distributions of heteroskedasticity robust wald statistics the imhof procedure is used to calculate the exact finite sample distributions of alternative heteroskedasticity robust wald type tests of scalar linear hypothesis in the normal linear model the tests are distinguished by the variance estimator that they use these include the white eicker and jackknife estimators the calculations demonstrate the importance of regression design in determining the quality of conventional first order asymptotic approximations to the null distributions of the tests

combined curvelet shrinkage and nonlinear anisotropic diffusion in this paper a diffusion based curvelet shrinkage is proposed for discontinuity preserving denoising using a combination of a new tight frame of curvelets with a nonlinear diffusion scheme in order to suppress the pseudo gibbs and curvelet like artifacts the conventional shrinkage results are further processed by a projected total variation diffusion in which only the insignificant curvelet coefficients or high frequency part of the signal are changed by use of a constrained projection numerical experiments from piecewise smooth to textured images show good performances of the proposed method to recover the shape of edges and important detailed components in comparison to some existing methods

glejser s test revisited godfrey 1996 journal of econometrics 72 275 299 has shown that the glejser test for heteroskedasticity is valid only under conditional symmetry here modifications of the glejser test are suggested the proposed test statistics are asymptotically valid even when the disturbances are not symmetrically distributed and can be used to test for heteroskedasticity when conditional location functions other than the conditional mean are estimated

asymmetric least squares estimation and testing this paper considers estimation and hypothesis tests for coefficients of linear regression models where the coefficient estimates are based on location measures defined by an asymmetric least squares criterion function these asymmetric least squares estimators have properties which are analogous to regression quantile estimators but are much simpler to calculate as are the corresponding test statistics the coefficient estimators can be used to construct test statistics for homoskedasticity and conditional symmetry of the error distribution and we find these tests compare quite favorably with other commonly used tests of these null hypotheses in terms of local relative efficiency consequently asymmetric least squares estimation provides a convenient and relatively efficient method of summarizing the conditional distribution of a dependent variable given the regressors and a means of testing whether a linear model is an adequate characterization of the typical value for this conditional distribution

a well balanced flow equation for noise removal and edge detection an anisotropic nonlinear diffusion equation for image restoration is presented the model has two terms the diffusion term and the forcing term the balance between these terms is made in a selective way in which boundary points and interior points of the objects that make up the image are treated differently the optimal smoothing time concept which allows for finding the ideal stop time for the evolution of the partial differential equation is also proposed numerical results show the proposed model s high performance

a generalized levene s scale test for variance heterogeneity in the presence of sample correlation and group uncertainty we generalize levene s test for variance scale heterogeneity between k groups for more complex data when there are sample correlation and group membership uncertainty following a two stage regression framework we show that least absolute deviation regression must be used in the stage 1 analysis to ensure a correct asymptotic k 12 k 1 distribution of the generalized scale gs test statistic we then show that the proposed gs test is independent of the generalized location test under the joint null hypothesis of no mean and no variance heterogeneity consequently we generalize the recently proposed joint location scale gjls test valuable in settings where there is an interaction effect but one interacting variable is not available we evaluate the proposed method via an extensive simulation study and two genetic association application studies

a study of several new and existing tests for heteroscedasticity in the general linear model abstract several optimum non parametric tests for heteroscedasticity are proposed and studied along with the tests introduced in the literature in terms of power and robustness properties it is found that all tests are reasonably robust to the ordinary least squares ols residual estimates number and character of the regressors only a few are robust to both the distributional and independence assumptions about the errors the power of tests can be improved with the ols residual estimates the increased sample size and the variability of the regressors it can be substantially reduced if the observations are not normally distributed and may increase or decrease if the errors are dependent each test is optimum to detect a specific form of heteroscedasticity and a serious power loss may occur if the underlying heteroscedasticity assumption in the data generation deviates from it