specification tests based on artificial regressions abstract many specification tests can be computed with artificial linear regressions designed to be used as calculating devices to obtain test statistics and other quantities of interest this article discusses the general principles that underlie all artificial regressions and the use of such regressions to compute lagrange multiplier and other specification tests based on estimates under the null hypothesis the generality and power of artificial regressions as a means of computing test statistics is demonstrated how durbin wu hausman conditional moment and other tests that are not explicitly lagrange multiplier tests may be computed is shown and several special cases that illustrate the general results and can be useful in practice are discussed these include tests of parameter restrictions in nonlinear regression models and tests of binary choice models such as the logit and probit models

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

optimality conditions for multiobjective programming with generalized i ρ θ convex set functions abstract necessary conditions for pareto optimality in multiobjective programming with subdifferentiable set functions are established in theorem 12 of h c lai and l j lin j math anal appl 132 1988 558 571 in this paper we establish some sufficient conditions under which a feasible solution of such a problem will be pareto optimal provided that a weaker convexity requirement is satisfied for instance i convexity is assumed for both objective and constraint set functions some duality models are also discussed wolfe type and mond weir type duality theorems are proved

analysis of multiresolution image denoising schemes using generalized gaussian and complexity priors research on universal and minimax wavelet shrinkage and thresholding methods has demonstrated near ideal estimation performance in various asymptotic frameworks however image processing practice has shown that universal thresholding methods are outperformed by simple bayesian estimators assuming independent wavelet coefficients and heavy tailed priors such as generalized gaussian distributions ggds in this paper we investigate various connections between shrinkage methods and maximum a posteriori map estimation using such priors in particular we state a simple condition under which map estimates are sparse we also introduce a new family of complexity priors based upon rissanen s universal prior on integers one particular estimator in this class outperforms conventional estimators based on earlier applications of the minimum description length mdl principle we develop analytical expressions for the shrinkage rules implied by ggd and complexity priors this allows us to show the equivalence between universal hard thresholding map estimation using a very heavy tailed ggd and mdl estimation using one of the new complexity priors theoretical analysis supported by numerous practical experiments shows the robustness of some of these estimates against mis specifications of the prior a basic concern in image processing applications

optimization theory for n set functions abstract an optimization theory is developed for functions of n sets optimality conditions are established and a lagrangian duality is obtained

testing for arch in the presence of a possibly misspecified conditional mean abstract ever since the development of the autoregressive conditional heteroskedasticity arch model engle 1982 testing for the presence of arch has become a routine diagnostic one popular method of testing for arch is t times the r2 from a regression of the squared residuals on p of its lags this test has been shown to have a lagrange multiplier interpretation and is asymptotically distributed as a 2 p random variable underlying this test is the assumption of a correctly specified conditional mean in this paper we consider the properties of the arch test when there is a possibly misspecified conditional mean examples of misspecification include omitted variables structural change and parameter instability we show that in general misspecification will lead to overrejection of the null hypothesis of conditional homoskedasticity we demonstrate the use of recursive residuals to improve the fit of a first stage conditional mean regression we illustrate these results via monte carlo simulations and consider two empirical examples

saddle points and lagrangian type duality for discrete minmax fractional subset programming problems with generalized convex functions abstract in this paper we present four sets of saddle point type optimality conditions construct two lagrangian type dual problems and prove weak and strong duality theorems for a discrete minmax fractional subset programming problem we establish these optimality and duality results under appropriate b convexity hypotheses

on the optimality conditions of vector valued n set functions abstract in a finite atomless measure space x the optimization problem of vector valued n set functions defined on a convex subfamily s of n is investigated the necessary and sufficient conditions of pareto optimal solution or proper r p solution of optimization problem with differentiable vector valued n set functions are given

optimality and duality for a multi objective programming problem involving generalized d type i and related n set functions in this paper we introduce several generalized convexity for a real valued set function and establish optimality and duality results for a multi objective programming problem involving generalized d type i and related n set functions

empirical bayes selection of wavelet thresholds this paper explores a class of empirical bayes methods for level dependent threshold selection in wavelet shrinkage the prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy tailed density the mixing weight or sparsity parameter for each level of the transform is chosen by marginal maximum likelihood if estimation is carried out using the posterior median this is a random thresholding procedure the estimation can also be carried out using other thresholding rules with the same threshold details of the calculations needed for implementing the procedure are included in practice the estimates are quick to compute and there is software available simulations on the standard model functions show excellent performance and applications to data drawn from various fields of application are used to explore the practical performance of the approach by using a general result on the risk of the corresponding marginal maximum likelihood approach for a single sequence overall bounds on the risk of the method are found subject to membership of the unknown function in one of a wide range of besov classes covering also the case of f of bounded variation the rates obtained are optimal for any value of the parameter p in 0 simultaneously for a wide range of loss functions each dominating the lq norm of the th derivative with 0 and 0 q 2 attention is paid to the distinction between sampling the unknown function within white noise and sampling at discrete points and between placing constraints on the function itself and on the discrete wavelet transform of its sequence of values at the observation points results for all relevant combinations of these scenarios are obtained in some cases a key feature of the theory is a particular boundary corrected wavelet basis details of which are discussed overall the approach described seems so far unique in combining the properties of fast computation good theoretical properties and good performance in simulations and in practice a key feature appears to be that the estimate of sparsity adapts to three different zones of estimation first where the signal is not sparse enough for thresholding to be of benefit second where an appropriately chosen threshold results in substantially improved estimation and third where the signal is so sparse that the zero estimate gives the optimum accuracy rate

distribution free estimation of some nonlinear panel data models this paper studies distribution free estimation of some multiplicative unobserved components panel data models one class of estimators requires only specification of the conditional mean in particular the multinomial quasi conditional maximum likelihood estimator is shown to be consistent when only the conditional mean in the unobserved effects model is correctly specified additional orthogonality conditions can be used in a method of moments framework a second class of problems specifies the conditional mean conditional variances and conditional covariances using the notion of a conditional linear predictor it is shown that specification of conditional second moments implies further orthogonality conditions in the observable data that can be exploited for efficiency gains this has applications to both count and gamma type panel data regression models

on multiple objective programming problems with set functions abstract the convexity of a subset of a algebra and the convexity of a set function on a convex subset are defined related properties are also examined a farkas minkowski theorem for set functions is then proved these results are used to characterize properly efficient solutions for multiple objective programming problems with set functions by associated scalar problems

diagnostic testing and evaluation of maximum likelihood models abstract the paper develops a unified theory of likelihood specification testing based on m estimators of auxiliary parameters the theory is sufficiently general to encompass a wide class of specification tests including moment based tests pearson type goodness of fit tests the information matrix test and the cox test the paper also presents a framework based on frechet differentiation for determining the effects of misspecification on the almost sure limits of parameter estimates and specification test statistics

testing for conditional heteroskedasticity with misspecified alternative hypotheses for the multiple linear regression model this paper examines the asymptotic behaviour of some tests for conditional heteroskedasticity when an alternative hypothesis is misspecified in the standard likelihood based framework a lagrange multiplier statistic based on a correctly specified alternative is ranked above one based on an overspecified alternative it is shown that this ranking does not hold for statistics that are robust to the form of conditional heterokurticity it is also shown that the ranking obtained in the standard likelihood based framework does not depend on a joint density being specified in its entirety the same ranking can be obtained when a type of information matrix equality holds

duality for generalized fractional programs involving n set functions abstract making use of a strong duality theorem for nonlinear programs involving n set functions we first establish a gordan type transposition theorem which is then utilized to construct a dual problem for a class of generalized fractional programming problems with n set functions as special cases of the main result we also obtain dual problems for discrete minmax and fractional programming problems

universal analytical forms for modeling image probabilities seeking probability models for images we employ a spectral approach where the images are decomposed using bandpass filters and probability models are imposed on the filter outputs also called spectral components we employ a two parameter family of probability densities called bessel k forms for modeling the marginal densities of the spectral components and demonstrate their fit to the observed histograms for video infrared and range images motivated by object based models for image analysis a relationship between the bessel parameters and the imaged objects is established using l sup 2 metric on the set of bessel k forms we propose a pseudometric on the image space for quantifying image similarities differences some applications including clutter classification and pruning of hypotheses for target recognition are presented

novel bayesian multiscale method for speckle removal in medical ultrasound images a novel speckle suppression method for medical ultrasound images is presented first the logarithmic transform of the original image is analyzed into the multiscale wavelet domain the authors show that the subband decompositions of ultrasound images have significantly non gaussian statistics that are best described by families of heavy tailed distributions such as the alpha stable then the authors design a bayesian estimator that exploits these statistics they use the alpha stable model to develop a blind noise removal processor that performs a nonlinear operation on the data finally the authors compare their technique with current state of the art soft and hard thresholding methods applied on actual ultrasound medical images and they quantify the achieved performance improvement

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

new sequential lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs in this paper a new sequential lagrange multiplier condition characterizing optimality without a constraint qualification for an abstract nonsmooth convex program is presented in terms of the subdifferentials and the epsilon subdifferentials a sequential condition involving only the subdifferentials but at nearby points to the minimizer for constraints is also derived for a smooth convex program the sequential condition yields a limiting kuhn tucker condition at nearby points without a constraint qualification it is shown how the sequential conditions are related to the standard lagrange multiplier condition applications to semidefinite programs semi infinite programs and semiconvex programs are given several numerical examples are discussed to illustrate the significance of the sequential conditions

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

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

on optimality and duality for multiobjective programming problems involving generalized d type i and related n set functions in this paper we establish some optimality and duality results under generalized convexity assumptions for a multiobjective programming problem involving generalized d type i and related n set functions

duality for a minimax programming problem containingn set functions abstract parameter necessary and sufficient optimality conditions for the discrete minimax programming problem with differentiable n set functions are established in zalmai optimization 20 1989 377 395 in this paper we establish nonparameter necessary and sufficient optimality conditions the nonparameter necessary optimality conditions suggest the establishment of two parameter free duality models for the discrete minimax programming problem with differentiable n set functions and the weak strong and strict converse duality theorems have been derived

econometric models for count data with an application to the patents r d relationship this paper focuses on developing and adapting statistical models of counts nonnegative integers in the context of panel data and using them to analyze the relationship between patents and r d expenditures since a variety of other economic data come in the form of repeated counts of some individual actions or events the methodology should have wide applications the statistical models we develop are applications and generalizations of the poisson distribution two important issues are i given the panel nature of our data how can we allow for separate persistent individual fixed or random effects ii how does one introduce the equivalent of disturbances in the equation into the analysis of poisson and other discrete probability functions the first problem is solved by conditioning on the total sum of outcomes over the observed years while the second problem is solved by introducing an additional source of randomness allowing the poisson parameter to be itself randomly distributed and compounding the two distributions lastly we develop a test statistic for the presence of serial correlation when fixed effects estimators are used in nonlinear conditional models

role of ρ η a invexity to ϵ optimality conditions for multiple objective fractional programming abstract based on a general framework for a class of a invex n set functions some results on the optimality conditions for multiple objective fractional programming problems are established the obtained results are not only general in nature but also unify results on generalized invexity to the context of multiple fractional programming

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

optimality and duality for multiobjective fractional programming involvingn set functions abstract we consider a multiobjective fractional programming problem mfp involving vector valued objective n set functions in which their numerators are different from each other but their denominators are the same by using the concept of proper efficiency we establish optimality conditions and duality relations for our problem mfp under convexity assumptions on objective and constrained functions

pseudo maximum likelihood methods applications to poisson models pseudo maximum likelihood techniques are applied to basic poisson models and to poisson models with specification errors in the latter case it is shown that consistent and asymptotically normal estimators can be obtained without specifying the p d f of the disturbances these estimators are compared both from the finite sample and the asymptotic point of view quasi generalized pml estimators which asymptotically dominate all pml estimators are also proposed finally bivariate and panel data poisson models are discussed the analysis of economic behavior often leads to the study of characteristics taking a small number of positive values the classical linear model is not adapted to explain how such discrete variables depend on other quantitative or qualitative variables the reasons are similar to those usually given in the case of an endogenous qualitative variable the shape of the observation set does not correspond to a linear model the assumption of normality of the disturbances cannot be made since the endogenous variables take a small number of values with strictly positive probabilities and the prediction formulae which are deduced from a linear model give impossible values in the models considered in the literature to describe discrete variables cox and lewis 2 el sayyad 3 frome kutner and beauchamp 4 gilbert 5 hausman hall and griliches 8 see also lancaster 12 the endogenous variable is assumed to have a poisson distribution conditional upon the exogenous variables the parameter of this distribution is a function of the values of the exogenous variables the choice of such a model is justified if the dependent variable counts the occurrence of a given event during a fixed period and if the usual assumptions of the poisson process are satisfied for instance the model is adapted to describe daily numbers of oil tankers arrivals in a port the number of accidents at work by factory or the number of patents applied for and received by firms hausman hall and griliches 8

epigraphs of convex set functions in this paper we characterize a convex set function by its epigraph the w semicontinuities for set functions are defined we identify a convex set function with a functional in l and show that the w closure of such a functional is a convex functional a fenchel duality theorem for set functions is then derived

matrix exponential garch i propose a new multivariate garch specification that maintains positive definiteness of the conditional covariance matrix the idea is to specify the dynamics in the matrix logarithm of the conditional covariance because the matrix exponential transformation ensures positive definiteness the dynamics can be specified without the positive definiteness constraint this affords a variety of specifications and in particular we can specify element by element the dynamics of the matrix logarithm i discuss specifications with leverage effects estimation with multivariate gaussian and t distributions and diagnostics that evaluate the appropriateness of the matrix exponential specification

bivariate shrinkage functions for wavelet based denoising exploiting interscale dependency most simple nonlinear thresholding rules for wavelet based denoising assume that the wavelet coefficients are independent however wavelet coefficients of natural images have significant dependencies we only consider the dependencies between the coefficients and their parents in detail for this purpose new non gaussian bivariate distributions are proposed and corresponding nonlinear threshold functions shrinkage functions are derived from the models using bayesian estimation theory the new shrinkage functions do not assume the independence of wavelet coefficients we show three image denoising examples in order to show the performance of these new bivariate shrinkage rules in the second example a simple subband dependent data driven image denoising system is described and compared with effective data driven techniques in the literature namely visushrink sureshrink bayesshrink and hidden markov models in the third example the same idea is applied to the dual tree complex wavelet coefficients

likelihood based estimation in a panel setting robustness redundancy and validity of copulas abstract this paper considers the estimation of likelihood based models in a panel setting that is we have panel data and for each time period separately we have a correctly specified model that could be estimated by mle we want to allow non independence over time this paper shows how to improve on the qmle it then considers mle based on joint distributions constructed using copulas it discusses the efficiency gain from using the true copula and shows that knowledge of the true copula is redundant only if the variance matrix of the relevant set of moment conditions is singular it also discusses the question of robustness against misspecification of the copula and proposes a test of the validity of the copula gmm methods are argued to be useful analytically and also for reasons of efficiency if the copula is robust but not correct

sufficiency criteria and duality for nonlinear programs involving n set functions abstract several sufficiency criteria and duality results are established under generalized convexity conditions for a class of nonlinear programming problems involving differentiable n set functions

nonlinear wavelet shrinkage with bayes rules and bayes factors abstract wavelet shrinkage the method proposed by the seminal work of donoho and johnstone is a disarmingly simple and efficient way of denoising data shrinking wavelet coefficients was proposed from several optimality criteria in this article a wavelet shrinkage by coherent bayesian inference in the wavelet domain is proposed the methods are tested on standard donoho johnstone test functions

bayesian wavelet based image denoising using the gauss hermite expansion the probability density functions pdfs of the wavelet coefficients play a key role in many wavelet based image processing algorithms such as denoising the conventional pdfs usually have a limited number of parameters that are calculated from the first few moments only consequently such pdfs cannot be made to fit very well with the empirical pdf of the wavelet coefficients of an image as a result the shrinkage function utilizing any of these density functions provides a substandard denoising performance in order for the probabilistic model of the image wavelet coefficients to be able to incorporate an appropriate number of parameters that are dependent on the higher order moments a pdf using a series expansion in terms of the hermite polynomials that are orthogonal with respect to the standard gaussian weight function is introduced a modification in the series function is introduced so that only a finite number of terms can be used to model the image wavelet coefficients ensuring at the same time the resulting pdf to be non negative it is shown that the proposed pdf matches the empirical one better than some of the standard ones such as the generalized gaussian or bessel k form pdf a bayesian image denoising technique is then proposed wherein the new pdf is exploited to statistically model the subband as well as the local neighboring image wavelet coefficients experimental results on several test images demonstrate that the proposed denoising method both in the subband adaptive and locally adaptive conditions provides a performance better than that of most of the methods that use pdfs with limited number of parameters

moreau rockafellar type theorem for convex set functions abstract let x be an atomless finite measure space and s a convex subfamily it is proved that the moreau rockafellar theorem f 1 f n f 1 f n holds for proper convex set functions f 1 f n and s if all set functions f i except possibly one are w lower semicontinuous on s as applications the kuhn tucker type condition for an optimal solution of convex programming problem with set functions and the fritz john type condition for an optimal solution of vector valued minimization problem for set functions are obtained

spatially adaptive wavelet thresholding with context modeling for image denoising the method of wavelet thresholding for removing noise or denoising has been researched extensively due to its effectiveness and simplicity much of the literature has focused on developing the best uniform threshold or best basis selection however not much has been done to make the threshold values adaptive to the spatially changing statistics of images such adaptivity can improve the wavelet thresholding performance because it allows additional local information of the image such as the identification of smooth or edge regions to be incorporated into the algorithm this work proposes a spatially adaptive wavelet thresholding method based on context modeling a common technique used in image compression to adapt the coder to changing image characteristics each wavelet coefficient is modeled as a random variable of a generalized gaussian distribution with an unknown parameter context modeling is used to estimate the parameter for each coefficient which is then used to adapt the thresholding strategy this spatially adaptive thresholding is extended to the overcomplete wavelet expansion which yields better results than the orthogonal transform experimental results show that spatially adaptive wavelet thresholding yields significantly superior image quality and lower mse than the best uniform thresholding with the original image assumed known

duality for minmaxb vex programming involvingn set functions abstract a minmax programming problem involving several b vex n set functions is considered necessary and sufficient optimality theorems and wolfe type duality results are established duality for the n set generalized minmax fractional programming problem is derived as a special case of the main problem

duality in mathematical programming of set functions on fenchel duality theorem abstract the optimization problem of a set function defined on a family a of measurable subsets in an atomless finite measure space x a m is investigated the generalized fenchel theorem is formulated and proved in this note

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

weak efficiency conditions for multiobjective fractional programming a general framework for a class of r h q invex functions is developed and then applied to establish some parametric sufficient efficiency conditions for multiobjective fractional programming toward achieving weakly e efficient solutions to multiobjective fractional programming problems the obtained results are general in nature to the sense of a wider generality and applications to other results on multiobjective fractional programming

efficiency conditions and duality models for multiobjective fractional subset programming problems with generalized ϝ α ϱ θ v convex functions abstract in this paper we first introduce a new class of generalized convex n set functions called v convex functions and then present numerous sets of parametric and semiparametric sufficient efficiency conditions under generalized v convexity assumptions for a multiobjective fractional subset programming problem moreover we construct three parametric and three semiparametric duality models and prove appropriate duality theorems

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

minimax estimation via wavelet shrinkage we attempt to recover an unknown function from noisy sampled data using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients the shrinkage can be tuned to be nearly minimax over any member of a wide range of triebel and besov type smoothness constraints and asymptotically minimax over besov bodies with p q linear estimates cannot achieve even the minimax rates over triebel and besov classes with p 2 so the method can significantly outperform every linear method e g kernel smoothing spline sieve in a minimax sense variants of our method based on simple threshold nonlinear estimators are nearly minimax our method possesses the interpretation of spatial adaptivity it reconstructs using a kernel which may vary in shape and bandwidth from point to point depending on the data least favorable distributions for certain of the triebel and besov scales generate objects with sparse wavelet transforms many real objects have similarly sparse transforms which suggests that these minimax results are relevant for practical problems sequels to this paper which was first drafted in november 1990 discuss practical implementation spatial adaptation properties universal near minimaxity and applications to inverse problems

inverse probability weighted estimation for general missing data problems abstract i study inverse probability weighted m estimation under a general missing data scheme examples include m estimation with missing data due to a censored survival time propensity score estimation of the average treatment effect in the linear exponential family and variable probability sampling with observed retention frequencies i extend an important result known to hold in special cases estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation for the treatment effect case the setup allows a general characterization of a double robustness result due to scharfstein et al 1999 rejoinder journal of the american statistical association 94 1135 1146

on minimax fractional programming of generalized convex set functions abstract we derive necessary and sufficient optimality conditions for the discrete minimax programming problem with subdifferentiable i convex set functions then we apply these optimality criteria to construct two models of parameter free dual problems and a third model of another dual problem we also establish weak strong and strictly converse duality theorems

duality theorems of vector valued n set functions abstract the wolfe and mond weir types of dual problems for convex vector valued n set functions are formulated and we prove the weak duality duality and converse duality theorems for these types of problems

parameter free sufficient optimality conditions and duality models for minmax fractional subset programming problems with generalized f ϱ θ convex functions abstract in this paper we present numerous sets of nonparametric sufficient optimality conditions and duality results under various generalized f convexity assumptions for a minmax fractional subset programming problem

lagrange duality in multiobjective fractional programming problems with n set functions in this paper lagrange multiplier theorems are developed for the multiobjective fractional programming problem involving n set functions a lagrange dual is introduced and duality results in terms of efficient solutions are established

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

adaptive wavelet thresholding for image denoising and compression the first part of this paper proposes an adaptive data driven threshold for image denoising via wavelet soft thresholding the threshold is derived in a bayesian framework and the prior used on the wavelet coefficients is the generalized gaussian distribution ggd widely used in image processing applications the proposed threshold is simple and closed form and it is adaptive to each subband because it depends on data driven estimates of the parameters experimental results show that the proposed method called bayesshrink is typically within 5 of the mse of the best soft thresholding benchmark with the image assumed known it also outperforms sureshrink donoho and johnstone 1994 1995 donoho 1995 most of the time the second part of the paper attempts to further validate claims that lossy compression can be used for denoising the bayesshrink threshold can aid in the parameter selection of a coder designed with the intention of denoising and thus achieving simultaneous denoising and compression specifically the zero zone in the quantization step of compression is analogous to the threshold value in the thresholding function the remaining coder design parameters are chosen based on a criterion derived from rissanen s minimum description length mdl principle experiments show that this compression method does indeed remove noise significantly especially for large noise power however it introduces quantization noise and should be used only if bitrate were an additional concern to denoising

wavelet shrinkage asymptopia much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects curves densities spectral densities images from noisy data a now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems unfortunately the results have rarely moved into practice for a variety of reasons among them being similarity to known methods computational intractability and lack of spatial adaptivity we discuss a method for curve estimation based on n noisy data translate the empirical wavelet coefficients towards the origin by an amount 2 log n n the proposal differs from those in current use is computationally practical and is spatially adaptive it thus avoids several of the previous objections further the method is nearly minimax both for a wide variety of loss functions pointwise error global error measured in l p norms pointwise and global error in estimation of derivatives and for a wide range of smoothness classes including standard holder and sobolev classes and bounded variation this is a much broader near optimality than anything previously proposed we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves finally the theory underlying the method is interesting as it exploits a correspondence between statistical questions and questions of optimal recovery and information based complexity

wavelet based statistical signal processing using hidden markov models wavelet based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly gaussian these models are unrealistic for many real world signals we develop a new framework for statistical signal processing based on wavelet domain hidden markov models hmms that concisely models the statistical dependencies and non gaussian statistics encountered in real world signals wavelet domain hmms are designed with the intrinsic properties of the wavelet transform in mind and provide powerful yet tractable probabilistic signal models efficient expectation maximization algorithms are developed for fitting the hmms to observational signal data the new framework is suitable for a wide range of applications including signal estimation detection classification prediction and even synthesis to demonstrate the utility of wavelet domain hmms we develop novel algorithms for signal denoising classification and detection

duality for multiobjectiveb vex programming involvingn set functions abstract in the present paper we consider a class of multiobjectiveb vex programming problems involving differentiableb vexn set functions and establish duality results in terms of properly efficient solutions further we relate the problem to a certain saddle point of a lagrangian and show multiobjective fractional program as a special case of the main problem

on the optimality of differentiable nonconvex n set functions abstract our main contribution is the extension of the concepts of quasiconvexity and pseudoconvexity to n set functions some properties of differentiable nonconvex n set functions are established necessary and sufficient conditions for the existence of an optimal solution of the nonconvex program with n set functions are characterized by derivatives of the n set functions involved a duality theorem for the nonconvex program with n set functions is also developed in this paper

optimality of differentiable vector valued n set functions abstract the necessary and sufficient conditions for the existence of an optimal solution of a vector valued n set functions optimization problem is obtained in this paper

wavelet denoising based on the map estimation using the bkf prior with application to images and eeg signals this paper presents a novel nonparametric bayesian estimator for signal and image denoising in the wavelet domain this approach uses a prior model of the wavelet coefficients designed to capture the sparseness of the wavelet expansion a new family of bessel k form bkf densities are designed to fit the observed histograms so as to provide a probabilistic model for the marginal densities of the wavelet coefficients this paper first shows how the bkf prior can characterize images belonging to besov spaces then a new hyper parameters estimator based on em algorithm is designed to estimate the parameters of the bkf density and it is compared with a cumulants based estimator exploiting this prior model another novel contribution is to design a bayesian denoiser based on the maximum a posteriori map estimation under the 0 1 loss function for which we formally establish the mathematical properties and derive a closed form expression finally a comparative study on a digitized database of natural images and biomedical signals shows the effectiveness of this new bayesian denoiser compared to other classical and bayesian denoising approaches results on biomedical data illustrate the method in the temporal as well as the time frequency domain

wavelet thresholding via a bayesian approach we discuss a bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression a prior distribution is imposed on the wavelet coefficients of the unknown response function designed to capture the sparseness of wavelet expansion that is common to most applications for the prior specified the posterior median yields a thresholding procedure our prior model for the underlying function can be adjusted to give functions falling in any specific besov space we establish a relationship between the hyperparameters of the prior model and the parameters of those besov spaces within which realizations from the prior will fall such a relationship gives insight into the meaning of the besov space parameters moreover the relationship established makes it possible in principle to incorporate prior knowledge about the function s regularity properties into the prior model for its wavelet coefficients however prior knowledge about a function s regularity properties might be difficult to elicit with this in mind we propose a standard choice of prior hyperparameters that works well in our examples several simulated examples are used to illustrate our method and comparisons are made with other thresholding methods we also present an application to a data set that was collected in an anaesthesiological study

analytical form for a bayesian wavelet estimator of images using the bessel k form densities a novel bayesian nonparametric estimator in the wavelet domain is presented in this approach a prior model is imposed on the wavelet coefficients designed to capture the sparseness of the wavelet expansion seeking probability models for the marginal densities of the wavelet coefficients the new family of bessel k forms bkf densities are shown to fit very well to the observed histograms exploiting this prior we designed a bayesian nonlinear denoiser and we derived a closed form for its expression we then compared it to other priors that have been introduced in the literature such as the generalized gaussian density ggd or the spl alpha stable models where no analytical form is available for the corresponding bayesian denoisers specifically the bkf model turns out to be a good compromise between these two extreme cases hyperbolic tails for the spl alpha stable and exponential tails for the ggd moreover we demonstrate a high degree of match between observed and estimated prior densities using the bkf model finally a comparative study is carried out to show the effectiveness of our denoiser which clearly outperforms the classical shrinkage or thresholding wavelet based techniques

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed