a linear programming approach for the weighted graph matching problem a linear programming lp approach is proposed for the weighted graph matching problem a linear program is obtained by formulating the graph matching problem in l sub 1 norm and then transforming the resulting quadratic optimization problem to a linear one the linear program is solved using a simplex based algorithm then approximate 0 1 integer solutions are obtained by applying the hungarian method on the real solutions of the linear program the complexity of the proposed algorithm is polynomial time and it is o n sup 6 l for matching graphs of size n the developed algorithm is compared to two other algorithms one is based on an eigendecomposition approach and the other on a symmetric polynomial transform experimental results showed that the lp approach is superior in matching graphs than both other methods

the application of generalized diagonal dominance to linear system stability theory abstract this paper shows that the well known diagonal dominance condition associated with rosenbrock s stability theorems is unnecessary and can be replaced by a less restrictive generalized diagonal dominance condition similar results are derived for generalized block diagonally dominant systems whenever possible graphical interpretations are given to facilitate the implementation of these ideas in computer aided design packages

nonparametric inference for periodic sequences this article proposes a nonparametric method for estimating the period and values of a periodic sequence when the data are evenly spaced in time the period is estimated by a leave out one cycle version of cross validation cv and complements the periodogram a widely used tool for period estimation the cv method is computationally simple and implicitly penalizes multiples of the smallest period leading to a virtually consistent estimator of integer periods this estimator is investigated both theoretically and by simulation we also propose a nonparametric test of the null hypothesis that the data have constant mean against the alternative that the sequence of means is periodic finally our methodology is demonstrated on three well known time series the sunspots and lynx trapping data and the el nino series of sea surface temperatures

a condition for robust stabilizability a family of linear time invariant finite dimensional plants is called robustly stabilizable if there exists a single controller that stabilizes each plant in the family a condition for robust stabilizability is given that requires the plant transmission zeros to remain in the left half complex plane and moreover imposes a restriction on the high frequency behavior of the plant transfer matrix

alternative goodness of fit tests for linear models fan and huang 2001 presented a goodness of fit test for linear models based on fourier transformations of the residuals of the fitted model we present two more theoretically appealing tests in which the fourier transforms are incorporated into a fitted model we show that when suitably normalized the new test statistics have the same asymptotic distribution as fan and huang s test we propose modifications to the asymptotic normalization constants to improve the small sample sizes of our tests while retaining their asymptotic distributions small sample sizes and powers are examined via simulations an illustration is given

a shape analysis model with applications to a character recognition system a method for the recognition of multifont printed characters is proposed giving emphasis to the identification of structural descriptions of character shapes using prototypes noise and shape variations are modeled as series of transformations from groups of features in the data to features in each prototype thus the method manages systematically the relative distortion between a candidate shape and its prototype accomplishing robustness to noise with less than two prototypes per class on average the method uses a flexible matching between components and a flexible grouping of the individual components to be matched a number of shape transformations are defined including filling of gaps so that the method handles broken characters also a measure of the amount of distortion that these transformations cause is given classification of character shapes is defined as a minimization problem among the possible transformations that map an input shape into prototypical shapes some tests with hand printed numerals confirmed the method s high robustness level

sieve empirical likelihood ratio tests for nonparametric functions generalized likelihood ratio statistics have been proposed in fan zhang and zhang ann statist 29 2001 153 193 as a generally applicable method for testing norparametic hypotheses about nonparametric functions the likelihood ratio statistics are constructed based on the assumption that the distributions of stochastic errors are in a certain parametric family we extend their work to the case where the error distribution is completely unspecified via newly proposed sieve empirical likelihood ratio selr tests the approach is also applied to test conditional estimating equations on the distributions of stochastic errors it is shown that the proposed selr statistics follow asymptotically resealed chi 2 distributions with the scale constants and the degrees of freedom being independent of the nuisance parameters this demonstrates that the wilks phenomenon observed in fan zhang and zhang ann statist 29 2001 153 193 continues to hold under more relaxed models and a larger class of techniques the asymptotic power of the proposed test is also derived which achieves the optimal rate for nonparametric hypothesis testing the proposed approach has two advantages over the generalized likelihood ratio method it requires one only to specify some conditional estimating equations rather than the entire distribution of the stochastic error and the procedure adapts automatically to the unknown error distribution including heteroscedasticity a simulation study is conducted to evaluate our proposed procedure empirically

graph matching relax at your own risk graph matching aligning a pair of graphs to minimize their edge disagreements has received wide spread attention from both theoretical and applied communities over the past several decades including combinatorics computer vision and connectomics its attention can be partially attributed to its computational difficulty although many heuristics have previously been proposed in the literature to approximately solve graph matching very few have any theoretical support for their performance a common technique is to relax the discrete problem to a continuous problem therefore enabling practitioners to bring gradient descent type algorithms to bear we prove that an indefinite relaxation when solved exactly almost always discovers the optimal permutation while a common convex relaxation almost always fails to discover the optimal permutation these theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance indeed experimental results illuminate and corroborate these theoretical findings demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches

smoothing parameter selection for power optimality in testing of regression curves abstract we consider selection of smoothing parameters to obtain optimal power in tests of regression curves we examine three tests and propose empirical smoothing parameters to maximize the power in each test we also show that the data based smoothing parameters converge to the optimal smoothing parameters as sample sizes get larger we conduct a simulation study for various classes of alternative showing the effectiveness of the proposed procedures

heteroscedastic one way anova and lack of fit tests recent articles have considered the asymptotic behavior of the one way analysis of variance anova f statistic when the number of levels or groups is large in these articles the results were obtained under the assumption of homoscedasticity and for the case when the sample or group sizes ni remain fixed as the number of groups a tends to infinity in this article we study both weighted and unweighted test statistics in the heteroscedastic case the unweighted statistic is new and can be used even with small group sizes we demonstrate that an asymptotic approximation to the distribution of the weighted statistic is possible only if the group sizes tend to infinity suitably fast in relation to a our investigation of local alternatives reveals a similarity between lack of fit tests for constant regression in the present case of replicated observations and the case of no replications which uses smoothing techniques the asymptotic theory uses a novel application of the projection principle to obtain

testing lack of fit in multiple regression summary we study lack of fit tests based on orthogonal series estimators a common feature of these tests is that they are functions of score statistics that employ data driven model dimensions the criteria used to select the dimension are score based versions of aic and bic the tests can be applied in a wide variety of settings including both continuous and discrete data with two or more covariates a model sequence i e a path in the alternative models space has to be chosen critical points and p values of the lack of fit tests can be obtained via asymptotic distribution theory or by use of the bootstrap data examples and a simulation study illustrate the applicability of the tests

almost decoupling of uncertain multivariable systems an effective almost decoupling theory using an internal model reference loop is developed for linear uncertain multivariable systems based on non negative matrix theory a useful design guide is derived to achieve the generalized diagonal dominance condition for the internal model reference loop using a perron root a sufficient condition is given to guarantee the inverse transfer matrix to be generalized diagonally dominant for all plants in a given family one of the main features of the proposed scheme is the reduction of uncertainty in the resultant compensated internal loop system which makes the subsequent design process of the individual channels using standard siso techniques much simpler

data driven smooth tests when the hypothesis is composite in recent years several authors have recommended smooth tests for testing goodness of fit however the number of components in the smooth test statistic should be chosen well otherwise considerable loss of power may occur schwarz s selection rule provides one such good choice earlier results on simple null hypotheses are extended here to composite hypotheses which tend to be of more practical interest for general composite hypotheses consistency of the data driven smooth tests holds at essentially any alternative monte carlo experiments on testing exponentiality and normality show that the data driven version of neyman s test compares well to other even specialized tests over a wide range of alternatives

multiscale testing of qualitative hypotheses suppose that one observes a process y on the unit interval where dy t n1 2f t dt dw t with an unknown function parameter f given scale parameter n 1 sample size and standard brownian motion w we propose two classes of tests of qualitative nonparametric hypotheses about f such as monotonicity or concavity these tests are asymptotically optimal and adaptive in a certain sense they are constructed via a new class of multiscale statistics and an extension of levy s modulus of continuity of brownian motion

residual variance and residual pattern in nonlinear regression summary a nonparametric estimator of residual variance in nonlinear regression is proposed it is based on local linear fitting asymptotically the estimator has a small bias but a larger variance compared with the parametric estimator in linear regression finite sample properties are investigated in a simulation study including a comparison with other nonparametric estimators the method is also useful for spotting heteroscedasticity and outliers in the residuals at an early stage of the data analysis a further application is checking the fit of parametric models this is illustrated for longitudinal growth data

model selection using wavelet decomposition and applications in this paper we discuss how to use wavelet decompositions to select a regression model the methodology relies on a minimum description length criterion which is used to determine the number of nonzero coefficients in the vector of wavelet coefficients consistency properties of the selection rule are established and simulation studies reveal information on the distribution of the minimum description length selector we then apply the selection rule to specific problems including testing for pure white noise the power of this test is investigated via simulation studies and the selection criterion is also applied to testing for no effect in nonparametric regression

spectral generalized multi dimensional scaling multidimensional scaling mds is a family of methods that embed a given set of points into a simple usually flat domain the points are assumed to be sampled from some metric space and the mapping attempts to preserve the distances between each pair of points in the set distances in the target space can be computed analytically in this setting generalized mds is an extension that allows mapping one metric space into another that is mds into target spaces in which distances are evaluated numerically rather than analytically here we propose an efficient approach for computing such mappings between surfaces based on their natural spectral decomposition where the surfaces are treated as sampled metric spaces the resulting spectral gmds procedure enables efficient embedding by incorporating smoothness of the metric structure into the problem thereby substantially reducing the complexity involved in its solution while practically overcoming its non convex nature the method is compared to existing techniques that compute dense correspondence between shapes numerical experiments of the proposed method demonstrate its efficiency and accuracy compared to state of the art approaches especially when isometry invariance is a dominant property

testing the fit of a parametric function abstract general methods for testing the fit of a parametric function are proposed the idea underlying each method is to accept the prescribed parametric model if and only if it is chosen by a model selection criterion several different selection criteria are considered including one based on a modified version of the akaike information criterion and others based on various score statistics the tests have a connection with nonparametric smoothing because they use orthogonal series estimators to detect departures from a parametric model an important aspect of the tests is that they can be applied in a wide variety of settings including generalized linear models spectral analysis the goodness of fit problem and longitudinal data analysis implementation using standard statistical software is straightforward asymptotic distribution theory for several test statistics is described and the tests are shown to be consistent against essentially any alternative hypothesis simulations and a data exampl

algebraic and topological aspects of quantitative feedback theory the current interest in robust control has called into question the applicability of the quantitative feedback theory qft robust design method introduced by horowitz a number of issues have been raised regarding inherent restrictions of both the design method and the uncertain plant set using a multivariable root locus technique extended to uncertain systems this paper shows that the qft assumptions are indeed not restrictive and are in fact equivalent to other well known conditions for robust stabilizability because qft is one of the very few methods to specifically address the quantitative robust performance issue these results should lead to better methods of developing new qft design software as well as improved robust control methods to satisfy a priori quantitative performance bounds

testing for no effect when estimating a smooth function by nonparametric regression a randomization approach abstract when a linear regression function is estimated by ordinary least squares the null hypothesis of no relationship between the response and the design variable can be tested by the normal theory f test this article describes a new test for use in the case in which a smooth regression function is estimated by a nonparametric procedure such as kernel estimation or local regression the test is constructed as an approximation to an exact permutation test the test statistic is the ratio of sums of squares that are defined by analogy to the analysis of variance the null permutation distribution of the test statistic is approximated by matching its exact mean and variance to the moments of a gamma distribution a simulation study shows that the approximation is excellent for several regression procedures and for normal heavy tailed and skewed error distributions simulation results are also used to investigate the power of the test as a function of the smoothing parameter the test is applied to dat

bandwidth choice for nonparametric regression this paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression we analyze a tapered fourier series estimate and discuss the relationship of this estimate to a kernel estimate we first consider a method based on an unbiased estimate of mean square error and show that the bandwidth thus chosen is asymptotically optimal other methods are examined as well and are shown to be asymptotically equivalent a small simulation shows however that for small or moderate sample size the methods perform quite differently

goodness of fit tests for parametric regression models several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives these tests formally check if the bias vector of residuals from parametric fits is negligible by using the adaptive neyman test and other methods the testing procedures formalize the traditional model diagnostic tools based on residual plots we examine the rates of contiguous alternatives that can be detected consistently by the adaptive neyman test applications of the procedures to the partially linear models are thoroughly discussed our simulation studies show that the new testing procedures are indeed powerful and omnibus the power of the proposed tests is comparable to the f test statistic even in the situations where the f test is known to be suitable and can be far more powerful than the f test statistic in other situations an application to testing linear models versus additive models is also discussed

a simple consistent bootstrap test for a parametric regression function abstract a simple consistent test is considered and a bootstrap method is proposed for testing a parametric regression functional form it is shown that the bootstrap method gives a more accurate approximation to the null distribution of the test than the asymptotic normal theory result we also propose a consistent test for testing a parametric partially linear model versus a semiparametric partially linear alternative monte carlo simulations suggest that the bootstrap test performs well based on wild bootstrap critical values

adaptive decoupling of multivariable systems for many industrial processes it is of interest to design a decoupling precompensator the precompensator makes it possible to design controllers based on single input single output models of the process a model of the process must be known to design the precompensator this paper shows how the precompensator can be designed adaptively using input output measurements the precompensator is first designed for the case when the process is known the adaptive precompensator is then constructed using the certainty equivalence principle the convergence properties and the implementation of the adaptive decoupler are discussed it is shown that the adaptive scheme will converge provided the system is persistently excited and that a suitable model structure is used in the estimation

testing the goodness of fit of a linear model via nonparametric regression techniques abstract this article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model the large sample properties of parametric goodness of fit tests for linearity are considered the inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression large sample theory is derived for two variants of this type of statistic the results demonstrate that such tests are consistent against all fixed smooth alternatives to linearity but are incapable of detecting local alternatives converging to a linear model at the parametric rate n 1 2 simulation experiments involving a test based on fitting cubic smoothing splines to residuals reveals that this test has good power properties against several reasonable alternatives

test of significance based on wavelet thresholding and neyman s truncation abstract traditional nonparametric tests such as the kolmogorov smirnov test and the cramer von mises test are based on the empirical distribution functions although these tests possess root n consistency they effectively use only information contained in the low frequencies this leads to low power in detecting fine features such as sharp and short aberrants as well as global features such as high frequency alternations the drawback can be repaired via smoothing based test statistics in this article we propose two such kind of test statistics based on the wavelet thresholding and the neyman truncation we provide extensive evidence to demonstrate that the proposed tests have higher power in detecting sharp peaks and high frequency alternations while maintaining the same capability in detecting smooth alternative densities as the traditional tests similar conclusions can be made for two sample nonparametric tests of distribution functions in that case the traditional linear rank tests such as th

commonality of cusum von neumann and smoothing based goodness of fit tests summary recent papers by munson jernigan 1989 and buckley 1991 propose nonparametric tests for the hypothesis of no predictor effect in regression the munson jernigan test is similar to the von neumann 1941 test while that of buckley is based on a functional of cusums these tests are shown to be special cases of a wider class of tests based on nonparametric function estimation ideas fourier analysis is used to qualitatively compare the munson jernigan and buckley tests with two new tests constructed from nonparametric smoothers their relative powers are then studied by means of large sample analysis and simulation the cusum test is the most powerful for very smooth departures from the no effect hypothesis while the new tests based on smoothing ideas are clearly superior when the alternative is high frequency

fingerprint identification using graph matching abstract a new algorithm for automated fingerprint encoding and matching is presented the algorithm is intended to be insensitive to imperfections introduced during fingerprint registration such as noise distortion and displacement a fingerprint is represented in the form of a graph whose nodes correspond to ridges in the print edges of the graph connect nodes that represent neighboring or intersecting ridges hence the graph structure captures the topological relationships within the fingerprint the algorithm has been implemented and tested using a library of real life fingerprint images

goodness of fit tests based on kullback leibler discrimination information we present a general methodology for developing asymptotically distribution free goodness of fit tests based on the kullback leibler discrimination information the tests are shown to be omnibus within an extremely large class of nonparametric global alternatives and to have good local power the proposed test procedure is a nonparametric extension of the classical neyman pearson log likelihood ratio test and is based on mth order spacings between order statistics cross validated by the observed log likelihood the developed method also generalizes cox s procedure of testing separate families and covers virtually all parametric families of distributions encountered in statistics it can also be viewed as a procedure based on sum log functionals of nonparametric density quantile estimators cross validated by the log likelihood with its good power properties the method provides an extremely simple and potentially much better alternative to the classical empirical distribution function edf based test procedures the important problem of selecting the order of spacings m in practice is also considered and a method based on maximizing the sample entropy constrained by the observed log likelihood is proposed this data driven method of choosing m is demonstrated by monte carlo simulations to be more powerful than deterministic choices of m and thus provides a practically useful tool for implementing our test procedure

matching hierarchical structures using association graphs it is well known that the problem of matching two relational structures can be posed as an equivalent problem of finding a maximal clique in a derived association graph however it is not clear how to apply this approach to computer vision problems where the graphs are hierarchically organized i e are trees since maximal cliques are not constrained to preserve the partial order we provide a solution to the problem of matching two trees by constructing the association graph using the graph theoretic concept of connectivity we prove that in the new formulation there is a one to one correspondence between maximal cliques and maximal subtree isomorphisms this allows us to cast the tree matching problem as an indefinite quadratic program using the motzkin straus theorem and we use replicator dynamical systems developed in theoretical biology to solve it such continuous solutions to discrete problems are attractive because they can motivate analog and biological implementations the framework is also extended to the matching of attributed trees by using weighted association graphs we illustrate the power of the approach by matching articulated and deformed shapes described by shock trees

semiparametric analysis of heterogeneous data using varying scale generalized linear models this article describes a class of heteroscedastic generalized linear regression models in which a subset of the regression parameters are rescaled nonparametrically and develops efficient semiparametric inferences for the parametric components of the models such models provide a means to adapt for heterogeneity in the data due to varying exposures varying levels of aggregation and so on the class of models considered includes generalized partially linear models and nonparametrically scaled link function models as special cases we present an algorithm to estimate the scale function nonparametrically and obtain asymptotic distribution theory for regression parameter estimates in particular we establish that the asymptotic covariance of the semiparametric estimator for the parametric part of the model achieves the semiparametric lower bound we also describe bootstrap based goodness of scale test we illustrate the methodology with simulations published data and data from collaborative research on ultrasound safety

an automatic portmanteau test for serial correlation this article introduces a data driven box pierce test for serial correlation the proposed test is very attractive compared to the existing ones in particular implementation of this test is extremely simple for two reasons rst the researcher does not need to specify the order of the autocorrelation tested since the test automatically chooses this number second its asymptotic null distribution is chi square with one degree of freedom so there is no need of using a bootstrap procedure to estimate the critical values in addition the test is consistent and robust to the presence of conditional heteroskedasticity of unknown form finally the proposed test presents higher power in simulations than the existing ones for models commonly employed in empirical nance

adaptive tests of linear hypotheses by model selection we propose a new test based on model selection methods for testing that the expectation of a gaussian vector with n independent components belongs to a linear subspace of r n against a nonparametric alternative the testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on the alternative the properties of the test are nonasymptotic and we prove that the test is rate optimal up to a possible log n factor over various classes of alternatives simultaneously we also provide a simulation study in order to evaluate the procedure when the purpose is to test goodness of fit in a regression model 1 introduction we consider the regression model

an algorithm for weighted sub graph matching based on gradient flows an algorithm for matching the weighted sub graphs based on gradient flows is proposed in this paper first the smaller and larger graphs for matching are represented by means of their weighted adjacency matrices then an objective function is introduced to measure the differences between two weighted adjacency matrices because the permutation matrix for graph matching is usually relaxed to an orthogonal matrix with non negative elements an optimization based approach is adopted to navigate the solution toward an appropriate permutation matrix to accomplish this goal two gradient flows in the space of orthogonal matrices are defined in such a way that they minimize the objective functions one minimizes the objective function in the space of orthogonal matrices and the other minimizes the distance of an orthogonal matrix from the set of permutations in addition two cost functions are introduced to force satisfaction approximately of the constraint that a translation matrix must have integer entries of different values the experimental results show that the proposed sub graph matching is feasible

structural matching in computer vision using probabilistic relaxation in this paper we develop the theory of probabilistic relaxation for matching features extracted from 2d images derive as limiting cases the various heuristic formulae used by researchers in matching problems and state the conditions under which they apply we successfully apply our theory to the problem of matching and recognizing aerial road network images based on road network models and to the problem of edge matching in a stereo pair for this purpose each line network is represented by an attributed relational graph where each node is a straight line segment characterized by certain attributes and related with every other node via a set of binary relations

achieving diagonal dominance there are many occasions when one would like to see whether a transfer function can be made diagonally dominant there is the obvious and important case of system design using rosenbrock s methods but one also wants to use diagonal dominance in a different manner in robustness studies and in several nonlinear system analysis techniques commonly the compensators or similarity transforms used to achieve dominance are designed in an ad hoc way this paper shows how in the particular case of diagonal compensators or similarity transforms there is a very easy way based on perron frobenius theory of obtaining optimal reduction in the off diagonal elements

new dominance concepts for multivariable control systems design this paper sets out a revised view of the classical diagonal dominance method for multivariable feedback systems the various types of dominance measure are unified by using one fundamental dominance theorem fd l it is shown that the fundamental dominance condition yields the smallest dominance measure when compared with all the known classical diagonal dominance measures in addition it is shown that the dominance measures such as row column generalized dominance and a few new ones are special cases and can be derived from this same fd theorem this improved dominance criterion also provides the sufficient condition for a system to be approximated by a nominal one in the sense that the stabilization of this nominal system will assure the stability of the original one finally a new type of dominance measure named l dominance is presented it has been shown that this new approach yields an even smaller dominance measure and that when it is applied to matrices with non positive off diagonal elements

asymptotically optimal difference based estimation of variance in nonparametric regression summary we define and compute asymptotically optimal difference sequences for estimating error variance in homoscedastic nonparametric regression our optimal difference sequences do not depend on unknowns such as the mean function and provide substantial improvements over the suboptimal sequences commonly used in practice for example in the case of normal data the usual variance estimator based on symmetric second order differences is only 64 efficient relative to the estimator based on optimal second order differences the efficiency of an optimal mth order difference estimator relative to the error sample variance is 2m 2m 1 again this is for normal data and increases as the tails of the error distribution become heavier

on convex relaxation of graph isomorphism graphs are a ubiquitous mathematical abstraction used in numerous problems in science and engineering of particular importance is the need to find the best structure preserving matching of graphs since graph matching gm is a computationally intractable problem numerous heuristics exist to approximate its solution an important class of gm heuristics is relaxation techniques based on replacing the original problem by a continuous convex program conditions for applicability or inapplicability of such convex relaxations are poorly understood in this study we propose easy to check spectral properties to characterize a wide family of graphs for which we prove equivalence of convex relaxation to the exact gm

structural tests in additive regression we consider the component analysis problem for a regression model with an additive structure the problem is to test whether some of the additive components are of polynomial structure e g linear without specifying the structure of the remaining components a particular case is the problem of selecting the significant covariates the method that we present is based on the wavelet transform using the haar basis which allows for applications under mild conditions on the design and smoothness of the regression function the results demonstrate that each component of the model can be tested with the rate corresponding to the case if all of the remaining components were known the proposed procedure is also computationally straightforward simulation results and a real data example about female labor supply demonstrate the test s good performance

the focused information criterion a variety of model selection criteria have been developed of general and specific types most of these aim at selecting a single model with good overall properties for example formulated via average prediction quality or shortest estimated overall distance to the true model the akaike the bayesian and the deviance information criteria along with many suitable variations are examples of such methods these methods are not concerned however with the actual use of the selected model which varies with context and application the present article takes the view that the model selector should instead focus on the parameter singled out for interest in particular a model that gives good precision for one estimand may be worse when used for inference for another estimand we develop a method that for a given focus parameter estimates the precision of any submodel based estimator the framework is that of large sample likelihood inference using an unbiased estimate of limiting risk we propose a foc

testing for additivity in nonparametric regression additive models are one means of assuaging the curse of dimensionality when nonparametric smoothing methods are used to estimate multivariable regression functions it is important to have methods for testing the fit of such models especially in high dimensions where visual assessment of fit becomes difficult new tests of additivity are proposed in this paper that derive from fourier series estimators with data driven smoothing parameters other tests related to the classical tukey test for additivity are also considered while the new tests are consistent against essentially any smooth alternative to additivity the tukey type tests are found to be inconsistent in certain situations asymptotic power of both varieties of tests is studied under local alternatives that tend toward additivity at a parametric rate and small sample power comparisons are carried out by means of a simulation study