a simple smooth backfitting method for additive models in this paper a new smooth backfitting estimate is proposed for additive regression models the estimate has the simple structure of nadaraya watson smooth backfitting but at the same time achieves the oracle property of local linear smooth backfitting each component is estimated with the same asymptotic accuracy as if the other components were known

the existence and asymptotic properties of a backfitting projection algorithm under weak conditions we derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function the procedure employs a recent projection interpretation of popular kernel estimators provided by mammen marron turlach and wand 1997 and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in bickel klaassen ritov and wellner 1993 our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components and in this sense improves on the method analysed in opsomer and ruppert 1997 we provide high level conditions independent of the sampling scheme we then verify that these conditions are satisfied in a regression and a time series autoregression under weak conditions

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

local polynomial regression analysis of clustered data this paper proposes a classical weighted least squares type of local polynomial smoothing for the analysis of clustered data with the key idea of using generalised inverses of correlation matrices the estimator has a simple closed form expression simplicity is achieved also for nonparametric generalised linear models with arbitrary link function via a transformation our approach can be characterised by local observations with local variances which yields intuitively correct results in the sense that correct incorrect specification of within cluster correlation has respective positive negative effects the approach is a natural extension of classical local polynomial smoothing consequently existing theory can be largely carried over and important issues such as bandwidth selection can be tackled in the classical fashion moreover the approach can handle various types of covariate such as cluster level subject level or partially cluster level numerical studies support the theoretical results the method is illustrated with a real example on luteinising hormone levels in cows

approaches to collective decision making with fuzzy preference relations abstract recent experimental studies show that the predictive accuracy of many of the solution concepts derived from the collective decision making theory leaves much to be desired in a previous paper the author attempted to explain some of the inaccuracies in terms of the fuzzy indifference regions of the individuals participating in the voting game this paper gives straightforward generalizations of the solutions concepts in terms of the fuzzy social or individual preference relations it turns out that some of these new solution concepts cotain their nonfuzzy counterparts as subsets others in turn are subsets of their nonfuzzy counterparts we also discuss a method of aggregating individual nonfuzzy preferences so as to get a fuzzy social preference relation and furthermore a nonfuzzy social choice set

stereoscopic ranging by matching image modulations we apply an am fm surface albedo model to analyze the projection of surface patterns viewed through a binocular camera system this is used to support the use of modulation based stereo matching where local image phase is used to compute stereo disparities the local image phase is an advantageous feature for image matching since the problem of computing disparities reduces to identifying local phase shifts between the stereoscopic image data local phase shifts however are problematic at high frequencies due to phase wrapping when disparities exceed spl plusmn spl pi we meld powerful multichannel gabor image demodulation techniques for multiscale coarse to fine computation of local image phase with a disparity channel model for depth computation the resulting framework unifies phase based matching approaches with am fm surface image models we demonstrate the concepts in a stereo algorithm that generates a dense accurate disparity map without the problems associated with phase wrapping

general transitivity conditions for fuzzy reciprocal preference matrices a reciprocal fuzzy matrix relation is a non negative matrix q qij such that qij qji 1 for all i j 1 2 n we define general transitivity conditions named fg transitivities for fuzzy reciprocal preference relations and show that they generalize some well known transitivities we also study relationships of these conditions with two models of rational preferences the so called utility model and the multidimensional model

nonparametric additive regression for repeatedly measured data summary we develop an easily computed smooth backfitting algorithm for additive model fitting in repeated measures problems our methodology easily copes with various settings such as when some covariates are the same over repeated response measurements we allow for a working covariance matrix for the regression errors showing that our method is most efficient when the correct covariance matrix is used the component functions achieve the known asymptotic variance lower bound for the scalar argument case smooth backfitting also leads directly to design independent biases in the local linear case simulations show our estimator has smaller variance than the usual kernel estimator this is also illustrated by an example from nutritional epidemiology

transitivity of fuzzy preference relations an empirical study based on an experiment we show that human preferences when represented by fuzzy relations may violate transitivity we define an index of transitivity and compute the degree to which the transitivity is violated

learning intransitive reciprocal relations with kernel methods abstract in different fields like decision making psychology game theory and biology it has been observed that paired comparison data like preference relations defined by humans and animals can be intransitive intransitive relations cannot be modeled with existing machine learning methods like ranking models because these models exhibit strong transitivity properties more specifically in a stochastic context where often the reciprocity property characterizes probabilistic relations such as choice probabilities it has been formally shown that ranking models always satisfy the well known strong stochastic transitivity property given this limitation of ranking models we present a new kernel function that together with the regularized least squares algorithm is capable of inferring intransitive reciprocal relations in problems where transitivity violations cannot be considered as noise in this approach it is the kernel function that defines the transition from learning transitive to learning intransitive relations and the kronecker product is introduced for representing the latter type of relations in addition we empirically demonstrate on two benchmark problems one in game theory and one in theoretical biology that our algorithm outperforms methods not capable of learning intransitive reciprocal relations

consistent models of transitivity for reciprocal preferences on a finite ordinal scale in this paper we consider a decision maker who shows his her preferences for different alternatives through a finite set of ordinal values we analyze the problem of consistency taking into account some transitivity properties within this framework these properties are based on the very general class of conjunctors on the set of ordinal values each reciprocal preference relation on a finite ordinal scale has both a crisp preference and a crisp indifference relation associated to it in a natural way taking this into account we have started by analyzing the problem of propagating transitivity from the preference relation on a finite ordinal scale to the crisp preference and indifference relations after that we carried out the analysis in the opposite direction we provide some necessary and sufficient conditions for that propagation and therefore we characterize the consistent class of conjunctors in each direction

color and depth priors in natural images natural scene statistics have played an increasingly important role in both our understanding of the function and evolution of the human vision system and in the development of modern image processing applications because range egocentric distance is arguably the most important thing a visual system must compute from an evolutionary perspective the joint statistics between image information color and luminance and range information are of particular interest it seems obvious that where there is a depth discontinuity there must be a higher probability of a brightness or color discontinuity too this is true but the more interesting case is in the other direction because image information is much more easily computed than range information the key conditional probabilities are those of finding a range discontinuity given an image discontinuity here the intuition is much weaker the plethora of shadows and textures in the natural environment imply that many image discontinuities must exist without corresponding changes in range in this paper we extend previous work in two ways we use as our starting point a very high quality data set of co registered color and range values collected specifically for this purpose and we evaluate the statistics of perceptually relevant chromatic information in addition to luminance range and binocular disparity information the most fundamental finding is that the probabilities of finding range changes do in fact depend in a useful and systematic way on color and luminance changes larger range changes are associated with larger image changes second we are able to parametrically model the prior marginal and conditional distributions of luminance color range and computed binocular disparity finally we provide a proof of principle that this information is useful by showing that our distribution models improve the performance of a bayesian stereo algorithm on an independent set of input images to summarize we show that there is useful information about range in very low level luminance and color information to a system sensitive to this statistical information it amounts to an additional and only recently appreciated depth cue and one that is trivial to compute from the image data we are confident that this information is robust in that we go to great effort and expense to collect very high quality raw data finally we demonstrate the practical utility of these findings by using them to improve the performance of a bayesian stereo algorithm

semiparametric and nonparametric regression analysis of longitudinal data this article deals with the regression analysis of repeated measurements taken at irregular and possibly subject specific time points the proposed semiparametric and nonparametric models postulate that the marginal distribution for the repeatedly measured response variable y at time t is related to the vector of possibly time varying covariates x through the equations e y t x t 0 t 0x t and e y t x t 0 t 0 t x t where 0 t is an arbitrary function of t 0 is a vector of constant regression coefficients and 0 t is a vector of time varying regression coefficients the stochastic structure of the process y is completely unspecified we develop a class of least squares type estimators for 0 which is proven to be n consistent and asymptotically normal with simple variance estimators furthermore we develop a closed form estimator for a cumulative function of 0 t which is shown to be n consistent and on proper normalization converges weakly to a zero mean gaussian pr

on the transitivity property abstract in this short note general transitivity properties of fuzzy binary relations are discussed it is shown that under some weak conditions any fuzzy binary relation can be regarded as a transitive one with respect to a properly chosen t norm a representation theorem for such relations is formulated

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

semiparametric regression for clustered data using generalized estimating equations we consider estimation in a semiparametric generalized linear model for clustered data using estimating equations our results apply to the case where the number of observations per cluster is finite whereas the number of clusters is large the mean of the outcome variable is of the form g xt t where g is a link function x and t are covariates is an unknown parameter vector and t is an unknown smooth function kernel estimating equations proposed previously in the literature are used to estimate the infinite dimensional nonparametric function t and a profile based estimating equation is used to estimate the finite dimensional parameter vector we show that for clustered data this conventional profile kernel method often fails to yield a n consistent estimator of along with appropriate inference unless working independence is assumed or t is artificially undersmoothed in which case asymptotic inference is possible to gain insight into these results we derive the se

fuzzy rationality measures fuzzy preference relations formalize intensity of individual preferences over fixed sets of alternatives it is therefore natural to extend to fuzzy preferences the notion of rationality or consistency with this goal in mind we address in this paper the problem of giving an axiomatic basis for defining the concept of fuzzy rationality specifically we establish a collection of conditions that any fuzzy rationality measure must satisfy some examples of fuzzy rationality measures are then given and analyzed

a rational consensus model in group decision making using linguistic assessments abstract a new consensus model for the consensus reaching process in a linguistic framework is presented in heterogeneous group decision making problems called rational consensus model it is guided by some linguistic consensus and linguistic consistency meaures all the measures are calculated from a set of linguistic preference relations used to provide experts opinions this consensus model allows more rational consensus solutions to be obtained and thus more human consistency to be incorporated in decision support systems

the self dual core and the anti self dual remainder of an aggregation operator in most decisional models based on pairwise comparison between alternatives the reciprocity of the individual preference representations expresses a natural assumption of rationality in those models self dual aggregation operators play a central role in so far as they preserve the reciprocity of the preference representations in the aggregation mechanism from individual to collective preferences in this paper we propose a simple method by which one can associate a self dual aggregation operator to any aggregation operator on the unit interval the resulting aggregation operator is said to be the self dual core of the original one and inherits most of its properties our method constitutes thus a new characterization of self duality with some technical advantages relatively to the traditional symmetric sums method due to silvert in our framework moreover every aggregation operator can be written as a sum of a self dual core and an anti self dual remainder which in some cases seems to give some indication on the dispersion of the variables in order to illustrate the method proposed we apply it to two important classes of continuous aggregation operators with the properties of idempotency symmetry and stability for translations the owa operators and the exponential quasiarithmetic means

preference relations on a set of fuzzy utilities as a basis for decision making abstract in fuzzy decision problems we often encounter situations of choosing among alternatives which are assigned fuzzy utilities these problems have been approached using fuzzy implications or direct comparisons among fuzzy utilities in the literature however there are few attempts to investigate the issues addressing reasonable choice or reasonable ordering using fuzzy sets theory this paper first introduces some fundamental properties of fuzzy binary relations and certain conditions of reasonable orderings of fuzzy utilities then a method for constructing a fuzzy preference relation on a given set of fuzzy utilities is proposed for the sake of rational decision making this procedure employs the concepts of the extended minimum and the hamming distance between the greatest upper sets or the greatest lower sets of fuzzy utilities finally it is shown that the proposed fuzzy preference relations have reasonable properties as fuzzy orderings for decision making

modeling rationality in a linguistic framework in classical decision theory there exists a large class of rationality models which try to capture different kinds of behavior when individuals compare by pairs a set of alternatives all these models assume that decision makers have dichotomous preferences however in real decisions individuals feel different degrees of preference in this paper we have checked the mentioned models in a real case where different kinds of linguistic preferences are allowed after the empirical analysis the main conclusion is that the fulfillment of rational conditions decreases when individuals have non extreme preferences based on the obtained empirical evidences we propose some classes of transitivity conditions in the framework of linguistic preferences

representation and construction of self dual aggregation operators abstract two different characterizations of self dual aggregation operators are available in the literature one based on c x y x x 1 y and one based on the arithmetic mean both approaches construct a self dual aggregation operator by combining an aggregation operator with its dual in this paper we fit these approaches into a more general framework and characterize n invariant aggregation operators with n an involutive negator various binary aggregation operators fulfilling some kind of symmetry w r t n and with a sufficiently large range can be used to combine an aggregation operator and its dual into an n invariant aggregation operator moreover using aggregation operators to construct n invariant aggregation operators seems rather restrictive it suffices to consider n ary operators fulfilling some weaker conditions special attention is drawn to the equivalence classes that arise as several of these n ary operators can yield the same n invariant aggregation operator

surfaces from stereo integrating feature matching disparity estimation and contour detection an approach is described that integrates the processes of feature matching contour detection and surface interpolation to determine the three dimensional distance or depth of objects from a stereo pair of images integration is necessary to ensure that the detected surfaces are smooth surface interpolation takes into account detected occluding and ridge contours in the scene interpolation is performed within regions enclosed by these contours planar and quadratic patches are used as local models of the surface occluded regions in the image are identified and are not used for matching and interpolation a coarse to fine algorithm is presented that generates a multiresolution hierarchy of surface maps one at each level of resolution experimental results are given for a variety of stereo images

rationality of fuzzy reciprocal preference relations we study relationships between different transitivity and acyclicity conditions for fuzzy reciprocal relations such conditions may be treated as rationality conditions for preferences described by such kind of relations

stochastic stereo matching over scale a stochastic optimization approach to stereo matching is presented unlike conventional correlation matching and feature matching the method provides a dense array of disparities eliminating the need for interpolation first the stereo matching problem is defined in terms of finding a disparity map that satisfies two competing constraints 1 matched points should have similar image intensity and 2 the disparity map should vary as slowly as possible these constraints are interpreted as specifying the potential energy of a system of oscillators ground states are approximated by a new variant of simulated annealing which has two important features first the microcanonical ensemble is simulated using a new algorithm that is more efficient and more easily implemented than the familiar metropolis algorithm which simulates the canonical ensemble secondly it uses a hierarchical coarse to fine control structure employing gaussian or laplacian pyramids of the stereo images in this way quickly computed results at low resolutions are used to initialize the system at higher resolutions

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

individual valued preferences and their aggregation consistency analysis in a real case in this paper we have analyzed the accomplishment of several consistency conditions in a real decision case a group of students showed their intensities of preference among the alternatives by means of linguistic labels represented by real numbers the absolute and relative fulfillments of some kinds of fuzzy transitivity properties have been studied for individual and collective preferences collective preferences have been obtained by means of a wide class of neutral and stable for translations aggregation rules which transports reciprocity from individual preferences to the collective preference we notice that in the real case studied the aggregate preferences reach higher consistency properties than individual preferences

estimating semiparametric arch models by kernel smoothing methods we investigate a class of semiparametric arch models that includes as a special case the partially nonparametric pnp model introduced by engle and ng 1993 and which allows for both flexible dynamics and flexible function form with regard to the news impact function we show that the functional part of the model satisfies a type ii linear integral equation and give simple conditions under which there is a unique solution we propose an estimation method that is based on kernel smoothing and profiled likelihood we establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model we also discuss efficiency of both the parametric part and the nonparametric part we investigate the performance of our procedures on simulated data and on a sample of s p500 index returns we find evidence of asymmetric news impact functions consistent with the parametric analysis

on choosing rationally when preferences are fuzzy abstract in real life exact choices are induced by fuzzy preferences these choices eventually satisfy certain plausible rationality properties several alternative rules for generating exact choices from fuzzy weak preference relations are introduced and the extent to which exact choice sets generated by these rules satisfy fairly weak rationality conditions is studied max min transitivity is shown to be crucial for obtaining a positive result

using chromatic information in dense stereo correspondence abstract the use of chromatic information in dense stereo correspondence is investigated specifically the chromatic photometric constraint which is used to specify a mathematical optimality criterion for solving the dense stereo correspondence problem is developed the result is a theoretical construction for developing dense stereo correspondence algorithms which use chromatic information the efficacy of using chromatic information via this construction is tested by implementing single and multi resolution versions of a stereo correspondence algorithm that uses simulated annealing as a means of solving the optimization problem results demonstrate that the use of chromatic information can significantly improve the performance of dense stereo correspondence

on a canonical representation of fuzzy numbers abstract fuzzy numbers and more generally linguistic values are approximate assessments given by experts and accepted by decision makers when obtaining more accurate values is impossible or unnecessary to simplify the task of representing and handling fuzzy numbers several authors have introduced real indices in order to capture the information contained in a fuzzy number in this paper we propose two parameters value and ambiguity for this purpose we use these parameters to obtain canonical representations and to deal with fuzzy numbers in decision making problems several examples illustrate these ideas

collective transitivity in majorities based on difference in support a common criticism to simple majority voting rule is the slight support that such rule demands to declare an alternative as a winner among the distinct majority rules used for diminishing this handicap we focus on majorities based on difference in support with these majorities voters are allowed to show intensities of preference among alternatives through reciprocal preference relations these majorities also take into account the difference in support between alternatives in order to select the winner in this paper we have provided some necessary and sufficient conditions for ensuring transitive collective decisions generated by majorities based on difference in support for all the profiles of individual reciprocal preference relations these conditions involve both the thresholds of support and some individual rationality assumptions that are related to transitivity in the framework of reciprocal preference relations