distribution theory for the studentized mean for long short and negative memory time series abstract we consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory short memory negative intermediate memory or is the first difference of such a process the rate of growth of this variance depends crucially on the type of memory and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically we also present asymptotic results for the case that the bandwidth is a fixed proportion of sample size extending known results to the case of flat top tapers we adopt the fixed proportion bandwidth perspective in our empirical section presenting two methods for estimating the limiting critical values both the subsampling method and a plug in approach simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean both methods perform well although the subsampling method appears to be better sized and provide a viable framework for conducting inference for the mean in summary we supply a unified asymptotic theory that covers all different types of memory under a single umbrella

least square completion and inconsistency repair methods for additively consistent fuzzy preference relations in this paper we explore the group decision making gdm problems with incomplete additively consistent fuzzy preference relations some properties of additively consistent fuzzy preference relations are also discussed a sufficient and necessary condition is proposed to keep the additive consistency of fuzzy preference relations methods for determining the priority weights of fuzzy preference relations are provided least square completion and inconsistency repair methods are developed to deal with incomplete and inconsistent fuzzy preference relations some numerical examples are also given to illustrate the proposed approaches

the continuous ordered weighted geometric operator and its application to decision making the aim of this paper is to develop a continuous ordered weighted geometric c owg operator which is based on the continuous ordered weighted averaging c owa operator recently introduced by the author and the geometric mean we study some desirable properties of the c owg operator and present its application to decision making with interval multiplicative preference relation and finally an illustrative example is pointed out

smoothing splines regression derivatives and deconvolution abstract the statistical properties of a cubic smoothing spline and its derivative are analyzed it is shown that unless unnatural boundary conditions hold the integrated squared bias is dominated by local effects near the boundary similar effects are shown to occur in the regularized solution of a translation kernel integral equation these results are derived by developing a fourier representation for a smoothing spline author

an optimization based approach to adjusting unbalanced linguistic preference relations to obtain a required consistency level in certain real decision making situations decision makers often feel more comfortable providing their knowledge and preferences in linguistic terms unbalanced linguistic term sets may be used in decision problems with preference relations however the lack of consistency in decision making with linguistic preference relations can lead to inconsistent conclusions based on the consistency measure of unbalanced linguistic preference relations this paper proposes an optimization based approach to improving the consistency level of unbalanced linguistic preference relations this consistency improving model preserves the utmost original knowledge and preferences in the process of improving consistency furthermore it guarantees that the elements in the optimal adjusted unbalanced linguistic preference relation are all simple unbalanced linguistic terms finally we propose a mixed 0 1 linear programming aimed to obtain the optimum solution to the proposed consistency improving model and to demonstrate its practicability

spline smoothing the equivalent variable kernel method on considere une approche spline pour la regression non parametrique et l estimation de courbe on montre que dans un certain sens le lissage spline correspond approximativement au lissage par une methode du noyau avec une largeur de bande dependant de la densite locale des points du plan de regression

remarks on functional canonical variates alternating least squares methods and ace we discuss properties of some data analytic methods which are intimately related to each other alternating least squares als correspondence analysis and more recently breiman and friedman s ace algorithm the application of these methods to regression produces nonparametric estimators of nonlinear transformations both of the response and the predictors we point out some anomalies as well as some curiosities in the mathematics of these methods and we relate them to some areas in computer aided tomography projection pursuit regression and nonlinear devices in the theory of noise

generalized additive models some applications abstract generalized additive models have the form x fj x j where might be the regression function in a multiple regression or the logistic transformation of the posterior probability pr y 1 x in a logistic regression in fact these models generalize the whole family of generalized linear models x x where x g x is some transformation of the regression function we use the local scoring algorithm to estimate the functions fj xj nonparametrically using a scatterplot smoother as a building block we demonstrate the models in two different analyses a nonparametric analysis of covariance and a logistic regression the procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in a standard linear analysis a variety of inferential tools have been developed to aid the analyst in assessing the relevance and significance of the estimated functions these include confidence curves degrees of freedom estimates and approximat

multitaper spectral estimation of power law processes in many branches of science particularly astronomy and geophysics power spectra of the form f sup spl beta where spl beta is a positive power law exponent are common this form of spectrum is characterized by a sharp increase in the spectral density as the frequency f decreases toward zero a power spectrum analysis method that has proven very powerful wherever the spectrum of interest is detailed and or varies rapidly with a large dynamic range is the multitaper method with multitaper spectral estimation a set of orthogonal tapers are applied to the time series and the resulting direct spectral estimators eigenspectra are averaged thus reducing the variance one class of processes with spectra of the power law type are fractionally differenced gaussian processes that are stationary and can model certain types of long range persistence spectral decay f sup spl beta can be modeled for 0 spl beta 1 estimation of the spectral slope parameter by regression on multitaper spectral ordinates is examined for this class of processes it is shown that multitapering or using sine or slepian tapers produces much better results than using the periodogram and is attractive compared with other competing methods the technique is applied to a geophysical estimation problem

automatic smoothing of regression functions in generalized linear models abstract we consider the penalized likelihood method for estimating nonparametric regression functions in generalized linear models nelder and wedderburn 1972 and present a generalized cross validation procedure for empirically assessing an appropriate amount of smoothing in these estimates asymptotic arguments and numerical simulations are used to show that the generalized cross validatory procedure preforms well from the point of view of a weighted mean squared error criterion the methodology adds to the battery of graphical tools for model building and checking within the generalized linear model framework included are two examples motivated by medical and horticultural applications

linear smoothers and additive models we study linear smoothers and their use in building nonparametric regression models in the first part of this paper we examine certain aspects of linear smoothers for scatterplots examples of these are the running mean and running line kernel and cubic spline smoothers the eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother and several other topics such as the number of degrees of freedom of a smoother are discussed in the second part of the paper we describe how linear smoothers can be used to estimate the additive model a powerful nonparametric regression model using the backfitting algorithm we show that backfitting is the gauss seidel iterative method for solving a set of normal equations associated with the additive model we provide conditions for consistency and nondegeneracy and prove convergence for the backfitting and related algorithms for a class of smoothers that includes cubic spline smoothers

saddlepoint approximations for short and long memory time series a frequency domain approach abstract saddlepoint techniques provide numerically accurate small sample approximations to the distribution of estimators and test statistics except for a few simple models these approximations are not available in the framework of stationary time series we contribute to fill this gap under short or long range serial dependence for gaussian and non gaussian processes we show how to derive and implement saddlepoint approximations for two relevant classes of frequency domain statistics ratio statistics and whittle s estimator we compare our new approximations to the ones obtained by the standard asymptotic theory and by two widely applied bootstrap methods the numerical exercises for whittle s estimator show that our approximations yield accuracy s improvements while preserving analytical tractability a real data example concludes the paper

multiplicative data envelopment analysis cross efficiency and stochastic weight space acceptability analysis for group decision making with interval multiplicative preference relations abstract to deal with group decision making gdm with interval multiplicative preference relations imprs this paper proposes a novel method based on multiplicative data envelopment analysis dea cross efficiency and stochastic weight space acceptability analysis we first develop a multiplicative dea model to evaluate the relative efficiency of all alternatives of a given multiplicative preference relation mpr then we present a method free from consistency adjustment to derive a priority vector using the multiplicative dea cross efficiency with respect to the given mpr for gdm with imprs we consider the decision makers weights as a uniform distribution for acceptability analysis a modified unacceptability index is further defined to measure the unlikeliness for a particular alternative in a particular rank finally we develop an assignment problem model to achieve an optimal ranking by minimizing the total rank unacceptability and to compute the expected priority vector of all alternatives numerical examples are provided to show the applicability and justifications of the proposed gdm method

exploring the nature of covariate effects in the proportional hazards model we discuss an exploratory technique for investigating the nature of covariate effects in cox s proportional hazards model this technique features an additive term sigma p1 fj chi ij in place of the usual linear term sigma p1 chi ij beta j where chi i1 chi i2 chi ip are covariate values for the ith individual the fj are unspecified smooth functions that are estimated using scatterplot smoothers these functions can be used for descriptive purposes or to suggest transformations of the covariates the estimation technique is a variation of the local scoring algorithm for generalized additive models hastie and tibshirani 1986 statistical science 1 297 318

fitting a bivariate additive model by local polynomial regression while the additive model is a popular nonparametric regression method many of its theoretical properties are not well understood especially when the backfitting algorithm is used for computation of the estimators this article explores those properties when the additive model is fitted by local polynomial regression sufficient conditions guaranteeing the asymptotic existence of unique estimators for the bivariate additive model are given asymptotic approximations to the bias and the variance of a homoscedastic bivariate additive model with local polynomial terms of odd and even degree are computed this model is shown to have the same rate of convergence as that of univariate local polynomial regression

prediction intervals for neural networks via nonlinear regression standard methods for computing prediction intervals in nonlinear regression can be effectively applied to neural networks when the number of training points is large simulations show however that these methods can generate unreliable prediction intervals on smaller datasets when the network is trained to convergence stopping the training algorithm prior to convergence to avoid overfitting reduces the effective number of parameters but can lead to prediction intervals that are too wide we present an alternative approach to estimating prediction intervals using weight decay to fit the network and show via a simulation study that this method may be effective in overcoming some of the shortcomings of the other approaches

maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models in practical applications of box jenkins autoregressive integrated moving average arima models the number of times that the observed time series must be differenced to achieve approximate stationarity is usually determined by careful but mostly informal analysis of the differenced series for many time series some differencing seems appropriate but taking the first or the second difference may be too strong as an alternative hosking and granger and joyeux proposed the use of fractional differences for 1 2 1 2 can be estimated by an approximate maximum likelihood method we thus obtain a unified approach to fitting traditional box jenkins arima processes as well as stationary and non stationary fractional arima processes a confidence interval for d can be given tests such as for unit roots in the autoregressive parameter or for stationarity follow immediately the resulting confidence intervals for the arma parameters take into account the additional uncertainty due to estimation of d a simple algorithm for calculating the estimate of d and the arma parameters is given simulations and two data examples illustrate the results

new decision making techniques and their application in the selection of financial products we develop a new approach that uses the ordered weighted averaging owa operator in the selection of financial products in doing so we introduce the ordered weighted averaging distance owad operator and the ordered weighted averaging adequacy coefficient owaac operator these aggregation operators are very useful for decision making problems because they establish a comparison between an ideal alternative and available options in order to find the optimal choice the objective of this new model is to manipulate the attitudinal character of previous methods based on distance measures so that the decision maker can select financial products according to his or her degree of optimism which is also known as the orness measure the main advantage of using the owa operator is that we can generate a parameterized family of aggregation operators between the maximum and the minimum thus the analysis developed in the decision process by the decision maker is much more complete because he or she is able to select the particular case in accordance with his or her interests in the aggregation process the paper ends with an illustrative example that shows results obtained by using different types of aggregation operators in the selection of financial products

information fusion methods based on physical laws we consider systems whose parameters satisfy certain easily computable physical laws each parameter is directly measured by a number of sensors or estimated using measurements or both the measurement process may introduce both systematic and random errors which may then propagate into the estimates furthermore the actual parameter values are not known since every parameter is measured or estimated which makes the existing sample based fusion methods inapplicable we propose a fusion method for combining the measurements and estimators based on the least violation of physical laws that relate the parameters under fairly general smoothness and nonsmoothness conditions on the physical laws we show the asymptotic convergence of our method and also derive distribution free performance bounds based on finite samples for suitable choices of the fuser classes we show that for each parameter the fused estimate is probabilistically at least as good as its best measurement as well as best estimate we illustrate the effectiveness of this method for a practical problem of fusing well log data in methane hydrate exploration

the variance profile the variance profile is defined as the power mean of the spectral density function of a stationary stochastic process it is a continuous and nondecreasing function of the power parameter p which returns the minimum of the spectrum p the interpolation error variance harmonic mean p 1 the prediction error variance geometric mean p 0 the unconditional variance arithmetic mean p 1 and the maximum of the spectrum p the variance profile provides a useful characterization of a stochastic process we focus in particular on the class of fractionally integrated processes moreover it enables a direct and immediate derivation of the szego kolmogorov formula and the interpolation error variance formula the article proposes a nonparametric estimator of the variance profile based on the power mean of the smoothed sample spectrum and proves its consistency and its asymptotic normality from the empirical standpoint we propose and illustrate the use of the variance profile for estimating th

nonparametric estimation and classification using radial basis function nets and empirical risk minimization studies convergence properties of radial basis function rbf networks for a large class of basis functions and reviews the methods and results related to this topic the authors obtain the network parameters through empirical risk minimization the authors show the optimal nets to be consistent in the problem of nonlinear function approximation and in nonparametric classification for the classification problem the authors consider two approaches the selection of the rbf classifier via nonlinear function estimation and the direct method of minimizing the empirical error probability the tools used in the analysis include distribution free nonasymptotic probability inequalities and covering numbers for classes of functions

a note on a goal programming model for incomplete interval multiplicative preference relations and its application in group decision making abstract in a recently published paper by liu et al liu f zhang w g wang z x 2012 a goal programming model for incomplete interval multiplicative preference relations and its application in group decision making european journal of operational research 218 747 754 two equations are introduced to define consistency of incomplete interval multiplicative preference relations imprs and employed to develop a goal programming model for estimating missing values this note illustrates that such consistency definition and estimation model are technically incorrect new transitivity conditions are proposed to define consistent imprs and a two stage goal programming approach is devised to estimate missing values for incomplete imprs

large sample properties of the periodogram estimator of seasonally persistent processes seasonally persistent models were first introduced by andel 1986 and gray et al 1989 to extend autoregressive moving average and fractionally differenced models and to encompass long memory quasi periodic behaviour these models are for certain ranges of parameters stationary and we prove here that the behaviour of the periodogram and other tapered estimators cannot be simply extended from the work of kunsch 1986 and hurvich beltrao 1993 on long memory induced by a pole at the origin we demonstrate that potentially large both positive and negative bias can be found from the same value of the long memory parameter and that the new distribution can be easily written down in the case of gaussian processes we also consider using both the cosine taper and the sine taper the extended least squares estimator is also considered in this context

uncertainty and rank order in the analytic hierarchy process abstract the analytic hierarchy process uses paired comparisons to derive a scale of relative importance for alternatives we investigate the effect of uncertainty in judgment on the stability of the rank order of alternatives the uncertainty experienced by decision makers in making comparisons is measured by associating with each judgment an interval of numerical values the approach leads to estimating the probability that an alternative or project exchanges rank with other projects these probabilities are then used to calculate the probability that project would change rank at all we combine the priority of importance of each project with the probability that it does not change rank to obtain the final ranking

flexible parsimonious smoothing and additive modeling a simple method is presented for fitting regression models that are nonlinear in the explanatory variables despite its simplicity or perhaps because of it the method has some powerful characteristics that cause it to be competitive with and often superior to more sophisticated techniques especially for small data sets in the presence of high noise

semiparametric estimates of the relation between weather and electricity sales abstract a nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data this accommodates introduction of covariates timing adjustments due to the actual billing schedules and serial correlation the procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross validation criterion introduced by craven and wahba 1979 estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

the optimal group continuous logarithm compatibility measure for interval multiplicative preference relations based on the cowga operator the calculation of compatibility measures is an important technique employed in group decision making with interval multiplicative preference relations in this paper a new compatibility measure called the continuous logarithm compatibility which considers risk attitudes in decision making based on the continuous ordered weighted geometric averaging cowga operator is introduced we also develop a group continuous compatibility model gcc model by minimizing the group continuous logarithm compatibility measure between the synthetic interval multiplicative preference relation and the continuous characteristic preference relation furthermore theoretical foundations are established for the proposed model such as the sufficient and necessary conditions for the existence of an optimal solution the conditions for the existence of a superior optimal solution and the conditions for the existence of redundant preference relations in addition we investigate certain conditions for which the optimal objective function of the gcc model guarantees its efficiency as the number of decision makers increases finally practical illustrative examples are examined to demonstrate the model and compare it with previous methods

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

induced 2 tuple linguistic generalized aggregation operators and their application in decision making the induced 2 tuple linguistic generalized ordered weighted averaging 2 tilgowa operator is presented this new aggregation operator extends previous approaches by using generalized means order inducing variables in the reordering of the arguments and linguistic information represented with the 2 tuple linguistic approach its main advantage is that it includes a wide range of linguistic aggregation operators thus its analyses can be seen from different perspectives and we obtain a much more complete picture of the situation considered and are able to select the alternative that best fits with our interests or beliefs we further generalize the 2 tilgowa by using quasi arithmetic means and choquet integrals the result is the quasi 2 tilowa operator and the 2 tuple linguistic induced quasi arithmetic choquet integral aggregation we conclude this paper by analysing the applicability of this new approach in a multi person linguistic decision making problem concerning product management

on unified model selection for stationary and nonstationary short and long memory autoregressive processes summary the question of model choice for the class of stationary and nonstationary fractional and nonfractional autoregressive processes is considered this class is defined by the property that the dth difference for 2 d oo is a stationary autoregressive process of order p0 00 a version of the akaike information criterion aic for determining an appropriate autoregressive order when d and the autoregressive parameters are estimated simultaneously by a maximum likelihood procedure beran 1995 is derived and shown to be of the same general form as for a stationary autoregressive process but with d treated as an additional estimated parameter moreover as in the stationary case this criterion is shown not to provide a consistent estimator of p0 the corresponding versions of the bic of schwarz 1978 and the hic of hannan quinn 1979 are shown to yield consistent estimators of po the results provide a unified treatment of fractional and nonfractional stationary and integrated nonstationary autoregressive models

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

regression by local fitting methods properties and computational algorithms abstract local regression is a procedure for estimating regression surfaces by the local fitting of linear or quadratic functions of the independent variables in a moving fashion that is analogous to how a moving average is computed for a time series the advantage of the methodology over the global fitting of parametric functions of the independent variables by least squares the current paradigm in regression studies is that a much wider class of regression functions can be estimated without distortion in this paper we discuss the methods their statistical properties and computational algorithms

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

a two stage logarithmic goal programming method for generating weights from interval comparison matrices a two stage logarithmic goal programming tlgp method is proposed to generate weights from interval comparison matrices which can be either consistent or inconsistent the first stage is devised to minimize the inconsistency of interval comparison matrices and the second stage is developed to generate priorities under the condition of minimal inconsistency the weights are assumed to be multiplicative rather than additive in the case of hierarchical structures a nonlinear programming method is used to aggregate local interval weights into global interval weights a simple yet practical preference ranking method is investigated to compare the interval weights of criteria or rank alternatives in a multiplicative aggregation process the proposed tlgp is also applicable to fuzzy comparison matrices when they are transformed into interval comparison matrices using a level sets and the extension principle six numerical examples including a group decision analysis problem with a group of comparison matrices a hierarchical decision problem and a fuzzy decision problem using fuzzy comparison matrix are examined to show the applications of the proposed methods comparisons with other existing procedures are made whenever possible

on fusers that perform better than best sensor in a multiple sensor system sensor s sub i i 1 2 n outputs y sup i spl isin 0 1 according to an unknown probability distribution p y sup i x in response to input x spl isin 0 1 we choose a fuser that combines the outputs of sensors from a function class f f 0 1 sup n spl rarr 0 1 by minimizing empirical error based on an i i d sample if f satisfies the isolation property we show that the fuser performs at least as well as the best sensor in a probably approximately correct sense several well known fusers such as linear combinations special potential functions and certain feedforward networks satisfy the isolation property

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

improving autocorrelation regression for the hurst parameter estimation of long range dependent time series based on golden section search abstract this article presents an improved autocorrelation correlation function acf regression method of estimating the hurst parameter of a time series with long range dependence lrd by using golden section search gss we shall show that the present method is substantially efficient than the conventional acf regression method of h estimation our research uses fractional gaussian noise as a data case but the method introduced is applicable to time series with lrd in general

continuous generalized owa operator and its application to decision making in this paper we present a new class of operators called the continuous generalized ordered weighted averaging c gowa operators which extends the continuous ordered weighted averaging operator to adapt to uncertain and complex situations in decision making we use differentiated aggregation method and produce special forms of c gowa operator in addition we apply the c gowa operator to the aggregation of multiple interval arguments and obtain a wide range of aggregation operators we especially discuss the controlling parameter and the selection of basic unit interval monotonic function introduced in the information aggregation to make it more feasible we further generalize the previous approaches by using choquet integral and quasi arithmetic means obtaining the combined continuous generalized choquet integral aggregation operator and the combined continuous quasi arithmetic choquet integral aggregation operator we also present some further extension by using hierarchical aggregation rules obtaining the ordered hierarchies of the combined c gowa operator meanwhile some desirable properties of these operators are investigated finally we give a numerical example to illustrate the application of these operators to group decision making with interval arguments

axiomatic property based consistency analysis and decision making with interval multiplicative reciprocal preference relations abstract this paper focuses on obtaining an interval extension of saaty s consistency and eliciting normalized interval weights in analytic form from interval multiplicative reciprocal preference relations imrprs as well as checking acceptability of imrprs four axiomatic properties are presented to characterize multiplicative consistency of imrprs the paper shows that six existing consistency definitions fail to satisfy all the four axiomatic properties a constrained interval multiplication based transitivity equation is devised and an interval matrix is constructed to capture original preferences and row uncertainty proportionalities of an imrpr based on the constructed interval matrix an ordinary interval multiplication based transitivity equation is developed to define consistency of imrprs a logarithmic least square model is established to find normalized interval weights from imrprs and its analytic solution is obtained by the lagrangian multiplier method the paper introduces an index to measure uniformity of row uncertainties in an imrpr and proposes a geometric consistency index to measure inconsistency of imrprs a novel method is put forward to determine acceptability of imrprs by checking acceptable consistency and acceptable uncertainty the proposed models are illustrated by eight numerical examples and a hierarchical multi criteria decision making problem dealing with recommending undergraduate students to graduate admission

a concise consensus support model for group decision making with reciprocal preference relations based on deviation measures supporting the process of consensus building has become a major research field in group decision making gdm the purpose of this paper is to present a consistency consensus based decision support model for gdm based on reciprocal preference relations inspired by the concept of a deviation measure between two matrices an individual consistency index and a group consensus index are presented in the support model a consistency control process is designed to make an inconsistent reciprocal preference relation one of acceptable consistency to achieve a predefined consensus level an interactive consensus reaching process is provided where the group reciprocal preference relation is seen as a reference when experts change their preferences theoretical foundations are then established for the proposed model the proposed model revises the original information in a simple and straightforward gradual way in the consensus process the individual rationality level in terms of consistency is maintained two examples are examined to demonstrate the model in practical problems

multiperson decision making based on multiplicative preference relations abstract a multiperson decision making problem where the information about the alternatives provided by the experts can be presented by means of different preference representation structures preference orderings utility functions and multiplicative preference relations is studied assuming the multiplicative preference relation as the uniform element of the preference representation a multiplicative decision model based on fuzzy majority is presented to choose the best alternatives in this decision model several transformation functions are obtained to relate preference orderings and utility functions with multiplicative preference relations the decision model uses the ordered weighted geometric operator to aggregate information and two choice degrees to rank the alternatives quantifier guided dominance degree and quantifier guided non dominance degree the consistency of the model is analysed to prove that it acts coherently

augmented partial residuals a simple way of encouraging a nonlinear effect in a regression model to show itself in a partial residual parres plot component plus residual plot is to include a single quadratic term in the regression it is computationally cheap to do this for each of the independent variables examples show that the resulting set of augmented partial residual plots gives insights that are not available from standard parres or added variable plots

decision theoretic generalizations of the pac model for neural net and other learning applications we describe a generalization of the pac learning model that is based on statistical decision theory in this model the learner receives randomly drawn examples each example consisting of an instance x in x and an outcome y in y and tries to find a hypothesis h x a where h in h that specifies the appropriate action a in a to take for each instance x in order to minimize the expectation of a loss l y a here x y and a are arbitrary sets l is a real valued function and examples are generated according to an arbitrary joint distribution on x times y special cases include the problem of learning a function from x into y the problem of learning the conditional probability distribution on y given x regression and the problem of learning a distribution on x density estimation we give theorems on the uniform convergence of empirical loss estimates to true expected loss rates for certain hypothesis spaces h and show how this implies learnability with bounded sample size disregarding computational complexity as an application we give distribution independent upper bounds on the sample size needed for learning with feedforward neural networks our theorems use a generalized notion of vc dimension that applies to classes of real valued functions adapted from pollard s work and a notion of capacity and metric dimension for classes of functions that map into a bounded metric space supersedes 89 30 and 90 52 also in information and computation vol 100 no 1 september 1992

wavelet packets of nonstationary random processes contributing factors for stationarity and decorrelation the paper addresses the analysis and interpretation of second order random processes by using the wavelet packet transform it is shown that statistical properties of the wavelet packet coefficients are specific to the filtering sequences characterizing wavelet packet paths these statistical properties also depend on the wavelet order and the form of the cumulants of the input random process the analysis performed points out the wavelet packet paths for which stationarization decorrelation and higher order dependency reduction are effective among the coefficients associated with these paths this analysis also highlights the presence of singular wavelet packet paths the paths such that stationarization does not occur and those for which dependency reduction is not expected through successive decompositions the focus of the paper is on understanding the role played by the parameters that govern stationarization and dependency reduction in the wavelet packet domain this is addressed with respect to semi analytical cumulant expansions for modeling different types of nonstatonarity and correlation structures the characterization obtained eases the interpretation of random signals and time series with respect to the statistical properties of their coefficients on the different wavelet packet paths

on comparing several spectral densities we investigated the problem of testing equality among spectral densities of several independent stationary processes our main methodological contribution is the introduction of a novel semiparametric log linear model that links all of the spectral densities under consideration this model is motivated by the asymptotic properties of the periodogram ordinates and specifies that the logarithmic ratio of g 1 spectral density functions with respect to the gth is linear in some parameters then the problem of testing equality of several spectral density functions is reduced to a parametric problem under this assumption the large sample theory of the maximum likelihood estimator was studied and it was found that the estimator is asymptotically normal even when the model is misspecified the development of the asymptotic theory is based on a new contrast function that might be useful for other spectral domain time series problems the results are applicable to a variety of models including linear and nonl

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

on a class of m estimators for gaussian long memory models summary we consider estimation for parametric stationary gaussian models with long memory the spectral density f x 0 is assumed to be characterised by a vector 0 01 022 03 om such that 02 he 1 1 and f x 0 is proportional to xl 2h as x tends to zero an approximate maximum likelihood estimator based on the autoregressive representation of the process is proposed its asymptotic distribution is derived more generally the approach leads to a class of m estimators for which a central limit theorem holds by choosing an appropriate t function robustness against additive outliers can be achieved while keeping high efficiency under the ideal model this is illustrated by a small simulation study a simple algorithm and an explicit formula for the efficiency and thus for choosing an appropriate tuning parameter are given for hampel s redescending function

consistency analysis and priority derivation of triangular fuzzy preference relations based on modal value and geometric mean existing consistency notions of triangular fuzzy preference relations tfprs are illustrated to be non robust new consistency and acceptable consistency definitions are put forward for tfprs we propose a notion of normalized triangular fuzzy multiplicative weights ntfmws transformation formulae are provided to convert ntfmws into consistent tfprs a logarithmic least square model is developed to derive a ntfmw vector from a tfpr triangular fuzzy preference relation tfpr is an effective framework to model pairwise estimations with imprecision and vagueness in order to obtain a reliable and rational decision result it is important to investigate consistency and priority derivation of tfprs the paper analyzes existing definitions and properties of consistent tfprs and illustrates that they have no invariance with respect to permutations of decision alternatives a new triangular fuzzy arithmetic based transitivity equation is introduced to define consistent tfprs the new transitivity equation reflects multiplicative consistency of modal values and multiplicative consistency of geometric means of triangular fuzzy estimations some properties are presented for consistent tfprs and a notion of acceptable consistency is put forward for tfprs geometric mean and uncertainty ratio based transformation formulae are devised to convert normalized triangular fuzzy multiplicative weights into consistent tfprs a logarithmic least square model is further established for deriving a normalized triangular fuzzy multiplicative weight vector from a tfpr with acceptable consistency a geometric mean based method is developed to compare and rank triangular fuzzy multiplicative weights three numerical examples including a group decision making problem are examined to demonstrate validity and advantages of the proposed models

a decision making model based on interval additive reciprocal matrices with additive approximation consistency abstract in order to capture the rationality experienced by decision makers in choosing the best alternative s of much interest is to study the consistency of preference relations in the analytic hierarchy process ahp when the typical ahp is extended by using fuzzy numbers to evaluate the opinions of decision makers the consistency of fuzzy judgments is worth to be considered in this paper we analyze some definitions of interval additive reciprocal matrices with additive consistency it is concluded that interval additive reciprocal matrices are inconsistent in essence the concept of additive approximation consistency of interval additive reciprocal matrices is proposed moreover a novel exchange method is designed to enumerate all permutations of alternatives for checking the approximation consistency by considering the randomness exhibited in pairwisely comparing alternatives a method of obtaining the interval weight vector is given a new algorithm of solving the decision making problem with interval additive reciprocal matrices is proposed finally two numerical examples are carried out to illustrate the new definition and some comparisons are offered

perceptual multi channel visual feature fusion for scene categorization abstract effectively recognizing sceneries from a variety of categories is an indispensable but challenging technique in computer vision and intelligent systems in this work we propose a novel image kernel based on human gaze shifting aiming at discovering the mechanism of humans perceiving visually semantically salient regions within a scenery more specifically we first design a weakly supervised embedding algorithm which projects the local image features i e graphlets in this work onto the pre defined semantic space thereby we describe each graphlet by multiple visual features at both low level and high level it is generally acknowledged that humans attend to only a few regions within a scenery thus we formulate a sparsity constrained graphlet ranking algorithm which incorporates visual clues at both the low level and the high level according to human visual perception these top ranked graphlets are either visually or semantically salient we sequentially connect them into a path which mimics human gaze shifting lastly a so called gaze shifting kernel gsk is calculated based on the learned paths from a collection of scene images and a kernel svm is employed for calculating the scene categories comprehensive experiments on a series of well known scene image sets shown the competitiveness and robustness of our gsk we also demonstrated the high consistency of the predicted path with real human gaze shifting path

fitting long memory models by generalized linear regression summary there is an increasing awareness of the importance of long memory models in statistical applications if long memory is present it has to be taken into account in order to obtain reliable tests and confidence intervals one obstacle to using models with long memory in routine statistical analysis has been the lack of easily available and sufficiently versatile statistical software here we propose a simple but flexible class of parametric models which can be used to model such behaviour we demonstrate that these models can be fitted by generalized linear regression standard statistical software packages can be used a data example is discussed

integrating multiplicative preference relations in a multipurpose decision making model based on fuzzy preference relations the aim of this paper is to study the integration of multiplicative preference relation as a preference representation structure in fuzzy multipurpose decision makingproblems assumingfuzzy multipurpose decision makingproblems under di4erent preference representation structures ordering utilities and fuzzy preference relations and using the fuzzy preference relations as uniform representation elements the multiplicative preference relations are incorporated in the decision problem by means of a transformation function between multiplicative and fuzzy preference relations a consistency study of this transformation function which demonstrates that it does not change the informative content of multiplicative preference relation is shown as a consequence a selection process based on fuzzy majority for multipurpose decision makingproblems under multiplicative preference relations is presented to design it an aggregation operator of information called ordered weighted geometric operator is introduced and two choice degrees the quanti7er guided dominance degree and the quanti7er guided non dominance degree are de7ned for multiplicative preference relations c 2001 elsevier science b v all rights reserved