elastic net oriented to fuzzy semiparametric regression model with fuzzy explanatory variables and fuzzy responses in the multivariate linear regression model it is desirable to include the important explanatory variables to achieve maximal prediction in this context the present paper is an attempt to extend the conventional elastic net multiple linear regression model adopted with a semiparametric method to fuzzy predictors and responses for this purpose kernel smoothing and elastic net penalized methods were combined to construct a novel variable selection method in a fuzzy multiple regression model some common goodness of fit criteria were also included to examine the performance of the proposed method the effectiveness of the proposed method was illustrated through three numerical examples including a simulation study and two practical cases the proposed method was also compared with several common fuzzy multiple regression models the numerical results clearly indicated that the proposed method is capable of providing sufficiently accurate results in cases where noninformative explanatory variables are removed from the model

an exponential type kernel robust regression model for interval valued variables abstract the presence of outliers is very common in regression problems and the use of robust regression methods is strongly recommended such that the bad fitted observations not affect the parameter estimates of the model interval valued variables are becoming common in data analysis problems since this type of data represents either the uncertainty existing in an error measurement or the natural variability present in the data regarding the presence of outliers in interval valued data sets few robust regression methods have been proposed in literature this paper introduces a new robust regression method for interval valued variables that penalizes the presence of outliers in the midpoints and or in the ranges of interval valued observations through the use of exponential type kernel functions thus the weight given to the midpoint and range of each interval valued observation is updated at each iteration in order to optimize a suitable objective function the convergence of the parameter estimation algorithm is guaranteed with a low computational cost a comparative study between the proposed method against some previous robust regression approaches for interval valued variables is also considered the performance of these methods are evaluated based on the bias and mean squared error mse of the parameter estimates for the midpoints and ranges of the intervals considering synthetic data sets with x space outliers y space outliers and leverage points different sample sizes and percentage of outliers in a monte carlo framework the results suggest that the proposed approach presents a competitive performance or best in comparison with the previous approaches on interval valued outliers scenarios that are comparable to those found in practices applications to real interval valued data sets corroborates the usefulness of the proposed method

multiple linear regression with some correlated errors classical and robust methods in this paper we consider classical and robust methods of estimation and diagnostics for the multiple linear regression model when some of the errors are correlated this work was motivated by the analysis of a medical data set from an observational study aimed at identifying factors affecting the outcome of a surgical method for the correction of scoliosis abnormal lateral spinal curvature there are 392 observations but some of them are on the same patient double curves it seems adequate to consider a multiple linear regression model but since it is not desirable to discard the double curves the assumption of non correlated errors is clearly violated and this is indeed confirmed by related diagnostics on the residuals durbin watson test a more appropriate model retains the linear structure but allows for non null correlation between the errors on the same patient we propose two different procedures for the estimation of the parameters of the linear model and the correlation parameters maximum likelihood assuming normal errors and a robustified version obtained by plugging in results from robust linear regression the latter procedure is designed to be resistant to outlying observations or error distributions with heavy tails and has produced the most satisfactory results for the analysed data set

high breakdown point and high efficiency robust estimates for regression a class of robust estimates for the linear model is introduced these estimates called mm estimates have simultaneously the following properties i they are highly efficient when the errors have a normal distribution and ii their breakdown point is 0 5 the mm estimates are defined by a three stage procedure in the first stage an initial regression estimate is computed which is consistent robust and with high breakdown point but not necessarily efficient in the second stage an m estimate of the errors scale is computed using residuals based on the initial estimate finally in the third stage an m estimate of the regression parameters based on a proper redescending psi function is computed consistency and asymptotical normality of the mm estimates assuming random carriers are proved a convergent iterative numerical algorithm is given finally the asymptotic biases under contamination of optimal bounded influence estimates and mm estimates are compared

fuzzy stage characteristic preserving product life cycle modeling abstract stage concerns have been important in product life cycles plc such concerns are stage identification stage related strategies and here newly introduced stage modeling stage modeling is concerned with not only modeling but also aggregation of individual stages in an overall influencing manner it not only preserves the respective characteristics of the stages but also may be explored for the stage related strategy issue later to date this aspect of plc modeling has not yet been explored in this paper a fuzzy plc modeling capable of preserving the fuzzy individual characteristics of the stages is proposed the various concepts such as boundary identification fuzzy stages modeling and stages inter influence functions are introduced and discussed finally to illustrate and support the approach a numerical example and a comparison with classical data analytic procedures segmented polynomial regression and autoregressive integrated moving average is provided

fuzzy linear regression with fuzzy intervals abstract in this paper we introduce a new class of fuzzy linear regression models based on tanaka s approach unlike in the tanaka model here all training data influence the estimated interval the crisp lp of tanaka s approach is generalized to a fuzzy linear programming problem with the proposed model an adaptation of the fuzzy regression equation to new data becomes possible

reduction to least squares estimates in multiple fuzzy regression analysis in this paper we deal with the problem of least squares multiple regression with fuzzy data the regression coefficients are assumed to be real crisp a formula for solving the regression coefficients in one variable models is derived if each independent variable is effective i e its corresponding regression coefficient is nonzero the multiple regression problem can be replaced with a 0 1 programming problem its optimal solution is easily computed finally we also propose effective algorithms to compute the regression coefficients in a general case

fuzzy nonparametric regression based on local linear smoothing technique in a great deal of literature on fuzzy regression analysis most of research has focused on some predefined parametric forms of fuzzy regression relationships especially on the fuzzy linear regression models in many practical situations it may be unrealistic to predetermine a fuzzy parametric regression relationship in this paper a fuzzy nonparametric model with crisp input and lr fuzzy output is considered and based on the distance measure for fuzzy numbers suggested by diamond p diamond fuzzy least squares information sciences 46 1988 141 157 the local linear smoothing technique in statistics with the cross validation procedure for selecting the optimal value of the smoothing parameter is fuzzified to fit this model some simulation experiments are conducted to examine the performance of the proposed method and three real world datasets are analyzed to illustrate the application of the proposed method the results demonstrate that the proposed method works quite well not only in producing satisfactory estimate of the fuzzy regression function but also in reducing the boundary effect significantly

a generic property of families of lagrangian systems we prove that a generic lagrangian has finitely many minimizing measures for every cohomology class

quantifying entanglement resources we present an overview of the quantitative theory of single copy entanglement in finite dimensional quantum systems in particular we emphasize the point of view that different entanglement measures quantify different types of resources which leads to a natural interdependence of entanglement classification and quantification apart from the theoretical basis we outline various methods for obtaining quantitative results on arbitrary mixed states this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders we prove a form of arnold diffusion in the a priori stable case let h 0 p epsilon h 1 theta p t quad theta in mathbb t n p in b n t in mathbb t mathbb r mathbb t be a nearly integrable system of arbitrary degrees of freedom n geqslant 2 with a strictly convex h0 we show that for a generic epsilon h 1 there exists an orbit theta p satisfying p t p 0 l h 1 0 where l h 1 is independent of epsilon the diffusion orbit travels along a codimension 1 resonance and the only obstruction to our construction is a finite set of additional resonances

developing a fuzzy bicluster regression to estimate heat tolerance in plants by chlorophyll fluorescence this paper presents a straightforward and useful fuzzy regression approach to estimate heat tolerance of plants by chlorophyll fluorescence measurement the chlorophyll fluorescence measurement is an indicator of functional change of photosynthesis and is sensitive to temperature using the fluorescence temperature curves the experimenter may determine the heat tolerance tc of plants by intersections of two linear regression lines however as traditional statistical regression analysis shows the experiment may contain uncertain factors or phenomena such as leaf nature and growth environment which concludes that data may vary among individual plants and different species this research presents a fuzzy bicluster regression fbcr analysis with genetic algorithms which helps derive a fuzzy intersection set and fuzzy heat tolerance of plants in addition to the traditional statistical regression analysis a fuzzy clustering concept and simultaneously optimal determination of data clusters is also developed especially when there are nonlinear inflections in data curves due to the imperative use of linear regression models the traditional regression analysis may become unable to sufficiently model the uncertainties exhibited the fbcr analysis can resolve this problem effectively due to the nonlinear tolerance of the system even in a linear model to demonstrate the fbcr analysis it was applied to estimate the heat tolerance of five plant species the results derived appeared to be more suitable than that of the conventional method the approach may provide a useful means for the experimenters to derive more credible results from their chlorophyll fluorescence temperature data

extrapolating internet users in taiwan by risk assessment abstract in a competitive environment most products usually have different stages of life cycle by different sales thus satisfying consumers requirements could make the product competitive from the experiences of experts the analytic hierarchy process has been used to analyze the expected range for a specified plc stage to enable a decision maker to derive proper marketing strategies however in decision theory the belfavior of a decision maker is always affected by her risk perception and risk propensity to result in different decision making in order to cope with this problem a fuzzy forecasting system to the risk perception and risk propensity is derived to extrapolate the internet users for a specified plc stage because of uncertainty and unknown system structure in the future

a generalized fuzzy weighted least squares regression abstract a fairly general fuzzy regression technique is proposed based on the least squares approach the main concept is to estimate the modal value and the spreads separately in order to do this the interactions between the modal value and the spreads are first analyzed in detail the advantages of this new fuzzy weighted least squares regression fwlsr approach are 1 the estimation of both non interactive and interactive fuzzy parameters can be performed by the same method 2 the decision makers confidence in the gathered data and in the established model can be incorporated into the process and 3 suspicious outliers or fuzzy outliers that is data points that are obviously and suspiciously lying outside the usual range can be treated and their effects can be reduced a numerical example is provided to show that the proposed method can be an effective computational tool in fuzzy regression analysis

on the maximum bias functions of mm estimates and constrained m estimates of regression we derive the maximum bias functions of the mm estimates and the constrained m estimates or cm estimates of regression and compare them to the maximum bias functions of the s estimates and the t estimates of regression in these comparisons the cm estimates tend to exhibit the most favorable bias robustness properties also under the gaussian model it is shown how one can construct a cm estimate which has a smaller maximum bias function than a given s estimate that is the resulting cm estimate dominates the s estimate in terms of maxbias and at the same time is considerably more efficient

a robust varying coefficient approach to fuzzy multiple regression model abstract the varying coefficient models are powerful tools for exploring the dynamic pattern between a response and a group of predictors in multiple regression models in addition robust regression is another solid approach in the regression analyses for cases whose data are contaminated with outliers or influential observations this paper proposed a novel varying coefficient model with exact predictors and fuzzy responses which can be used in cases where outliers occur in the data set for this purpose a locally weighted approximation idea and a popular m estimator were combined to estimate unknown fuzzy nonparametric varying coefficients some common goodness of fit criteria including an outlier detection criterion were also applied to examine the performance of the proposed method the effectiveness of the presented method was then illustrated through two numerical examples including a simulation study it was also compared with several common fuzzy multiple regression models the numerical results clearly indicate that the proposed method is not sensitive to the outliers moreover compared to the available fuzzy multiple regressions with constant coefficients the proposed fuzzy varying coefficient model managed to provide more accurate results

fuzzy least squares linear regression analysis for fuzzy input output data a fuzzy regression model is used in evaluating the functional relationship between the dependent and independent variables in a fuzzy environment most fuzzy regression models are considered to be fuzzy outputs and parameters but non fuzzy crisp inputs in general there are two approaches in the analysis of fuzzy regression models linear programming based methods and fuzzy least squares methods in 1992 sakawa and yano considered fuzzy linear regression models with fuzzy outputs fuzzy parameters and also fuzzy inputs they formulated multiobjective programming methods for the model estimation along with a linear programming based approach in this paper two estimation methods along with a fuzzy least squares approach are proposed these proposed methods can be effectively used for the parameter estimation comparisons are also made between them

outlier detection using nonconvex penalized regression this article studies the outlier detection problem from the standpoint of penalized regression in the regression model we add one mean shift parameter for each of the n data points we then apply a regularization favoring a sparse vector of mean shift parameters the usual l1 penalty yields a convex criterion but fails to deliver a robust estimator the l1 penalty corresponds to soft thresholding we introduce a thresholding denoted by based iterative procedure for outlier detection ipod a version based on hard thresholding correctly identifies outliers on some hard test problems we describe the connection between ipod and m estimators our proposed method has one tuning parameter with which to both identify outliers and estimate regression coefficients a data dependent choice can be made based on the bayes information criterion the tuned ipod shows outstanding performance in identifying outliers in various situations compared with other existing approaches in addition ipod is much

linear regression analysis for fuzzy input and output data using the extension principle abstract the method for obtaining the fuzzy least squares estimators with the help of the extension principle in fuzzy sets theory is proposed the membership functions of fuzzy least squares estimators will be constructed according to the usual least squares estimators in order to obtain the membership value of any given value taken from the fuzzy least squares estimator optimization problems have to be solved we also provide the methodology for evaluating the predicted fuzzy output from the given fuzzy input data

on the hausdorff dimension of the mather quotient under appropriate assumptions on the dimension of the ambient manifold and the regularity of the hamiltonian we show that the mather quotient is small in term of hausdorff dimension then we present applications in dynamics

fuzzy regression models using the least squares method based on the concept of distance fuzzy regression models are developed to construct the relationship between explanatory variables and responses in a fuzzy environment in order to increase the explanatory performance of the model the least squares method is applied to determine the numeric coefficients based on the concept of distance unlike most existing approaches the numeric coefficients in the proposed model can have negative values the proposed model minimizes total estimation error in terms of the sum of the average squared distance between the observed and estimated responses based on a few alpha cuts the proposed approach is not limited to triangular fuzzy numbers it can be used to carry out a large number of fuzzy observations efficiently because the model is based on traditional statistical methods comparisons with existing methods show that based on the total estimation error using the mean squared error and kim and bishu s criterion the explanatory performance of the proposed model is satisfactory

efficient bounded influence regression estimation abstract the least squares estimator for in the classical linear regression model is strongly efficient under certain conditions however in the presence of heavy tailed errors and or anomalous data the least squares efficiency can be markedly reduced in this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first order condition for strong efficiency subject to the constraint we then show that the estimator is asymptotically normal the article concludes with an outline of an algorithm for computing a bounded influence regression estimator and with an example comparing least squares robust regression as developed by huber and the estimator proposed in this article

a partial robust ridge based regression model with fuzzy predictors responses abstract this paper extends the conventional semi parametric partial linear regression model with fuzzy predictors and fuzzy response in cases where 1 outliers occur in data set 2 multicollinearity exists in predictors for this purpose the classical kernel fitting method is first extended for estimating unknown fuzzy smooth function then inspired by the conventional local linear smoothing method a kernel based weighted criterion is suggested for determining the exact coefficients on the basis of ridge methodology some common goodness of fit criteria are also used to examine the performance of the proposed method the effectiveness of the proposed method is then illustrated through two numerical examples including a simulation study the proposed method is also compared with some common fuzzy multiple regression models with fuzzy predictors and fuzzy responses the numerical results clearly indicate that 1 the proposed method is not sensitive to the outliers 2 the proposed method provides sufficiently accurate results in cases where multicollinearity happens among predictors and 3 comparing to existing fuzzy multiple regressions the proposed model provides more efficient predictions

estimation following a sequentially designed experiment abstract we investigate the design of experiments for the nonparametric estimation of the root of an unknown regression function approaches to this problem include the robbins monro 1951 venter 1967 and lai robbins 1979 1981 stochastic approximation procedures and wu s 1985 1986 sequential maximum likelihood estimators because the regression function is not assumed to belong to a parametric family only experimentation near to the root is informative and the sequential design should converge to the root after the sequential design has been generated there are at least two distinct methods for estimation of the root a estimate the root by the last design point or b fit a parametric model except for ruppert 1988 and simulation studies by bodt 1985 and bodt and tingey 1990 all studies known to us of stochastic approximation procedures used the last design point as the estimator wu 1985 1986 fit a generalized linear model when the last design point is the estimator then cle

least squares model fitting to fuzzy vector data abstract we consider model fitting problems in which the mathematical model of an observed event is a system of equations involving model parameters and observables and in which the data are fuzzy vectors such problems naturally arise in applications when data are scarce and information is vague about distributions of variances that are contained in the observations then it may only be possible to obtain estimates of membership functions of the data a model can be fitted to such data by maximizing the membership values of the adjusted observations we achieve this by minimizing the sum of squares of the deviations of the membership values from one the optimization problem simplifies significantly if the membership functions of the fuzzy vectors belong to a class of conical functions which are defined in terms of an elliptic norm properties of these functions are discussed and a membership propagation formula derived which component wise obeys the extension principle the least squares model fitting to the described fuzzy vector data deviates in important aspects from ordinary least squares one obtains as a solution a fuzzy model parameter vector and a number of indicators which describe the quality of the fit viz the grade of compatibility between data and model their discord and dilators of model and data membership functions these new concepts are illustrated and discussed in the context of an example from a terminal ballistics problem

fuzzy least absolute deviations regression and the conflicting trends in fuzzy parameters a general fuzzy linear model for fuzzy regression analysis was first formulated based on both this general model and a fuzzy difference ranking method 1 2 approaches for fuzzy least squares regression and fuzzy least absolute value deviations regression were proposed the former approach resulted in a nonlinear programming problem while the latter resulted linear numerical examples were solved by using the absolute deviations approach to illustrate the problems of conflicting trends and ways to at least partially overcome these problems furthermore these examples showed that the absolute deviations formulation forms an effective computational tool

fuzzy strategic replacement analysis abstract this paper presents a fuzzy methodology for replacement of equipment issues such as fuzzy modeling of degradation parameters and determining fuzzy strategic replacement and economic lives are extensively discussed for the strategic purpose addible market and cost effects from the replacements against the counterpart i e the existing equipment cost and market obsolescence are modeled fuzzily and interactively in addition to the equipment deterioration both the standard fuzzy arithmetic and here re termed requisite constraint vertex fuzzy arithmetic or the vertex method are applied and investigated two numerical examples and the results are provided

a nonparametric kernel approach to interval valued data analysis this article concerns datasets in which variables are in the form of intervals which are obtained by aggregating information about variables from a larger dataset we propose to view the observed set of hyper rectangles as an empirical histogram and to use a gaussian kernel type estimator to approximate its underlying distribution in a nonparametric way we apply this idea to both univariate density estimation and regression problems unlike many existing methods used in regression analysis the proposed method can estimate the conditional distribution of the response variable for any given set of predictors even when some of them are not interval valued empirical studies show that the proposed approach has a great flexibility in various scenarios with complex relationships between the location and width of intervals of the response and predictor variables

off the beaten track a new linear model for interval data abstract we propose a new linear regression model for interval valued variables the model uses quantile functions to represent the intervals thereby considering the distributions within them in this paper we study the special case where the uniform distribution is assumed in each observed interval and we analyze the extension to the symmetric triangular distribution the parameters of the model are obtained solving a constrained quadratic optimization problem that uses the mallows distance between quantile functions as in the classical case a goodness of fit measure is deduced two applications on up to date fields are presented one predicting duration of unemployment and the other allowing forecasting burned area by forest fires

fuzzy linear regression models with least square errors to estimate the parameters of fuzzy linear regression models with fuzzy output and crisp inputs we develop a mathematical programming model in this paper the method is constructed on the basis of minimizing the square of the total difference between observed and estimated spread values or in other words minimizing the least square errors the advantage of the proposed approach is its simplicity in programming and computation as well as its performance to compare the performance of the proposed approach with the other methods two examples are presented

geometry of arnold diffusion the goal of this paper is to present to nonspecialists what is perhaps the simplest possible geometrical picture explaining the mechanism of arnold diffusion we choose to speak of a specific model that of geometric rays in a periodic optical medium this model is equivalent to that of a particle in a periodic potential in mathbb r n with energy prescribed and to the geodesic flow in a riemannian metric on mathbb r n

change of variance sensitivities in regression analysis the change of variance function is defined for estimators of regression coefficients both an unstandardized and a standardized form of the change of variance sensitivity are introduced and their relation with the corresponding gross error sensitivities is investigated the problems of optimal robustness lead to the hampel krasker and the krasker welsch estimators at the same time also the scale parameter has to be estimated robustly by means of the change of variance sensitivity optimal robust redescending scale estimators are constructed

smoothing parameter selection in nonparametric regression using an improved akaike information criterion summary many different methods have been proposed to construct nonparametric estimates of a smooth regression function including local polynomial convolution kernel and smoothing spline estimators each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set in this paper an improved version of a criterion based on the akaike information criterion aic termed aicc is derived and examined as a way to choose the smoothing parameter unlike plug in methods aicc can be used to choose smoothing parameters for any linear smoother including local quadratic and smoothing spline estimators the use of aicc avoids the large variability and tendency to undersmooth compared with the actual minimizer of average squared error seen when other classical approaches such as generalized cross validation or the aic are used to choose the smoothing parameter monte carlo simulations demonstrate that the aicc based smoothing parameter is competitive with a plug in method assuming that one exists when the plug in method works well but also performs well when the plug in approach fails or is unavailable

multiobjective fuzzy regression with central tendency and possibilistic properties a multiobjective fuzzy regression model mofr is developed this mofr model combines central tendency and possibilistic properties of statistical and fuzzy regressions and overcomes several shortcomings of these two approaches a new class of distance measure for two intervals that takes into account all the points in both intervals is introduced the methodology is illustrated by numerical examples

bootstrapping robust estimates of regression we introduce a new computer intensive method to estimate the distribution of robust regression estimates the basic idea behind our method is to bootstrap a reweighted representation of the estimates to obtain a bootstrap method that is asymptotically correct we include the auxiliary scale estimate in our reweighted representation of the estimates our method is computationally simple because for each bootstrap sample we only have to solve a linear system of equations the weights we use are decreasing functions of the absolute value of the residuals and hence outlying observations receive small weights this results in a bootstrap method that is resistant to the presence of outliers in the data the breakdown points of the quantile estimates derived with this method are higher than those obtained with the bootstrap we illustrate our method on two datasets and we report the results of a monte carlo experiment on confidence intervals for the parameters of the linear model

classification of arbitrary multipartite entangled states under local unitary equivalence we propose a practical method for finding the canonical forms of arbitrary dimensional multipartite entangled states either pure or mixed by extending the technique developed in one of our recent works the canonical forms for the mixed n partite entangled states are constructed where they have inherited local unitary symmetries from their corresponding n 1 pure state counterparts a systematic scheme to express the local symmetries of the canonical form is also presented which provides a feasible way of verifying the local unitary equivalence for two multipartite entangled states

robust fuzzy regression analysis in this paper we propose a robust fuzzy linear regression model based on the least median squares weighted least squares lms wls estimation procedure the proposed model is general enough to deal with data contaminated by outliers due to measurement errors or extracted from highly skewed or heavy tailed distributions we also define suitable goodness of fit indices useful to evaluate the performances of the proposed model the effectiveness of our model in reducing the outliers influence is shown by using applicative examples based both on simulated and real data and by a simulation study

identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters abstract we have already discussed several models of the possibilities linear regression analysis under the assumption that probabilitioes parameters in the models are non interactive i e the possibilistic distribution of parameters is defined by minimum operators in this paper quadratic membership functions as defined by a celmi s are considered to propose an identification method of interactive fuzzy parameters in possibilistic linear systems our method can be reduced to linear programming so that it is very easy to obtain the posssibilistic distribution of parameters

fuzzy regression in hydrology a general methodology for fuzzy regression is developed and illustrated by an actual hydrological case study fuzzy regression may be used whenever a relationship between variables is imprecise and or data are inaccurate and or sample sizes are insufficient in such cases fuzzy regression may be used as a complement or an alternative to statistical regression analysis in fuzzy regression several goodness of fit criteria may be used such as the maximum average vagueness criterion and the prediction vagueness criterion the technique is illustrated by means of a case study involving the relationship between soil electrical resistivity and hydraulic permeability this relationship is imprecise and based on only a few data points in the present case a curvilinear relationship is fitted using fuzzy regression with six calculated resistivities and six measured permeabilities prediction vagueness criteria appears to yield a more robust fuzzy regression than the maximum average vagueness criteria potential application areas of fuzzy regression in hydrology are discussed further the methodology is relatively simple and the results can be interpreted to provide a valuable hydrological decision making aid

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

from the statistics of data to the statistics of knowledge symbolic data analysis increasingly datasets are so large they must be summarized in some fashion so that the resulting summary dataset is of a more manageable size while still retaining as much knowledge inherent to the entire dataset as possible one consequence of this situation is that the data may no longer be formatted as single values such as is the case for classical data but rather may be represented by lists intervals distributions and the like these summarized data are examples of symbolic data this article looks at the concept of symbolic data in general and then attempts to review the methods currently available to analyze such data it quickly becomes clear that the range of methodologies available draws analogies with developments before 1900 that formed a foundation for the inferential statistics of the 1900s methods largely limited to small by comparison datasets and classical data formats the scarcity of available methodologies for symbolic data also becomes clear and so draws attention to an enor

an orderwise polynomial regression procedure for fuzzy data a procedure for polynomial fit with fuzzy data is presented as in real case studies there is often dependence between modes and spreads we propose a regression polynomial model capable to take into account possible interactions between the estimated spreads and modes this method finds applications in several fields such as reliability quality control psychometrics marketing image processing etc an application to a software reliability problem is also presented

robust variable selection with exponential squared loss robust variable selection procedures through penalized regression have been gaining increased attention in the literature they can be used to perform variable selection and are expected to yield robust estimates however to the best of our knowledge the robustness of those penalized regression procedures has not been well characterized in this article we propose a class of penalized robust regression estimators based on exponential squared loss the motivation for this new procedure is that it enables us to characterize its robustness in a way that has not been done for the existing procedures while its performance is near optimal and superior to some recently developed methods specifically under defined regularity conditions our estimators are consistent and possess the oracle property importantly we show that our estimators can achieve the highest asymptotic breakdown point of 1 2 and that their influence functions are bounded with respect to the outliers in either the response or the covari

resolution of fuzzy regression model abstract fuzzy linear regression was originally introduced by tanaka et al to cope with different types of input output information several approaches to fuzzy linear regression have been proposed in this paper a type of problem with crisp input and fuzzy output described by tanaka is considered of which a modified fuzzy least square method was proposed for solution it shows that with such an approach the predictability in the new model is better than tanaka s and its computation efficiency is better than the conventional fuzzy least square method

a geometrical approach to monotone functions in r n this paper is concerned with the fine properties of monotone func tions on r n we study the continuity and differentiability properties of these functions the approximability properties the structure of the distributional derivatives and of the weak jacobians moreover we exhibit an example of a monotone function u which is the gradient of a c 1 convex function and

robust regression using repeated medians abstract the repeated median algorithm is a robustified u statistic in which nested medians replace the single mean unlike many generalizations of the univariate median repeated median estimates maintain the high 50 breakdown value and can resist the effects of outliers even when they comprise nearly half of the data because they are calculated directly not iteratively repeated median procedures can be used as starting values for iterative robust estimation methods for bivariate linear regression with symmetric errors repeated median estimates are unbiased and fisher consistent and their efficiency under gaussian sampling can be comparable to the efficiency of the univariate median author

closing aubry sets ii given a tonelli hamiltonian h t m of class ck with k 2 we prove the following results 1 assume there exist a recurrent point of the projected aubry set and a critical viscosity subsolution u such that u is a c1 critical solution in an open neighborhood of the positive orbit of suppose further that u is c2 at then there exists a ck potential v m small in c2 topology for which the aubry set of the new hamiltonian h v is either an equilibrium point or a periodic orbit 2 if m is two dimensional 1 holds replacing c1 critical solution c2 at by cm3 critical subsolution these results can be considered as a first step through the attempt of proving the mane s conjecture in c2 topology in a second paper 27 we will generalize 2 to arbitrary dimension moreover such an extension will need the introduction of some new techniques which will allow us to prove in 27 the mane s density conjecture in c1 topology our proofs are based on a combination of techniques coming from finite dimensional control theory and hamilton jacobi theory together with some of the ideas that were used to prove c1 closing lemmas for dynamical systems 2014 wiley periodicals inc

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

mane s conjectures in codimension 1 we prove mane s conjectures 9 in the context of codimension 1 aubry mather theory 2011 wiley periodicals inc

a new kind of lax oleinik type operator with parameters for time periodic positive definite lagrangian systems in this paper we introduce a new kind of lax oleinik type operator with parameters associated with positive definite lagrangian systems for both the time periodic case and the time independent case on one hand the family of new lax oleinik type operators with an arbitrary u in c m mathbb r 1 as initial condition converges to a backward weak kam solution in the time periodic case while it was shown by fathi and mather that there is no such convergence of the lax oleinik semigroup on the other hand the family of new lax oleinik type operators with an arbitrary u in c m mathbb r 1 as initial condition converges to a backward weak kam solution faster than the lax oleinik semigroup in the time independent case

properties of certain fuzzy linear regression methods abstract fuzzy linear regression was originally introduced by tanaka uejima and asai ieee trans systems man cybern 12 1982 903 907 in subsequent years several different approaches to fuzzy linear regression have been proposed the purpose of this paper is to review and examine some of these formulations to discuss their strengths and weaknesses relative to each other and to suggest possible improvements in addition we compare and contrast these methods to the method of ordinary least squares regression

dependency between degree of fit and input noise in fuzzy linear regression using non symmetric fuzzy triangular coefficients fuzzy linear regression flr model can be thought of as a fuzzy variation of classical linear regression model it has been widely studied and applied in diverse fields when noise exists in data it is a very meaningful topic to reveal the dependency between the parameter h i e the threshold value used to measure degree of fit in flr model and the input noise in this paper the flr model is first extended to its regularized version i e regularized fuzzy linear regression rflr model so as to enhance its generalization capability then rflr model is explained as the corresponding equivalent maximum a posteriori map problem finally the general dependency relationship that the parameter h with noisy input should follow is derived particular attention is paid to the regression model using non symmetric fuzzy triangular coefficients it turns out that with the existence of typical gaussian noisy input the parameter h is inversely proportional to the input noise our experimental results here also confirm this theoretical claim obviously this theoretical result will be helpful to make a good choice for the parameter h and to apply flr techniques effectively in practical applications

on the number of mather measures of lagrangian systems in 1996 ricardo ricardo mane discovered that mather measures are in fact the minimizers of a universal infinite dimensional linear programming problem this fundamental result has many applications of which one of the most important is to the estimates of the generic number of mather measures mane obtained the first estimation of that sort by using finite dimensional approximations recently we were able with gonzalo contreras to use this method of finite dimensional approximation in order to solve a conjecture of john mather concerning the generic number of mather measures for families of lagrangian systems in the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem we use a notion of countably rectifiable sets of finite codimension in banach and frechet spaces which may deserve independent interest

complete set of operational measures for the characterization of three qubit entanglement we characterize the entanglement contained in a pure three qubit state via operational entanglement measures to this end we derive a new decomposition for arbitrary three qubit states which is characterized by five parameters up to local unitary operations we show that these parameters are uniquely determined by bipartite entanglement measures these quantities measure the entanglement required to generate the state following a particular preparation procedure and have a clear physical meaning moreover we show that the classification of states obtained in this way is strongly related to the one obtained when considering general local operations and classical communication

multidimensional least squares fitting with a fuzzy model the aim of this paper is to deal with the question of fuzzy multivariable linear regression by least squares similar to the traditional least squares method we develop a fuzzy analogue by a distance defined on a fuzzy number space and propose a fuzzy multivariable linear regression model it is shown that the model has a unique solution and the solution can be given in an analytic expression in this paper we also give an index to evaluate the goodness of fit between the observed value and the estimated value

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

asymptotic behavior of general m estimates for regression and scale with random carriers let xini y i be a sequence of independent identically distributed random variables where x i r p and y i r and let r p be an unknown vector such that y i x i u i where u i is independent of x i and has distribution function f u where 0 is an unknown parameter this paper deals with a general class of m estimates of regression and scale defined as solutions of the system sum limits i phi text x i r i x i 0 sum limits i chi r i 0 where r y i xi1 with r p r r and r r this class contains estimators of proposed by huber mallows and krasker and welsch the consistency and asymptotic normality of the general m estimators are proved assuming general regularity conditions on and and assuming the joint distribution of x i y i to fulfill the model only approximately

propagation of singularities for weak kam solutions and barrier functions this paper studies the structure of the singular set points of nondifferentiability of viscosity solutions to hamilton jacobi equations associated with general mechanical systems on the n torus first using the level set method we characterize the propagation of singularities along generalized characteristics then we obtain a local propagation result for singularities of weak kam solutions in the supercritical case finally we apply such a result to study the propagation of singularities for barrier functions

on assessing the h value in fuzzy linear regression abstract there are certain circumstances under which the application of statistical regression is not appropriate or even feasible because it makes rigid assumptions about the statistical properties of the model fuzzy regression a nonparametric method can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise and variables are interacting in an uncertain qualitative and fuzzy way thus it may have considerable practical applications in many management and engineering problems in this paper the relationship among the h value membership function shape and spreads of fuzzy parameters in fuzzy linear regression is determined and the sensitivity of the spread with respect to the h value and membership function shape is examined the spread of a fuzzy parameter increases as a higher value of h and or a decreasingly concave or increasingly convex membership function is employed by utilizing the relationship among the h value membership function and spreads of the fuzzy parameters a systematic approach to assessing a proper h parameter value is also developed the approach developed and illustrated enables a decision maker s beliefs regarding the shape and range of the possibility distribution of the model to be reflected more systematically and consequently should yield more reliable and realistic results from fuzzy regression the resulging regressing equations could for example also be used as constraints in a fuzzy mathematical optimization model such as in quality function deployment