quantitative weights and aggregation based on the strong idempotency of aggregation operators quantitative weights are incorporated into the fusion process our general method is compared with some previous specific cases more details about weighted aggregation based on some penalty function is given further weighted integral based aggregation linked to quantifier based fuzzy measures is investigated especially weighted owa operators several examples are included

modelling of covariance structures in generalised estimating equations for longitudinal data summary when used for modelling longitudinal data generalised estimating equations specify a working structure for the within subject covariance matrices aiming to produce efficient parameter estimators however misspecification of the working covariance structure may lead to a large loss of efficiency of the estimators of the mean parameters in this paper we propose an approach for joint modelling of the mean and covariance structures of longitudinal data within the framework of generalised estimating equations the resulting estimators for the mean and covariance parameters are shown to be consistent and asymptotically normally distributed real data analysis and simulation studies show that the proposed approach yields efficient estimators for both the mean and covariance parameters

induced weighted operators based on dissimilarity functions based on the minimization considering dissimilarity function d x y f x f y 2 induced ordered weighted averaging operators iowa and induced ordered generalized mixture operators iom g are discussed in general these operators need not be monotone non decreasing thus they need not be the aggregation operators this paper introduces conditions for their monotonicity and weak monotonicity several examples are included

computation of the generalized inverse of a polynomial matrix and applications abstract the computation of the generalized inverse of a constant matrix is utilized in finding the generalized inverse and its laurent expansion of a nonregular polynomial matrix the proposed algorithm constitutes a generalization of the algorithm proposed by fragulis et al for regular polynomial matrices and gives rise to numerous applications in multivariable system analysis

an alternative definition of finite sample breakdown point with applications to regression model estimators abstract we propose an alternative definition of the finite sample breakdown point this breakdown point is invariant with respect to reparameterization and compatible with the donoho huber breakdown point in linear regression situations it also overcomes certain limitations of the definition proposed by stromberg and ruppert and can be used in a wide range of estimation problems we investigate the breakdown properties of some nonlinear regression estimators these results alert us to the danger of using familiar m estimators with data sets containing outliers and to the advantages of using estimators based on hampel s proposal such as s estimators

full rank and determinantal representation of the drazin inverse abstract in this article we introduce a full rank representation of the drazin inverse a d of a given complex matrix a which is based on an arbitrary full rank decomposition of a l l k where k is the index of a using this general representation we introduce a determinantal representation of the drazin inverse more precisely we represent elements of the drazin inverse a d as a fraction of two expressions involving minors of the order rank a k k ind a taken from the matrices a and rank invariant powers a l l k also we examine conditions for the existence of the drazin inverse for matrices whose elements are taken from an integral domain finally a few correlations between the minors of the drazin inverse a d powers of the drazin inverse and the minors of the matrix a k k ind a are explicitly derived

toward a general theory of information aggregation abstract information aggregation is a pervasive issue in the field of decision making in this paper we begin an attempt to develop a comprehensive theory of this process we investigate the use of a penalty function to help guide in the aggregation process it is suggested that an aggregated value which violates a given piece of data is charged a penalty the problem of aggregation can be seen as finding the aggregated value with the least penalty we show that logical inference systems are characterized by infinite penalty functions this implies that deviation from the data are not easily accepted probability theory is characterized by equal finite penalty costs nonmonotonic logics appear to be characterized by a case in which we have at least two different levels of penalties of differing magnitudes we discuss the relationship between the relevance or bearing a piece of data has on the problem and the penalty cost associated with it we see the central role of the intersection operation

breakdown robustness of tests abstract power and level breakdown functions of a test statistic are introduced to obtain a unified analysis of local stability as typified by the influence function and global stability as illustrated by the breakdown point the power breakdown function gives the amount of contamination of each alternative distribution that can carry the test statistic to a null value the level breakdown function gives the amount of contamination of a null distribution that can carry the test statistic to each value in the alternative space in many cases the breakdown function bears an inverse relationship to the maximum bias as a function of the contamination as the maximum bias is not invariant to one to one transformations however equivalent test statistics can have different scales for bias a distinct advantage of the inverse scale is the invariance of the breakdown functions to such transformations the resulting stability curves depend on the parameters in a way analogous to the power curve the slopes o

breakdown and groups the concept of breakdown point was introduced by hampel ph d dissertation 1968 univ california berkeley ann math statist 42 1971 1887 1896 and developed further by among others huber robust statistics 1981 wiley new york and donoho and huber in a festschrift for erich l lehmann 1983 157 184 wadsworth belmont ca it has proved most successful in the context of location scale and regression problems attempts to extend the concept to other situations have not met with general acceptance in this paper we argue that this is connected to the fact that in the location scale and regression problems the translation and affine groups give rise to a definition of equivariance for statistical functionals comparisons in terms of breakdown points seem only useful when restricted to equivariant functionals and even here the connection between breakdown and equivariance is a tenuous one institute of mathematical statistics 2005

robust estimation for arma models this paper introduces a new class of robust estimates for arma models they are m estimates but the residuals are computed so the effect of one outlier is limited to the period where it occurs these estimates are closely related to those based on a robust filter but they have two important advantages they are consistent and the asymptotic theory is tractable we perform a monte carlo where we show that these estimates compare favorably with respect to standard m estimates and to estimates based on a diagnostic procedure

qualitative robustness for stochastic processes in this paper we generalize hampel s concept of qualitative robustness of a sequence of estimators to the case of stochastic processes with non i i d observations defining appropriate metrics between samples we also present a different approach to qualitative robustness which formalizes the notion of resistance we give two definitions based on this approach strong and weak resistance we show that for estimating a finite dimensional real parameter pi robustness is equivalent to weak resistance and in the i i d case is also equivalent to strong resistance finally we prove the strong resistance of a class of estimators which includes common gm estimates for linear models and autoregressive processes

aggregation functions based on penalties this article studies a large class of averaging aggregation functions based on minimizing a distance from the vector of inputs or equivalently minimizing a penalty imposed for deviations of individual inputs from the aggregated value we provide a systematization of various types of penalty based aggregation functions and show how many special cases arise as the result we show how new aggregation functions can be constructed either analytically or numerically and provide many examples we establish connection with the maximum likelihood principle and present tools for averaging experimental noisy data with distinct noise distributions

lever aggregation operators we make use of the physical concept of lever to generalize well known operators based on weights all these operators can be understood as levers in equilibrium with weights masses located at the points in 0 1 that opinions represent

symbolic computation of weighted moore penrose inverse using partitioning method abstract we propose a method and algorithm for computing the weighted moore penrose inverse of one variable rational matrices continuing this idea we develop an algorithm for computing the weighted moore penrose inverse of one variable polynomial matrix these methods and algorithms are generalizations of the method for computing the weighted moore penrose inverse for constant matrices originated in wang and chen g r wang y l chen a recursive algorithm for computing the weighted moore penrose inverse a mn j comput math 4 1986 74 85 and the partitioning method for computing the moore penrose inverse of rational and polynomial matrices introduced in stanimirovic and tasic p s stanimirovic m b tasic partitioning method for rational and polynomial matrices appl math comput 155 2004 137 163 algorithms are implemented in the symbolic computational package mathematica

representation and approximation of the outer inverse at s 2 of a matrix a abstract in this paper we establish a basic representation and a representation theorem for the outer inverse a t s 2 of a matrix a which is the matrix x satisfying xax x r x t and n x s we develop several specific representations and iterative methods for a t s 2 we show that this representation includes many of the traditional generalized inverses and outer inverses and the relation of our results to these outer inverses will be explored

high breakdown point conditional dispersion estimation with application to s p 500 daily returns volatility we show that quasi maximum likelihood qml estimators for conditional dispersion models can be severely affected by a small number of outliers such as market crashes and rallies and we propose new estimation strategies the two stage hampel estimators and two stage s estimators resistant to the effects of outliers and study the properties of these estimators we apply our methods to estimate models of the conditional volatility of the daily returns of the s p 500 cash index series in contrast to qml estimators our proposed method resists outliers revealing an informative new picture of volatility dynamics during typical daily market activity

semiparametric robust estimation of truncated and censored regression models many estimation methods of truncated and censored regression models such as the maximum likelihood and symmetrically censored least squares scls are sensitive to outliers and data contamination as we document therefore we propose a semiparametric general trimmed estimator gte of truncated and censored regression which is highly robust but relatively imprecise to improve its performance we also propose data adaptive and one step trimmed estimators we derive the robust and asymptotic properties of all proposed estimators and show that the one step estimators e g one step scls are as robust as gte and are asymptotically equivalent to the original estimator e g scls the finite sample properties of existing and proposed estimators are studied by means of monte carlo simulations

comprehensive definitions of breakdown points for independent and dependent observations summary we provide a new definition of breakdown in finite samples with an extension to asymptotic breakdown previous definitions centre on defining a critical region for either the parameter or the objective function if for a particular outlier configuration the critical region is entered breakdown is said to occur in contrast with the traditional approach we leave the definition of the critical region implicit our proposal encompasses previous definitions of breakdown in linear and non linear regression settings in some cases it leads to a different and more intuitive notion of breakdown than other procedures that are available an important advantage of our new definition is that it also applies to models for dependent observations where current definitions of breakdown typically fail we illustrate our suggestion by using examples from linear and non linear regression and time series

computation of the inverse of a polynomial matrix and evaluation of its laurent expansion abstract an algorithm is given which constitutes a generalization of the algorithm for the inversion of a pencil se a due to mertzios 1984 in the case of general systems described in differential operator form recursive formulae are obtained for the calculation of both the coefficient matrices of the adjoint of the polynomial matrix as well as for the coefficients of the characteristic polynomial of the polynomial matrix a simple method is also presented that allows the evaluation of the laurent expansion for the inverse of a polynomial matrix of any order specifically an arma model is given for the computation of the coefficient matrices of the laurent expansion in terms of the coefficient matrices of the polynomial matrix without inverting the latter the laurent expansion of a polynomial matrix is used for the analysis and synthesis of the polynomial matrix descriptions that constitute a further generalization of the singular or generalized systems

a characterization and representation of the generalized inverse a 2 t s and its applications abstract this paper presents an explicit expression for the generalized inverse a 2 t s based on this we established the characterization the representation theorem and the limiting process for a 2 t s as an application we estimate the error bound of the iterative method for approximating a 2 t s

symbolic and recursive computation of different types of generalized inverses abstract we propose a method and algorithm for recursive computation of different classes of generalized inverses of a given one variable rational matrix and corresponding algorithm for polynomial matrix these methods and algorithms are generalizations of the method for computing the generalized inverses for constant matrices originated in f e udwadia r e kalaba a unified approach for the recursive determination of generalized inverses comp math appl 37 1999 125 130 and the partitioning method for computing the generalized inverses of rational and polynomial matrices introduced in p s stanimirovic m b tasic partitioning method for rational and polynomial matrices appl math comput 155 2004 137 163 m b tasic p s stanimirovic m d petkovic symbolic computation of weighted moore penrose inverse using partitioning method appl math comput 189 2007 615 640 algorithms are implemented in the symbolic computational package mathematica

full rank representation of generalized inverse at s 2 and its application in this paper we introduce a full rank representation of the generalized inverse a t s 2 of a given complex matrix a which is based on an arbitrary full rank decomposition of g where g is a matrix such that r g t and n g s using this representation we introduce the minor of the generalized inverse a t s 2 as a special case of the minor a determinantal representation of the generalized inverse a t s 2 is obtained as an application we use an example to demonstrate that this representation is correct

lower bounds for contamination bias globally minimax versus locally linear estimation we study how robust estimators can be in parametric families obtaining a lower bound on the contamination bias of an estimator that holds for a wide class of parametric families this lower bound includes as a special case the bound used to establish that the median is bias minimax among location equivariant estimators and it is tight or nearly tight in a variety of other settings such as scale estimation discrete exponential families and multiple linear regression the minimum variation distance estimator has contamination bias within a dimension free factor of this bound a second lower bound applies to locally linear estimates and implies that such estimates cannot be bias minimax among all fisher consistent estimates in higher dimensions in linear regression this class of estimates includes the familiar m estimates gm estimates and s estimates in discrete exponential families yet another lower bound implies that the proportion of zeros estimate has minimax bias if the median of the distribution is zero a common situation in some fields this bound also implies that the information standardized sensitivity of every fisher consistent estimate of the poisson mean and of the binomial proportion is unbounded

an improved method for the computation of the moore penrose inverse matrix abstract in this article we provide a fast computational method in order to calculate the moore penrose inverse of singular square matrices and of rectangular matrices the proposed method proves to be much faster and has significantly better accuracy than the already proposed methods while works for full and sparse matrices

partitioning method for rational and polynomial matrices we propose an extension of the grevile s partitioning method for computing the moore penrose inverse which is applicable to the set of rational matrices also we develop an algorithm for computing the moore penrose inverse of given one variable polynomial matrix which is based on the grevile s method major problems arising in the implementation of this method are repetitive recomputations of the same values and simplification of rational and polynomial expressions which contain unknown variable these algorithms are implemented in the symbolic computational package mathematica

on the definition of penalty functions in data aggregation abstract in this paper we point out several problems in the different definitions and related results of penalty functions found in the literature then we propose a new standard definition of penalty functions that overcomes such problems some results related to averaging aggregation functions in terms of penalty functions are presented as the characterization of averaging aggregation functions based on penalty functions some examples are shown as the penalty functions based on spread measures which happen to be continuous we also discuss the definition of quasi penalty functions in order to deal with non monotonic or weakly directionally monotonic averaging functions

breakdown in nonlinear regression abstract the breakdown point is considered an important measure of the robustness of a linear regression estimator this article addresses the concept of breakdown in nonlinear regression because it is not invariant to nonlinear reparameterization the usual definition of the breakdown point in linear regression is inadequate for nonlinear regression the original definition of breakdown due to hampel is more suitable for nonlinear problems but may indicate breakdown when the fitted values change very little we introduce breakdown functions which measure breakdown of the fitted values using the breakdown functions we introduce a new definition of the breakdown point for the linear regression model our definition of the breakdown point coincides with the usual definition for linear regression as well as with hampel s definition for most nonlinear regression functions we show that the breakdown point of the least squares estimator is 1 n we prove that for a large class of unbounded regression func

breakdown properties of location m estimators in this article we consider the asymptotic behavior of three kinds of sample breakdown points it is shown that for the location m estimator with bounded objective function both the addition sample breakdown point and the simplified replacement sample breakdown point strongly converge to the gross error asymptotic breakdown point whereas the replacement sample breakdown point strongly converges to a smaller value in addition it is proved that under some regularity conditions these sample breakdown points are asymptotically normal the addition sample breakdown point has a smaller asymptotic variance than the simplified replacement sample breakdown point for the commonly used redescending m estimators of location numerical results indicate that among the three kinds of sample breakdown points the replacement sample breakdown point has the largest asymptotic variance

generalized mixture operators using weighting functions a comparative study with wa and owa abstract in the context of multiple attribute decision making we present an aggregation scheme based on generalized mixture operators using weighting functions and we compare it with two standard aggregation methods weighted averaging and ordered weighted averaging specifically we consider linear and quadratic weight generating functions that penalize bad attribute performances and reward good attribute performances an illustrative example borrowed from the literature is used to perform the operators comparison we believe that this comparative study will highlight the potential and flexibility of generalized mixture operators using weighting functions that depend on attribute performances

effective partitioning method for computing weighted moore penrose inverse we introduce a method and an algorithm for computing the weighted moore penrose inverse of multiple variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices these methods and algorithms are generalizations of algorithms developed in m b tasic p s stanimirovic m d petkovic symbolic computation of weighted moore penrose inverse using partitioning method appl math comput 189 2007 615 640 to multiple variable rational and polynomial matrices and improvements of these algorithms on sparse matrices also these methods are generalizations of the partitioning method for computing the moore penrose inverse of rational and polynomial matrices introduced in p s stanimirovic m b tasic partitioning method for rational and polynomial matrices appl math comput 155 2004 137 163 m d petkovic p s stanimirovic symbolic computation of the moore penrose inverse using partitioning method internat j comput math 82 2005 355 367 to the case of weighted moore penrose inverse algorithms are implemented in the symbolic computational package mathematica

deviation based aggregation functions abstract based on the original idea of daroczy deviation functions expressing the deviation of two real values x and y are generalized into basic moderate deviation functions subsequently a new type of deviation based aggregation function is introduced studied and exemplified our approach generalizes among others several types of mixture operators and can be seen as an alternative to penalty based constructions of aggregation functions

robust variable selection in semiparametric mean covariance regression for longitudinal data analysis this paper considers robust semiparametric smooth threshold generalized estimating equations for the analysis of longitudinal data based on the modified cholesky decomposition and b spline approximations the proposed method can automatically eliminate inactive predictors by setting the corresponding parameters to be zero and simultaneously estimate the mean regression coefficients generalized autoregressive coefficients and innovation variances in order to overcome the outliers in either the response or and the covariate domain we use a bounded score function and leverage based weights to achieve better robustness moreover the proposed estimators have desired large sample properties including consistency and oracle property finally monte carlo simulation studies are conducted to investigate the robustness and efficiency of the proposed method under different contaminations

symbolic computation of at s 2 inverses using qdr factorization abstract efficient evaluation of the full rank qdr decomposition is established a method and algorithm for efficient symbolic computation of a t s 2 inverses of a given rational matrix a is defined using the full rank qdr decomposition of an appropriate rational matrix w the algorithm is implemented using mathematica s ability to deal with symbolic expressions as well as with numbers examples including polynomial and rational matrices are presented some comparisons with well known methods for symbolic evaluation of generalized inverses are obtained

aggregation with generalized mixture operators using weighting functions this paper regards weighted aggregation operators in multiple attribute decision making and its main goal is to investigate ways in which weights can depend on the satisfaction degrees of the various attributes criteria we propose and discuss two types of weighting functions that penalize poorly satisfied attributes and reward well satisfied attributes we discuss in detail the characteristics and properties of both functions moreover we present an illustrative example to clarify the use and behaviour of such weighting functions comparing the results with those of standard weighted averaging operators

the generalized bott duffin inverse and its applications abstract the generalized bott duffin inverse a l of a with respect to a subspace l is defined and by means of it a unified treatment of a class of linear systems and extreme value problems with equality constraints is given

breakdown points for maximum likelihood estimators of location scale mixtures ml estimation based on mixtures of normal distributions is a widely used tool for cluster analysis however a single outlier can make the parameter estimation of at least one of the mixture components break down among others the estimation of mixtures of t distributions by mclachlan and peel finite mixture models 2000 wiley new york and the addition of a further mixture component accounting for noise by fraley and raftery the computer j 41 1998 578 588 were suggested as more robust alternatives in this paper the definition of an adequate robustness measure for cluster analysis is discussed and bounds for the breakdown points of the mentioned methods are given it turns out that the two alternatives while adding stability in the presence of outliers of moderate size do not possess a substantially better breakdown behavior than estimation based on normal mixtures if the number of clusters s is treated as fixed r additional points suffice for all three methods to let the parameters of r clusters explode only in the case of r s is this not possible for t mixtures the ability to estimate the number of mixture components for example by use of the bayesian information criterion of schwarz ann statist 6 1978 461 464 and to isolate gross outliers as clusters of one point is crucial for an improved breakdown behavior of all three techniques furthermore a mixture of normals with an improper uniform distribution is proposed to achieve more robustness in the case of a fixed number of components