migrative uninorms and nullnorms over t norms and t conorms in this paper the notions of migrative uninorms and nullnorms over a fixed t norm t and over a fixed t conorm s are introduced and studied all cases when the uninorm u lies in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations of u and t and for all possible combinations of u and s a similar study is done for nullnorms

quasi and pseudo inverses of monotone functions and the construction of t norms abstract several properties of quasi and pseudo inverses of a non decreasing real function are discussed based on a result of schweizer and sklar for a given triangular norm t and non decreasing function f a construction method leading to a commutative fully ordered semigroup on the unit interval is given a similar construction based on the pseudo inverse implies that the resulting operation will be bounded from above by the minimum but then the associativity may be violated several sufficient conditions for constructing new t norms from a given one and a non decreasing function f based on its quasi inverses and on its pseudo inverse respectively are discussed together with illustrative examples

fitting regression models to case control data by maximum likelihood summary we consider fitting categorical regression models to data obtained by either stratified or nonstratified case control or response selective sampling from a finite population with known population totals in each response category with certain models such as the logistic with appropriate constant terms a method variously known as conditional maximum likelihood breslow cain 1988 or pseudo conditional likelihood wild 1991 which involves the prospective fitting of a pseudo model results in maximum likelihood estimates of case control data we extend these results by showing the maximum likelihood estimates for any model can be found by iterating this process with a simple updating of offset parameters attention is also paid to estimation of the asymptotic covariance matrix one benefit of the results of this paper is the ability to obtain maximum likelihood estimates of the parameters of logistic models for stratified case control studies compare breslow cain 1988 scott wild 1991 using an ordinary logistic regression program even when the stratum constants are modelled

associative monotonic operations in fuzzy set theory abstract the properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets on fuzzy numbers and on fuzzy probabilistic sets

new algorithms for euclidean distance transformation of an n dimensional digitized picture with applications abstract in this paper we propose a new method to obtain the euclidean distance transformation and the voronoi diagram based on the exact euclidean metric for an n dimensional picture we present four algorithms to perform the transformation which are constructed by the serial composition of n dimensional filters when performed by a general purpose computer they are faster than the method by h yamada for a two dimensional picture those algorithms require only one n dimensional array for storing input output pictures and a single one dimensional array for a work area if an input picture needs not be preserved

a linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions a sequential algorithm is presented for computing the exact euclidean distance transform dt of a k dimensional binary image in time linear in the total number of voxels n the algorithm which is based on dimensionality reduction and partial voronoi diagram construction can be used for computing the dt for a wide class of distance functions including the l sub p and chamfer metrics at each dimension level the dt is computed by constructing the intersection of the voronoi diagram whose sites are the feature voxels with each row of the image this construction is performed efficiently by using the dt in the next lower dimension the correctness and linear time complexity are demonstrated analytically and verified experimentally the algorithm may be of practical value since it is relatively simple and easy to implement and it is relatively fast not only does it run in o n time but the time constant is small a simple modification of the algorithm computes the weighted euclidean dt which is useful for images with anisotropic voxel dimensions a parallel version of the algorithm runs in o n p time with p processors

sequentially additive nonignorable missing data modelling using auxiliary marginal information summarywe study a class of missingness mechanisms referred to as sequentially additive nonignorable for modelling multivariate data with item nonresponse these mechanisms explicitly allow the probability of nonresponse for each variable to depend on the value of that variable thereby representing nonignorable missingness mechanisms these missing data models are identified by making use of auxiliary information on marginal distributions such as marginal probabilities for multivariate categorical variables or moments for numeric variables we prove identification results and illustrate the use of these mechanisms in an application

maximum likelihood estimation of logistic regression parameters under two phase outcome dependent sampling summary outcome dependent sampling increases the efficiency of studies of rare outcomes examples being case control studies in epidemiology and choice based sampling in econometrics two phase or double sampling is a standard technique for drawing efficient stratified samples we develop maximum likelihood estimation of logistic regression coefficients for a hybrid two phase outcome dependent sampling design an algorithm is given for determining the estimates by repeated fitting of ordinary logistic regression models simulation results demonstrate the efficiency loss associated with alternative pseudolikelihood and weighted likelihood methods for certain data configurations these results provide an efficient solution to the measurement error problem with validation sampling based on a discrete surrogate

on the structure of special classes of uninorms in this paper the concept of the reidemeister closure condition is adopted in order to characterize associativity of uninorms with a special attention paid to the class of representable uninorms thus conditions replacing the associativity requirement for such uninorms are given further the attention is focused on the uninorms where the underlying t norm and t conorm are idempotent or induce an involutive negator based on the aforementioned results the structure of these classes of uninorms is fully described

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

discrete aggregation operators with annihilator abstract mas et al have investigated a special kind of commutative and associative aggregation operators with annihilator on the unit interval 0 1 which includes s uninorms s nullnorms t uninorms t nullnorms bi uninorms and bi nullnorms this paper is devoted to extending this kind of operators from the unit interval 0 1 to a finite chain a characterization of this kind of operators on a finite chain is given including some examples this class of operators can be viewed as a generalization of both uninorms and nullnorms on a finite chain

the distributive equations for idempotent uninorms and nullnorms the distributive equations only involving idempotent uninorms and nullnorms are investigated the following two cases are proved i as for a nullnorm with an idempotent uninorm having distributivity the necessary and sufficient conditions are given ii as for an idempotent uninorm with a nullnorm having distributivity the necessary and sufficient conditions are given also

uninorms on bounded lattices we study uninorms on bounded lattices we show the existence of uninorms with the neutral element which is different from the top element and the bottom element using the fact that the t norms and t conorms on arbitrary lattice l always exist as a by product we give a method of constructing uninorms using this method we obtain also the smallest uninorm and the greatest uninorm with a given neutral element e

a unified approach to regression analysis under double sampling designs we propose a unified approach to the estimation of regression parameters under double sampling designs in which a primary sample consisting of data on the rough or proxy measures for the response and or explanatory variables as well as a validation subsample consisting of data on the exact measurements are available we assume that the validation sample is a simple random subsample from the primary sample our proposal utilizes a specific parametric model to extract the partial information contained in the primary sample the resulting estimator is consistent even if such a model is misspecified and it achieves higher asymptotic efficiency than the estimator based only on the validation data specific cases are discussed to illustrate the application of the estimator proposed

a model calibration approach to using complete auxiliary information from survey data suppose that the finite population consists of n identifiable units associated with the ith unit are the study variable yi and a vector of auxiliary variables xi the values x1 x2 xn are known for the entire population i e complete but yi is known only if the ith unit is selected in the sample one of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage in this article a unified model assisted framework has been attempted using a proposed model calibration technique the proposed model calibration estimators can handle any linear or nonlinear working models and reduce to the conventional calibration estimators of deville and sarndal and or the generalized regression estimators in the linear model case the pseudoempirical maximum likelihood estimator of chen and sitter when used in this setting gives an estimator that is asymptotically equivalent to the model calibration estimator but with positive weights some existing estimators

weighted ordinal means the concept of weighted ordinal arithmetic means and other related weighted ordinal means is studied based on the relevant results on the scale 0 1 new types of weighted ordinal means are proposed in some cases these ordinal means coincide with those proposed by godo and torra but not in the case when ordinal means introduced by them are not idempotent based on divisible ordinal t conorms and modifying the approach of godo and torra we show how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t conorms on 0 1 and divisible ordinal t conorms

on the distributivity of uninorms over nullnorms this paper investigates the functional equation of distributivity of uninorms over nullnorms we consider the case where the uninorm is continuous in 0 1 2 or is representable it has been proved that the absorbing element of the nullnorm is an idempotent element of the uninorm if the distributive equation holds and then combining the structures of the uninorm and the nullnorm we give the characterization of the pair of the functions of the uninorm and the nullnorm moreover when the nullnorm is continuous we obtain the sufficient and necessary conditions under which the distributive equation holds

convex combinations in terms of triangular norms a characterization of idempotent bisymmetrical and self dual compensatory operators it is observed that most of the well known compensatory operators are defined in terms of convex transformations of the values of triangular norms and conorms or other operators in this paper the characterization and the applicability of parametrized operators constructed again in terms of triangular norms and conorms but as transformations of their arguments are studied it turns out that these operators are closely related to the ordinary convex combination moreover when idempotency is required these operators can be characterized algebraically as bisymmetrical and self dual operators that satisfy the cancellation law

on migrativity property for uninorms recently u 0 migrative uninorms u were introduced and discussed where u and u 0 are two uninorms with neutral element e in this paper we will further study u 2 migrative uninorms u 1 where u 1 and u 2 are two uninorms with different neutral elements e 1 and e 2 respectively all cases when the uninorm u 1 and u 2 are in different families out of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for some possible combinations of u 1 and u 2

linear time euclidean distance transform algorithms two linear time and hence asymptotically optimal algorithms for computing the euclidean distance transform of a two dimensional binary image are presented the algorithms are based on the construction and regular sampling of the voronoi diagram whose sites consist of the unit feature pixels in the image the first algorithm which is of primarily theoretical interest constructs the complete voronoi diagram the second more practical algorithm constructs the voronoi diagram where it intersects the horizontal lines passing through the image pixel centers extensions to higher dimensional images and to other distance functions are also discussed

level dependent sugeno integral in this paper a new concept of level dependent sugeno integral is introduced and it is used to represent comonotone maxitive aggregation functions acting on a complete scale k the relationship between the level dependent sugeno integral and some other types of fuzzy integrals is shown and properties of the level dependent sugeno integral are discussed several examples show that the level dependent sugeno integral can have different aggregation attitudes for low input values than for high input values and thus overcome problems that arise while using the sugeno integral

generalized integration model for improved statistical inference by leveraging external summary data summarymeta analysis has become a powerful tool for improving inference by gathering evidence from multiple sources it pools summary level data from different studies to improve estimation efficiency with the assumption that all participating studies are analysed under the same statistical model it is challenging to integrate external summary data calculated from different models with a newly conducted internal study in which individual level data are collected we develop a novel statistical inference framework that can effectively synthesize internal and external data for the integrative analysis the new framework is versatile enough to assimilate various types of summary data from multiple sources we establish asymptotic properties for the proposed procedure and prove that the new estimate is theoretically more efficient than the internal data based maximum likelihood estimate as well as a recently developed constrained maximum likelihood approach that incorporates the external information we illustrate an application of our method by evaluating cervical cancer risk using data from a large cervical screening program

on locally internal monotonic operations this paper deals with monotonic binary operations f 0 1 2 0 1 with the property called locally internal property that the value at any point x y is always one of its arguments x y after stating a theorem that characterizes this kind of operations some special cases are studied in detail by considering additional properties of the operation commutativity existence of a neutral element and associativity in case of locally internal associative monotonic operations with neutral element a characterization theorem gives an improvement of a well known theorem of czogala and drewniak on idempotent associative and increasing operations with neutral element as well as an improvement of a characterization theorem for left and right continuous idempotent uninorms

on distributivity equations for uninorms over semi t operators recently dryga generalized nullnorms and t operators and introduced semi t operators by eliminating commutativity from the axioms of t operators distributivity equations were investigated in families of certain operations e g triangular norms conorms uninorms and nullnorms or called t operators in this paper we give out the solutions of distributivity equations for uninorms over semi t operators previous results about distributivity equations for uninorms over nullnorms can be obtained as corollaries

the modularity condition for uninorms revisited abstract functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory the modularity equation is a kind of restricted general associative equations in the literature the already known results concerning the modularity equation for two uninorms are based on the assumption that both uninorms lie in one of the most studied classes of uninorms in this study we explore the modularity equation involving uninorms in a most general setting specifically we investigate the modularity between two uninorms in the cases when one uninorm belongs to any of the most studied classes of uninorms but the other one is any uninorm with no further assumptions further many new solutions appear from this new point of view that were not included in previous approaches

transfer stable aggregation functions on finite lattices abstract the paper by z kurac 2019 deals with a new property the so called transfer stability characterizing the arithmetic mean with this property it is possible to define special forms of arithmetic mean on finite chains the idempotence property was required for this definition in this paper we neglect this necessity and deal only with transfer stable aggregation functions thanks to this fact it is possible to define these aggregation functions on any finite lattice hereinafter lattice and not only on finite chains transfer stable aggregation functions can be defined on any finite lattice nevertheless there is a subclass of finite lattices the so called transfer stable lattices where the behavior of the transfer stable aggregation functions is simply described because the transfer stability classes are linearly ordered therefore the main goal of this paper is characterization of these transfer stable lattices the second half of the paper deals with some useful properties associated with the lattice of all k ary transfer stable aggregation functions

uninorms on bounded lattices constructed by t norms and t subconorms abstract the construction of uninorms on bounded lattices has been a attractive research area in this paper we introduce some new classes of uninorms on bounded lattices via t subnorms and t subconorms with a neutral element e under some constraints we also give some illustrative examples to help understand the structure of these new uninorms moreover we provide an answer to the open problem raised by cayli in 2019 finally the differences between our methods and existing approaches are assessed

regression for ordinal variables without underlying continuous variables several techniques exist nowadays for continuous i e numerical data analysis and modeling however although part of the information gathered by companies statistical offices and other institutions is numerical a large part of it is represented using categorical variables in ordinal or nominal scales techniques for model building on categorical data are required to take advantage of such a wealth of information in this paper current approaches to regression for ordinal data are reviewed and a new proposal is described which has the advantage of not assuming any latent continuous variable underlying the dependent ordinal variable estimation in the new approach can be implemented using genetic algorithms an artificial example is presented to illustrate the feasibility of the proposal

a characterization of a class of uninorms with continuous underlying operators in this paper all uninorms locally internal in the region a e given by the complement in 0 1 2 of 0 e 2 e 1 2 where e is the neutral element of the uninorm having continuous underlying operators are studied and characterized by distinguishing some cases when the underlying t norm and t conorm are not given by ordinal sums it is proved that uninorms locally internal in a e are in fact all possible uninorms with these underlying operators except when both the t norm and the t conorm are strict in which case there is also the class of representable uninorms leading to a finite number of possibilities when at least one of the continuous underlying operators is given by an ordinal sum again there are other possible uninorms than those that are locally internal in a e but all uninorms with this property are also characterized in this case infinitely many possibilities can appear depending on the set of idempotent elements of the uninorm

fast distance transformation on irregular two dimensional grids in this article we propose a new fast algorithm to compute the squared euclidean distance transform e 2dt on every two dimensional 2 d irregular isothetic grids regular square grids quadtree based grids etc our new fast algorithm is an extension of the e 2dt method proposed by breu et al 3 it is based on the implicit order of the cells in the grid and builds a partial voronoi diagram of the centers of background cells thanks to a data structure of lists we compare the execution time of our method with the ones of others approaches we developed in previous works in those experiments we consider various kinds of classical 2 d grids in imagery to show the interest of our methodology and to point out its robustness we also show that our method may be interesting regarding an application where we extract an adaptive medial axis construction based on a quadtree decomposition scheme

a characterization of discrete uninorms having smooth underlying operators in this paper discrete uninorms u such that their underlying t norm t and t conorm s are smooth are characterized the different cases combining when t is the minimum or the ukasiewicz t norm and s is the maximum or the ukasiewicz t conorm are given separately and the number of discrete uninorms with these underlying operators is given the same is done for the general case when t and or s are smooth but ordinal sums

visual characterization of associative quasitrivial nondecreasing operations on finite chains abstract in this paper we provide visual characterization of associative quasitrivial nondecreasing operations on finite chains we also provide a characterization of bisymmetric quasitrivial nondecreasing binary operations on finite chains finally we estimate the number of operations belonging to the previous classes

a new linguistic computational model based on discrete fuzzy numbers for computing with words in recent years several different linguistic computational models for dealing with linguistic information in processes of computing with words have been proposed however until now all of them rely on the special semantics of the linguistic terms usually fuzzy numbers in the unit interval and the linguistic aggregation operators are based on aggregation operators in 0 1 in this paper a linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is presented ensuring the accuracy and consistency of the model in this framework no underlying membership functions are needed and several aggregation operators defined on the set of all discrete fuzzy numbers are presented these aggregation operators are constructed from aggregation operators defined on a finite chain in accordance with the granularity of the linguistic term set finally an example of a multi expert decision making problem in a hierarchical multi granular linguistic context is given to illustrate the applicability of the proposed method and its advantages

transfer stable means on finite chains abstract according to 5 the arithmetic mean is a function characterized by four features it is non decreasing idempotent symmetric and additive the first three of them can be naturally converted to the theory of posets but the last one generally can not due to this problem we will replace it with another suitable property which is called transfer stability however we do not get the exact arithmetic mean but some approximation these functions will be called transfer stable means the first aim of the paper is to show that transfer stable means on a finite chain form a lattice which is isomorphic to the direct power of a finite chain the second goal is to create a generating set of transfer stable means i e means that can generate all other transfer stable means of the same arity by classical composition of functions the last goal deals with question of how to generate all transfer stable means of any arity by binary transfer stable means only for this problem we define special transfer stable means composition

c sets of n uninorms the concept of n uninorms was introduced in our earlier paper which is based on the existence of an n neutral element for an associative monotone non decreasing in both variables and commutative amc binary operator on 0 1 there it was shown that the number of subclasses of n uninorms is the n 1 th catalan number an expression for the arbitrary member of each subclass was also given which is recursive in nature in this paper we introduce a unique ordered set of distinct integers between 0 and n called c sets for each subclass of n uninorms this enables us to 1 obtain an expression for arbitrary member of each subclass which is non recursive in nature 2 identify the minimum and the maximum members in general and of idempotent members in particular in each subclass 3 relate c sets of de morgan pairs for strict negation of n uninorms from different subclasses 4 convert theoretical results into construction procedures which are algorithmic in nature in process we generalize some of the existing results for uninorms in the literature

smooth t subnorms on finite scales in this work smooth t subnorms and boundary weak t norms bwt norms defined on a finite chain are studied in the smooth case it is proved that smooth bwt norms reduces to smooth t norms whereas a classification of smooth t subnorms as ordinal sums of a smooth t norm and an archimedean smooth t subnorm is proved in a similar way as in the case of 0 1 with respect to archimedean smooth t subnorms some cases depending on their zero region are considered classifying all of them in some cases and some specific families in others

kernel aggregation functions on finite scales constructions from their marginals abstract the study of discrete aggregation functions those defined on a finite chain with some kind of smoothness has been extensively developed in last years many different kinds of aggregation functions have been characterized in this context in this paper discrete aggregation functions with the kernel property which implies the smoothness property are investigated some properties and characterizations as well as some construction methods for this kind of discrete aggregation functions are studied it is also investigated when the marginal functions of a discrete kernel aggregation function fully determine it

semiparametric methods for response selective and missing data problems in regression summary suppose that data are generated according to the model f ylx 0 g x where y is a response and x are covariates we derive and compare semiparametric likelihood and pseudolikelihood methods for estimating 0 for situations in which units generated are not fully observed and in which it is impossible or undesirable to model the covariate distribution the probability that a unit is fully observed may depend on y and there may be a subset of covariates which is observed only for a subsample of individuals our key assumptions are that the probability that a unit has missing data depends only on which of a finite number of strata that y x belongs to and that the stratum membership is observed for every unit applications include case control studies in epidemiology field reliability studies and broad classes of missing data and measurement error problems our results make fully efficient estimation of 0 feasible and they generalize and provide insight into a variety of methods that have been proposed for specific problems

characterizing set valued functions of uninorms with continuous underlying t norm and t conorm abstract the uninorms with continuous underlying functions were characterized by their set of discontinuity points in the previous work of the author using the characterizing set valued function in this paper properties of this characterizing set valued function are studied it is shown that the type of the monotonicity of such a set valued function is always changed in idempotent points of the corresponding uninorm several additional properties of the characterizing set valued function of a uninorm with continuous underlying functions are shown and an example is included results shown in this paper are used for a complete characterization of uninorms with continuous underlying functions via the ordinal sum construction which is shown in the consecutive paper

the distributivity equation for uninorms revisited abstract the distributivity equation has been widely studied involving different classes of aggregation functions from t norms and t conorms to uninorms nullnorms and generalizations of them it is important in the framework of logical connectives because of its applications in fuzzy logic and approximate reasoning as well as in image processing since uninorms have been used in these topics the study of the distributivity between two uninorms becomes specially interesting in a recent paper by the same authors the already known solutions were compiled and completed when the first uninorm is in any of the most studied classes of uninorms and the second uninorm is anyone in this paper we want to achieve this study by focusing on the reverse direction that is for the cases when the second uninorm lies in any of the most studied classes of uninorms and the first one is any uninorm we show along the paper that this new point of view leads to many new solutions

optimal separable algorithms to compute the reverse euclidean distance transformation and discrete medial axis in arbitrary dimension in binary images the distance transformation dt and the geometrical skeleton extraction are classic tools for shape analysis in this paper we present time optimal algorithms to solve the reverse euclidean distance transformation and the reversible medial axis extraction problems for d dimensional images we also present a d dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape

on properties of uninorms locally internal on the boundary abstract recently a class of uninorms locally internal on the boundary was proposed by mas et al during the study of the migrativity property for uninorms in this paper some properties of this class of uninorms are presented and the characterizations are obtained for different cases

copula like operations on finite settings this paper deals with discrete copulas considered as a class of binary aggregation operators on a finite chain a representation theorem by means of permutation matrices is given from this characterization we study the structure of associative discrete copulas and a theorem of decomposition of any discrete copula in terms of associative discrete copulas is obtained finally some aspects concerning their extension to copulas are dealt with

an extension of the migrative property for uninorms in this paper the notion of a migrative uninorms over a fixed uninorm u 0 with the same neutral element is introduced all uninorms u that are a migrative over a uninorm u 0 are studied all cases when u and u 0 have continuous underlying operations and belong to any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations

properties of uninorms with the underlying operations given as ordinal sums abstract uninorms as mixed aggregation operations on the unit interval have been widely used as logical connectives in fuzzy set theory this paper presents some properties of uninorms for which the underlying operations are given as ordinal sums specially we present the relations between two arbitrary summands and the value on cartesian product of their underlying intervals one in 0 e and the other in e 1 where e is neutral element of the uninorm whose results bring us a step closer to the structure of uninorms that have continuous underlying operations as a byproduct we characterize several special classes of uninorms that are different from the well studied classes of uninorms

using discrete fuzzy numbers in the aggregation of incomplete qualitative information in this article discrete fuzzy numbers are used to model complete and incomplete qualitative information and some methods to aggregate this kind of information are proposed when the support of discrete fuzzy numbers is a closed interval of the chain l n 0 1 n they can be interpreted as linguistic expert valuations that increase the flexibility of the elicitation of qualitative information based on linguistic terms on the other hand when the support is not an interval of l n the corresponding discrete fuzzy number can be interpreted as an incomplete linguistic expert valuation in order to aggregate this kind of information we propose two different methods one of them deals with the construction of aggregation functions on the set of discrete fuzzy numbers from discrete aggregation functions defined on l n the other one presents several procedures for estimating the missing information based on the so called discrete associations finally the proposed aggregation methods are used in a multi expert decision making problem and a concrete example is given

aggregation of subjective evaluations based on discrete fuzzy numbers in this paper aggregation functions defined on the set of all discrete fuzzy numbers whose support is a subset of consecutive natural numbers are introduced and the particular cases of uninorms and nullnorms are studied in detail these aggregation functions are constructed from discrete aggregation functions defined on a finite chain and they are applied to the aggregation of subjective evaluations

benchmarking small area estimators this paper considers benchmarking issues in the context of small area estimation we find optimal estimators within the class of benchmarked linear estimators under linear constraints this extends existing results for external and internal benchmarking and also links the two necessary and sufficient conditions for self benchmarking are found for an augmented model most results of this paper are found using ideas of orthogonal projection copyright 2013 oxford university press

the distributivity equations for semi t operators over uninorms recently the distributivity equation was discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms or called t operators in this paper we describe the solutions of distributivity for semi t operators over uninorms previous results about distributivity for nullnorms over uninorms can be obtained as a corollary

aggregation under uncertainty basic uncertain information bui in the form langle x c rangle where x in 0 1 is an observed datum and c in 0 1 is its reliability is discussed and studied the concept of bui s aggregation is introduced and some construction methods are proposed and exemplified the connection with interval valued data and their aggregation is also discussed

finding a minimum medial axis of a discrete shape is np hard the medial axis is a classical representation of digital objects widely used in many applications however such a set of balls may not be optimal subsets of the medial axis may exist without changing the reversivility of the input shape representation in this article we first prove that finding a minimum medial axis is an np hard problem for the euclidean distance then we compare two algorithms which compute an approximation of the minimum medial axis one of them providing bounded approximation results

aggregation functions on the set of discrete fuzzy numbers defined from a pair of discrete aggregations abstract in this paper we propose a method to construct aggregation functions on the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers from a couple of discrete aggregation functions the interest on these discrete fuzzy numbers lies on the fact that they can be interpreted as linguistic expert valuations that increase the flexibility of the elicitation of qualitative information based on linguistic terms finally a linguistic decision making model based on a pair of aggregation functions defined on discrete fuzzy numbers is given

miscellanea combining parametric and empirical likelihoods imbens lancaster 1994 pointed out that census reports can be interpreted as providing nearly exact knowledge of moments of the marginal distribution of economic variables in this paper we show that empirical likelihood can effectively incorporate auxiliary information like this as long as it can be summarised as unbiased estimating equations by combining empirical and parametric likelihoods we show that the combined likelihood can produce valid inferences for the underlying parameters a wilks type theorem is proved for the combined likelihood ratio statistic simulation results demonstrate that the performance of the combined likelihood ratio confidence intervals is better than conventional confidence intervals that use a normal approximation

characterizations of idempotent discrete uninorms in this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only conservativeness symmetry and nondecreasing monotonicity we also provide an alternative characterization involving the bisymmetry property finally we provide a graphical characterization of these operations in terms of their contour plots and we mention a few open questions for further research

a semiparametric mixture approach to case control studies with errors in covariables abstract methods are devised for estimating the parameters of a prospective logistic model in a case control study with dichotomous response d that depends on a covariate x for a portion of the sample both the gold standard x and a surrogate covariate w are available however for the greater portion of the data only the surrogate covariate w is available by using a mixture model the relationship between the true covariate and the response can be modeled appropriately for both types of data the likelihood depends on the marginal distribution of x and the measurement error density w x d the latter is modeled parametrically based on the validation sample the marginal distribution of the true covariate is modeled using a nonparametric mixture distribution in this way we can improve the efficiency and reduce the bias of the parameter estimates the results also apply when there is no validation data provided the error distribution is known or estimated from an independent data source many of the

generalized meta analysis for multiple regression models across studies with disparate covariate information meta analysis is widely popular for synthesizing information on common parameters of interest across multiple studies because of its logistical convenience and statistical efficiency we develop a generalized meta analysis approach to combining information on multivariate regression parameters across multiple studies that have varying levels of covariate information using algebraic relationships among regression parameters in different dimensions we specify a set of moment equations for estimating parameters of a maximal model through information available from sets of parameter estimates for a series of reduced models from the different studies the specification of the equations requires a reference dataset for estimating the joint distribution of the covariates we propose to solve these equations using the generalized method of moments approach with the optimal weighting of the equations taking into account uncertainty associated with estimates of the parameters of the reduced models we describe extensions of the iterated reweighted least squares algorithm for fitting generalized linear regression models using the proposed framework based on the same moment equations we also develop a diagnostic test for detecting violations of underlying model assumptions such as those arising from heterogeneity in the underlying study populations the proposed methods are illustrated with extensive simulation studies and a real data example involving the development of a breast cancer risk prediction model using disparate risk factor information from multiple studies

regranulation a granular algorithm enabling communication between granular worlds abstract in this paper we describe a granular algorithm for translating information between two granular worlds represented as fuzzy rulebases these granular worlds are defined on the same universe of discourse but employ different granulations of this universe in order to translate information from one granular world to the other we must regranulate the information so that it matches the information granularity of the target world this is accomplished through the use of a first order interpolation algorithm implemented using linguistic arithmetic a set of elementary granular computing operations we first demonstrate this algorithm by studying the common fuzzy pd rulebase at several different granularities and conclude that the 3 3 granulation may be too coarse for this objective we then examine the question of what the natural granularity of a system might be this is studied through a 10 fold cross validation experiment involving three different granulations of the same underlying mapping for the problem under consideration we find that a 7 7 granulation appears to be the minimum necessary precision

a measure of variance for hierarchical nominal attributes the need for measuring the dispersion of nominal categorical attributes appears in several applications like clustering or data anonymization for a nominal attribute whose categories can be hierarchically classified a measure of the variance of a sample drawn from that attribute is proposed which takes the attribute s hierarchy into account the new measure is the reciprocal of consanguinity the less related the nominal categories in the sample the higher the measured variance for non hierarchical nominal attributes the proposed measure yields results consistent with previous diversity indicators applications of the new nominal variance measure to economic diversity measurement and data anonymization are also discussed

characterizing autodistributive aggregation operations defined on finite linearly ordered scales abstract observe that for continuous strictly increasing binary means defined on a unit interval autodistributivity and bisymmetry are equivalent bisymmetric aggregation operations defined on finite linearly ordered scales have been studied in the past and their behavior is unlike that of corresponding operations defined on the unit interval 0 1 this paper investigates two families of autodistributive aggregation operations defined on finite linearly ordered scales one with a neutral element and the other under some partial smoothness related conditions the former is fully described as the family of idempotent uninorms and the latter is completely characterized as the family of idempotent t operators through these results we can deduce that compared with bisymmetry autodistributivity is much stronger and the behavior of autodistributive aggregation operations defined on finite linearly ordered scales is significantly different from that of corresponding operations defined on 0 1

migrativity property for uninorms and semi t operators in this paper the notions of migrative uninorms over semi t operators and migrative semi t operators over uninorms are introduced and investigated all solutions of the migrativity equations for all possible combinations of semi t operators and uninorms are characterized

calibration estimators in survey sampling abstract this article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information estimation is equivalent to attaching weights to the survey data we focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations we briefly mention an application to the case in which the information consists of known marginal counts in a two or multi way table known as generalized raking the general regression estimator greg was conceived with multivariate auxiliary information in mind ordinarily this estimator is justified by a regression relationship between the study variable y and the auxiliary vector x but we note that the greg can be derived by a different route by focusing instead on the weights the ordinary sampling weights of the kth observation is 1 k where k is the inclusion probabilit

distributivity and conditional distributivity of a uninorm and a continuous t conorm the open problem recalled by klement in the linz2000 closing session related to distributivity and conditional distributivity of a uninorm and a continuous t conorm is solved for the most usual known classes of uninorms from the obtained results it is deduced that distributivity and conditional distributivity are equivalent for these cases it is remarkable that solutions appear involving not only strict t conorms but also ordinal sums of the maximum with a strict t conorm conversely the distributivity of a t conorm over a uninorm is also studied leading only to already known solutions moreover the dual case of distributivity and conditional distributivity involving uninorms and continuous t norms is also solved proving again the equivalence of both kinds of distributivities

using covariate specific disease prevalence information to increase the power of case control studies public registration databases and large cohort studies provide vital information on disease prevalence at various levels of a risk factor this auxiliary information can be helpful in conducting statistical inference in a new study we aim to develop a statistical procedure that improves the efficiency of the logistic regression model for a case control study by utilizing auxiliary information on covariate specific disease prevalence via a series of unbiased estimating equations we adopt empirical likelihood for statistical inference and demonstrate its advantages through simulation and an application

on the distributivity property for uninorms abstract distributivity between two operations is a property that was already posed many years ago and that is especially interesting in the framework of logical connectives for this reason the distributivity property has been extensively studied for several families of operations like triangular norms and conorms some kinds of uninorms and nullnorms also called t operators and even for some generalizations of them in this paper we investigate the distributivity equation involving two uninorms lying in any one of the most studied classes of uninorms leading to many new solutions

optimal calibration estimators in survey sampling we show that the model calibration estimator for the finite population mean which was proposed by wu sitter 2001 through an intuitive argument is optimal among a class of calibration estimators we also present optimal calibration estimators for the finite population distribution function the population variance the variance of a linear estimator and other quadratic finite population functions under a unified framework the proposed calibration estimators are optimal under the true model but remain design consistent even if the working model is misspecified a limited simulation study shows that the improvement of these optimal estimators over the conventional ones can be substantial the question of when and how auxiliary information can be used for both the estimation of the population mean using a generalised regression estimator and the estimation of its variance through calibration is addressed clearly under the proposed general methodology some fundamental issues in using auxiliary information from survey data are also addressed in the context of optimal estimation

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

on the discrete bisymmetry it is known that bisymmetry generalizes the simultaneous commutativity and associativity in the framework of the unit interval in this work we will completely characterize two classes of bisymmetric aggregation operators one with a neutral element and the other with the vertical and horizontal sections of the idempotent elements being smooth on a finite chain but not necessarily smooth and commutative thus the previous results based on the smoothness that is known as a very restrictive condition are improved for example there is only one smooth archimedean t norm on a finite chain in this paper the discrete bisymmetric aggregation operators are explored without the limit of the smoothness as a by product it is deduced that for smooth aggregation operators on a finite chain the bisymmetry is equivalent to the commutativity and associativity which improves the conclusion obtained by mas et al that associativity and bisymmetry are equivalent for commutative smooth aggregation operators on a finite chain

on bisymmetric operators on a finite chain the bisymmetry property is studied for operators defined on a finite chain in particular a characterization of all bisymmetric commutative and smooth binary operators is given it is deduced from this characterization that bisymmetry and associativity are equivalent for finite chains under these additional conditions

some properties of idempotent uninorms on a special class of bounded lattices abstract binary operations have many applications in fuzzy set theory one of them is uninorms in this paper we study some properties of idempotent uninorms on bounded lattices it is shown that idempotent uninorms on an arbitrary bounded lattice need not always be internal with the extended definition of the term internal we give a sufficient condition for the bounded lattice to any idempotent uninorm be internal in addition that it is given many properties of idempotent uninorms in this case

a single point characterization of representable uninorms we study uninorms of which both the underlying t norm and underlying t conorm are strict such uninorms are the only candidates for being representable by an additive generator we prove that the representability of such a uninorm depends solely on its value at a single arbitrary point in the remaining open part of the unit square more explicitly such a uninorm turns out to be representable if and only if this single value is located strictly between the minimum and the maximum of the corresponding arguments if this single value coincides with one of these bounds then the value of the uninorm at any point in the remaining open part is determined by the same bound

novel two phase sampling designs for studying binary outcomes in biomedical cohort studies for assessing the association between an outcome variable and a set of covariates usually some covariates can only be measured on a subgroup of study subjects an important design question is which subjects to select into the subgroup to increase statistical efficiency when the outcome is binary one may adopt a case control sampling design or a balanced case control design where cases and controls are further matched on a small number of complete discrete covariates while the latter achieves success in estimating odds ratio or parameters for the matching covariates similar two phase design options have not been explored for the remaining covariates especially the incompletely collected ones this is of great importance in studies where the covariates of interest cannot be completely collected to this end assuming that an external model is available to relate the outcome and complete covariates we propose a novel sampling scheme that oversamples cases and controls with worse goodness of fit based on the external model and further matches them on complete covariates similarly to the balanced design we develop a pseudolikelihood method for estimating or parameters through simulation studies and explorations in a real cohort study we find that our design generally leads to reduced asymptotic variances of the or estimates and the reduction for the matching covariates is comparable to that of the balanced design

the median and its extensions we review various representations of the median and related aggregation functions an advantage of the median is that it discards extreme values of the inputs and hence exhibits a better central tendency than the arithmetic mean however the value of the median depends on only one or two central inputs our aim is to design median like aggregation functions whose value depends on several central inputs such functions will preserve the stability of the median against extreme values but will take more inputs into account a method based on graduation curves is presented

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

k maxitive aggregation functions abstract inspired by the idea of k maxitive measures we introduce and study k maxitive aggregation functions in particular 1 maxitive aggregation functions are shown to be just maxitive aggregation functions i e maxima of distorted inputs we introduce among others a representation of symmetric k maxitive aggregation functions moreover we show that for any k maxitive capacity and the smallest universal integral based on an arbitrary fixed semicopula including the sugeno and shilkret integrals the resulting aggregation function is k maxitive

constrained maximum likelihood estimation for model calibration using summary level information from external big data sources information from various public and private data sources of extremely large sample sizes are now increasingly available for research purposes statistical methods are needed for using information from such big data sources while analyzing data from individual studies that may collect more detailed information required for addressing specific hypotheses of interest in this article we consider the problem of building regression models based on individual level data from an internal study while using summary level information such as information on parameters for reduced models from an external big data source we identify a set of very general constraints that link internal and external models these constraints are used to develop a framework for semiparametric maximum likelihood inference that allows the distribution of covariates to be estimated using either the internal sample or an external reference sample we develop extensions for handling complex stratified sampling designs such as case co

on a family of multivariate copulas for aggregation processes we introduce a family of multivariate copulas a special type of n ary aggregation operations depending on a univariate function this family is used in the construction of a special aggregation operation that satisfies a lipschitz condition several examples are provided and some statistical properties are studied