an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

an affine invariant bivariate version of the sign test abstract the generalized median of h oja yields a notion of bivariate quantile and in turn an affine invariant bivariate analogue of the sign test its properties include a simple null covariance formula facilitating a permutation or sign change test in the case of bivariate symmetry normal efficiency coinciding with that of the oja median and bounded influence hence strong robustness author

efficient estimation for the proportional hazards model with interval censoring the maximum likelihood estimator mle for the proportional hazards model with case 1 interval censored data is studied it is shown that the mle for the regression parameter is asymptotically normal with n convergence rate and achieves the information bound even though the mle for the baseline cumulative hazard function only converges at n 1 3 rate estimation of the asymptotic variance matrix for the mle of the regression parameter is also considered to prove our main results we also establish a general theorem showing that the mle of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the mle of the infinite dimensional parameter converges at a rate slower than n the results are iliustrated by applying them to a data set from a tumorigenicity study

on certain bivariate sign tests and medians abstract brown and hettmansperger proposed an affine invariant bivariate analogue of the sign test the os test based on the generalized median of oja on the other hand oja and nyblom introduced a family of locally most powerful affine invariant sign tests in the case of elliptic distributions the locally most powerful blumen s test and the os test are shown to be asymptotically equivalent formulas for calculating asymptotic relative efficiencies of the os test and the oja bivariate median are given it is shown that if the contours of a distribution are of a similar shape the relative efficiencies of the os test and blumen s test depend on the distribution only through the shape of the contours for the power family of contours x 1 p x 2 p c p 0 numerical calculations show that the efficiency of the os test relative to blumen s test attains its minimum 1 as p 2 spherical elliptic case and increases to infinity as p 0 in the bivariate laplace case with independent marginals p

rank based optimal tests of the adequacy of an elliptic varma model we are deriving optimal rank based tests for the adequacy of a vector autoregressive moving average varma model with elliptically contoured innovation density these tests are based on the ranks of pseudo mahalanobis distances and on narmed residuals computed from tyler s ann statist 15 1987 234 251 scatter matrix they generalize the univariate signed rank procedures proposed by hallin and puri j multivariate anal 39 1991 1 29 two types of optimality properties are considered both in the local and asymptotic sense a la le cam a fixed score procedures local asymptotic minimaxity at selected radial densities and b estimated score procedures local asymptotic minimaxity uniform over a class f of radial densities contrary to their classical counterparts based on cross covariance matrices these tests remain valid under arbitrary elliptically symmetric innovation densities including those with infinite variance and heavy tails we show that the ares of our fixed score procedures with respect to traditional gaussian methods are the same as for the tests of randomness proposed in hallin and paindaveine bernoulli 8 2002b 787 815 the multivariate serial extensions of the classical chernoff savage and hodges lehmann results obtained there thus also hold here in particular the van der waerden versions of our tests are uniformly more powerful than those based on cross covariances as for our estimated score procedures they are fully adaptive hence uniformly optimal over the class of innovation densities satisfying the required technical assomptions

optimal tests for multivariate location based on interdirections and pseudo mahalanobis ranks we propose a family of tests based on randies 1989 concept of inter directions and the ranks of pseudo mahalanobis distances computed with respect to a multivariate m estimator of scatter due to tyler 1987 for the multivariate one sample problem under elliptical symmetry these tests which generalize the univariate signed rank tests are affine invariant depending on the score function considered van der waerden laplace they allow for locally asymptotically maximin tests at selected densities multivariate normal multivariate double exponential local powers and asymptotic relative efficiencies are derived with respect to hotelling s test randies 1989 multivariate sign test peters and randies 1990 wilcoxon type test and with respect to the oja median tests we moreover extend to the multivariate setting two famous univariate results the traditional chemoff savage 1958 property showing that hotelling s traditional procedure is uniformly dominated in the pitman sense by the van der waerden version of our tests and the celebrated hodges lehmann 1956 864 result providing for any fixed space dimension k the lower bound for the asymptotic relative efficiency of wilcoxon type tests with respect to hotelling s these asymptotic results are confirmed by a monte carlo investigation and application to a real data set

bivariate nonparametric tests for the one sample location problem abstract many nonparametric competitors to hotelling s t2 test lack t 2 s property of invariance under linear transformations such tests have power and efficiency that depend on the direction of shift and the covariance matrix of the alternative distribution this article modifies a previously proposed bivariate sign test and signed rank test to overcome this difficulty asymptotic results and a monte carlo study indicate that the efficiency and small sample power of the new procedures compare favorably to those of the original tests an example illustrates the application of the new procedures

weighted logrank tests for interval censored data when assessment times depend on treatment we consider weighted logrank tests for interval censored data when assessment times may depend on treatment and for each individual we only use the two assessment times that bracket the event of interest it is known that treating finite right endpoints as observed events can substantially inflate the type i error rate under assessment treatment dependence atd but the validity of several other implementations of weighted logrank tests score tests permutation tests multiple imputation tests has not been studied in this situation with a bounded number of unique assessment times the score test under the grouped continuous model retains the type i error rate asymptotically under atd however although the approximate permutation test based on the permutation central limit theorem is not asymptotically valid under every atd scenario we show through simulation that in many atd scenarios it retains the type i error rate better than the score test we show a case where the approximate permutation test retains the type i error rate when the exact permutation test does not we study and modify the multiple imputation logrank tests of huang lee and yu 2008 statistics in medicine 27 3217 3226 showing that the distribution of the rank like scores asymptotically does not depend on the assessment times we show through simulations that our modifications of the multiple imputation logrank tests retain the type i error rate in all cases studied even with atd and a small number of individuals in each treatment group simulations were performed using the interval r package us government work in the public domain

interdirection tests for simple repeated measures designs abstract interdirection tests are proposed for a simple repeated measures design the test statistics proposed are applications of the one sample interdirection sign test and interdirection signed rank test to a repeated measurement setting the interdirection sign test has a small sample distribution free property and includes the two sided univariate sign test and blumen s bivariate sign test as special cases the interdirection signed rank test includes the two sided univariate wilcoxon signed rank test as a special case the proposed statistics are shown to have a limiting x p 1 2 null distribution when the underlying distribution is elliptically symmetric in addition the asymptotic distributions of the proposed statistics under certain contiguous alternatives are obtained for elliptically symmetric distributions with a particular density function form pitman asymptotic relative efficiencies and monte carlo studies show the proposed interdirection tests to be robust as compared to several competito

multivariate location estimation using extension of r estimates through u statistics type approach we consider a class of u statistics type estimates for multivariate location the estimates extend some r estimates to multivariate data in particular the class of estimates includes the multivariate median considered by gini and galvani 1929 and haldane 1948 and a multivariate extension of the well known hodges lehmann 1963 estimate we explore large sample behavior of these estimates by deriving a bahadur type representation for them in the process of developing these asymptotic results we observe some interesting phenomena that closely resemble the famous shrinkage phenomenon observed by stein 1956 in high dimensions interestingly the phenomena that we observe here occur even in dimension d 2

a probabilistic definition of a nonconvex fuzzy cardinality the existing methods to assess the cardinality of a fuzzy set with finite support are intended to preserve the properties of classical cardinality in particular the main objective of researchers in this area has been to ensure the convexity of fuzzy cardinalities in order to preserve some properties based on the addition of cardinalities such as the additivity property we have found that in order to solve many real world problems such as the induction of fuzzy rules in data mining convex cardinalities are not always appropriate in this paper we propose a possibilistic and a probabilistic cardinality of a fuzzy set with finite support these cardinalities are not convex in general but they are most suitable for solving problems and contrary to the generalizing opinion they are found to be more intuitive for humans their suitability relies mainly on the fact that they assume dependency among objects with respect to the property to be in a fuzzy set the cardinality measures are generalized to relative ones among pairs of fuzzy sets we also introduce a definition of the entropy of a fuzzy set by using one of our probabilistic measures finally a fuzzy ranking of the cardinality of fuzzy sets is proposed and a definition of graded equipotency is introduced

comparisons of tests for the presence of random walk coefficients in a simple linear model abstract the locally most powerful test is derived for the hypothesis that the regression coefficients are constant over time against the alternative that they vary according to the random walk process when the regression equation contains the constant term only comparisons are made with the tests suggested by lamotte and mcwhorter 1978 these are based on exact powers and on three different types of asymptotic efficiencies including the classical pitman and bahadur approaches and the new one due to gregory 1980 the concept of the bahadur efficiency is extended to cover also the random slopes suggestions are made for choosing the test

a nonparametric test of independence between two vectors abstract a new statistic qcirc n based on interdirections is proposed for testing whether two vector valued quantities are dependent the statistic which has an intuitive invariance property reduces to the quadrant statistic when the two quantities are each univariate under the null hypothesis of independence qcirc n has a limiting chi squared distribution when each vector is elliptically symmetric the new statistic is compared to the classical normal theory competitor wilks likelihood ratio criterion and a componentwise quadrant statistic using a novel model of dependence between the vectors pitman asymptotic relative efficiencies are s are computed the pitman are s indicate that qcirc n compares favorably to wilks likelihood ratio criterion when the vectors have heavy tailed elliptically symmetric distributions and is uniformly better than the componentwise quadrant statistic when the vectors are spherically symmetric a simulation study demonstrates that qcirc n performs better t

a semiparametric proportional odds regression model for the analysis of current status data abstract an approach to covariate analysis of current status data is described the method is applicable when the logit of the conditional probability of survival given the covariates is some increasing function of time plus a linear combination of the covariates the approach is based on approximating the infinite dimensional nuisance parameter the baseline log odds of failure with a step function and carrying out a maximum likelihood procedure the resulting finite dimensional parameter estimates for the regression parameters are shown to be asymptotically normal and semiparametric efficient numerical studies with small and moderate samples are discussed

nonparametric methods for survival sacrifice experiments in many carcinogenicity studies the time to disease occurrence is not clinically observable a survival sacrifice experiment is considered for nonparametric inference about the rate of disease occurrence a multistate model for disease development and death is considered and an algorithm of the em type for maximum likelihood estimation is obtained questions of identifiability and estimability are addressed under the model interval hazards for disease occurrence are identifiable for intervals defined by the sacrifice times a score test is developed appropriate for the comparison of two groups with respect to disease development without need of any assumption concerning lethality of the disease concerned

on an adaptive transformation retransformation estimate of multivariate location an affine equivariant estimate of multivariate location based on an adaptive transformation and retransformation approach is studied the work is primarily motivated by earlier work on different versions of the multivariate median and their properties we explore an issue related to efficiency and equivariance that was originally raised by bickel and subsequently investigated by brown and hettmansperger our estimate has better asymptotic performance than the vector of co ordinatewise medians when the variables are substantially correlated the finite sample performance of the estimate is investigated by using monte carlo simulations some examples are presented to demonstrate the effect of the adaptive transformation retransformation strategy in the construction of multivariate location estimates for real data

a multivariate signed rank test for the one sample location problem abstract an affine invariant signed rank test is proposed for the one sample multivariate location problem the test suggested is a modification of randles s multivariate sign test based on interdirections which extends blumen s bivariate procedure to the multidimensional setting comparisons are made between the proposed statistic and several competitors via pitman asymptotic relative efficiencies and monte carlo results the signed rank statistic appears to be robust it performs better than its competitors when the distribution is light tailed and virtually as well as hotelling s t 2 under multivariate normality for heavy tailed distributions the signed rank statistic performs better than hotelling s t 2 but not as well as randles s statistic

affine invariant rank methods in the bivariate location model abstract the generalized multivariate median of h oja is used to define a multivariate notion of quantile or rank and to define a measure of scatter of multivariate linear models the latter when applied to the one and two sample bivariate location models yields affine invariant analogs of the wilcoxon rank sum and signed rank tests and of the corresponding estimates additional keywords dispersion measures rank statics author

a wilcoxon mann whitney type test for infinite dimensional data the wilcoxon mann whitney test is a robust competitor of the t test in the univariate setting for finite dimensional multivariate non gaussian data several extensions of the wilcoxon mann whitney test have been shown to outperform hotelling s t 2 test in this paper we study a wilcoxon mann whitney type test based on spatial ranks in infinite dimensional spaces we investigate its asymptotic properties and compare it with several existing tests the proposed test is shown to be robust with respect to outliers and to have better power than some competitors for certain distributions with heavy tails we study its performance using real and simulated data

on multivariate runs tests for randomness this paper proposes several extensions of the concept of runs to the multivariate setup and studies the resulting tests of multivariate randomness against serial dependence two types of multivariate runs are defined i an elliptical extension of the spherical runs proposed by marden 1999 and ii an original concept of matrix valued runs the resulting runs tests themselves exist in various versions one of which is a function of the number of data based hyperplanes separating pairs of observations only all proposed multivariate runs tests are affine invariant and highly robust in particular they allow for heteroscedasticity and do not require any moment assumption their limiting distributions are derived under the null hypothesis and under sequences of local vector arma alternatives asymptotic relative efficiencies with respect to gaussian portmanteau tests are computed and show that while marden type runs tests suffer severe consistency problems tests based on matrix valued runs perform u

a nonparametric test for panel count data summary panel count data arise when a recurrent event is under investigation and each study subject is observed only at discrete time points in this situation observed data include only the numbers of occurrences of the event of interest between observation time points and no information is available on subjects between their observation time points we propose a nonparametric test for comparing the point processes characterising the recurrent event when only panel count data are available the asymptotic distribution of the test statistic is derived and a simulation study is conducted to evaluate its performance the method is illustrated using data from a medical follow up study

sign tests in multidimension inference based on the geometry of the data cloud abstract multivariate sign tests attracted several statisticians in the past and it is evident from recent nonparametric literature that they still continue to draw attention one of the most important features of the univariate sign test is that it does not involve much technical assumptions or complicacy and this makes it quite popular among statistics users in this article we have come up with a new method for constructing multivariate sign tests that have reasonable statistical properties and can be used conveniently to solve one sample location problems our principal strategy here is to make a wise utilization of certain geometric structures in the constellation of data points for making inference about the location of their distribution as we proceed with the development of a fairly broad and general methodology we indicate its relationship with previous work done by others and sometimes attempt to unify some of the earlier ideas in particular we pick up some well known tests for uniform dis

multivariate nonparametric tests of independence new test statistics are proposed for testing whether two random vectors are independent gieser and randles as well as taskinen kankainen and oja have introduced and discussed multivariate extensions of the quadrant test of blomqvist this article serves as a sequel to this work and presents new multivariate extensions of kendall s tau and spearman s rho statistics two different approaches are discussed first interdirection proportions are used to estimate the cosines of angles between centered observation vectors and between differences of observation vectors second covariances between affine equivariant multivariate signs and ranks are used the test statistics arising from these two approaches appear to be asymptotically equivalent if each vector is elliptically symmetric the spatial sign versions are easy to compute for data in common dimensions and they provide practical robust alternatives to normal theory methods asymptotic theory is developed to approximate the finite sample null distr

generalized multiset theory abstract the paper gives a formal axiomatic theory of collections such that elements may occur some number of times in these collections and this number is allowed to be an arbitrary real number e g a negative one the presented theory is a generalization of multiset theories and some fuzzy set theories some important consequences of the theory are revealed among potential applications of the theory expressing of vague properties and relations is anticipated the usefulness of the theory and its consequences for applications involving vague properties is demonstrated by an example of multi criteria decision making based on vague properties of alternatives

on a geometric notion of quantiles for multivariate data abstract an extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered the approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles both of which have been extensively studied in the literature these geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other l estimates of multivariate location and they lead to a directional notion of central and extreme points in a multidimensional setup such quantiles can be defined as meaningful and natural objects even in infinite dimensional hilbert and banach spaces and they yield an effective generalization of quantile regression in multiresponse linear model problems desirable equivariance properties are shown to hold for these multivariate quantiles and issues related to their computation for data in finite dimensional spaces are discussed n 1 2 consistenc

tests for high dimensional data based on means spatial signs and spatial ranks tests based on sample mean vectors and sample spatial signs have been studied in the recent literature for high dimensional data with the dimension larger than the sample size for suitable sequences of alternatives we show that the powers of the mean based tests and the tests based on spatial signs and ranks tend to be same as the data dimension grows to infinity for any sample size when the coordinate variables satisfy appropriate mixing conditions further their limiting powers do not depend on the heaviness of the tails of the distributions this is in striking contrast to the asymptotic results obtained in the classical multivariate setup on the other hand we show that in the presence of stronger dependence among the coordinate variables the spatial sign and rank based tests for high dimensional data can be asymptotically more powerful than the mean based tests if in addition to the data dimension the sample size also grows to infinity the sizes of some mean based tests for high dimensional data studied in the recent literature are observed to be significantly different from their nominal levels this is due to the inadequacy of the asymptotic approximations used for the distributions of those test statistics however our asymptotic approximations for the tests based on spatial signs and ranks are observed to work well when the tests are applied on a variety of simulated and real datasets

the set of fuzzy rational numbers and flexible querying a fuzzy bag is a bag in which each occurrence of an element is associated with a grade of membership this notion can be viewed as a generalization of the concepts of set fuzzy set and bag the set of fuzzy integers n f provides a general characterization in which all these different concepts are treated in a uniform way and can then be composed in the field of databases the use of fuzzy bags is motivated by their ability to manage both quantities and preferences however n f becomes too restricted a framework when dealing with queries based on difference or division operations so a more general structure based on the set of fuzzy relative integers z f in which exact differences can be performed has been first developed in this paper we carry on with this approach and we extend z f to the set of fuzzy rational numbers q f this context leads to define a closed system of multiplicative operations and allows to perform exact divisions applied to flexible querying of databases q f and the notion of division on fuzzy numbers allow to generalize the relational division they define a sound basis for queries involving ratios between quantities

a distribution free multivariate sign test based on interdirections abstract distribution free tests are investigated for the one sample multivariate location problem counts called interdirections which measure the angular distance between two observation vectors relative to the positions of the other observations are introduced these counts are invariant under nonsingular linear transformations and have a small sample distribution free property over a broad class of population models called distributions with elliptical directions which includes all elliptically symmetric populations and many skewed populations a sign test based on interdirections is described including as special cases the two sided univariate sign test and blumen s bivariate sign test the statistic is shown to have a limiting 2 p null distribution and because it is based on interdirections it is also seen to be invariant and to have a small sample distribution free property pitman asymptotic relative efficiencies and a monte carlo study show the test to perform well compared with hotell

an approach to multivariate rank tests in multivariate analysis of variance abstract a class of multivariate rank like quantities is defined and used to develop multivariate tests to mimic popular one dimensional rank tests such as the mann whitney wilcoxon two sample test the jonckheere terpstra test for trend and the kruskal wallis one way analysis of variance test tests in one way analysis of variance are developed based on qualitative orthogonal contrasts allowing decomposition of an overall statistic into asymptotically independent components based on the contrasts the class of tests includes the usual normal theory tests and the componentwise rank tests but the main focus is on the tests based on a particular definition of multivariate rank a study of the pitman efficiency of the latter tests to those based on multivariate medians shows them to be superior at the normal slightly heavy tailed and light tailed distributions whereas the median based tests are superior for heavy tails these results are analogous to the univariate case

on the theory of bags and lists abstract in this paper the concept of bag space has been introduced the concept of bag complement is redefined suitably and some theorems involving bag operations have been established the concept of the theory of lists which is a generalization of the theory of bags has been redefined and many existing and new results have been established based upon this new definition

rl bags a conceptual level based approach to fuzzy bags in this paper we claim that though algebraically well defined bags are not well suited for representing and reasoning with real world information and we propose suitable alternatives we extend the same discussion to the fuzzy case in which membership of elements to bags is gradual extending the proposed alternatives there are two main ideas behind our approach the first is that in general the elements of a bag can be identified and are distinguishable in the real world and when this is not the case we are facing a problem of representation of partial knowledge i e we have a lack of information under this consideration we discuss and criticize the usual operations for bags the second is to manage the fuzziness by levels using a recent level based representation approach that extends that of fuzzy sets and keeps all the properties of the crisp case the classical notion of bag can be seen in our approach as a bag summary we propose a new model that generalizes the existing approach defining new operations from this new perspective we also propose how to deal with fuzziness and incompleteness following our approach doing a review of the existing approaches and applications concerning bags

on the limiting distributions of multivariate depth based rank sum statistics and related tests a depth based rank sum statistic for multivariate data introduced by liu and singh j amer statist assoc 88 1993 252 260 as an extension of the wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies those applications however are based on a conjectured limiting distribution provided by liu and singh j amer statist assoc 88 1993 252 260 the present paper proves the conjecture under general regularity conditions and therefore validates various applications of the rank sum statistic in the literature the paper also shows that the corresponding rank sum tests can be more powerful than hotelling s t 2 test and some commonly used multivariate rank tests in detecting location scale changes in multivariate distributions

estimates of regression coefficients based on the sign covariance matrix the influence function and asymptotic theory are developed to consider robustness and limiting efficiencies of the scm regression estimate the estimate is shown to be consistent with a limiting multinormal distribution the influence function as a function of the length of the contamination vector is shown to be linear in elliptic cases for the least squares ls estimate it is quadratic the asymptotic relative efficiencies with respect to the ls estimate are given in the multivariate normal as well as the t distribution cases the scm regression estimate is highly efficient in the multivariate normal case and for heavy tailed distributions it performs better than the ls estimate simulations are used to consider finite sample efficiencies with similar results the theory is illustrated with an example

on fuzzy bags and their application to flexible querying an issue in extending database management functionalities is to increase the expressiveness of query languages flexible querying enables users to express preferences inside requirements and priorities inside compound queries the answers are then qualified and sorted out the fuzzy sets theory offers a general framework for dealing with flexible queries moreover the bag type plays an important role in databases systems taking into account both flexible queries and bags define fuzzy bags a new approach of this concept based on the notion of fuzzy cardinalities is presented in this paper fuzzy cardinalities provide a general framework in which different collection types set fuzzy set bag and fuzzy bag are treated in a uniform way and can then be composed we show how they can be used to build up flexible queries and to manipulate both quantitative and qualitative information on the elements of collections

modelling tumour biology progression relationships in screening trials there has been some recent work in the statistical literature for modelling the relationship between tumour biology properties and tumour progression in screening trials while non parametric methods have been proposed for estimation of the tumour size distribution at which metastatic transition occurs their asymptotic properties have not been studied in addition no testing or regression methods are available so that potential confounders and prognostic factors can be adjusted for we develop a unified approach to non parametric and semi parametric analysis of modelling tumour size metastasis data in this article an association between the models considered by previous authors with survival data structures is discussed based on this relationship we develop non parametric testing procedures and semi parametric regression methodology of modelling the effect of size of tumour on the probability at which metastatic transitions occur in two situations asymptotic properties of these estimators are provided the proposed methodology is applied to data from a screening study in lung cancer

on a notion of data depth based on random simplices for a distribution f on mathbb r p and a point x in mathbb r p the simplical depth d x is introduced which is the probability that the point x is contained inside a random simplex whose vertices are p 1 independent observations from f mathematically and heuristically it is argued that d x indeed can be viewed as a measure of depth of the point x with respect to f an empirical version of d cdot gives rise to a natural ordering of the data points from the center outward the ordering thus obtained leads to the introduction of multivariate generalizations of the univariate sample median and l statistics this generalized sample median and l statistics are affine equivariant

a framework for multiset merging information fusion is a research area that investigates how to combine information provided by independent sources into one piece of information several aspects of this topic have already been studied leading to amongst others aggregation operators in bounded lattices and merge functions of propositional belief bases in this paper information fusion is investigated in the context of coreferent objects which are pieces of data in an information system that refer to the same real world entity the fundamental operator in our approach is a merge function that maps a multiset of coreferent objects onto a single object which is called the solution we investigate the specific case where objects themselves are multisets which can be applied to problems such as multi document summarization mds and fusion of duplicate graphs e g xml documents our approach involves the definition of quality measures that express the correctness and the completeness of a given solution we show how a solution can be found that optimizes a balance between correctness and completeness merge functions that result in such a solution are called f optimal merge functions and we investigate their properties

a comparison of tumour incidence analyses applicable in single sacrifice animal experiments monte carlo methods are used to evaluate the operating characteristics of several trend tests for comparing incidence rates of occult tumours the candidate tests are applicable in long term animal experiments that have just one sacrifice time and no information on cause of death when survival decreases with dose and the tumour is lethal the tests that do not adjust for survival or that assume tumours are non lethal behave conservatively whereas the test that assumes tumours are rapidly lethal rejects the hypothesis of equal incidence rates too frequently the only test which consistently operates at the correct level is one that specifies a constant difference between the death rates for animals with and without the tumour surprisingly the test that specifies a constant ratio of these death rates often is conservative finally a test based on a simple modification of the unadjusted test which accounts for differential mortality by scaling down the size of the risk set performs reasonably well in many cases among the tests that operate at the proper level the constant risk difference test consistently exhibits high power across a wide range of situations

nonparametric inference for stochastic linear hypotheses application to high dimensional data summary the mann whitney wilcoxon rank sum test is limited to comparison of two groups with univariate responses in this paper we introduce a class of stochastic linear hypotheses that addresses these limitations within a nonparametric setting we formulate hypotheses for simultaneous comparisons of several multivariate response groups without modelling the response distributions inference is developed based on u statistics theory and an exchangeability assumption the latter condition is required to identify testable hypotheses for high dimensional response vectors such as those arising in genomic and psychosocial research the methodology is illustrated with two real data applications

bbtopsis a bag based technique for order preference by similarity to ideal solution abstract this contribution explores the way of accomplishing a topsis ranking of various submitted variants taking into account a our newly developed notions of variant superiority inferiority and noninferiority multiattribute canonical fuzzy bags defined on attributes and b making use of bag metrics to compute the relative closeness of the different variants to an ideal solution in particular we prove the existence and the uniqueness of a bag metric fulfilling a number of interesting properties

fuzzy bags and applications abstract based upon r r yager s concept of bags 1 a definition of fuzzy bags and corresponding operations such as peak value grade of concentration as well as the relative cardinality is introduced here several examples are also given to show the usefulness of fuzzy bags

a practical affine equivariant multivariate median summary a robust affine equivariant estimator of location for multivariate data is proposed which becomes the univariate median for data of dimension one the estimator is robust in the sense that it has a bounded influence function a positive breakdown value and has high efficiency compared to the sample mean for heavy tailed distributions perhaps its greatest strength is that unlike other affine equivariant multivariate medians it is easily computed for data in any practical dimension

graphics for the multivariate two sample problem abstract some graphical methods for comparing multivariate samples are presented these methods are based on minimal spanning tree techniques developed for multivariate two sample tests the utility of these methods is illustrated through examples using both real and artificial data

inference on multivariate m estimators based on bivariate censored data consider two random variables subject to random right censoring for example the survival times of twins or two recurrence times of a certain disease recorded on the same individual of interest is the estimation of a multivariate m functional of these two random variables asymptotic results for the proposed estimator are established under general conditions on the criterion function of the m estimator the obtained results include the asymptotic normality of the estimator its local power and construction of a confidence region our primary example of interest is the bivariate l1 median we compare the small sample behavior of this estimator with that of the vector of marginal medians by means of a simulation study finally we consider a dataset on kidney dialysis patients and estimate the median time to two different infections for these individuals

a distribution free two sample run test applicable to high dimensional data we propose a multivariate generalization of the univariate two sample run test based on the shortest hamiltonian path the proposed test is distribution free in finite samples while most existing two sample tests perform poorly or are even inapplicable to high dimensional data our test can be conveniently used in high dimension low sample size situations we investigate its power when the sample size remains fixed and the dimension of the data grows to infinity simulated and real datasets demonstrate our method s superiority over existing nonparametric two sample tests

affine invariant multivariate one sample signed rank tests abstract brown and hettmansperger introduced affine invariant bivariate analogs of the sign rank and signed rank tests based on the oja median in this article affine invariant k variate extensions of the one sample signed rank test and the hodges lehmann estimate are considered the necessary distribution theory is developed and asymptotic pitman efficiencies with respect to hotelling s t 2 test under multivariate t distributions are tabulated an application of the signed rank tests to a repeated measurement setting is presented

on directional regression for dimension reduction we introduce directional regression dr as a method for dimension reduction like contour regression dr is derived from empirical directions but achieves higher accuracy and requires substantially less computation dr naturally synthesizes the dimension reduction estimators based on conditional moments such as sliced inverse regression and sliced average variance estimation and in doing so combines the advantages of these methods under mild conditions it provides exhaustive and consistent estimate of the dimension reduction space we develop the asymptotic distribution of the dr estimator and from that a sequential test procedure to determine the dimension of the central space we compare the performance of dr with that of existing methods by simulation and find strong evidence of its advantage over a wide range of models finally we apply dr to analyze a data set concerning the identification of hand written digits

a nonparametric test for comparing two samples where all observations are either left or right censored the situation is considered where the status of the individuals under study is assessed only once during their lifetime and as a consequence the observed time to an event of interest is either left or right censored nonparametric estimation of the time to event distribution is reviewed and a nonparametric two sample test is proposed the performance of the test is illustrated by simulations and by a numerical example

affine invariant multivariate multisample sign tests summary invariant sign type tests for the multivariate multisample location models are developed the definition of sign is based on the oja criterion function emphasis is on the twosample location model and the associated equivariant estimate of shift asymptotic theory is developed to provide large sample approximations for the null distribution of the test and to provide a framework for a discussion of efficiency tests are then developed for the one way and two way lay outs

rank tests for main and interaction effects in analysis of variance abstract a class of rank tests for analysis of variance based on linear functions of the wilcoxon mann whitney statistics between cells is studied this class includes many popular procedures assuming a location family model a condition for optimal pitman efficacy of tests of main effects in this class is given tests for main effects in two way layouts that achieve this optimality are shown to improve on previous proposals when the sample sizes are unbalanced nested orthogonal contrasts are introduced that can be used to decompose the overall test statistics into independent components to assess the contribution of individual contrasts a new definition of interaction appropriate for rank based analysis of variance is suggested and test procedures are proposed

sieve maximum likelihood regression analysis of dependent current status data current status data occur in contexts including demographic studies and tumorigenicity experiments in such cases each subject is observed only once and the failure time of interest is either left or right censored kalbfleisch prentice 2002 many methods have been developed for the analysis of such data huang 1996 sun 2006 most of which assume that the failure time and the observation time are independent completely or given covariates in this paper we present a sieve maximum likelihood approach for current status data when independence does not hold a copula model and monotone i splines are used and the asymptotic properties of the resulting estimators are established in particular the estimated regression parameters are shown to be semiparametrically efficient an illustrative example is provided

representation by levels an alternative to fuzzy sets for fuzzy data mining abstract in this paper we describe and discuss the main contributions of the representation by levels approach to fuzzy data mining representation by levels is an alternative representation of fuzziness in information and data which is complementary to fuzzy sets in the sense that it provides tools and algebraic structures beyond the capabilities of fuzzy set theories based on t norms t conorms and fuzzy negations our approach allows to extend any crisp mining technique to the fuzzy case in a simple way keeping all the properties of the crisp technique we illustrate our discussion with examples and existing approaches based on representation by levels to fuzzy association rules and the related issues of mining exception anomalous rules and mining fuzzy bag databases

a multivariate sign ewma control chart nonparametric control charts are useful in statistical process control spc when there is a lack of or limited knowledge about the underlying process distribution especially when the process measurement is multivariate this article develops a new multivariate spc methodology for monitoring location parameters it is based on adapting a powerful multivariate sign test to online sequential monitoring the weighted version of the sign test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control ewma scheme which results in a nonparametric counterpart of the classical multivariate ewma mewma it is affine invariant and has a strictly distribution free property over a broad class of population models that is the in control ic run length distribution can attain or is always very close to the nominal one when using the same control limit designed for a multivariate normal distribution moreover when the process distribution comes from the elli

testing for deterministic linear trend in time series abstract most powerful tests are derived for the hypothesis that deterministic linear trend occurs in time series against the alternative that trend consists of random walk subject to drift comparisons of these tests and of the tests suggested by lamotte and mcwhorter 1978 are made in terms of exact powers and pitman asymptotic relative efficiencies

on the efficiency of multivariate spatial sign and rank tests conditionally and asymptotically distribution free rotation but not scale invariant competitors of the well known hotelling s t 2 tests in this paper efficiency results are found in the one sample location case but they natu rally hold in the multivariate two sample multisample and general linear model case the lack of means of fully ordering or ranking observations in the multivariate setting seems at first sight to be an obstacle to generalizing the concepts of sign and rank and signed rank however these concepts can be defined also by using l criterion functions as follows consider k 1 variate observations y y utilizing the euclidean distance y s 1 n 2 2 1r2 y q qy the three objective functions 1 k t y s s y y i i i i i

likelihood based inference for monotone response models the behavior of maximum likelihood estimates mles and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied this class of problems differs radically from the usual parametric or semiparametric situations in that the mle of the monotone function at a point converges to the truth at rate n 1 3 slower than the usual n rate with a non gaussian limit distribution a framework for likelihood based estimation of monotone functions is developed and limit theorems describing the behavior of the mles and the likelihood ratio statistic are established in particular the likelihood ratio statistic is found to be asymptotically pivotal with a limit distribution that is no longer 2 but can be explicitly characterized in terms of a functional of brownian motion applications of the main results are presented and potential extensions discussed

nonparametric methods for analyzing incomplete nondecreasing repeated measurements in comparing the effectiveness of two treatments suppose that nondecreasing repeated measurements of the same characteristic are scheduled to be taken over a common set of time points for each study subject a class of univariate one sided global asymptotically distribution free tests is proposed to test the equality of the two treatments the test procedures allow different patterns of missing observations in the two groups to be compared although the missing data mechanism is required to be independent of the observations in each treatment group test based point and interval estimators of the global treatment difference are given multiple inference procedures are also provided to examine the time trend of treatment differences over the entire study the proposed methods are illustrated by an example from a bladder cancer study

a quality index based on data depth and multivariate rank tests let f and g be the distribution functions of two given populations on rp p 1 we introduce and study a parameter q q f g which measures the overall outlyingness of population g relative to population f the parameter q can be defined using any concept of data depth its value ranges from 0 to 1 and is 5 when f and g are identical we show that within the dass of elliptical distributions when g departs from f in location or g has a larger spread or both the value of q dwindles down from 5 hence q can be used to detect the loss of accuracy or precision of a manufacturing process and thus it should serve as an important measure in quality assurance this in fact is the reason why we refer to q as a quality index in this article in addition to studying the properties of q we provide an exact rank test for testing q 5 vs q 5 this can be viewed as a multivariate analog of wilcoxon s rank sum test the tests proposed here have power against location change and scale increase simultaneo

the analysis of current status data on point processes abstract this article considers the analysis of event count data in which each subject is observed at only one time point and no information is available on subjects between their entry time and observation points this type of data often referred to as current status data arises frequently for example in demography epidemiology and reliability studies statistical methods for the analysis of current status data from point processes are proposed specifically a statistic for testing the equality of the mean functions of point processes is presented and its asymptotic distribution obtained for illustration the proposed method is used to analyze multiple tumor data from a tumorgenicity experiment with focus on the comparison of tumor growth rates in male and female rats the adequacy of the asymptotic distribution of the test statistic is evaluated in a small simulation study power comparisons with the usual parametric model are also obtained finally some possible directions for further research

a nonparametric test for current status data with unequal censoring nonparametric tests for the comparison of different treatments based on current status data are proposed for this problem most methods proposed in the literature require that observation times on all subjects follow the same distribution in other words censoring distributions are identical between the treatment groups in this paper we focus on the situation where the censoring distributions may be different for subjects in different treatment groups and the test that can take this unequal censoring into account is given the asymptotic distribution of the test proposed is derived the method proposed is applied to data arising from a tumorigenicity experiment

semiparametrically efficient rank based inference for shape i optimal rank based tests for sphericity we propose a class of rank based procedures for testing that the shape matrix v of an elliptical distribution with unspecified center of symmetry scale and radial density has some fixed value v 0 this includes for v 0 i k the problem of testing for sphericity as an important particular case the proposed tests are invariant under translations monotone radial transformations rotations and reflections with respect to the estimated center of symmetry they are valid without any moment assumption for adequately chosen scores they are locally asymptotically maximin in the le cam sense at given radial densities they are strictly distribution free when the center of symmetry is specified and asymptotically so when it must be estimated the multivariate ranks used throughout are those of the distances in the metric associated with the null value v 0 of the shape matrix between the observations and the estimated center of the distribution local powers against elliptical alternatives and asymptotic relative efficiencies ares are derived with respect to the adjusted mauchly test a modified version of the gaussian likelihood ratio procedure proposed by muirhead and waternaux biometrika 67 1980 31 43 or equivalently with respect to an extension of the test for sphericity introduced by john biometrika 59 1972 169 173 for gaussian scores these ares are uniformly larger than one irrespective of the actual radial density necessary and or sufficient conditions for consistency under nonlocal possibly nonelliptical alternatives are given finite sample performance is investigated via a monte carlo study

nonparametric comparison of survival functions based on interval censored data with unequal censoring nonparametric comparison of survival functions is one of the most commonly required task in failure time studies such as clinical trials and for this many procedures have been developed under various situations this paper considers a situation that often occurs in practice but has not been discussed much the comparison based on interval censored data in the presence of unequal censoring that is one observes only interval censored data and the distributions of or the mechanisms behind censoring variables may depend on treatments and thus be different for the subjects in different treatment groups for the problem a test procedure is developed that takes into account the difference between the distributions of the censoring variables and the asymptotic normality of the test statistics is given for the assessment of the performance of the procedure a simulation study is conducted and suggests that it works well for practical situations an illustrative example is provided copyright 2017 john wiley sons ltd

gradual numbers and their application to fuzzy interval analysis in this paper we introduce a new way of looking at fuzzy intervals instead of considering them as fuzzy sets we see them as crisp sets of entities we call gradual real numbers they are a gradual extension of real numbers not of intervals such a concept is apparently missing in fuzzy set theory gradual numbers basically have the same algebraic properties as real numbers but they are functions a fuzzy interval is then viewed as a pair of fuzzy thresholds which are monotonic gradual real numbers this view enables interval analysis to be directly extended to fuzzy intervals without resorting to alpha cuts in agreement with zadeh s extension principle several results show that interval analysis methods can be directly adapted to fuzzy interval computation where end points of intervals are changed into left and right fuzzy bounds our approach is illustrated on two known problems computing fuzzy weighted averages and determining fuzzy floats and latest starting times in activity network scheduling

bivariate sign tests abstract in this article the bivariate location problem is treated new appealing bivariate analogs of the univariate sign tests are proposed for testing the null hypothesis concerning the unknown symmetry center these tests remain unaltered under any nonsingular linear transformation from these promising findings a whole family of locally most powerful invariant sign tests is introduced the tests proposed earlier blumen 1958 hodges 1955 are specific members of this family for example blumen s test appears to be optimal against bivariate normal or any other elliptic alternatives the limiting distributions are derived both under the null hypothesis and under the contiguous alternatives these limiting distributions are then used to derive asymptotic relative efficiencies it is found that blumen s test has the efficiency 785 relative to hotelling s test against bivariate normal alternatives for other locally most powerful sign tests the corresponding efficiency depends on the significance leve

a simpler affine invariant multivariate distribution free sign test abstract a simpler multivariate sign test is proposed that uses the transformation retransformation approach of chakraborty chaudhuri and oja together with a directional transformation due to tyler this produces a multivariate sign test that is practical to apply to data of any dimension makes minimal assumptions about the underlying distribution and has a small sample distribution free property over a broad class of population models it is shown to perform very well in comparison to hotelling s t 2 and other multivariate sign tests for heavy tailed and skewed distributions