pairwise versus joint ranking another look at the kruskal wallis statistic summary a test statistic for the k sample location problem is constructed by appropriately combining all pairwise two sample wilcoxon tests the result is an analogue of the kruskal wallis statistic in the sense that the pitman asymptotic relative efficiency between the two is one however the approximate bahadur efficiency of the analogue relative to the kruskal wallis statistic is shown to be greater than or equal to one at every alternative the standard k sample linear rank statistics for testing equality of the location parameters of k populations are based on the joint ranking of the observations in the combined samples it is also possible to construct k sample test statistics in this setting by combining all k k 1 pairwise two sample linear rank statistics this can be done to yield analogues to the standard k sample linear rank statistics in the sense that the pitman asymptotic relative efficiency between such a pair is one this is referred to as the pairwise rank approach and we note that the question of pairwise versus joint ranking has recently received attention in the multiple comparisons literature as well as by for example koziol reid 1977 voshaar 1980 fligner 1984 or fairley pearl 1984 in 2 the pairwise rank analogue of the kruskal wallis 1952 statistic is developed although the pitman efficiency between the procedures is one the approximate bahadur 1960 efficiency of the pairwise rank analogue relative to the kruskal wallis test is shown to be greater than or equal to one at every alternative a simple algebraic relationship between the kruskal wallis statistic and its analogue is established which helps to explain these efficiency results the technique for constructing pairwise rank analogues in the general scores case is also considered section 3 describes other problems in which it may be fruitful to create k sample statistics through appropriate combinations of two sample statistics

classification of sequentially weakly continuous jb triples let d be the open unit ball of a jb triple a and let aut d be the group of all biholomorphic automorphisms of d it is shown that every element of aut d is sequentially weakly continuous if and only if every primitive ideal of a is a maximal closed ideal and a is a type i jbw triple without infinite spin part implications for general structure theory are explored in particular it is deduced that every jb triple a contains a smallest ideal j for which the sequentially weakly continuous biholomorphic automorphisms of the open unit ball of a j are all linear

morse index of some min max critical points i application to multiplicity results on donne un resultat general sur des bornes inferieures pour des indices de morse de points critiques obtenus par des principes de min max en combinant cette information avec une inegalite semiclassique on obtient des estimations pointues sur la croissance de certaines valeurs critiques a partir desquelles on deduit de nouveaux resultats de multiplicite pour des solutions d equations elliptiques semi lineaires d ordre 2

images of contractive projections on operator algebras it is shown that if p is a weak continuous contractive projection on a jbw triple m then p m is of type i or semifinite respectively if m is of the corresponding type we also show that p m has no infinite spin part if m is a type i von neumann algebra

probabilistic index models summary we present a semiparametric statistical model for the probabilistic index which can be defined as p y y a where y and y a are independent random response variables associated with covariate patterns x and x a respectively a link function defines the relationship between the probabilistic index and a linear predictor asymptotic normality of the estimators and consistency of the covariance matrix estimator are established through semiparametric theory the model is illustrated with several examples and the estimation theory is validated in a simulation study

on closed test procedures for dose response analysis this paper concerns the testing of a dose response effect in medical studies we consider two situations the first is when the drug effect on a parameter of interest is likely to increase or decrease with increasing doses we propose a procedure based on the closure principle of peritz combined with an application of a closed testing procedure of marcus et al to a test proposed by turkey et al the second situation is the analysis of a drug effect where one might observe a reversal at higher doses for this situation we propose simultaneous examination of contrasts among the doses at each of several stages of the testing scheme we calculate critical values for this procedure incorporating the correlation structure among the contrasts both procedures strongly control the family wise error rate at the pre determined alpha level they also provide information about the shape of the dose response lacking in other commonly used procedures for testing against an ordered alternative hypothesis we illustrate the procedures on two datasets

john w tukey s contributions to multiple comparisons this article provides a historical overview of the philosophical theoretical and practical contributions made by john tukey to the field of simultaneous inference his early work culminating in the monograph the problem of multiple comparisons established him as one of the pioneers in the field investing it with both academic respectability and a focus on practical problems for many years afterward tukey only published sporadically in the area but remained convinced that multiplicity issues were of fundamental importance during the last decade of his life tukey again devoted substantial attention to multiplicity experimenting with different graphical representations of multiple comparison procedures and exploring the implications of new approaches to controlling family wise error rates he leaves a rich legacy that should engage and inspire statisticians for many years to come

state spaces of jb triples an atomic decomposition is proved for banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process this is then applied to yield under appropriate assumptions geometric characterizations up to isometry of the unit ball of the dual space of a jb triple and up to complete isometry of one sided ideals in c algebras

centralisers of spaces of symmetric tensor products and applications we show that the centraliser of the space of n fold symmetric injective tensors n 2 on a real banach space is trivial with a geometric condition on the set of extreme points of its dual the space of integral polynomials we obtain the same result for complex banach spaces we give some applications of this results to centralisers of spaces of homogeneous polynomials and complex banach spaces in addition we derive a banach stone theorem for spaces of vector valued approximable polynomials

complexity an interpretability criterion for multiple comparisons abstract this article deals with multiple comparison methods for a set of populations which can be described in terms of testing hypotheses of homogeneity of subsets criteria for evaluating procedures are defined in terms of the set of outcomes of all tests termed the pattern of decisions in particular complexity is introduced as a new criterion based on interpretability of that pattern the criteria are defined and discussed in a general framework and then applied to the comparison of normal means for the cases considered results favor an f over a range procedure and are mixed in the comparison of the f and the range procedure with a new gap procedure

isometries between spaces of homogeneous polynomials abstract we derive banach stone theorems for spaces of homogeneous polynomials we show that every isometric isomorphism between the spaces of homogeneous approximable polynomials on real banach spaces e and f is induced by an isometric isomorphism of e onto f with an additional geometric condition we obtain the analogous result in the complex case isometries between spaces of homogeneous integral polynomials and between the spaces of all n homogeneous polynomials are also investigated

nonradial solutions of elliptic weighted superlinear problems in bounded symmetric domains abstract the present work has two objectives first we prove that a weighted superlinear elliptic problem has infinitely many nonradial solutions in the unit ball second we obtain the same conclusion in annuli for a more general nonlinearity which also involves a weight we use a lower estimate of the energy level of radial solutions with k 1 zeros in the interior of the domain and a simple counting uniqueness results due to tanaka 14 2008 and 13 2007 are very useful in our approach

boundedness of completely additive measures with application to 2 local triple derivations we prove a jordan version of dorofeev s boundedness theorem for completely additive measures and use it to show that every not necessarily linear nor continuous 2 local triple derivation on a continuous jbw triple is a triple derivation 2 local triple derivations are well understood on von neumann algebras jbw triples which are properly defined in section i are intimately related to infinite dimensional holomorphy and include von neumann algebras as special cases in particular continuous jbw triples can be realized as subspaces of continuous von neumann algebras which are stable for the triple product xy z zy x and closed in the weak operator topology

multiple comparisons by rerandomization tests abstract classical methods of simultaneous inference cannot be used with rerandomization tests without risking excessive type i errors this is illustrated by examples that show some published methods to be invalid for multiple comparisons however the use of stepwise procedures is shown to remain valid with rerandomization tests in particular this article advocates an adaptation of begun and gabriel s 1981 technique and provides the algorithm for using it

on multiple comparisons in the randomization analysis of growth and response curves two multiple comparisons procedures are suggested for supplementing randomization analysis of growth and response curves one controls the experimentwise type i error rate for all possible contrast curves via an extension of the scheffe method the other controls a family of type i error rates via a stepwise testing procedure both can be approximated by standard f tests without costly recomputation of all of the test statistics for a large number of permutations

the range of a structural projection abstract let a be a jbw triple a linear subspace j of a is called an inner ideal in a provided that the subspace j a j is contained in j a subtriple b in a is said to be complemented if a b ker b where ker b a a b a b 0 a complemented subtriple in a is a weak closed inner ideal a linear projection on a is said to be structural if for all elements a b and c in a formula the range of a structural projection is a complemented subtriple and conversely a complemented subtriple is the range of a unique structural projection we analyze the structure of the weak closed inner ideal generated by two arbitrary tripotents in a jbw triple in terms of the simultaneous peirce spaces of three suitably chosen pairwise compatible tripotents this result is then used to show that every weak closed inner ideal j in a jbw triple a is a complemented subtriple in a and therefore the range of a unique structural projection on a as an application structural projections on w algebras are considered

multiple testing in clinical trials the basic ideas of multiple testing are outlined and the problem of how to control the probability of erroneous decisions is discussed the main emphasis is on the concept of the multiple level of significance controlling the experiment or family error in the strong sense which can be achieved by applying the principle of closed tests various practical situations encountered in multiple testing in clinical trials are considered more than one end point more than two treatments such as comparisons with a single control comparisons using ordered alternatives all pairwise comparisons and contrast methods and more than one trial tests based on global statistics the union intersection principle and other criteria are discussed the application of the multiple test concept in sequential sampling is investigated finally some comments are made on multiple power multiple confidence intervals and directed decisions

grothendieck s inequalities for real and complex jbw triples we prove that if m 4 1 2 3 and e 0 if v and w are complex jbw triples with preduals v andw respectively and if u is a separately weak continuous bilinear form on v w then there exist norm one functionals 1 2 v and 1 2 w satisfying u x y m u x 2 2 e 2 x 2 1 1 2 y 2 2 e 2 y 2 1 1 2 for all x y v w here for a norm one functional on a complex jb triple v stands for the prehilertian seminorm on v associated to in bf1 we arrive in this grothendieck s inequality through results of c h chu b iochum and g loupias cil and a corrected version of the little grothendieck s inequality for complex jb triples due to t barton and y friedman bf1 we also obtain extensions of these results to the setting of real jb triples 2000 mathematics subject classification 17c65 46k70 46l05 46l10 and 46l70

uniqueness of large radial solutions and existence of nonradial solutions for a superlinear dirichlet problem in annulii abstract here we establish the existence of infinitely many nonradial solutions for a superlinear dirichlet problem in annulii our proof relies on estimating the number of radial solutions having a prescribed number of nodal regions we prove that for k 0 large there exist exactly two radial solutions with k nodal regions connected components of x u x 0 the problem need not be homogeneous

robust rank procedures for the behrens fisher problem abstract the problem of testing for equality of the medians of two populations is considered the standard distribution free tests for this problem require that the two populations have the same shape to maintain their nominal significance level under the null hypothesis a method is given to modify many of these tests so they can be used to test for equality of the medians with fewer assumptions on the shapes of the two populations the method is demonstrated using the mann whitney wilcoxon statistic

on the power of tests for multiple comparison of three normal means abstract this article gives theoretical reasons for the findings of a simulation study by shaffer 1981 two well established procedures for multiple comparison of three normal means are compared an f procedure and an r procedure it turns out that for a large set of parameters the average number of rejected pairwise hypotheses is larger when the f procedure is applied to achieve our result we have to prove a special instance of a conjecture by david lachenbruch and brandis 1972

finite tripotents and finite jbw triples abstract we study two natural preorders on the set of tripotents in a jb triple defined in terms of their peirce decomposition and weaker than the standard partial order we further introduce and investigate the notion of finiteness for tripotents in jbw triples which is a natural generalization of finiteness for projections in von neumann algebras we analyze the preorders in detail using the standard representation of jbw triples we also provide a refined version of this representation in particular a decomposition of any jbw triple into its finite and properly infinite parts since a jbw algebra is finite if and only if the extreme points of its unit ball are just unitaries our notion of finiteness differs from the concept of modularity widely used in jordan structures so far the exact relationship of these two notions is clarified in the last section

conjugacy of involutive antiautomorphisms of von neumann algebras department of mathematics university of oslo blindern oslo 3 norway communicated by a cannes received may 5 1984 accepted july 7 1984 specialized to the factor case the main result is as follows let m be a factor and a a involutive antiautomorphisms of m let m denote the jordan algebra ms xe m x x q x i 1 2 then a and gin are conjugate if and only if m and m z are isomorphic as jordan algebras thus many nonisomorphic jw algebras may generate the same von neumann algebra

stepwise multiple test procedures and control of directional errors one of the most difficult problems occurring with stepwise multiple test procedures for a set of two sided hypotheses is the control of directional errors if rejection of a hypothesis is accomplished with a directional decision in this paper we generalize a result for so called step down procedures derived by shaffer to a large class of stepwise or closed multiple test procedures in a unifying way we obtain results for a large class of order statistics procedures including step down as well as step up procedures hochberg rom but also a procedure of hommel based on critical values derived by simes our method of proof is also applicable in situations where directional decisions are mainly based on conditionally independent t statistics a closed f test procedure applicable in regression models with orthogonal design the modified s method of scheffe applicable in the analysis of variance and fisher s lsd test for the comparison of three means will be considered in more detail

infinitely many solutions for some nonlinear elliptic problems in symmetrical domains on considere le probleme aux valeurs limites u u u u 2 2 0 u h 0 1 ou r n est un domaine borne n 3 2 2n n 2 est l exposant critique pour le plongement de sobolev et est un parametre positif reel on demontre l existence d une infinite de solutions quand a de bonnes symetries

a comparison of one sided methods to identify significant individual outcomes in a multiple outcome setting stepwise tests or global tests with closed testing we compare two approaches to the identification of individual significant outcomes when a comparison of two groups involves multiple outcome variables the approaches are all designed to control the familywise error rate fwe with any subset of the null hypotheses being true in the strong sense the first approach is initially to use a global test of the overall hypothesis that the groups are equivalent for all variables followed by an application of the closed testing algorithm of marcus peritz and gabriel the global tests considered here are ordinary least squares ols generalized least squares gls an approximation to a likelihood ratio test alr and a new test based on an approximation to the most powerful similar test for simple alternatives the second approach is that of stepwise testing which tests the univariate hypotheses in a specific order with appropriate adjustment to the univariate p values for multiplicity the stepwise tests considered include both step down and step up tests of a general type and likewise permutation tests that incorporate the dependence structure of the data we illustrate the tests with two examples of birth outcomes a comparison of cocaine exposed new borns to control new borns on neurobehavioural and physical growth variables and in a separate study a comparison of babies born to diabetic mothers and babies born to non diabetic mothers on minor malformations after describing the methods and analysing the birth outcome data we use simulations on gaussian data to provide guidelines for the use of these procedures in terms of power and computation

a note on two sided distribution free treatment versus control multiple comparisons abstract distribution free treatment versus control multiple comparison procedures using joint ranking and pairwise ranking are compared the pairwise ranking method is extended to allow for all contrast comparisons among the treatments and the control the author shows by counterexample that the joint ranking method does not control the maximum type 1 error rate

measures of weak non compactness in preduals of von neumann algebras and jbw triples abstract we prove among other results that three standard measures of weak non compactness coincide in preduals of jbw triples this result is new even for preduals of von neumann algebras we further provide a characterization of jbw triples with strongly wcg predual and describe the order of seminorms defining the strong topology as a byproduct we improve a characterization of weakly compact subsets of a jbw triple predual providing so a proof for a conjecture open for almost eighteen years on weakly compact operators from a jb triple into a complex banach space

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

some new inequalities for the range distribution with application to the determination of optimum significance levels of multiple range tests abstract a problem arising in multiple range tests is the monotonicity of the defining critical values which ws first treated by lehmann and shaffer 1977 this article proves a general inequality for the distribution function of the range which guarantees the monotonicity of a special set of critical values it also discusses the relation to some other inequalities the importance of these inequalities is pointed out in considering some concepts of admissibility and optimality of multiple range tests

contractive projections and operator spaces parallel to the study of finite dimensional banach spaces there is a growing interest in the corresponding local theory of operator spaces we define a family of hilbertian operator spaces h k n 1 k n generalizing the row and column hilbert spaces r n and c n and we show that an atomic subspace x c b h that is the range of a contractive projection on b h is isometrically completely contractive to an sum of the h k n and cartan factors of types 1 to 4 in particular for finite dimensional x this answers a question posed by oikhberg and rosenthal explicit in the proof is a classification up to complete isometry of atomic w closed jw triples without an infinite dimensional rank 1 w closed ideal

closure of the newman keuls multiple comparisons procedure abstract closure of the family of hypotheses tested by the newman keuls procedure has been proposed in order to avoid excessive type i errors this proposal is examined in some detail and a practical procedure for carrying it out is described and programmed in fortran the relation of such closure to other multiple comparison procedures is discussed and its relatively high power is pointed out

multiple comparison methods for means multiple comparison methods mcms are used to investigate differences between pairs of population means or more generally between subsets of population means using sample data although several such methods are commonly available in statistical software packages users may be poorly informed about the appropriate method s to use and or the correct way to interpret the results this paper classifies the mcms and presents the important methods for each class both simulated and real data are used to compare methods and emphasis is placed on correct application and interpretation we include suggestions for choosing the best method mathematica programs developed by the authors are used to compare mcms by taking advantage of mathematica s notebook structure an interested student can use these programs to explore the subject more deeply the programs and examples used in the article are available at http www cs gasou edu faculty rafter mcmm