testing and selecting for equivalence with respect to a control abstract the problem of equivalence assessment of several treatments with a control is considered the first approach uses a hypothesis testing formulation in which the alternative states global equivalence with respect to a family of distributions with location parameter a test based on a two sided many one statistic is proposed least favorable parameter configuration results are presented as being necessary to evaluate critical values and to determine sample sizes implied by certain power requirements when planning experiments the second approach concerns a stepwise selection procedure the goal is to select a subset of treatments containing all those actually equivalent to the control in the absence of global equivalence the normal case is dealt with in detail for randomized block designs as well as for one way layouts concerning the test problem optimal allocations of total sample sizes are determined to guarantee specified power requirements for the one way layout

a problem of time in the multiplicative scheme for the n site hopper quantum measure theory qmt is an approach to quantum mechanics based on the path integral in which quantum theory is conceived of as a generalised stochastic process one of the postulates of qmt is that events with zero quantum measure do not occur however this is not sufficient to give a full picture of the quantum world determining the other postulates is a work in progress and this paper investigates a proposal called the multiplicative scheme for qmt in which the physical world corresponds essentially to a set of histories from the path integral this scheme is applied to sorkin s n site hopper a discrete unitary model of a single particle on a ring of n sites motivated by free schrodinger propagation it is shown that the multiplicative scheme s global features lead to the conclusion that no non trivial time finite event can occur

an upper bound for codes for the noisy two access binary adder channel corresp using earlier methods a combinatorial upper bound is derived for c cdot d where c d is a delta decodable code pair for the noisy two access binary adder channel asymptotically this bound reduces to r 1 r 2 leq frac 3 2 e log 2 e frac 1 2 e log 2 1 2e frac 1 2 e h frac 1 2 e frac 1 2 h 2e where e lfloor delta 1 2 rfloor n n rightarrow infty and r 1 resp r 2 is the rate of the code c resp d

unimodality convexity and applications properties of univariate unimodal distributions concepts of multivariate unimodality some more notions of unimodality unimodality for discrete distributions unimodality of infinitely divisible distributions unimodality and notions of dependence ordering of distributions by peakedness applications of unimodality in statistical inference convexity in reliability theory appendix

quantum measure and integration theory this article begins with a review of quantum measure spaces quantum forms and indefinite inner product spaces are then discussed the main part of the paper introduces a quantum integral and derives some of its properties the quantum integral s form for simple functions is characterized and it is shown that the quantum integral generalizes the lebesgue integral a bounded monotone convergence theorem for quantum integrals is obtained and it is shown that a radon nikodym type theorem does not hold for quantum measures as an example a quantum lebesgue integral on the real line is considered

assessing nonsuperiority noninferiority or equivalence when comparing two regression models over a restricted covariate region in many scientific problems the purpose of the comparison of two regression models which describe the relationship between a same response variable and several same covariates for two different groups is to demonstrate that one model is no higher than the other by a negligible amount or to demonstrate that the models have only negligible differences and so they can be regarded as describing practically the same relationship between the response variable and the covariates in this article methods based on one sided pointwise confidence bands are proposed for assessing the nonsuperiority of one model to the other and for assessing the equivalence of two regression models examples from qt qtc study and from drug stability study are used to illustrate the methods

simultaneous confidence bands for a percentile hyper plane with covariates constrained in a restricted range abstract a simultaneous confidence band provides useful information about the plausible range of the unknown regression model in several recent papers confidence bands have been used for various inferential purposes see for example liu et al 2004 2005 2009 2010 2012 2014 liu and hayter 2007 1 liu and lin 2009 piegorsch et al 2005 han et al 2015 and zhou 2017 the construction of simultaneous confidence bands has a long history going back to working and hotelling 1929 2 and is often difficult when the region over which a confidence band is required is restricted and the number of predictor variables is greater than one in this paper we have developed methods to construct simultaneous confidence bands for a percentile hyper plane these methods allow us to construct the bands over arbitrary intervals either finite or infinite they also allow us to construct the type i and type ii bands in order to get an idea of the efficiency of these bands we have also developed the confidence sets for the bands and have compared the bands under the minimum volume confidence set optimality criterion the proposed methods are illustrated by an example

berezin integrals and poisson processes we show that the calculation of berezin integrals over anticommuting variables can be reduced to the evaluation of expectations of functionals of poisson processes via an appropriate feynman kac formula in this way the tools of ordinary analysis can be applied to berezin integrals and as an example we prove a simple upper bound possible applications of our results are briefly mentioned

the maximum familywise error rate of fisher s least significant difference test abstract in this article an investigation is made of the maximum familywise error rate mfwer of fisher s least significant difference lsd test for testing the equality of k population means in a one way layout an exact expression for the mfwer is derived see theorem 1 for all balanced models and for an unbalanced model with k 3 populations type i models a close upper bound for the mfwer is derived for all unbalanced models with four or more populations type ii models these expressions are used to illustrate that the mfwer may greatly exceed the nominal size of the lsd test in addition a simple modification of the lsd test is proposed to control the mfwer this modified procedure has mfwer equal to the nominal level for type i models and no greater than for type ii models theorem 2 and is therefore recommended as an improvement over the lsd test the key to the analysis is two theorems concerning the ranges of independent normal random variables which are contained in the append

a multiple comparison procedure for hypotheses with gatekeeping structure we develop gatekeeping procedures that focus on comparing multiple treatments with a control when there are multiple endpoints our procedures utilize estimated correlations among individual test statistics without parametric assumptions we make comparisons with other gatekeeping procedures with respect to properties of the trade off in statistical power between families of hypotheses we introduce a reward function to facilitate these comparisons we illustrate our methods by simulation and an analysis of data from a randomized multi armed clinical trial copyright 2013 oxford university press

detecting dose response with contrasts analyses of dose response studies should separate the question of the existence of a dose response relationship from questions of functional form and finding the optimal dose a well chosen contrast among the estimated effects of the studied doses can make a powerful test for detecting the existence of a dose response relationship a contrast based test attains its greatest power when the pattern of the coefficients has the same shape as the true dose response relationship however it loses power when the contrast shape and the true dose response shape are not similar thus a primary test based on a single contrast is often risky two or more appropriately chosen contrasts can assure sufficient power to justify the cost of a multiplicity adjustment an example shows the success of a two contrast procedure in detecting dose response which had frustrated several standard procedures

a bell inequality analog in quantum measure theory one obtains bell s inequalities if one posits a hypothetical joint probability distribution or measure whose marginals yield the probabilities produced by the spin measurements in question the existence of a joint measure is in turn equivalent to a certain causality condition known as screening off we show that if one assumes more generally a joint quantal measure or decoherence functional one obtains instead an analogous inequality weaker by a factor of the proof of this tsirel son inequality is geometrical and rests on the possibility of associating a hilbert space to any strongly positive quantal measure these results lead both to a question does a joint measure follow from some quantal analog of screening off and to the observation that non contextual hidden variables are viable in histories based quantum mechanics even if they are excluded classically

quantum dynamics without the wavefunction when suitably generalized and interpreted the path integral offers an alternative to the more familiar quantal formalism based on state vectors self adjoint operators and external observers mathematically one generalizes the path integral as propagator to a quantal measure on the space of all conceivable worlds and this generalized measure expresses the dynamics or law of motion of the theory much as wiener measure expresses the dynamics of brownian motion within such histories based schemes new and more realistic possibilities open up for resolving the philosophical problems of the state vector formalism in particular one can dispense with the need for external agents by locating the predictive content of in its sets of measure zero such sets are to be precluded but unrestricted application of this rule engenders contradictions one possible response would remove the contradictions by circumscribing the application of the preclusion concept another response more in the tradition of quantum logic would accommodate the contradictions by dualizing to a space of co events and effectively identifying reality with an element of this dual space

exact simultaneous confidence intervals for multiple comparisons among three or four mean values abstract a procedure for constructing exact simultaneous confidence intervals for a finite set of multiple comparisons among three or four groups is presented these confidence intervals are hyperbolic and based on an unbiased estimator of the mean values having a normal distribution with covariance matrix 2v where v is an arbitrary known positive definite matrix this procedure is used to study the amount of conservativeness of tukey kramer intervals for pairwise comparisons in an unbalanced one way analysis of variance design

simultaneous confidence bands for linear regression with heteroscedastic errors abstract the scheffe method may be used to construct simultaneous confidence bands for a regression surface for the whole predictor space when the bands need only hold for a subset of that space previous authors have described how the bands can be appropriately narrowed while still maintaining the desired level of confidence data with heteroscedastic errors occur often and unless some transformation is feasible there is no obvious way to construct bands using the current methods this article shows how to construct approximate simultaneous confidence bands when the errors are heteroscedastic and symmetric the method works when the weights are known or unknown and have to be estimated the region in which the bands must hold can be quite general and will work for any linear unbiased estimate of the regression surface the method can even be extended to linear estimates with a small amount of bias such as nonparametric kernel regression smoothers

step up multiple testing of parameters with unequally correlated estimates we consider the problem of simultaneously testing k or to 2 hypotheses on parameters theta 1 theta k using test statistics t 1 t k such that a specified familywise error rate alpha is achieved dunnett and tamhane 1992a proposed a step up multiple test procedure in which testing starts with the hypothesis corresponding to the least significant test statistic and proceeds towards the most significant stopping the first time a significant test result is obtained and rejecting the hypotheses corresponding to that and any remaining test statistics the parameter estimates used in the t statistics were assumed to be normally distributed with a common variance which was a known multiple of an unknown sigma 2 and known correlations which were equal in the present article we show how the procedure can be extended to include unequally correlated parameter estimates unequal correlations occur for example in experiments involving comparisons among treatment groups with unequal sample sizes we also compare the step up and step down multiple testing approaches and discuss applications to some biopharmaceutical testing problems

super quantum measures on effect algebras with the riesz decomposition properties we give one basis of the space of super quantum measures on finite effect algebras with the riesz decomposition properties rdp for short then we prove that the super quantum measures and quantum interference functions on finite effect algebras with the rdp are determined each other at last we investigate the relationships between the super quantum measures and the diagonally positive signed measures on finite effect algebras with the rdp in detail

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

implementing optimal allocation in sequential binary response experiments for sequential experiments with k treatments we establish two formal optimization criteria to find optimal allocation strategies both criteria involve the sample sizes on each treatment and a concave noncentrality parameter from a multivariate test we show that these two criteria are equivalent we apply this result to specific questions 1 how do we maximize power of a multivariate test of homogeneity with binary response and 2 for fixed power how do we minimize expected treatment failures because the solutions depend on unknown parameters we describe a response adaptive randomization procedure that targets the optimal allocation and provides increases in power along the lines of 2 4 over complete randomization for equal allocation the increase in power contradicts the conclusions of other authors who have explored other randomization procedures for k 2 and have found that the variability induced by randomization negates any benefit of targeting an optimal allocation

using confidence intervals to compare several correlated areas under the receiver operating characteristic curves the performance of a diagnostic tool yielding quantitative or ordinal measurements is often assessed in terms of its area under the receiver operating characteristic curve auc as new diagnostic tools are constantly being developed a frequently occurring task is to compare multiple aucs as derived from the same group of subjects for this purpose previous methods have usually used an omnibus chi square test which may not be very informative we present here methods for comparing several correlated aucs using simultaneous confidence intervals to improve small sample properties we adopt the method of variance estimates recovery in which confidence limits for each auc are obtained on the basis of the logit and inverse hyperbolic sine transformations a simulation study demonstrates the superior performance of the proposed approach the methods are illustrated with two examples

an anhomomorphic logic for quantum mechanics although various schemes for anhomomorphic logics for quantum mechanics have been considered in the past we shall mainly concentrate on the quadratic or grade 2 scheme in this scheme the grade 2 truth functions are called coevents we discuss properties of coevents projections on the space of coevents and the master observable we show that the set of projections forms an orthomodular poset we introduce the concept of precluding coevents and show that this is stronger than the previously studied concept of preclusive coevents precluding coevents are defined naturally in terms of the master observable a result that exhibits a duality between preclusive and precluding coevents is given some simple examples are presented

multiple testing of general contrasts powerful improvements are possible for multiple testing procedures when the hypotheses are logically related closed testing with exhaustive tests provides a unifying framework for developing such procedures but can be computationally difficult and can be nonmonotonic in p values royen introduced a truncated closed testing method for the case of all pairwise comparisons in the analysis of variance that is monotonic in p values shaffer developed a similar truncated procedure for more general comparisons but using bonferroni tests rather than exhaustive tests and westfall extended shaffer s method to allow exhaustive tests this article extends royen s method to general contrasts and proves that it is equivalent to the extended shaffer procedure for k contrasts the method generally requires evaluation of o 2k critical values that correspond to subset intersection hypotheses and is computationally infeasible for large k the set of intersections is represented using a tree structure and a

an exact confidence set for a maximum point of a univariate polynomial function in a given interval construction of a confidence set for a maximum point of a function is an important statistical problem which has many applications in this article an exact 1 confidence set is provided for a maximum point of a univariate polynomial function in a given interval it is shown how the construction method can readily be applied to many parametric and semiparametric regression models involving a univariate polynomial function examples are given to illustrate this confidence set and to demonstrate that it can be substantially narrower and so better than the only other confidence set available in the statistical literature that guarantees 1 confidence level

a bayesian credible subgroups approach to identifying patient subgroups with positive treatment effects many new experimental treatments benefit only a subset of the population identifying the baseline covariate profiles of patients who benefit from such a treatment rather than determining whether or not the treatment has a population level effect can substantially lessen the risk in undertaking a clinical trial and expose fewer patients to treatments that do not benefit them the standard analyses for identifying patient subgroups that benefit from an experimental treatment either do not account for multiplicity or focus on testing for the presence of treatment covariate interactions rather than the resulting individualized treatment effects we propose a bayesian credible subgroups method to identify two bounding subgroups for the benefiting subgroup one for which it is likely that all members simultaneously have a treatment effect exceeding a specified threshold and another for which it is likely that no members do we examine frequentist properties of the credible subgroups method via simulations and illustrate the approach using data from an alzheimer s disease treatment trial we conclude with a discussion of the advantages and limitations of this approach to identifying patients for whom the treatment is beneficial

pairwise comparisons of generally correlated means abstract a commonly occurring statistical inference problem in practice is that of making simultaneous comparisons among three or more treatment means i 1 i k for certain experimental designs one way to do this the t method proposed by tukey 1953 constructs simultaneous confidence intervals for all pairwise differences of the treatment means i j 1 i j k i j the joint confidence level of these confidence intervals however depends in a very complicated fashion on the covariance structure of the treatment mean estimates i and therefore for designs where the covariance structure is not simple the joint confidence level is not readily apparent in general this is the case for any unbalanced design or for designs in which the treatment mean estimates i have unequal correlations tukey conjectured in 1953 that whatever the correlation structure of the treatment mean estimates i the t method would always provide a conservative set of confidence intervals that is that th

sample size for equivalence trials a case study from a vaccine lot consistency trial for some trials simple but subtle assumptions can have a profound impact on the size of the trial a case in point is a vaccine lot consistency or equivalence trial standard sample size formulas used for designing lot consistency trials rely on only one component of variation namely the variation in antibody titers within lots the other component the variation in the means of titers between lots is assumed to be equal to zero in reality some amount of variation between lots however small will be present even under the best manufacturing practices using data from a published lot consistency trial we demonstrate that when the between lot variation is only 0 5 per cent of the total variation the increase in the sample size is nearly 300 per cent when compared with the size assuming that the lots are identical the increase in the sample size is so pronounced that in order to maintain power one is led to consider a less stringent criterion for demonstration of lot consistency the appropriate sample size formula that is a function of both components of variation is provided we also discuss the increase in the sample size due to correlated comparisons arising from three pairs of lots as a function of the between lot variance

symmetric multilinear forms and polarization of polynomials we study a generalization of the classical correspondence between homogeneous quadratic polynomials quadratic forms and symmetric alternating bilinear forms to forms in n variables the main tool is combinatorial polarization and the approach is applicable even when n is not invertible in the underlying field

a step up multiple test procedure abstract we consider the problem of simultaneously testing k 2 hypotheses on parameters 1 k in a typical application the s may be a set of contrasts for instance a set of orthogonal contrasts among population means or a set of differences between k treatment means and a standard treatment mean it is assumed that least squares estimators 1 k are available that are jointly normally distributed with a common variance known up to a scalar namely the error variance 2 and a common known correlation an independent 2 distributed unbiased estimator of 2 is also assumed to be available we propose a step up multiple test procedure for this problem which tests the t statistics for the k hypotheses in order starting with the least significant one and continues as long as an acceptance occurs by contrast the step down approach which is usually used starts with the most significant and continues as long as a rejection occurs critical constants required by this step up procedure to co

step down multiple tests for comparing treatments with a control in unbalanced one way layouts we show how a well known multiple step down significance testing procedure for comparing treatments with a control in balanced one way layouts can be applied in unbalanced layouts unequal sample sizes for the treatments the method we describe has the advantage that it provides p values for each treatment versus control comparison that take account of the multiple step down testing nature of the procedure these joint p values can be used with any value of alpha the fixed type i family wise error rate bound that may be specified by the investigator to determine the p values it is necessary to compute a multivariate student t integral for which a computer program is available this procedure is more powerful than the step down bonferroni procedure of holm and the single step procedure of dunnett an example from the pharmaceutical literature is used to illustrate the procedure

monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics abstract the technique of monte carlo mc tests dwass 1957 annals of mathematical statistics 28 181 187 barnard 1963 journal of the royal statistical society series b 25 294 provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated when no nuisance parameter is involved we extend this method in two ways first by allowing for mc tests based on exchangeable possibly discrete test statistics second by generalizing it to statistics whose null distribution involves nuisance parameters maximized mc mmc tests simplified asymptotically justified versions of the mmc method are also proposed these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics

using common random numbers and control variates in multiple comparison procedures this paper considers the determination of the relative merits of two or more system designs via stochastic simulation experiments by constructing simultaneous interval estimates of certain differences in expected performance tukey s all pairwise comparisons procedure hsu s multiple comparisons with the best procedure and dunnett s multiple comparisons with a control procedure are standard methods for making such comparisons we propose refinements for all three procedures through the use of two variance reduction techniques common random numbers and control variates we show that the proposed procedures are better than the standard multiple comparison procedures in the sense that they have a larger probability of containing the true difference and at the same time not containing zero when a difference exists

inclusion exclusion bonferroni identities and inequalities for discrete tube like problems via euler characteristics identity for the union of finitely many balls in d dimensional euclidean space with a single correction term this result also holds in the d dimensional sphere these results form the basis for a discrete theory of tubes which up to now has been continuous in nature the spherical result is used to give a simulation method for finding critical probabilities for multiple comparisons procedures and a computer program implementing the method is described numerical results are presented which demonstrate that in the tails of the distribution probability estimates based on the method tend to exhibit less variability than estimates based on naive simulation 1 introduction this paper touches on several areas of mathematics statistics and elementary probability theory the main results are somewhat technical in proof but easily stated consider a finite collection of measurable subsets ai n the classical inclusion exclusion identity is n

consistent histories and the interpretation of quantum mechanics the usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times called consistent histories through a criterion which ensures that within limits which are explicitly defined within the formalism classical rules for probabilities are satisfied the interpretive scheme which results is applicable to closed isolated quantum systems is explicitly independent of the sense of time i e past and future can be interchanged has no need for wave function collapse makes no reference to processes of measurement though it can be used to analyze such processes and can be applied to sequences of microscopic or macroscopic events or both as long as the mathematical condition of consistency is satisfied when applied to appropriate macroscopic events it appears to yield the same answers as other interpretative schemes for standard quantum mechanics though from a different point of view which avoids the conceptual difficulties which are sometimes thought to require reference to conscious observers or classical apparatus

a path length inequality for the multivariate t distribution with applications to multiple comparisons abstract this article presents a new inequality for the multivariate t distribution which implies a new method for multiple comparisons whose foundation rests on a recent inequality due to naiman the new method is promising in view of the fact that it utilizes information estimator intercorrelations ignored by the most widely used multiple comparison methods yet is not computationally prohibitive requiring only the numerical evaluation of a single one dimensional integral in this article the validity of the new method in the normal theoretic general linear model is established and efficiency studies relative to the methods of scheffe bonferroni sidak and hunter worsley are presented the new method is shown to always improve on scheffe s method the new method is also shown to perform well that is to lead to a smaller critical point than its competitors with low degrees of freedom but the method is not as efficient as the hunter worsley method for high degrees of freedom in addition the me

equivalence and interval testing for lehmann s alternative abstract equivalence and interval tests for lehmann s alternative that extend the well known savage test for one sided hypotheses are proposed the proposed tests are shown to be unbiased with a strictly unimodal power function provided the sample sizes in both treatment groups are equal by means of a numerical investigation of the bias in the case of unequal sample sizes that are not too far apart the suggested tests still turn out to provide practicable solutions because the computational effort to perform the suggested tests is considerable tables containing the critical values are displayed to perform these tests easily a numerical analysis of the power function of the interval test establishes this procedure as a powerful tool for detection of a significantly relevant difference in the small sample case in contrast to the case of interval testing the fact arises that the performance of a powerful equivalence study under lehmann s alternative requires an extensive amount of data because the p

exact simultaneous confidence intervals for pairwise comparisons of three normal means abstract the problem of simultaneously estimating the pairwise differences of means of three independent normal populations with equal variances is considered a computational method involving a bivariate t density is used to form confidence intervals with simultaneous coverage probability equal to 1 a for equal sample sizes the method is the tukey studentized range procedure with unequal sample sizes the method is superior to the various generalized tukey methods a table of probability points is presented for small sample sizes a large sample approximation based on the bivariate normal and studentized range distributions is given

multiple comparisons with a control in response surface methodology quadratic response surface methodology often focuses on finding the levels of some coded predictor variables x x l x 2 x k that optimize the expected value of a response variable y typically the experimenter starts from some best guess or control combination of the predictors usually coded to x 0 and performs an experiment varying them in a region around this center point the question of interest addressed here is whether any x in the experimental region provides an e y preferable to that of the control and if so by what amount this article approaches the question via simultaneous confidence intervals for e y x e y 0 for all x within a specified distance of 0 exact results for the quadratic regression case k 1 are obtained using existing results for linear regression a conservative solution for rotatable designs in k 1 predictors is obtained using a result of casella and strawderman several examples are provided

upper bounds on c_2 for a uniquely decodable code pair c_1 c_2 for a two access binary adder channel an algebraic and a combinatorial upper bound are derived on c 2 given the code c 1 where c l c 2 is a uniquely decodable code pair c 1 c 2 for a two access binary adder channel a uniquely decodable code with rate pair 0 5170 0 7814 is also described

quantum reality filters an anhomomorphic logic is the set of all possible realities for a quantum system our main goal is to find the actual reality for the system reality filters are employed to eliminate unwanted potential realities until only a remains in this paper we consider three reality filters that are constructed by means of quantum integrals a quantum measure can generate or actualize a if a is a quantum integral with respect to for a density function f over events a in this sense is an average of the truth values of with weights given by f we mainly discuss relations between these filters and their existence and uniqueness properties for example we show that a quadratic reality generated by a quantum measure is unique in this case we obtain the unique actual quadratic reality

simultaneous confidence bands for linear regression and smoothing suppose we observe y i f x i varepsilon i i 1 ldots n we wish to find approximate 1 alpha simultaneous confidence regions for f x x in mathscr x our regions will be centered around linear estimates hat f x of nonparametric or nonparametric f x there is a large amount of previous work on this subject substantial restrictions have been usually placed on some or all of the dimensionality of x the class of functions f that can be considered the class of linear estimates hat f and the region mathscr x the method we present is an approximation to the tube formula dn can be used for multidimensional x and a wide class of linear estimates by considering the effect of bias we are able to relax assumptions on the class of functions f which are considered simultaneous and numerical computations are used to illustrate the performance

simultaneous estimation and prediction using the expected coverage measure criterion on utilise des methodes d invariance pour construire des procedures minimax dans les modeles lineaires multivariables

exact simultaneous confidence bands for a collection of univariate polynomials in regression analysis we discuss a simple simulation method for construction of exact confidence bands having a pre assigned confidence level simultaneously for several regression functions which are univariate polynomials in the predictors this is accomplished by combining and extending existing results in a manner that permits both finite and infinite ranges for individual predictor variables we illustrate the method for a logistic regression model with both dichotomous and continuous predictors

confidence bands for regression functions abstract a method for obtaining conservative confidence bands for regression functions in low dimensions is given of particular importance is the applicability of the method to nonparametric regression computations examples and comparisons indicate the effectiveness of the method

optimum partition procedures for separating good and bad treatments abstract this article considers partitioning a given set of competing treatments into two subsets with the purpose of separating good and bad treatments the qualities good and bad are defined in terms of the parameter vector of the underlying distribution family regarding the probability of an incorrect partition within the class of so called natural procedures minimax solutions are derived under suitable distributional assumptions these results extend previous investigations to the larger family of quasi concave distributions it is shown that the multivariate noncentral t distribution with v degrees of freedom is 1 v concave and hence quasi concave thus the unknown variance case in a normal distribution setup is covered as a special application specifically for partitioning with respect to a control the presented minimax results are used in the unknown variance case to determine optimal allocations of total sample sizes that guarantee a correct partition at a preassigned confidence lev

minimum area confidence set optimality for confidence bands in simple linear regression the average width of a simultaneous confidence band has been used by several authors e g naiman and piegorsch as a criterion for the comparison of different confidence bands in this article the area of the confidence set that corresponds to a confidence band is used as a new criterion for simple linear regression comparisons have been carried out under this new criterion between hyperbolic bands two segment bands and three segment bands which include constant width bands as special cases it is found that if one requires a confidence band over the whole range of the covariate then the best confidence band is given by the working and hotelling hyperbolic band furthermore if one needs a confidence band over a finite interval of the covariate then a restricted hyperbolic band can again be recommended although a three segment band may be very slightly superior in certain cases

a multiple comparisons procedure for use in conjunction with the benard van elteren test summary the benard van elteren test statistic is a generalization of the friedman test statistic that permits multiple and unequal replicates per treatment per block a multiple comparisons procedure for pairwise comparisons of treatments is developed for use in conjunction with the benard van elteren test this procedure is applied to an example arising from a clinical trial sufficient conditions for use of this multiple comparisons procedure are given with examples of designs for which these conditions are met this multiple comparisons procedure is shown to be identical to a procedure developed by nemenyi unpublished doctoral thesis princeton university 1963 presented by hollander and wolfe 1973 nonparametric statistical methods new york wiley for the randomized complete block design with one replicate per treatment per block and to a procedure given by campbell 1980 in proceedings of the american statistical association section on statistical education 24 27 for the balanced incomplete block design

generalizations of k order additive discrete fuzzy measures abstract two types of generalizations of k order additive discrete fuzzy measures recently introduced by grabisch are shown first a special type of discrete fuzzy measures generalizing the pseudo additive measures with respect to a pan addition is introduced following the ideas of grabisch a mobius like transformation of discrete fuzzy measures is presented and an evaluation formula for the corresponding choquet like integral is given including the sugeno integral next k order additive fuzzy measures on general spaces are introduced combination of both generalizations is discussed and several open problems are addressed

combining the advantages of one sided and two sided test procedures for comparing several treatment effects abstract we consider the one way layout for comparing k treatment effects i 1 i k hayter earlier proposed a one sided studentized range test osrt for testing the null hypothesis h o 1 2 k against the simple ordered alternative ha 1 2 k with at least one strict inequality the osrt gives a set of simultaneous confidence intervals for all ordered pairwise differences j i i 0 but provides two sided finite confidence intervals if the sample averages are all far apart

pooling batches in drug stability study by using constant width simultaneous confidence bands one important study objective in drug stability studies is to estimate the shelf life of a drug a key statistical problem involved in this is how to assess the practical equivalence of different batches of the same drug so that different batches can be subgrouped to produce a single shelf life for the drug in this paper constant width simultaneous confidence bands are proposed to quantify the magnitude of difference between different batches with a particular view to establish the practical equivalence of different batches this approach is suitable for the situation that the intercepts and slopes of the regression lines for the batches cannot be assumed to be equal it is shown how constant width simultaneous confidence bands can be easily constructed for the multiple comparison of several general linear regression models in particular it is shown that constant width simultaneous confidence bands have a better chance to establish the equivalence than and so are preferable to the hyperbola shaped simultaneous confidence bands considered j am stat assoc 2004 99 395 403

a generalized tukey conjecture for multiple comparisons among mean vectors abstract in this article the tukey kramer procedure for multiple comparisons of pairwise differences of mean vectors in multivariate normal distributions is considered a multivariate version of the tukey kramer procedure is presented and a generalized tukey conjecture of the conservativeness of the simultaneous confidence intervals for all pairwise comparisons by this procedure is affirmatively proved in the case of three correlated mean vectors some properties of the multivariate tukey kramer procedure are also presented and simulation results for some selected parameters are given

nonhomogeneous trellis codes for the quasi synchronous multiple access binary adder channel with two users a trellis code is em homogeneous if the number of branches emanating from each node or state in the trellis diagram is constant for example convolutional codes are linear homogeneous trellis codes a trellis code is em nonhomogeneous if the number of branches emanating from each node in the trellis diagram is not the same the two user binary adder channel is a multiple access channel with two binary inputs x 1 and x 2 and one ternary output y x 1 x 2 where the addition is done in the real number field the adder channel is synchronous if both encoders and the decoder maintain block frame synchronism it is quasi synchronous if the encoders do not start their blocks at the same time but the decoder knows the position of each block the difference between the starting times of the blocks is called the slippage the channel is asynchronous if no block synchronism exists among the encoders and the decoder some uniquely decodable code pairs c 1 c 2 are presented that can be used to transmit information reliably over the quasi synchronous binary adder channel with two users one of the codes is a nonhomogeneous trellis code the other is a common block code our code rates are better than deaett wolf codes and are close to or equal to the asymptotic rates of kasami em et al a method for calculating the rates of nonhomogeneous trellis codes is described an algorithm for finding more uniquely decodable code pairs for the quasi synchronous binary adder channel is formulated

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

the efficiency of simulation based multiple comparisons a frequently encountered problem in practice is that of simultaneous interval estimation of p linear combinations of a parameter beta in the setting of or equivalent to a univariate linear model this problem has been solved adequately only in a few settings when the covariance matrix of the estimator is diagonal in other cases conservative solutions can be obtained by the methods of scheffe bonferroni or sidak 1967 journal of the american statistical association 62 626 633 here we investigate the efficiency of using a simulated critical point for exact intervals which has been suggested before but never put to serious test we find the simulation based method to be completely reliable and essentially exact sample size savings are substantial in our settings 3 19 over the sidak method 4 37 over the bonferroni method and 27 33 over the scheffe method we illustrate the efficiency and flexibility of the simulation based method with case studies in physiology and marine ecology

graph theoretic approaches to the code construction for the two user multiple access binary adder channel we relate coding for the two user multiple access binary adder channel to a problem in graph theory known as the independent set problem graph theoretic approaches to coding for both synchronized and nonsynchronized two user adder channels are presented using the tu an theorem on the independence number of a simple graph we are able to improve the lower bounds on the achievable rates of uniquely and delta decodable codes for the synchronized adder channel derived by kasami and lin we are also able to derive lower bounds on the achievable rates of uniquely decodable codes for the nonsynchronized adder channel we show that the rates of deaett wolf codes for the nonsynchronized adder channel fall below the bounds synchronizing sequences for the nonsynchronized adder channel are constructed

average width optimality for confidence bands in simple linear regression abstract the problem of constructing optimal confidence bands for a simple linear regression over the whole real line is considered optimality is defined as minimization of the average width of the bands weighted by a normalized function this weight function is presented as an indicator of experimental interest in the varying width of the band a comparison between the commonly seen hyperbolic bands and segmented line bands is presented

exact confidence bands for linear regression over intervals abstract exact simultaneous confidence intervals and bands for the regression line on a set cx in simple linear regression have been known only when cx is a finite set with one or two points or when cx is a finite or infinite interval otherwise conservative bands have been used in this article we present a method for constructing exact confidence bands on an arbitrary finite union of intervals or points also tables are provided for cases of finite cx with three points and of cx an interval

control charts for detecting cyclical behavior one way that a process can be out of statistical control is that the process mean can follow a cyclical pattern over time this out of control condition leads to increased variability in the variable of interest over any production interval recently a control chart based on a common time series technique the periodogram was proposed as a means of detecting cyclical behavior of the process mean we show that this control chart is not able to detect certain periodicities and that it does not make use of all available information when multiple observations are taken at each sampling time using a multiple regression approach we present modifications of the periodogram approach that produce control charts sensitive to a wider range of periodicities and use all available information we compare the average run lengths of the procedures

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

multiple comparison of several linear regression models research on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means several years ago spurrier considered the multiple comparison of several simple linear regression lines he constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range when the models have the same design matrices this article extends spurrier s work in several directions first multiple linear regression models are considered and the design matrices are allowed to be different second the predictor variables are either unconstrained or constrained to finite intervals third the types of comparison allowed can be very flexible including pairwise many one and successive two simulation methods are proposed for the calculation of critical constants the methodologies are illustrated with examples

monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem the choquet sugeno and shilkret integrals with respect to monotone measures as well as their generalization the universal integral stand for a useful tool in decision support systems in this paper we propose a general construction method for aggregation operators that may be used in assessing output of scientists we show that the most often currently used indices of bibliometric impact like hirsch s h woeginger s w egghe s g kosmulski s maxprod and similar constructions may be obtained by means of our framework moreover the model easily leads to some new very interesting functions

simultaneous confidence intervals for pairwise multiple comparisons in a two way unbalanced design turkey s 1953 the problem of multiple comparisons unpublished report princeton university procedure is widely used for pairwise multiple comparisons in one way anova it provides exact simultaneous pairwise confidence intervals spci for balanced designs and conservative spci for unbalanced designs in this paper we will extend turkey s procedure to two way unbalanced designs both the exact and the conservative methods will be introduced the application of the new procedure is illustrated with sample data from two experiments

an improved gt2 method for simultaneous confidence intervals on pairwise differences the problem of pairwise comparisons of three parameters is considered it is assumed that a set of unbiased estimators of these parameters has a trivariate normal distribution with covariance matrix 2 b where b is a known positive definite matrix a probability inequality sharper than that used by hochberg 1974 is discussed based on this inequality it is possible to achieve simultaneous confidence intervals uniformly shorter than those arising from the gt2 method these new intervals are also generally shorter than the intervals arising from scheffe s method and from the bonferroni inequality in addition these new intervals are at times shorter than those from kramer s method when the latter method is appropriate

quantum integrals and anhomomorphic logics the basic arena for a probabilistic structure is a set a of events corresponding to a is a dual structure a of coevents we call a an anhomomorphic logic and the coevents are given by truth functions from a to the two element boolean algebra z2 0 1 one of the main goals of a physical theory is to describe physical reality and a coevent a z2 provides such a description in the sense that an event a a actually occurs if and only if a 1 the quantum integral over an event a with respect to a coevent is defined and its properties are treated integrals with respect to various coevents are computed quantum systems are frequently described by a quantum measure which gives the propensity a that an event a occurs for a if a 0 whenever a 0 we say that is preclusive preclusivity is a reality filter because it eliminates coevents that do not describe a possible reality for the system a quantum measure that can be represented as a quantum integral with respect to a coevent i

finite sample properties and asymptotic efficiency of monte carlo tests on donne une approche unifiee qui couvre le cas d une distribution nulle arbitraire afin d etudier les proprietes statistiques des tests de monte carlo

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

a one sided studentized range test for testing against a simple ordered alternative abstract consider the usual balanced one way fixed effects analysis of variance anova model x ij i e ij 1 j n 1 i k where the e ij are independent n 0 sgrave 2 random variables and i is the mean of the ith treatment 1 i k the i and sgrave 2 are unknown parameters let x i be the sample mean of the ith treatment based on n observations 1 i k and let s 2 be an unbiased estimate of sgrave 2 which is distributed independently of the x i as a 2 2 v v random variable usually the anova mean squared error with v k n 1 df is used as the estimate s 2 a problem that has received considerable attention is that of testing the null hypothesis h 0 1 k against the simple ordered alternative hypothesis h a 1 k with at least one strict inequality see e g barlow bartholomew bremner and brunk 1972 and robertson wright and dykstra 1988 various test procedures have been proposed for this problem such as the likelihood ratio test

atoms of weakly null additive monotone measures and integrals in this paper we prove some properties of atoms of weakly null additive monotone measures by using the regularity and weak null additivity a sin gleton characterization of atoms of monotone measures on a metric space is shown it is a generalization of previous results obtained by pap the calculation of the sugeno integral and the choquet integral over an atom is also presented respectively similar results for recently introduced universal integral are also given following these results it is shown that the sugeno integral and the choquet integral over an atom of monotone measure is maxitive linear and standard linear respectively convergence theorems for the sugeno integral and the choquet integral over an atom of a monotone measure are also shown

the kochen specker theorem revisited in quantum measure theory the kochen specker theorem is widely interpreted to imply that non contextual hidden variable theories that agree with the predictions of copenhagen quantum mechanics are impossible the import of the theorem for a novel observer independent interpretation of quantum mechanics due to sorkin is investigated

a statistical assessment of clinical equivalence an observed confidence distribution is proposed as a measure of strength of evidence for practically equivalent efficacies of two treatments the concept is independent of prior opinions about relevant sizes of a difference in efficacy it also avoids retrospective power calculations for trials with missed recruitment goals and allows combination of the confidence from independent experiments

a proof of the conjecture that the tukey kramer multiple comparisons procedure is conservative in this paper we present a first general proof of tukey s 1953 conjecture concerning the extension of the tukey multiple comparisons procedure to the case of unequal sample sizes thereby proving that the so called tukey kramer procedure is conservative in all cases also a brief history of the conjecture is given and some extensions and further problems concerning the procedure are discussed

pairwise comparisons with ordered categorical data clinical trials frequently involve pairwise comparisons of different treatments to evaluate their relative efficacy in this study we examine methods for conducting pairwise tests of treatments with ordered categorical responses a modified version of the wilcoxon mann whitney test based on a logistic regression model assuming proportional odds is a popular choice for comparing two treatments this paper discusses the extension of this test to pairwise comparisons involving more than two treatments however when the proportional odds assumption is not valid the wilcoxon mann whitney type test procedure cannot control the overall type i error rate at the prespecified level of significance we therefore propose a better strategy in which a latent normal model is employed we presented a simulated comparative study of power and the overall type i error rate to illustrate the superiority of the latent normal model examples are also given for illustrative purposes copyright 2013 john wiley sons ltd

on the structure of the k additive fuzzy measures in this paper we present some results concerning the vertices of the set of fuzzy measures being at most k additive we provide an algorithm to compute them we give some examples of the results obtained with this algorithm and give lower bounds on the number of vertices for the n 1 additive case proving that it grows much faster than the number of vertices of the general fuzzy measures the results in the paper suggest that the structure of k additive measures might be more complex than expected from their definition and in particular that they are more complex than general fuzzy measures

multiplicative interaction in network meta analysis meta analysis of a set of clinical trials is usually conducted using a linear predictor with additive effects representing treatments and trials additivity is a strong assumption in this paper we consider models for two or more treatments that involve multiplicative terms for interaction between treatment and trial multiplicative models provide information on the sensitivity of each treatment effect relative to the trial effect in developing these models we make use of a two way analysis of variance approach to meta analysis and consider fixed or random trial effects it is shown using two examples that models with multiplicative terms may fit better than purely additive models and provide insight into the nature of the trial effect we also show how to model inconsistency using multiplicative terms copyright 2014 john wiley sons ltd

equivalence with respect to a control stepwise tests summary the problem of selecting those treatments which are equivalent or bioequivalent to a control treatment is investigated by using single step step down and step up multipletesting procedures for each of the tests considered the null hypothesis is that of nonequivalence and the hypotheses are rejected in either a single step or a stepwise fashion while controlling the familywise error rate the single step procedure is based on expanded confidence intervals as discussed by bofinger the step down procedure is based on the method of naik and the step up procedure on the method of dunnett and tamhane almost all the critical constants used in the procedures are based on tables already published

hilbert spaces from path integrals it is shown that a hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental the decoherence functional provides the inner product on this history hilbert space it is also shown that the history hilbert space is the standard hilbert space in the case of non relativistic quantum mechanics

improved multiple comparisons with a control in response surface analysis quadratic response surface methodology often focuses on finding the levels of some coded predictor variables x x 1 x 2 x k that optimize the expected value of a response variable y typically the experimenter starts from some best guess or control combination of the predictors usually coded to x 0 and performs an experiment varying them in a region around this center point the question of interest addressed here is whether any x in the experimental region provides a long run mean response e y preferable to that of the control and if so by what amount this article approaches this question via simultaneous confidence intervals for x e y x e y 0 for all x within a specified distance of 0 a new method for two or more predictors is introduced that gives sharper intervals than the scheffe method and also the sa and edwards adaptation of the casella and strawderman method the new method does not require a rotatable design and allows for one sided simultaneous bounds for x appr

confidence sets for optimal factor levels of a response surface construction of confidence sets for the optimal factor levels is an important topic in response surfaces methodology in wan et al 2015 an exact 1 confidence set has been provided for a maximum or minimum point i e an optimal factor level of a univariate polynomial function in a given interval in this article the method has been extended to construct an exact 1 confidence set for the optimal factor levels of response surfaces the construction method is readily applied to many parametric and semiparametric regression models involving a quadratic function a conservative confidence set has been provided as an intermediate step in the construction of the exact confidence set two examples are given to illustrate the application of the confidence sets the comparison between confidence sets indicates that our exact confidence set is better than the only other confidence set available in the statistical literature that guarantees the 1 confidence level