fuzzy nilpotent algebra abstract we define the concept of fuzzy nilpotent algebra prove that the homomorphic inverse image of a fuzzy nilpotent algebra is also nilpotent and study the intersection and union of fuzzy nilpotent algebras

hierarchical testing in the high dimensional setting with correlated variables we propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high dimensional linear model in presence of highly correlated variables as is very common in high dimensional data it seems indispensable to go beyond an approach of inferring individual regression coefficients and we show that detecting smallest groups of variables mtds minimal true detections is realistic thanks to the hierarchy among the groups of variables powerful multiple testing adjustment is possible which leads to a data driven choice of the resolution level for the groups our procedure based on repeated sample splitting is shown to asymptotically control the familywise error rate and we provide empirical results for simulated and real data which complement the theoretical analysis supplementary materials for this article are available online

front speed enhancement by incompressible flows in three or higher dimensions we study in dimensions n 3 the family of first integrals of an incompressible flow these are h 1 rm loc functions whose level surfaces are tangential to the streamlines of the advective incompressible field one main motivation for this study comes from earlier results proving that the existence of nontrivial first integrals of an incompressible flow q is the main key that leads to a linear speed up by a large advection of pulsating traveling fronts solving a reaction advection diffusion equation in a periodic heterogeneous framework the family of first integrals is not well understood in dimensions n 3 due to the randomness of the trajectories of q and this is in contrast with the case n 2 by looking at the domain of propagation as a union of different components produced by the advective field we provide more information about first integrals and we give a class of incompressible flows which exhibit ergodic components of positive lebesgue measure and hence are not shear flows and which under certain sharp geometric conditions speed up the kpp fronts linearly with respect to the large amplitude in the proofs we establish a link between incompressibility ergodicity first integrals and the dimension to give a sharp condition about the asymptotic behavior of the minimal kpp speed in terms of the configuration of ergodic components

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

characterization of dose response relationships inferred by statistically significant trend tests summary a method is proposed for classifying various experimental outcomes associated with statistically significant trend tests according to a set of results of sequential testing within a family of closed under intersections one sided tests the intent of the procedure is to characterize the general shape of implied dose response relationships taking care neither to inflate the false positive type i error rate by overtesting nor to sacrifice power by overadjusting for mulitple comparisons

comparability of segmented line regression models segmented line regression models which are composed of continuous linear phases have been applied to describe changes in rate trend patterns in this article we propose a procedure to compare two segmented line regression functions specifically to test i whether the two segmented line regression functions are identical or ii whether the two mean functions are parallel allowing different intercepts a general form of the test statistic is described and then the permutation procedure is proposed to estimate the p value of the test the permutation test is compared to an approximate f test in terms of the p value estimation and the performance of the permutation test is studied via simulations the tests are applied to compare female lung cancer mortality rates between two registry areas and also to compare female breast cancer mortality rates between two states

swarm intelligence and evolutionary algorithms the popularity of metaheuristics especially swarm intelligence and evolutionary algorithms has increased rapidly over the last two decades numerous algorithms are proposed each year and progressively more novel applications are being found however different metaheuristics are often compared by their performance on problems with an arbitrarily fixed number of allowed function calls there are surprisingly few papers that explore the relationship between the relative performance of numerous metaheuristics on versatile numerical real world problems and the number of allowed function calls in this study the performance of 33 various metaheuristics proposed between 1960 and 2016 have been tested on 22 numerical real world problems from different fields of science with the maximum number of function calls varying between 5000 and 500 000 it is confirmed that the algorithms that succeed in comparisons when the computational budget is low are among the poorest performers when the computational budget is high and vice versa among the tested variants particle swarm optimization algorithms and some new types of metaheuristics perform relatively better when the number of allowed function calls is low whereas differential evolution and genetic algorithms perform better relative to other algorithms when the computational budget is large it is difficult to find any metaheuristic that would perform adequately over all of the numbers of function calls tested it was also found that some algorithms may become completely unreliable on specific real world problems even though they perform reasonably on others

an improved bonferroni inequality and applications summary we present an improved bonferroni inequality which gives an upper bound for the probability of the union of an arbitrary sequence of events the bound is constructed in terms of the joint probability of pairs of events which are represented by edges on a graph examples of applications to periodicity location shift detection kolmogorovsmirnov tests and outlier detection are given

dose finding strategies involving interim analyses and unbalanced treatment allocation dose finding studies usually require the application of multiple test procedures mtp a variety of procedures is available for data analyses focusing on testing only subset hypotheses of interest requires only limited adjustment specific strategies based on mtp in particular closed test procedures which also consider dropping dose groups and unequal group sizes lead to substantial reduction in total sample size of course strategies discussed here can be extended to comparisons of more than five groups and they may be generalized to cover equivalence tests too for example one may want to demonstrate therapeutical equivalence of two dose regimens like b i d and o d administrations of the drug

a computational study of residual kpp front speeds in time periodic cellular flows in the small diffusion limit abstract the minimal speeds c of the kolmogorov petrovsky piskunov kpp fronts at small diffusion 1 in a class of time periodic cellular flows with chaotic streamlines is investigated in this paper the variational principle of c reduces the computation to that of a principle eigenvalue problem on a periodic domain of a linear advection diffusion operator with space time periodic coefficients and small diffusion to solve the advection dominated time dependent eigenvalue problem efficiently over large time a combination of spectral methods and finite element as well as the associated fast solvers are utilized to accelerate computation in contrast to the scaling c o 1 4 in steady cellular flows a new relation c o 1 as 1 is revealed in the time periodic cellular flows due to the presence of chaotic streamlines residual propagation speed emerges from the lagrangian chaos which is quantified as a sub diffusion process

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

speed up of combustion fronts in shear flows this paper is concerned with the analysis of speed up of reaction diffusion advection traveling fronts in infinite cylinders with periodic boundary conditions the advection is a shear flow with a large amplitude and the reaction is nonnegative with either positive or zero ignition temperature the unique or minimal speeds of the traveling fronts are proved to be asymptotically linear in the flow amplitude as the latter goes to infinity solving an open problem from berestycki nonlinear pdes in condensed matter and reactive flows kluwer doordrecht 2003 the asymptotic growth rate is characterized explicitly as the unique or minimal speed of traveling fronts for a limiting degenerate problem and the convergence of the regular traveling fronts to the degenerate ones is proved for positive ignition temperatures under an additional hormander type condition on the flow

pulsating type entire solutions of monostable reaction advection diffusion equations in periodic excitable media abstract we establish the existence of pulsating type entire solutions of reaction advection diffusion equations with monostable nonlinearities in a periodic framework here the nonlinearities include the classic kpp case the pulsating type entire solutions are defined in the whole space and for all time t r by studying a pulsating traveling front connecting a constant unstable stationary state to a stable stationary state which is allowed to be a positive function we proved that there exist pulsating type entire solutions behaving as two pulsating traveling fronts coming from both directions and approaching each other the key techniques are to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions

semiparametric bayes multiple testing applications to tumor data in national toxicology program ntp studies investigators want to assess whether a test agent is carcinogenic overall and specific to certain tumor types while estimating the dose response profiles because there are potentially correlations among the tumors a joint inference is preferred to separate univariate analyses for each tumor type in this regard we propose a random effect logistic model with a matrix of coefficients representing log odds ratios for the adjacent dose groups for tumors at different sites we propose appropriate nonparametric priors for these coefficients to characterize the correlations and to allow borrowing of information across different dose groups and tumor types global and local hypotheses can be easily evaluated by summarizing the output of a single monte carlo markov chain mcmc two multiple testing procedures are applied for testing local hypotheses based on the posterior probabilities of local alternatives simulation studies are conducted and an ntp tumor data set is analyzed illustrating the proposed approach

constructing multiple test procedures for partially ordered hypothesis sets a popular method to control multiplicity in confirmatory clinical trials is to use a so called hierarchical or fixed sequence test procedure this requires that the null hypotheses are ordered a priori for example in order of clinical importance the procedure tests the hypotheses in this order using level tests until one is not rejected it then stops so that no subsequent hypotheses are eligible for rejection this procedure strongly controls the familywise error rate fwe that is to say the probability that any true hypotheses are rejected this paper describes a simple generalization of this approach in which the null hypotheses are partially ordered it is convenient to display the partial ordering in a directed acyclic graph dag we consider sequentially rejective procedures based on the partial ordering in which a hypothesis is tested only when all preceding hypotheses have been tested and rejected in general such procedures do not control the fwe but it is shown that when certain intersection hypotheses are added strong control of the fwe is obtained the purpose of the method is to construct inference strategies for confirmatory clinical trials that better reflect the trial objectives copyright 2007 john wiley sons ltd

information ratio test for model misspecification in quasi likelihood inference in this article we focus on the circumstances in quasi likelihood inference that the estimation accuracy of mean structure parameters is guaranteed by correct specification of the first moment but the estimation efficiency could be diminished due to misspecification of the second moment we propose an information ratio ir statistic to test for model misspecification of the variance covariance structure through a comparison between two forms of information matrix the negative sensitivity matrix and the variability matrix we establish asymptotic distributions of the proposed ir test statistics we also suggest an approximation to the asymptotic distribution of the ir statistic via a perturbation resampling method moreover we propose a selection criterion based on the ir test to select the best fitting variance covariance structure from a class of candidates through simulation studies it is shown that the ir statistic provides a powerful statistical tool to detect different scenarios of misspecific

a boundary layer theory for diffusively perturbed transport around a heteroclinic cycle we consider a two dimensional transport equation subject to small diffusive perturbations the transport equation is given by a hamiltonian flow near a compact and connected heteroclinic cycle we investigate approximately harmonic functions corresponding to the generator of the perturbed transport equation in particular we investigate such functions in the boundary layer near the heteroclinic cycle the space of these functions gives information about the likelihood of a particle moving a mesoscopic distance into one of the regions where the transport equation corresponds to periodic oscillations i e a well of the hamiltonian we find that we can construct such approximately harmonic functions which can be used as corrector functions in certain averaging questions when certain macroscopic gluing conditions are satisfied this provides a different perspective on some previous work of freidlin and wentzell on stochastic averaging of hamiltonian systems 2004 wiley periodicals inc

extinction versus persistence in strong oscillating flows in this paper we give some conditions for finite time extinction or persistence of the solutions of diffusion advection equations in strong and oscillating flows under dirichlet boundary conditions the enhancement of the diffusion rate depends on the interplay between strong advection and time homogenization and in particular on the ratio between the strength of the flow and its frequency parameter quantitative estimates of this ratio which depend on the geometry of the domain are provided in the case of a uniform flow in the general time space dependent case the finite time behavior of the solutions is related to the existence of first integrals of the flow

modified sequentially rejective multiple test procedures abstract suppose that n hypotheses h 1 h 2 h n with associated test statistics t 1 t 2 t n are to be tested by a procedure with experimentwise significance level the probability of rejecting one or more true hypotheses smaller than or equal to some specified value a commonly used procedure satisfying this condition is the bonferroni b procedure which consists of rejecting h i for any i iff the associated test statistic t i is significant at the level n holm 1979 introduced a modified bonferroni procedure with greater power than the b procedure under holm s sequentially rejective bonferroni srb procedure if any hypothesis is rejected at the level n the denominator of for the next test is n 1 and the criterion continues to be modified in a stagewise manner with the denominator of reduced by 1 each time a hypothesis is rejected so that tests can be conducted at successively higher significance levels holm proved that the experimentwise significance level

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

clustering of trend data using joinpoint regression models in this paper we propose methods to cluster groups of two dimensional data whose mean functions are piecewise linear into several clusters with common characteristics such as the same slopes to fit segmented line regression models with common features for each possible cluster we use a restricted least squares method in implementing the restricted least squares method we estimate the maximum number of segments in each cluster by using both the permutation test method and the bayes information criterion method and then propose to use the bayes information criterion to determine the number of clusters for a more effective implementation of the clustering algorithm we propose a measure of the minimum distance worth detecting and illustrate its use in two examples we summarize simulation results to study properties of the proposed methods and also prove the consistency of the cluster grouping estimated with a given number of clusters the presentation and examples in this paper focus on the segmented line regression model with the ordered values of the independent variable which has been the model of interest in cancer trend analysis but the proposed method can be applied to a general model with design points either ordered or unordered copyright 2014 john wiley sons ltd

computing reactive front speeds in random flows by variational principle we study reactive front speeds in randomly perturbed cellular flows using a variational representation for the front speed we develop this representation into a computational tool for computing the front speeds without resorting to closure approximations we demonstrate that the front speeds depend on flow statistics and topologies in a complex and dramatic manner

estimating average annual per cent change in trend analysis trends in incidence or mortality rates over a specified time interval are usually described by the conventional annual per cent change capc under the assumption of a constant rate of change when this assumption does not hold over the entire time interval the trend may be characterized using the annual per cent changes from segmented analysis sapcs this approach assumes that the change in rates is constant over each time partition defined by the transition points but varies among different time partitions different groups e g racial subgroups however may have different transition points and thus different time partitions over which they have constant rates of change making comparison of sapcs problematic across groups over a common time interval of interest e g the past 10 years we propose a new measure the average annual per cent change aapc which uses sapcs to summarize and compare trends for a specific time period the advantage of the proposed aapc is that it takes into account the trend transitions whereas capc does not and can lead to erroneous conclusions in addition when the trend is constant over the entire time interval of interest the aapc has the advantage of reducing to both capc and sapc moreover because the estimated aapc is based on the segmented analysis over the entire data series any selected subinterval within a single time partition will yield the same aapc estimate that is it will be equal to the estimated sapc for that time partition the capc however is re estimated using data only from that selected subinterval thus its estimate may be sensitive to the subinterval selected the aapc estimation has been incorporated into the segmented regression free software joinpoint which is used by many registries throughout the world for characterizing trends in cancer rates copyright 2009 john wiley sons ltd

monte carlo evaluation of resampling based hypothesis tests abstract monte carlo estimation of the power of tests that require resampling can be very computationally intensive it is possible to reduce the size of the inner resampling loop as long as the resulting estimator of power can be corrected for bias a simple linear extrapolation method is shown to perform well in correcting for bias and thus reduces computation time in monte carlo power studies

random perturbations of 2 dimensional hamiltonian flows we consider the motion of a particle in a periodic two dimensional flow perturbed by small molecular diffusion the flow is generated by a divergence free zero mean vector field the long time behavior corresponds to the behavior of the homogenized process that is diffusion process with the constant diffusion matrix effective diffusivity we obtain the asymptotics of the effective diffusivity when the molecular diffusion tends to zero

some metaheuristics should be simplified abstract users have a large and constantly increasing number of optimization metaheuristics at their disposal in pursuit of ever better approaches popular and successful methods are often improved a number of times in a row or various methods are hybridized one should however pay attention to whether such deliberately improved or hybridized methods do not become unnecessarily complicated or if some of their elements do not introduce a structural bias in the first case the algorithm should be simplified by eliminating the unneeded elements this will make it more clear to the users and as shown in this study may even improve the results in the second case operators that are responsible for over frequent sampling of some part of the search space have to be removed in this study we address the problem of over complexity of metaheuristics focusing on two joint winners of the cec2016 competition on single objective numerical optimization l shade epsin and umoea ii algorithms it is shown that each of them includes a procedure which introduces a structural bias by attracting population towards the origin o as discussed in the text in the case of seven out of 30 benchmark problems considered in the cec2016 competition the objective function values in the origin o are better than those found by the vast majority of algorithms hence structural bias affects the results obtained by l shade epsin and umoea ii in this work we simplify both algorithms by removing operators that are the main cause of structural bias further we show that in the l shade epsin algorithm the ensemble sinusoidal adaptation mechanism of control parameter f that is used during the first half of the search is not needed slightly better results on both artificial benchmarks used in the cec2016 competition and on a wide set of real world problems may be obtained if during that period of the search the value of f is simply set to 0 5 such a simplified algorithm is competitive against a large number of metaheuristics and may be much easier for the users to understand

shortcuts for locally consonant closed test procedures the closed testing principle provides a general and simple framework to construct powerful multiple test procedures for k elementary null hypotheses while controlling the familywise error rate in the strong sense however the closed testing principle has the disadvantage of leading to the evaluation of o 2k intersection hypotheses multiple test procedures based on the closed testing principle may thus require substantial computational efforts consonant closed test procedures for unrestricted hypotheses have the advantage of rejecting at least one elementary null hypothesis whenever the global null hypothesis is rejected and thus admit shortcuts of size k if the elementary null hypotheses are restricted by logical constraints the closure of common tests such as max t or min p tests may not be consonant in the usual sense in this article we introduce a weaker consonance property denoted as local consonance and show that many closed test procedures with restricted hypotheses satisfy this condition

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

a note on multiple testing procedures in dose finding it is shown that in some recently proposed multiple test procedures for dose finding tamhane hochberg and dunnett 1996 biometrics 52 21 37 strong control of the familywise error is only guaranteed if order relations are assumed to hold among the means procedures that can be applied safely without assuming any restrictions on the means can be based on the classical many one comparisons of doses with the zero dose

multiple test procedures in clinical dose finding studies abstract test procedures in clinical dose finding studies are considered when it can be assumed that increasing dose levels lead to a larger or at least equal efficacy if one is interested in various comparisons within the set of dose levels one arrives at a problem of multiple testing against ordered alternatives some multiple test procedures controlling the multiple level of significance are compared in a simulation study it follows that a simple procedure that only uses comparisons between neighboring dose levels can be recommended the degree of approximation of this bonferroni type procedure is investigated under normal assumptions

a powerful approach to the study of moderate effect modification in observational studies effect modification means the magnitude or stability of a treatment effect varies as a function of an observed covariate generally larger and more stable treatment effects are insensitive to larger biases from unmeasured covariates so a causal conclusion may be considerably firmer if this pattern is noted if it occurs we propose a new strategy called the submax method that combines exploratory and confirmatory efforts to determine whether there is stronger evidence of causality that is greater insensitivity to unmeasured confounding in some subgroups of individuals it uses the joint distribution of test statistics that split the data in various ways based on certain observed covariates for l binary covariates the method splits the population l times into two subpopulations perhaps first men and women perhaps then smokers and nonsmokers computing a test statistic from each subpopulation and appends the test statistic for the whole population making 2 l 1 test statistics in total although l binary covariates define 2 l interaction groups only 2 l 1 tests are performed and at least l 1 of these tests use at least half of the data the submax method achieves the highest design sensitivity and the highest bahadur efficiency of its component tests moreover the form of the test is sufficiently tractable that its large sample power may be studied analytically the simulation suggests that the submax method exhibits superior performance in comparison with an approach using cart when there is effect modification of moderate size using data from the nhanes i epidemiologic follow up survey an observational study of the effects of physical activity on survival is used to illustrate the method the method is implemented in the r package submax which contains the nhanes example an online appendix provides simulation results and further analysis of the example

fuzzy algebras over fuzzy fields redefined abstract first we point out that nanda s 1986 definition of fuzzy field was irrational hence the definition of fuzzy algebras over fuzzy fields 1990 was also irrational secondly we redefined fuzzy fields and fuzzy algebras over fuzzy fields finally we prove without any restriction that homomorphic images of fuzzy algebras form are fuzzy algebra

existence and nonexistence of traveling waves and reaction diffusion front propagation in periodic media we review the existence results of traveling wave solutions to the reaction diffusion equations with periodic diffusion convection coefficients and combustion bistable nonlinearities we prove that whenever traveling waves exist the solutions of the initial value problem with either frontlike or pulselike data propagate with the constant effective speeds of traveling waves in all suitable directions in the case of bistable nonlinearity and one space dimension we give an example of nonexistence of traveling waves which causes quenching localization of wavefront propagation quenching localization only occurs when the variations of the media from their constant mean values are large enough our related numerical results also provide evidence for this phenomenon in the parameter regimes not covered by the analytical example finally we comment on the role of the effective wave speeds in determining the effective wavefront equation hamilton jacobi equation of the reactiondiffusion equations under the small diffusion fast reaction limit with a formal geometric optics expansion

semiparametric comparison of regression curves the comparison of nonparametric regression curves is considered it is assumed that there are parametric possibly nonlinear transformations of the axes which map one curve into the other estimation and testing of the parameters in the transformations are studied the rate of convergence is n 1 2 although the nonparametric components of the model typically have a rate slower than that a statistic is provided for testing the validity of a given completely parametric model

diffusion advection in cellular flows with large peclet numbers for periodic two dimensional cellular flows in incompressible fluids we provide explicit upper and lower estimates of the effective diffusivity which have the correct scaling behavior for large peclet numbers we demonstrate that all allowed scaling laws can occur the bounds prove that there is no residual diffusion in the infinite peclet number limit for holder continuous flows answering a problem posed by kozlov

boundary layers for cellular flows at high peclet numbers we analyze the behavior of solutions of steady advection diffusion problems in bounded domains with prescribed dirichlet data when the peclet number pe 1 is large we show that the solution converges to a constant in each flow cell outside a boundary layer of width o 1 2 pe 1 around the flow separatrices we construct an dependent approximate water pipe problem purely inside the boundary layer that provides a good approximation of the solution of the full problem but has independent computational cost we also define an asymptotic problem on the graph of streamline separatrices and show that solution of the water pipe problem itself may be approximated by an asymptotic independent problem on this graph finally we show that the dirichlet to neumann map of the water pipe problem approximates the dirichlet to neumann map of the separatrix problem with an error independent of the flow outside the boundary layers 2004 wiley periodicals inc

the sequential rejection principle of familywise error control closed testing and partitioning are recognized as fundamental principles of familywise error control in this paper we argue that sequential rejection can be considered equally fundamental as a general principle of multiple testing we present a general sequentially rejective multiple testing procedure and show that many well known familywise error controlling methods can be constructed as special cases of this procedure among which are the procedures of holm shaffer and hochberg parallel and serial gatekeeping procedures modern procedures for multiple testing in graphs resampling based multiple testing procedures and even the closed testing and partitioning procedures themselves we also give a general proof that sequentially rejective multiple testing procedures strongly control the familywise error if they fulfill simple criteria of monotonicity of the critical values and a limited form of weak familywise error control in each single step the sequential rejection principle gives a novel theoretical perspective on many well known multiple testing procedures emphasizing the sequential aspect its main practical usefulness is for the development of multiple testing procedures for null hypotheses possibly logically related that are structured in a graph we illustrate this by presenting a uniform improvement of a recently published procedure

the effect of simulation order on level accuracy and power of monte carlo tests we discuss the effect of simulation order on level accuracy and power of monte carlo tests in a very general setting both parametric problems with or without nuisance parameters and nonparametric problems are treated by a single unifying argument it is shown that if the level of a monte carlo test is known only nominally not precisely then the level error of a monte carlo test is an order of magnitude less than that of the corresponding asymptotic test this result is available whenever the test statistic is asymptotically pivotal even if the number of simulations is held fixed as the sample size n increases it implies that monte carlo methods are a real alternative to asymptotic methods we also show that even if the number of simulations is held fixed a monte carlo test is able to distinguish between the null hypothesis and alternative hypotheses distant n 12 from the null

bootstrap test for difference between means in nonparametric regression abstract a bootstrap test is proposed for detecting a difference between two mean functions in the setting of nonparametric regression error distributions in the regression model are permitted to be arbitrary and unequal the test enjoys power properties akin to those in a parametric setting in the sense that it can distinguish between regression functions distant only n 1 2 apart where n is the sample size it has exceptional level accuracy with level error of only n 2 and uses a very accurate estimate of the critical point of an exact test being in error by only n 3 2 under the null hypothesis the test admits several generalizations for example to the case of testing for differences between several regression means this is a nonparametric regression analog of analysis of variance a simulation study using n as small as 15 corroborates the asymptotic result on level accuracy of the bootstrap test applications are illustrated with an example involving acid rain data

allocation of effort in monte carlo simulation for power of permutation tests abstract consider a randomization test in which an observed statistic is compared to a null distribution constructed by first drawing a random sample from the set of all possible permutations of the data and then calculating the statistic anew for each member of the random sample if the power of such a test is investigated by simulation the computer code must have two main loops in the outer loop which has o iterations data are generated under a specific alternative hypothesis for each outer iteration there are i inner iterations in each of which the data are permuted and the statistic calculated assume that the costs of inner and outer iterations are known and the total cost of the study is fixed so that i and o are constrained by o io for fixed this article considers what the optimal choice for i is in a mean squared sense a general expression is derived for the mean squared error of the distribution of p values if the alternative hypothesis is close to the null the optimal c

permutation tests for joinpoint regression with applications to cancer rates the identification of changes in the recent trend is an important issue in the analysis of cancer mortality and incidence data we apply a joinpoint regression model to describe such continuous changes and use the grid search method to fit the regression function with unknown joinpoints assuming constant variance and uncorrelated errors we find the number of significant joinpoints by performing several permutation tests each of which has a correct significance level asymptotically each p value is found using monte carlo methods and the overall asymptotic significance level is maintained through a bonferroni correction these tests are extended to the situation with non constant variance to handle rates with poisson variation and possibly autocorrelated errors the performance of these tests are studied via simulations and the tests are applied to u s prostate cancer incidence and mortality rates

boundary layers and kpp fronts in a cellular flow we study an eigenvalue problem associated with a reaction diffusion advection equation of the kpp type in a cellular flow we obtain upper and lower bounds on the eigenvalues in the regime of a large flow amplitude a 1 it follows that the minimal pulsating traveling front speed c a satisfies the upper and lower bounds c1a1 4 c a c2a1 4 physically the speed enhancement is related to the boundary layer structure of the associated eigenfunction accordingly we establish an averaging along the streamlines principle for the unique positive eigenfunction

test of significance when data are curves abstract with modern technology massive data can easily be collected in a form of multiple sets of curves new statistical challenge includes testing whether there is any statistically significant difference among these sets of curves in this article we propose some new tests for comparing two groups of curves based on the adaptive neyman test and the wavelet thresholding techniques introduced earlier by fan we demonstrate that these tests inherit the properties outlined by fan and that they are simple and powerful for detecting differences between two sets of curves we then further generalize the idea to compare multiple sets of curves resulting in an adaptive high dimensional analysis of variance called hanova these newly developed techniques are illustrated by using a dataset on pizza commercials where observations are curves and an analysis of cornea topography in ophthalmology where images of individuals are observed a simulation example is also presented to illustrate the power of the adapti

smooth tests for the zero inflated poisson distribution in this article we construct three smooth goodness of fit tests for testing for the zero inflated poisson zip distribution against general smooth alternatives in the sense of neyman we apply our tests to a data set previously claimed to be zip distributed and show that the zip is not a good model to describe the data at rejection of the null hypothesis of zip the individual components of the test statistic which are directly related to interpretable parameters in a smooth model may be used to gain insight into an alternative distribution

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

large multiple neighborhood search for the clustered vehicle routing problem abstract the clustered vehicle routing problem is a variant of the classical capacitated vehicle routing problem in which customers are partitioned into clusters and it is assumed that each cluster must have been served completely before the next cluster is served this decomposes the problem into three subproblems i e the assignment of clusters to routes the routing inside each cluster and the sequencing of the clusters in the routes the second task requires the solution of several hamiltonian path problems one for each possibility to route through the cluster we pre compute the hamiltonian paths for every pair of customers of each cluster we present a large multiple neighborhood search which makes use of multiple cluster destroy and repair operators and a variable neighborhood descent vnd for post optimization the vnd is based on classical neighborhoods such as relocate 2 opt and swap all working on the cluster level and a generalization of the balas simonetti neighborhood modifying simultaneously the intra cluster routings and the sequence of clusters in a route computational results with our new approach compare favorably to existing approaches from the literature

on adjusting p values for multiplicity response 1 the development of proc multtest while controversial the use of multiplicity adjustments has gained acceptance recently in varied fields of scientific endeavor and their associated publications multiplicity adjustments have been considered important in pharmaceutical safety determinations involving multiple endpoints such as in adverse events analysis of clinical trials and in animal carcinogenicity studies in situations where the compound tested is completely safe it is likely to observe false positive indications of one or more untoward outcomes when unadjusted testing methods are used multiplicity adjustment is also important in epidemiology and other complicated areas of data analysis as it offers protection against conclusions that are driven by excessive data mining multiplicity concerns in toxicology and clinical trials prompted the development of the sas procedure proc multtest which calculates adjusted p values for a user supplied family of tests in a wide variety of applications biometrics readers will be interested to know that this software is readily available to calculate many but not all of the multiplicity adjusted p values described by wright 1992 in addition the software incorporates many improvements and enhancements such as the ability to incorporate correlations and nonnormal distributions the development of proc multtest started in may 1987 one of us westfall presented a resampling approach to calculating adjusted p values for multiple tests in multivariate binomial models with special application to the animal carcinogenicity problem the talk was entitled multivariate binomial testing and was given as the keynote address for the midwestern biopharmaceutical statistics workshop mbsw held in muncie indiana similar approaches to the same problem were developed concurrently and independently all of which have been published farrar and crump 1988 heyse and rom 1988 westfall and young 1989 an interesting biometrics connection should be mentioned here dr young thought that westfall s 1985 publication concerning simultaneous inference with multivariate binary data might be applied to the multiplicity problem in animal carcinogenicity studies dr young therefore invited dr westfall to speak at the mbsw conference on this application the initial precursor to proc multtest called proc mbin was developed in 1988 we wrote the specifications for the software and the coding was performed by youling lin at texas tech university under the auspices of the pharmaceutical manufacturing association a consortium of drug companies offered financial and intellectual support for the project specific individuals and companies who contributed are listed below in the acknowledgements section the development proceeded through a series of meetings at national and regional statistics conferences attendees included representatives from the funding organizations and from the united states food and drug administration from the outset it was decided that the primary form of output from the software would be the adjusted p value for the reasons wright describes in his opening paragraph the procedure proc mbin was described by westfall lin and young 1989 and was donated to sas institute inc the software performed multiplicity adjustments for multiple tests z score or exact permutation tests in multivariate possibly stratified multiple group binary outcome situations the main feature of the output of this software was the use of adjusted p values to summarize many statistical tests single step resampling bootstrap or permutation bonferroni and sidak methods were used to calculate the adjustments the tabular form of the output was much like tables 2 and 3 of wright showing unadjusted p values which we called raw p values side by side with various types of adjusted p values

multiple test procedures for dose finding the problem of identifying the lowest dose level for which the mean response differs from that at the zero dose level is considered a general framework for stepwise testing procedures that use contrasts among the dose level means is proposed using this framework several new procedures are derived these and some existing procedures including that of williams 1971 biometrics 27 103 117 1972 biometrics 28 519 531 are compared analytically and by an extensive simulation study for the normal theory balanced one way layout case it is pointed out that the procedures based on the so called step and basin contrasts proposed by ruberg 1989 journal of american statistical association 84 816 822 have excessively high type i familywise error rates fwes and hence they should not be used some findings of the simulation study are as follows for monotone dose mean configurations williams procedure and two step down test procedures based on helmert and linear contrasts offer the best performance for nonmonotone dose mean configurations the performance of williams procedure does degrade somewhat but the other two procedures are still the best for more complex designs a simple step down test procedure that uses any alpha level tests not necessarily t tests to compare each dose level with the zero dose level controls the fwe and is the only alternative available but its power is rather low especially under nonmonotone configurations step up procedures are generally dominated by step down procedures when the same contrasts are used although the differences are not great

multiple testing of general contrasts using logical constraints and correlations abstract use of logical constraints among hypotheses and correlations among test statistics can greatly improve the power of step down tests an algorithm for uncovering these logically constrained subsets in a given dataset is described the multiple testing results are summarized using adjusted p values which incorporate the relevant dependence structures and logical constraints these adjusted p values are computed consistently and efficiently using a generalized least squares hybrid of simple and control variate monte carlo methods and the results are compared to alternative stepwise testing procedures

multiplicity adjustment for multiple endpoints in clinical trials with multiple doses of an active treatment frequently multiple doses of an active treatment and multiple endpoints are simultaneously considered in the designs of clinical trials for these trials traditional multiplicity adjustment procedures such as bonferroni hochberg and hommel procedures can be applied when treating the comparisons of different doses to the control on all endpoints at the same level however these approaches will not take into account the possible dose response relationship on each endpoint and therefore are less specific and may have lower power to gain power in this paper we consider the problem as a two dimensional multiplicity problem one dimension concerns the multiple doses and the other dimension concerns the multiple endpoints we propose procedures which consider the dose order to form the closure of the procedures and control the family wise type i error rate in a strong sense for this two dimensional problem numerical examples show that procedures proposed in this paper in general have higher power than the commonly used procedures e g the regular hochberg procedure especially for comparing the higher dose to the control

testing for treatment and interaction effects in semi parametric analysis of covariance semi parametric regression models assume that the effects of covariates on the mean response are additive we propose a test of additivity when there is one continuous covariate and a group indicator at p fixed points the differences of the within group kernel estimates of the means are calculated and the likelihood ratio test that the p differences have a constant mean is formed the kernel bandwidth and the location of the p fixed points are chosen to give the test good power performance of the proposed test is compared with parametric and non parametric tests of additivity published in 2001 by john wiley sons ltd

elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena this paper is concerned with the asymptotic behaviour of the principal eigenvalue of some linear elliptic equations in the limit of high first order coefficients roughly speaking one of the main results says that the principal eigenvalue with dirichlet boundary conditions is bounded as the amplitude of the coefficients of the first order derivatives goes to infinity if and only if the associated dynamical system has a first integral and the limiting eigenvalue is then determined through the minimization of the dirichlet functional over all first integrals a parabolic version of these results as well as other results for more general equations are given some of the main consequences concern the influence of high advection or drift on the speed of propagation of pulsating travelling fronts

sharp asymptotics for kpp pulsating front speed up and diffusion enhancement by flows we study kpp pulsating front speed up and effective diffusivity enhancement by general periodic incompressible flows we prove the existence of and determine the limits c e a a and de a a2 as the flow amplitude a with c e a the minimal front speed and de a the effective diffusivity in direction e

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

sequential implementation of monte carlo tests with uniformly bounded resampling risk this paper introduces an open ended sequential algorithm for computing the p value of a test using monte carlo simulation it guarantees that the resampling risk the probability of a different decision than the one based on the theoretical p value is uniformly bounded by an arbitrarily small constant previously suggested sequential or nonsequential algorithms using a bounded sample size do not have this property although the algorithm is open ended the expected number of steps is finite except when the p value is on the threshold between rejecting and not rejecting the algorithm is suitable as standard for implementing tests that require re sampling it can also be used in other situations to check whether a test is conservative iteratively to implement double bootstrap tests and to determine the sample size required for a certain power an r package implementing the sequential algorithm is available online

the ios test for model misspecification a new test of model misspecification is proposed based on the ratio of in sample and out of sample likelihoods the test is broadly applicable and in simple problems approximates well known intuitive methods using jackknife influence curve approximations it is shown that the test statistic can be viewed asymptotically as a multiplicative contrast between two estimates of the information matrix both of which are consistent under correct model specification this approximation is used to show that the statistic is asymptotically normally distributed although it is suggested that p values be computed using the parametric bootstrap the resulting methodology is demonstrated with various examples and simulations involving both discrete and continuous data

goodness of fit for generalized linear latent variables models generalized linear latent variables models gllvm enable the modeling of relationships between manifest and latent variables where the manifest variables are distributed according to a distribution of the exponential family e g binomial or normal and to the multinomial distribution for ordinal manifest variables these models are widely used in social sciences to test the appropriateness of a particular model one needs to define a goodness of fit test statistic gfi in the normal case one can use a likelihood ratio test or a modified version proposed by satorra and bentler 2001 s b gfi that compares the sample covariance matrix to the estimated covariance matrix induced by the model in the binary case pearson type test statistics can be used if the number of observations is sufficiently large in the other cases including the case of mixed types of manifest variables there exists gfi based on a comparison between a pseudo sample covariance and the model covariance of the manifest vari

score tests for dose effect in the presence of non responders when only a certain proportion of subjects respond to treatment responders or may never experience an event of interest thus cured mixture models often lead to increased understanding of the treatment or disease process this paper focuses on hypothesis testing in a dose response framework and shows that increased power is possible by using a mixture model where both the logit of the response rate and the response mean are linear functions of the dose level three score tests are developed for testing an overall effect and permutation methods are used to control the type i error extensive simulations establish the power properties of the tests and show that our proposed score test has the best performance the approach is illustrated by a multi country clinical trial of rapid acting intramuscular olanzapine copyright 2004 john wiley sons ltd

a numerical study of turbulent flame speeds of curvature and strain g equations in cellular flows abstract we study front speeds of curvature and strain g equations arising in turbulent combustion these g equations are hamilton jacobi type level set partial differential equations pdes with non coercive hamiltonians and degenerate nonlinear second order diffusion the hamiltonian of a strain g equation is also non convex numerical computation is performed based on monotone discretization and weighted essentially nonoscillatory weno approximation of transformed g equations on a fixed periodic domain the advection field in the computation is a two dimensional hamiltonian flow consisting of a periodic array of counter rotating vortices or cellular flows depending on whether the evolution is predominantly in the hyperbolic or parabolic regimes suitable explicit and semi implicit time stepping methods are chosen the turbulent flame speeds are computed as the linear growth rates of large time solutions a new nonlinear parabolic pde is proposed for the reinitialization of level set functions to prevent piling up of multiple bundles of level sets on the periodic domain we found that the turbulent flame speed s t of the curvature g equation is enhanced as the intensity a of cellular flows increases at a rate between those of the inviscid and viscous g equations the s t of the strain g equation increases in small a decreases in larger a then drops down to zero at a large enough but finite value a the flame front ceases to propagate at this critical intensity a and is quenched by the cellular flow