modeling tumor onset and multiplicity using transition models with latent variables summary we describe a method for modeling carcinogenicity from animal studies where the data consist of counts of the number of tumors present over time the research is motivated by applications to transgenic rodent studies which have emerged as an alternative to chronic bioassays for screening possible carcinogens in transgenic mouse studies the endpoint of interest is frequently skin papilloma with weekly examinations determining how many papillomas each animal has at a particular point in time it is assumed that each animal has two unobservable latent variables at each time point the first indicates whether or not the tumors are in a multiplying state and the second is the potential number of additional tumors if the tumors are in a multiplying state the product of these variables follows a zero inflated poisson distribution and the em algorithm can be used to maximize the observed data pseudo likelihood based on the latent variables a generalized estimating equations robust variance estimator adjusts for dependency among outcomes within individual animals the method is applied to testing for a dose related trend in both tumor incidence and multiplicity in carcinogenicity studies

mean field upper and lower bounds on lyapunov exponents we extend the supersymmetric field theory formulation of random walks in random po tentials developed in earlier papers we obtain the mean field rate of decay for the squared green s function at the critical energy this requires studying supersymmetric field theories which are quar tic in the grassmann variables we also obtain both the mean field upper and lower bounds at the critical energy for lyapunov exponents for unbounded potentials the upper bound part extends the corresponding result in an earlier work

bayesian inferences on umbrella orderings in regression applications with categorical predictors interest often focuses on comparing the null hypothesis of homogeneity to an ordered alternative this article proposes a bayesian approach for addressing this problem in the setting of normal linear and probit regression models the regression coefficients are assigned a conditionally conjugate prior density consisting of mixtures of point masses at 0 and truncated normal densities with a possibly unknown changepoint parameter included to accommodate umbrella ordering two strategies of prior elicitation are considered 1 a bayesian bonferroni approach in which the probability of the global null hypothesis is specified and local hypotheses are considered independent and 2 an approach which treats these probabilities as random a single gibbs sampling chain can be used to obtain posterior probabilities for the different hypotheses and to estimate regression coefficients and predictive quantities either by model averaging or under the preferred hypothesis the methods are applied to data from a carcinogenesis study

new characterizations of the region of complete localization for random schrodinger operators we study the region of complete localization in a class of random operators which includes random schrodinger operators with anderson type potentials and classical wave operators in random media as well as the anderson tight binding model we establish new characterizations or criteria for this region of complete localization given either by the decay of eigenfunction correlations or by the decay of fermi projections these are necessary and sufficient conditions for the random operator to exhibit complete localization in this energy region using the first type of characterization we prove that in the region of complete localization the random operator has eigenvalues with finite multiplicity

hermitian k theory of the integers rognes and weibel used voevodsky s work on the milnor conjecture to deduce the strong dwyer friedlander form of the lichtenbaum quillen conjecture at the prime 2 in consequence the 2 completion of the classifying space for algebraic k theory of the integers z 1 2 can be expressed as a fiber product of well understood spaces bo and bgl f3 over bu similar results are now obtained for hermitian k theory and the classifying spaces of the integral symplectic and orthogonal groups for the integers z 1 2 this leads to computations of the 2 primary hermitian k groups and affirmation of the lichtenbaum quillen conjecture in the framework of hermitian k theory

weak disorder localization and lifshitz tails this paper is devoted to the study of localization of discrete random schrodinger hamiltonians in the weak disorder regime consider an i i d anderson model and assume that its left spectral edge is 0 let be the coupling constant measuring the strength of the disorder for small we prove a lifshitz tail type estimate and use it to derive localization in a band starting at 0 going up to a distance of the average of the potential in this energy region we show that the localization length at energy e is bounded from above by a constant times the square root of the distance between e and the average of the potential

rank based tests for dose finding in nonmonotonic dose response settings summary lim and wolfe 1997 biometrics53 410 418 proposed rank based multiple test procedures for identifying the dose levels that are more effective than the zero dose control in randomized complete block designs when it can be assumed that the efficacy of the increasing dose levels is monotonically increasing up to a point followed by a monotonic decrease modifications of the lim wolfe tests are suggested that provide more practical and powerful alternatives two numerical examples are illustrated and the results of a monte carlo power study are presented

tests for patterned alternatives in k sample problems abstract this article suggests nonparametric methods of testing for a patterned alternative as an example suppose that we suspect that with increasing age one s ability to perform a certain job tends to improve but that after some point advancing age tends to mean diminishing performance suppose that n employees are grouped by age into k groups and employees job performances are ranked from 1 to n viewing performance as the dependent variable the particular pattern of increasing group locations followed by decreasing group locations is called an umbrella pattern the tests proposed herein allow the experimenter to test for this or any pattern of his choice given k groups let denote the mean rank of the data in group j considering only statistics of the form where aj 0 we find a statistic having maximum asymptotic local power and greatest efficiency when the alternative hypothesis consists of a specific pattern the case in which the researcher specifies a vague pattern is handled by

zero inflated poisson regression with an application to defects in manufacturing zero inflated poisson zip regression is a model for count data with excess zeros it assumes that with probability p the only possible observation is 0 and with probability 1 p a poisson random variable is observed for example when manufacturing equipment is properly aligned defects may be nearly impossible but when it is misaligned defects may occur according to a poisson distribution both the probability p of the perfect zero defect state and the mean number of defects in the imperfect state may depend on covariates sometimes p and are unrelated other times p is a simple function of such as p l 1 t for an unknown constant t in either case zip regression models are easy to fit the maximum likelihood estimates mle s are approximately normal in large samples and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the mle s simulations suggest that the confidence intervals based on likelihood ratio test

k sample rank tests for umbrella alternatives abstract distribution free test procedures are proposed for the k sample problem where the alternatives of interest are of the form f 1 x fl x fk x for all x with at least one strict inequality these are referred to as umbrella alternatives and both the l point of umbrella known and l unknown settings are considered small sample null distributions are discussed and the results of a monte carlo power study are presented a detailed example illustrating the use of the unknown umbrella point procedure is also given

a characterization of the anderson metal insulator transport transition we investigate the anderson metal insulator transition for random schrodinger operators we define the strong insulator region to be the part of the spectrum where the random operator exhibits strong dynamical localization in the hilbert schmidt norm we introduce a local transport exponent e and set the weak metallic transport region to be the part of the spectrum with nontrivial transport i e e 0 we prove that these insulator and metallic regions are complementary sets in the spectrum of the random operator and that the local transport exponent e provides a characterization of the metal insulator transport transition moreover we show that if there is such a transition then e has to be discontinuous at a transport mobility edge more precisely we show that if the transport is nontrivial then e 1 2d where d is the space dimension these results follow from a proof that slow transport of quantum waves in random media implies the starting hypothesis for the authors bootstrap multiscale analysis we also conclude that the strong insulator region coincides with the part of the spectrum where we can perform a bootstrap multiscale analysis proving that the multiscale analysis is valid all the way up to a transport mobility edge

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

a new proof of localization in the anderson tight binding model we give a new proof of exponential localization in the anderson tight binding model which uses many ideas of the frohlich martinelli scoppola and spencer proof but is technically simpler particularly the probabilistic estimates

localization and universality of poisson statistics for the multidimensional anderson model at weak disorder we prove anderson localization with the mean field lyapunov exponent and poisson statistics for eigenvalue spacing for the multi dimensional anderson model at weak disorder these results are obtained by developing the supersymmetric formalism initiated in w1 see also sjw rid

the homotopy fixed point theorem and the quillen lichtenbaum conjecture in hermitian k theory abstract we settle two conjectures for computing higher grothendieck witt groups also known as hermitian k groups of noetherian schemes x under some mild conditions it is shown that the comparison map from the hermitian k theory of x to the homotopy fixed points of k theory under the natural z 2 action is a 2 adic equivalence we also prove that the mod 2 comparison map between the hermitian k theory of x and its etale version is an isomorphism on homotopy groups in the same range as for the quillen lichtenbaum conjecture in k theory applications compute higher grothendieck witt groups of complex algebraic varieties and rings of 2 integers in number fields and hence values of dedekind zeta functions

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

a test of homogeneity of odds ratios against order restrictions abstract this article deals with testing the homogeneity of the odds ratios 1 k taken relative to the first column of a given 2 k 1 cross classification table of ordinal variables against a partial order restriction the inference of these odds ratios is considered on an extended hypergeometric distribution a conditional distribution of cell frequencies n 2l n 2k say given both marginal totals take a transformation such that the order restriction on the odds ratios tends to be in some linear inequalities restriction on means of the n 2j s based on the conditional distribution a test is proposed from the transformation as a one sided likelihood ratio test in the normal case and its asymptotic null distribution is the 2 distribution the test is applied to a numerical example and its power is compared with mantel s test and the ordinary 2 test in practice many odds ratios exhibit a trend for example there is usually a simple order on the odds ratios 1 1 k in the

expansion of the almost sure spectrum in the weak disorder regime abstract the spectrum of random ergodic schrodinger type operators is almost surely a deterministic subset of the real line the random operator can be considered as a perturbation of a periodic one as soon as the disorder is switched on via a global coupling constant the spectrum expands we estimate how much the spectrum expands at its bottom for operators on l 2 z d

dynamical delocalization in random landau hamiltonians we prove the existence of dynamical delocalization for random landau hamiltonians near each landau level since typically there is dynamical localization at the edges of each disordered broadened landau band this implies the existence of at least one dynamical mobility edge at each landau band namely a boundary point between the localization and delocalization regimes which we prove to converge to the corresponding landau level as either the magnetic field goes to infinity or the disorder goes to zero in this article we prove the existence of dynamical delocalization for random landau hamiltonians near each landau level more precisely we prove that for these two dimensional hamiltonians there exists at least one energy e near each landau level such that e 1 where e the local transport exponent introduced in gk5 is a measure of the rate of transport in wave packets with spectral support near e since typically there is dynamical localization at the edges of each disordered broadened landau band this implies the existence of at least one dynamical mobility edge at each landau band namely a boundary point between the localization and delocalization regimes which we prove to converge to the corresponding landau level as either the magnetic field goes to infinity or the disorder goes to zero random landau hamiltonians are the subject of intensive study due to their links with the integer quantum hall e ect kli for which von klitzing received the 1985 nobel prize in physics they describe an electron moving in a very thin flat conductor with impurities under the influence of a constant magnetic field perpendicular to the plane of the conductor and play an important role in the understanding of the quantum hall e ect l aoa t h nt ku be avss bees laughlin s argument l as pointed out by halperin h uses the assumption that under weak disorder and strong magnetic field the energy spectrum consists of bands of extended states separated

a comparison of tests for restricted orderings in the three class case a variety of methods for comparing three distributions have been proposed in the literature these methods assess the same null hypothesis of equal distributions but differ in the alternative hypothesis they consider the alternative hypothesis can be that measurements from the three classes are distributed according to unequal distributions or that measurements between the three classes follow a specific monotone ordering an inverse u shaped umbrella ordering or a u shaped tree ordering this paper compares these tests with respect to power and test size under different simulation scenarios in addition the methods are illustrated in two applications generated by different research questions with data from three classes suggesting monotone and umbrella orders additionally proposals for the appropriate application of these tests are provided

local fluctuation of the spectrum of a multidimensional anderson tight binding model we consider the anderson tight binding modelh v acting inl 2 z d and its restrictionh to finite hypercubes z d herev v x x z d is a random potential consisting of independent identically distributed random variables let e j j be the eigenvalues ofh and let j e e j e j 1 be its rescaled eigenvalues then assuming that the exponential decay of the fractional moment of the green function holds for complex energies neare and that the density of statesn e exists ate we shall prove that the random sequence j e j considered as a point process onr 1 converges weakly to the stationary poisson point process with intensity measuren e dx as gets large thus extending the result of molchanov proved for a one dimensional continuum random schrodinger operator on the other hand the exponential decay of the fractional moment of the green function was established recently by aizenman molchanov and graf as a technical lemma for proving anderson localization at large disorder or at extreme energy thus our result in this paper can be summarized as follows near the energye where anderson localization is expected there is no correlation between eigenvalues ofh if is large

nonparametric identification of the minimum effective dose summary we consider identifying the minimum effective dose med in a dose response study where the med is denned to be the lowest dose level producing an effect over that of the zero dose control proposed herein is a nonparametric procedure based on the mann whitney statistic incorporated with the step down closed testing scheme a numerical example demonstrates the feasibility of the proposed nonparametric procedure finally the comparative results of a monte carlo level and power study for small sample sizes are presented and discussed

a comparison of tests for the k sample non decreasing alternative this paper compares by means of monte carlo simulations three non parametric tests to detect a non decreasing trend in location parameters the three tests are the jonckheere terpstra test the cuzick test and the le test we estimated power for each test across a wide variety of non decreasing location parameters under four different types of distributions none of the tests produced an overwhelmingly higher power over their two competitors

the local structure of the spectrum of the one dimensional schrodinger operator let h v frac d text 2 dt text 2 q t omega be an one dimensional random schrodinger operator in 2 v v with the classical boundary conditions the random potentialq t has a formq t f x t wherex t is a brownian motion on the compact riemannian manifoldk andf k r 1 is a smooth morse function mathop min limits k f 0 let n v delta sum limits ei v in delta 1 where 0 e i v are the eigenvalues ofh v the main result theorem 1 of this paper is the following ifv e 0 0 k z anda 0 a is a fixed constant then p left n v left e 0 frac a 2v e 0 frac a 2v right k right xrightarrow v to infty e an e 0 an e 0 k k wheren e 0 is a limit state density ofh v v this theorem mean that there is no repulsion between energy levels of the operatorh v v the second result theorem 2 describes the phenomen of the repulsion of the corresponding wave functions

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

mean field bounds on lyapunov exponents in z d at the critical energy we further develop the supersymmetric formalism initiated in w1 see also sjw we obtain the optimal mean field bounds at the critical energy for lyapunov exponents of random walks in random potentials in z d at weak disorder this extends some of the results in w1

singular continuous spectrum under rank one perturbations and localization for random hamiltonians we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic for a in terms of the spectral measure d a we give necessary and sufficient conditions for a p to have empty singular continuous spectrum or to have only point spectrum for a e we apply these results to questions of localization in the one and multi dimensional anderson models

recursive nonparametric testing for dose response relaflonships subject to downturns at high doses summary a general recursive strategy is introduced to test nonparametrically for an increasing dose response relationship when a downturn in response at high doses is possible a specific implementation involving a test of jonckheere 1954 and terpstra 1952 is considered and its size and power properties are investigated via monte carlo methods data from mutation research illustrate the phenomenon of concern

hermitian k theory and 2 regularity for totally real number fields we completely determine the 2 primary torsion subgroups of the hermitian k groups of rings of 2 integers in totally real 2 regular number fields the result is almost periodic with period 8 moreover the 2 regular case is precisely the class of totally real number fields that have homotopy cartesian bokstedt square relating the k theory of the 2 integers to that of the fields of real and complex numbers and finite fields we also identify the homotopy fibers of the forgetful and hyperbolic maps relating hermitian and algebraic k theory the result is then exactly periodic of period 8 in the orthogonal case in both the orthogonal and symplectic cases we prove a 2 primary hermitian homotopy limit conjecture for these rings

effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable we consider three commonly used statistical tests for assessing the association between an explanatory variable and a measured binary or survival time response variable and investigate the loss in efficiency from mismodelling or mismeasuring the explanatory variable with respect to mismodelling we examine the consequences of using an incorrect dose metameter in a test for trend of mismodelling a continuous explanatory variable and of discretizing a continuous explanatory variable we also examine the consequences of classification errors for a discrete explanatory variable and of measurement errors for a continuous explanatory variable for all three statistical tests the asymptotic relative efficiency are corresponding to each type of mis specification equals the square of the correlation between the correct and fitted form of the explanatory variable this result is evaluated numerically for the different types of mis specification to provide insight into the selection of tests the interpretation of results and the design of studies where the correct explanatory variable cannot be measured exactly

localization at large disorder and at extreme energies an elementary derivation the work presents a short proof of localization under the conditions of either strong disorder 0 or extreme energies for a wide class of self adjoint operators with random matrix elements acting inl 2 spaces a prototypical example is the discrete schrodinger operatorh u 0 x v x onz d d 1 withu 0 x a specified background potential and v x generated as random variables the general results apply to operators with replaced by a non local self adjoint operatort whose matrix elements satisfy y t x y s const uniformly inx for somes 1 localization means here that within a specified energy range the spectrum ofh is of the pure point type or equivalently the wave functions do not spread indefinitely under the unitary time evolution generated byh the effect is produced by strong disorder in either the potential or in the off diagonal matrix elementst x y under rapid decay oft x y the corresponding eigenfunctions are also proven to decay exponentially the method is based on resolvent techniques the central technical ideas include the use of low moments of the resolvent kernel i e g e x y s withs small enough 1 to avoid the divergence caused by the distribution s cauchy tails and an effective use of the simple form of the dependence ofg e x y on the individual matrix elements ofh in elucidating the implications of the fundamental equation h e g e x x 0 x x0 this approach simplifies previous derivations of localization results avoiding the small denominator difficulties which have been hitherto encountered in the subject it also yields some new results which include localization under the following sets of conditions i potentials with an inhomogeneous non random partu 0 x ii the bethe lattice iii operators with very slow decay in the off diagonal terms t x y 1 x y d e and iv localization produced by disordered boundary conditions

nonparametric testing for dose response curves subject to downturns asymptotic power considerations dose response experiments are widely used in scientific research and nonmonotone dose response curves are commonly observed a class of nonparametric tests for dose response curves subject to downturns at high doses is examined via its asymptotic properties this class includes the well known jonckheere terpstra test as a limiting case the analysis indicates that the jonckheere terpstra test lacks robustness to a downturn in the dose response and that other members of the class provide superior overall performance a result concerning u statistics in locally asymptotically normal families of distributions facilitates the derivation of the asymptotic power function for the class of tests under consideration this result may also be used to obtain asymptotic power functions for other tests based on u statistics for instance the mann whitney wilcoxon test the accuracy of the asymptotic approximation is examined via monte carlo simulation and is found to be quite good for moderate sample sizes suggesting that the approximation might reasonably be used for sample size determinations

nonparametric analysis for doubly ordered two way contingency tables tsujitani 1992 biometrics 48 267 269 and kateri 1993 biometrics 49 950 951 considered analyses for two way contingency tables in this reader reaction a nonparametric analysis using mnidrank scores is given this analysis can be interpreted in terms of bivariate moments does not make model assumptions takes into account the ordinal nature of the data and allows monte carlo p values to be given

confidence subset containing the unknown peaks of an umbrella ordering abstract umbrella ordering has received considerable attention in the statistical literature during the past 15 years however there is still no solution to the important problem of estimating the unknown peaks of an umbrella ordering this article discusses confidence estimation of the unknown peaks a random subset of all of the treatments that contains the unknown peaks of an umbrella ordering with any prespecified confidence level is considered the proposed order restricted confidence subset theory explicitly utilizes the order information and has several advantages for umbrella orderings over the usual subset selection theory the utility and general applicability of the proposed method is shown by its applications in various experimental designs assuming normal or other location scale distributions with known or unknown variances examples based on real data are provided

testing trend for count data with extra poisson variability summary trend tests for monotone trend or umbrella trend monotone upward changing to monotone downward or vise versa in count data are proposed when the data exhibit extra poisson variability the proposed tests which are called the gs1 test and the gs2 test are constructed by applying an orthonormal score vector to a generalized score test under an rth order log linear model these tests are compared by simulation with the cochran armitage test and the quasi likelihood test of piegorsch and bailer 1997 statastics for enuiron mental biology and toxicology it is shown that the cochran armitage test should not be used under the existence of extra poisson variability that for detecting monotone trend the gs1 test is superior to the others and that the gs2 test has high power to detect an umbrella response

confidence bands for logistic regression with restricted predictor variables confidence bands are constructed for the logistic response function when there is an interval restriction on each of the predictor variables the construction involves application of a general fitting procedure using scheffe s s method described by casella and strawderman 1980 journal of the american statistical association 75 862 868 specific details are given for the case of one predictor variable along with details for a fixed width alternative to the s method bands in the one predictor case monte carlo results suggest that both bands are conservative for small sample sizes such as n 25 by n 200 the s method s coverage probabilities are seen to attain their nominal levels while the fixed width bands remain conservative the procedures are exemplified with data from a genetic toxicology experiment

eigenvalue statistics for lattice hamiltonian with off diagonal disorder this short note deals with a certain kind of lattice hamiltonian with off diagonal disorder based on the exponential decay of the fractional moment of the green function we are able to prove that the properly rescaled eigenvalues of the random hamiltonian are distributed as a poisson point process with intensity measure given by the density of states one of the key step in this proof is the minami type estimate as a crucial ingredient we also use the minami type estimate to study some important properties of the random hamiltonian such as multiplicity of the eigenvalues and quantitative estimate of the localization centers

the homotopy limit problem for hermitian k theory equivariant motivic homotopy theory and motivic real cobordism abstract the homotopy limit problem for karoubi s hermitian k theory karoubi 1980 26 was posed by thomason 1983 44 there is a canonical map from algebraic hermitian k theory to the z 2 homotopy fixed points of algebraic k theory the problem asks roughly how close this map is to being an isomorphism specifically after completion at 2 in this paper we solve this problem completely for fields of characteristic 0 theorems 16 20 we show that the 2 completed map is an isomorphism for fields f of characteristic 0 which satisfy cd 2 f i but not in general

a regression framework for rank tests based on the probabilistic index model we demonstrate how many classical rank tests such as the wilcoxon mann whitney kruskal wallis and friedman test can be embedded in a statistical modeling framework and how the method can be used to construct new rank tests in addition to hypothesis testing the method allows for estimating effect sizes with an informative interpretation resulting in a better understanding of the data supplementary materials for this article are available online

finiteness theorems for the shifted witt and higher grothendieck witt groups of arithmetic schemes abstract for smooth varieties over finite fields we prove that the shifted aka derived witt groups of surfaces are finite and the higher grothendieck witt groups aka hermitian k theory of curves are finitely generated for more general arithmetic schemes we give conditional results for example finite generation of the motivic cohomology groups implies finite generation of the grothendieck witt groups

a central limit theorem for products of random matrices and goe statistics for the anderson model on long boxes we consider products of random matrices that are small independent identically distributed perturbations of a fixed matrix mathcal t 0 focusing on the eigenvalues of mathcal t 0 of a particular size we obtain a limit to a sde in a critical scaling previous results required mathcal t 0 to be a conjugated unitary matrix so it could not have eigenvalues of different modulus from the result we can also obtain a limit sde for the markov process given by the action of the random products on the flag manifold applying the result to random schrodinger operators we can improve some results by valko and virag showing goe statistics for the rescaled eigenvalue process of a sequence of anderson models on long boxes in particular we solve a problem posed in their work

a comparison of several methods to test for the existence of a monotonic dose response relationship in clinical and epidemiological studies the mantel extension chi square test for overall trend and an asymptotically equivalent test based on logistic regression are commonly used to test for a monotonic dose response relationship between exposure and disease in epidemiological and clinical studies however these tests present two important disadvantages as they i make the restrictive assumption of a parametric model of linear form on the logit scale and ii impose the a priori choice of scores to code for the exposure categories indeed the linear assumption if made incorrectly can lead to an invalid conclusion and the choice of scores lends arbitrariness to the test results some alternative tests have been proposed in the literature we have considered several of these tests namely one based on isotonic regression the t test based on contrasts and a recently published test based on adjacent contrasts dosemeci benichou test the aim of our study was to compare the statistical properties type i error and power of these tests and of the commonly used mantel extension test for overall trend we generated cohort and case control data and considered one and two sided versions of the tests moreover we studied the tests under the null hypothesis of no relationship between exposure and disease and under various alternative patterns of monotonic or non monotonic dose response relationships this study confirms that the commonly used trend tests can lead to erroneous conclusion of a monotonic dose response relationship the test based on isotonic regression does not represent a favourable alternative as it tends to be too powerful in case of non monotonic dose response relationship patterns the tests based on contrasts seem to possess more favourable properties by combining close to nominal type i error high power for monotonic alternatives and low power for non monotonic alternatives

the equations for the moduli space of n points on the line a central question in invariant theory is that of determining the relations among invariants geometric invariant theory git quotients come with a natural ample line bundle and hence often a natural projective embedding this question translates to determining the equations of the moduli space under this embedding this article deals with one of the most classical quotients the space of ordered points on the projective line we show that under any weighting of the points this quotient is cut out scheme theoretically by a particularly simple set of quadric relations with the single exception of the segre cubic threefold the space of six points with equal weight we also show that the ideal of relations is generated in degree at most four and we give an explicit description of the generators if all the weights are even e g in the case of equal weight for odd n then we show that the ideal of relations is generated by quadrics

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

analyzing excessive no changes in clinical trials with clustered data this article considers clinical trials in which the efficacy measure is taken from several sites within each patient such as the alveolar bone height of the tooth sites or bone mineral densities of the lumbar spine sites since usually only a small portion of these sites will exhibit changes the conventional method using per patient average gives a diluted result due to excessive no changes in the data different methods have been proposed for this type of data in the case where the observations are mutually independent this includes the popular two part model lachenbruch 2001 statistics in medicine 20 1215 1234 2002 statistical methods in medical research 11 297 302 which is related to the composite approach for discrete and continuous data in shih and quan 1997 statistics in medicine16 1225 1239 2001 statistica sinica 11 53 62 in this article we model the data with excessive zeros no changes in clustered data using a mixture of distributions and taking into account possible measurement errors this mixture model includes the two part model as a special case when one component of the mixture degenerates

localization of classical waves i acoustic waves we consider classical acoustic waves in a medium described by a position dependent mass density x we assume that x is a reandom perturbation of a periodic function 0 x and that the periodic acoustic operator a 0 nabla cdot tfrac 1 varrho 0 x nabla has a gap in the spectrum we prove the existence of localized waves i e finite energy solutions of the acoustic equations with the property that almost all of the wave s energy remains in a fixed bounded region of space at all times with probability one localization of acoustic waves is a consequence of anderson localization for the self adjoint operators a nabla cdot tfrac 1 varrho 0 x nabla onl2 d we prove that in the random medium described by x the random operatora exhibits anderson localization inside the gap in the spectrum ofa0 this is shown even in situations when the gap is totally filled by the spectrum of the random opertor we can prescribe random environments that ensure localization in almost the whole gap

the stable mapping class group and q ℂp in t2 it was shown that the classifying space of the stable mapping class groups after plus construction b has an infinite loop space structure this result and the tools developed in bm to analyse transfer maps are used here to show the following splitting theorem let p p e 0 e p 2 be the adams splitting of the p completed suspension spectrum of p then for some infinite loop space w p b p e 0 e p 3 w p where e i denotes the infinite loop space associated to the spectrum e i the homology of e i is known and as a corollary one obtains large families of torsion classes in the homology of the stable mapping class group this splitting also detects all the miller morita mumford classes our results suggest a homotopy theoretic refinement of the mumford conjecture the above p adic splitting uses a certain infinite loop map b p 1 that induces an isomorphims in rational cohomology precisely if the mumford conjecture is true we suggest that might be a homotopy equivalence

tests for order restrictions in binary data in this article a general procedure is presented for testing for equality of k independent binary response probabilities against any given ordered alternative the proposed methodology is based on an estimation procedure developed in hwang and peddada 1994 annals of statistics 22 67 93 and can be used for a very broad class of order restrictions the procedure is illustrated through application to two data sets that correspond to three commonly encountered order restrictions simple tree order simple order and down turn order

comparing groups with umbrella orderings abstract one commonly observed response pattern in a one factor design with ordered treatment levels is the umbrella or unimodal ordering in which the response variable increases with an increase in the treatment level up to a point then decreases with further increase in the treatment level the turning point is called the peak of an umbrella ordering in many practical settings there are two or more different populations with umbrella orderings and it is of interest to compare these populations in this article likelihood ratio tests are developed for testing whether two groups with umbrella orderings have the same peaks three cases are considered variances known variances unknown and different for each group and variances unknown and the same for both groups extensions to randomized block designs and to a more general class of testing problems are discussed

analyses for binomial data with application to the fluctuation test for mutagenicity s umma ry the fluctuation test proposed by green muriel and bridges 1976 mutation research 38 33 42 a short term microbial test for mutagenicity yields binomial observations for which the probability of success varies with the background mutation rate the total number of microbial growth cycles for which a microbe is at risk of mutation and the rate of induced mutation for the compound being tested a standard one tailed two sample binomial test is preferable to the two tailed test adopted by green et al for analyzing data from a control versus single positive dose fluctuation test based on exact power computations recommendations are offered for the design of such a fluctuation test a simple method of guarding against the impact of a small number of aberrant observations in a multisample binomial problem is studied it is applicable to the fluctuation test when the protocol involves replicate measurements finally the case of more than one positive dose of the test compound is investigated two statistical tests for this situation both extensions of the one tailed two sample test are extensively compared a departure from monotonicity at high doses has a more serious effect on the power of the regression test than on that of the isotonic test a variant of the isotonic test based on the angular transformation should be avoided

the stable mapping class group of simply connected 4 manifolds we consider mapping class groups m 0diff m fix m of smooth compact simply connected oriented 4 manifolds m bounded by a collection of 3 spheres we show that if m contains cp 2 or cp 2 as a connected summand then all dehn twists around 3 spheres are trivial and furthermore m is independent of the number of boundary components by repackaging classical results in surgery and handlebody theory from wall kreck and quinn we show that the natural homomor phism from the mapping class group to the group of automorphisms of the intersection form becomes an isomorphism after stabilization with respect to connected sum with cp 2 cp 2 we next consider the 3 1 dimensional cobordism 2 category c of 3 spheres 4 manifolds as above and enriched with isotopy classes of diffeomorphisms as 2 morphisms we identify the homotopy type of the classifying space of this cat egory as the hermitian algebraic k theory of the integers we also comment on versions of these results for simply connected spin 4 manifolds finally we observe that a related 4 manifold operad detects infinite loop spaces

bootstrap multiscale analysis and localization in random media we introduce an enhanced multiscale analysis that yields subexponentially decaying probabilities for bad events for quantum and classical waves in random media we obtain exponential decay for the resolvent of the corresponding random operators in boxes of side l with probability higher than 1 e l for any 0 1 the starting hypothesis for the enhanced multiscale analysis only requires the verification of polynomial decay of the finite volume resolvent at some sufficiently large scale with probability bigger than 1 d is the dimension note that from the same starting hypothesis we get conclusions that are valid for any 0 1 this is achieved by the repeated use of a bootstrap argument as an application we use a generalized eigenfunction expansion to obtain strong dynamical localization of any order in the hilbert schmidt norm and better estimates on the behavior of the eigenfunctions

the ames salmonella microsome mutagenicity assay issues of inference and validation abstract the importance of chemically induced mutation for human health is discussed briefly and the biological basis for the primary in vitro assay for mutagenicity the ames salmonella microsome assay is reviewed a previous analysis for ames test data based on two mathematical models of the competing risks of mutation and toxicity is shown to have inflated false positive rates a reason for this is the existence of local singularities in the fisher information matrix a new likelihood ratio test incorporating a pretest of a nuisance parameter is proposed and its size is validated with replicated experimental data through an analysis based on a finite mixture of binomials model

distinguishing effects on tumor multiplicity and growth rate in chemoprevention experiments in some types of cancer chemoprevention experiments and short term carcinogenicity bioassays the data consist of the number of observed tumors per animal and the times at which these tumors were first detected in such studies there is interest in distinguishing between treatment effects on the number of tumors induced by a known carcinogen and treatment effects on the tumor growth rate since animals may die before all induced tumors reach a detectable size separation of these effects can be difficult this paper describes a flexible parametric model for data of this type under our model the tumor detection times are realizations of a delayed poisson process that is characterized by the age specific tumor induction rate and a random latency interval between tumor induction and detection the model accommodates distinct treatment and animal specific effects on the number of induced tumors multiplicity and the time to tumor detection growth rate a gibbs sampler is developed for estimation of the posterior distributions of the parameters the methods are illustrated through application to data from a breast cancer chemoprevention experiment

smoothness of the density of states in the anderson model at high disorder we prove smoothness of the density of states in the anderson model at high disorder for a class of potential distributions that include the uniform distribution