fixed width multiple comparison procedures using common random numbers for steady state simulations abstract suppose that there are k 2 different systems i e stochastic processes where each system has an unknown steady state mean performance we consider the problem of running a two stage simulation using common random numbers to construct fixed width confidence intervals for two multiple comparison problems under the assumptions that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem and that the asymptotic covariance matrix satisfies a condition known as sphericity we prove that our confidence intervals are asymptotically valid as the desired half width of the confidence intervals tend to zero we develop both absolute and relative width confidence intervals empirical results are presented indicating the procedures robustness to violations of the sphericity assumption

is the selected population the best random variables x i sim n theta i 1 i 1 2 cdots k are observed suppose x s is the largest observation if the inference theta s max i neq s theta i is made whenever x s max i neq s x i c then the probability of a false inference is maximized when two theta i are equal and the rest are infty equivalently the inference can be made whenever a two sample two sided test for difference of means based on the largest two observations would reject the hypothesis of no difference the result also holds in the case of unknown estimable common variance and in fact for location families with monotone likelihood ratio

identification for control optimal input design with respect to a worst case nu gap cost function parameter identification experiments deliver an identified model together with an ellipsoidal uncertainty region in parameter space the objective of robust controller design is thus to stabilize all plants in the identified uncertainty region the subject of the present contribution is to design an identification experiment such that the worst case nu gap over all plants in the resulting uncertainty region between the identified plant and plants in this region is as small as possible the experiment design is performed via input power spectrum optimization two cost functions are investigated which represent different levels of trade off between accuracy and computational complexity it is shown that the input optimization problem with respect to these cost functions is amenable to standard numerical algorithms used in convex analysis

algebraic invariants for right angled artin groups a finite simplicial graph determines a right angled artin group g with generators corresponding to the vertices of and with a relation w w for each pair of adjacent vertices we compute the lower central series quotients the chen quotients and the first resonance variety of g directly from the graph

a new procedure for selecting good populations summary suppose we have k normal populations with means ii1 k and common unknown variance o2 a population is good if its mean exceeds u k 1 where p k is the largest of the u s a procedure is proposed to select a subset of populations satisfying the requirement that the probability of including all good populations exceeds a prespecified value p simultaneous inference that can be made with the selection procedure is considered furthermore if populations with means below p k e2 are bad where 92 el a selection procedure is proposed and a sample size is determined so that the probability of either omitting a good population or selecting a bad population is less than or equal to 1 p

multiple comparison procedures for steady state simulations suppose that there are k 2 different systems i e stochastic processes where each system has an unknown steady state mean performance and unknown asymptotic variance we allow for the asymptotic variances to be unequal and for the distributions of the k systems to be different we consider the problem of running independent single stage simulations to make multiple comparisons of the steady state means of the different systems we derive asymptotically valid as the run lengths of the simulations of the systems tend to infinity simultaneous confidence intervals for each of the following problems all pairwise comparisons of means all contrasts multiple comparisons with a control and multiple comparisons with the best our confidence intervals are based on standardized time series methods and we establish the asymptotic validity of each under the sole assumption that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem although simulation is the context of this paper the results naturally apply to asymptotically stationary time series

simultaneous confidence intervals for all distances from the best in practice comparisons with the best are often the ones of primary interest in this paper parametric and nonparametric simultaneous upper confidence intervals for all distances from the best are derived under the location model their improvement upon the results of bechhofer 1954 gupta 1956 1965 fabian 1962 and desu 1970 in the parametric case is discussed in the nonparametric case no comparable confidence statements were available previously

graphical procedures for multiple comparisons under general dependence abstractit has been more than half a century since tukey first introduced graphical displays that relate nonoverlap of confidence intervals to statistically significant differences between parameter estimates in this article we show how tukey s graphical overlap procedure can be modified to accommodate general forms of dependence within and across samples we also develop a procedure that can be used to more effectively resolve rankings within the tails of the distributions of parameter values thereby generalizing existing methods for multiple comparisons with the best we show that these new procedures retain the simplicity of tukey s original procedure while maintaining asymptotic control of the familywise error rate under very general conditions simple examples are used throughout to illustrate the procedures supplementary materials for this article are available online

a useful input parameterization for optimal experiment design optimal inputs are usually determined by minimizing a scalar valued function of the inverse fisher information matrix the function should be monotonically increasing this is the case e g for the trace and the determinant the minimization must be performed under some constraints to prevent the input or output amplitude to blow up in this note it is proved that assuming open loop experiments the optimal input signal can be realized as a certain arma process of low order or at least can be approximated with any degree of accuracy by such a process this allows the optimal input design problem to be reformulated as a standard static optimization problem of low dimension

simple and robust experiment design for system identification using fractional models this paper tackles the problems of simple and robust experiment design for system identification using elementary fractional models it is based on a frequency domain approach and allows to determine the best sine input signal maximizing d optimality criterion of the parameters inverse covariance matrix in different contexts first a single parameter any of the parameters of the elementary fractional model is assumed to be unknown next any combination of two and then three parameters are supposed to be unknown finally the problem of robust experiment design is treated when a bounded interval of the estimated parameters is known in the same contexts

coherence subgroup separability and metacyclic structures for a class of cyclically presented groups abstract we study a class m of cyclically presented groups that includes both finite and infinite groups and is defined by a certain combinatorial condition on the defining relations this class includes many finite metacyclic generalized fibonacci groups that have been previously identified in the literature by analyzing their shift extensions we show that the groups in the class m are coherent subgroup separable satisfy the tits alternative possess finite index subgroups of geometric dimension at most two and that their finite subgroups are all metacyclic many of the groups in m are virtually free some are free products of metacyclic groups and free groups and some have geometric dimension two we classify the finite groups that occur in m giving extensive details about the metacyclic structures that occur and we use this to prove an earlier conjecture concerning cyclically presented groups in which the relators are positive words of length three we show that any finite group in the class m that has fixed point free shift automorphism must be cyclic

graphs and separability properties of groups abstract a group g is lerf locally extended residually finite if for any finitely generated subgroup s of g and for any g s there exists a finite index subgroup s 0 of g which contains s but not g using graph theoretical methods we give algorithms for constructing finite index subgroups in amalgamated free products of groups with good separability properties we prove that a free product of a free group and a lerf group amalgamated over a cyclic subgroup maximal in the free factor is lerf the maximality condition cannot be removed because adjunction of roots does not preserve property lerf we also give short proofs of some old theorems about separability properties of groups including a theorem of brunner burns and solitar that a free product of free groups amalgamated over a cyclic subgroup is lerf

identification for control optimal input intended to identify a minimum variance controller it is well known that the quality of the parameters identified during an identification experiment depends on the applied excitation signal prediction error identification using full order parametric models delivers an ellipsoidal region in which the true parameters lie with some prescribed probability level this ellipsoidal region is determined by the covariance matrix of the parameters input design strategies aim at the minimization of some measure of this covariance matrix we show that it is possible to optimize the input in an identification experiment with respect to a performance cost function of a closed loop system involving explicitly the dependence of the designed controller on the identified model in the present contribution we focus on finding the optimal input for the estimation of the parameters of a minimum variance controller without the intermediate step of first minimizing some measure of the model parameter accuracy we do this in conjunction with using covariance formulas which are not asymptotic in the model order which is rather new in the domain of optimal input design the identification procedure is performed in closed loop besides optimizing the input power spectrum for the identification experiment we also address the question of optimality of the controller it is a wide belief that the minimum variance controller should be the optimal choice since we perform an experiment for designing a minimum variance controller however we show that this may not always be the case but rather depends on the model structure

multiple comparisons with the best treatment abstract let 1 2 k be k 2 sources of observations treatments populations and suppose the goodness of treatment i is characterized by the size of an unknown real valued parameter i let k max1 i k i if i is preferred to j when i j the parameters i k i i 1 2 k reflect in an inverse sense the goodness of each treatment relative to the best treatment a general technique for obtaining simultaneous confidence intervals on the i is demonstrated with several examples this technique can be applied in any setting where comparison with control intervals can be computed regarding any j as the control these results have special importance in ranking and selection problems in that the process of generating upper bounds on the i generates traditional confidence statements of both the indifference zone and the subset selection schools simultaneously as established by hsu 1981

closed loop experiment design for linear time invariant dynamical systems via lmis all stationary experimental conditions corresponding to a discrete time linear time invariant causal internally stable closed loop with real rational system and feedback controller are characterized using the youla kucera parametrization finite dimensional parametrizations of the input spectrum and the youla kucera parameter allow a wide range of closed loop experiment design problems based on the asymptotic in the sample size covariance matrix for the estimated parameters to be recast as computationally tractable convex optimization problems such as semi definite programs in particular for box jenkins models a finite dimensional parametrization is provided which is able to generate all possible asymptotic covariance matrices as a special case the very common situation of a fixed controller during the identification experiment can be handled and optimal reference signal spectra can be computed subject to closed loop signal constraints finally a brief numerical comparison with closed loop experiment design based on a high model order variance expression is presented

morse theory and finiteness properties of groups we examine the finiteness properties of certain subgroups of right angled artin groups in particular we find an example of a group that is of type fp z but is not finitely presented

constrained simultaneous confidence intervals for multiple comparisons with the best for comparing k treatment effects 01 02 ok often the parameters of primary interest are 0i maxeioi0 i 1 k in this article we develop constrained 100p two sided simultaneous confidence intervals for 0i maxj i0j which we refer to as constrained mcb intervals it turns out that the lower bounds of the intervals imply indifference zone selection inference and the upper bounds of these intervals imply subset selection inference each given at the same confidence level 100p as mcb we also extend our

input design as a tool to improve the convergence of pem the prediction error method pem is related to an optimization problem built on input output data collected from the system to be identified it is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and or the search space is constrained to a nonconvex set the shape of the cost function and hence the difficulty in solving the optimization problem depends directly on the experimental conditions more specifically on the spectrum of the input output data collected from the system therefore it seems plausible to improve the convergence to the global minimum by properly choosing the spectrum of the input in this paper we address this problem we present a condition for convergence to the global minimum of the cost function and propose its inclusion in the input design we present the application of the proposed approach to case studies where the algorithms tend to get trapped in nonglobal minima

closed loop optimal experiment design solution via moment extension we consider optimal experiment design for parametric prediction error system identification of linear time invariant multiple input multiple output systems in closed loop when the true system is in the model set the optimization is performed jointly over the controller and the spectrum of the external excitation which can be reparametrized as a joint spectral density matrix the optimal solution consists of first computing a finite set of generalized moments of this spectrum as the solution of a semi definite program a second step then consists of constructing a spectrum that matches this finite set of optimal moments and satisfies some constraints due to the particular closed loop nature of the optimization problem this problem can be seen as a moment extension problem under constraints here we first show that the so called central extension always satisfies these constraints leading to a constructive procedure for the optimal controller and excitation spectrum we then show that one can construct a broader set of parametrized optimal solutions that also satisfy the constraints the additional degrees of freedom can then be used to achieve additional objectives

sequential implementation of stepwise procedures for identifying the maximum tolerated dose this article considers the problem of finding the maximum tolerated dose mtd of a drug in human trials the mtd is defined as the maximum test dose with toxicity probability less than or equal to a target toxicity rate we adopt the multiple test framework with step down tests used in an escalation stage and step up tests used in a deescalation stage to allow sequential dose assignments for ethical purposes by formulating the estimation problem as a testing problem the proposed procedures formally control the error probability of selecting an unsafe dose in addition we can control the probability of correctly selecting the mtd under a parameter subspace where no toxicity probability lies in an interval bracketed by the target toxicity rate and an unacceptably high toxicity rate the so called indifference zone this frequentist property which is currently lacking in the conduct of dose finding trials in humans is appealing from a regulatory standpoint we give the general expressions of the se

parabolic and quasiparabolic subgroups of free partially commutative groups let be a finite graph and g be the corresponding free partially commutative group in this paper we study subgroups generated by vertices of the graph which we call canonical parabolic subgroups a natural extension of the definition leads to canonical quasiparabolic subgroups it is shown that the centralisers of subsets of g are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions

optimal confidence sets bioequivalence and the limacon of pascal abstract we begin with a decision theoretic investigation into confidence sets that minimize expected volume at a given parameter value such sets are constructed by inverting a family of uniformly most powerful tests and hence they also enjoy the optimality property of being uniformly most accurate in addition these sets possess bayesian optimal volume properties and represent the first case to our knowledge of a frequentist 1 confidence set that possesses a bayesian optimality property the hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing our sets are optimal for testing bioequivalence in certain settings in the case of the normal distribution the optimal set is a curve known as the limacon of pascal we illustrate the use of these curves with a biopharmaceutical example

on the profinite topology of right angled artin groups abstract in the present work we give necessary and sufficient conditions on the graph of a right angled artin group that determine whether the group is subgroup separable or not moreover we investigate the profinite topology of f 2 f 2 and we show that the profinite topology of the above group is strongly connected with the profinite topology of f 2

simultaneous inference with respect to the best treatment in block designs in many practical situations only inference concerning the unknown best treatment and comparisons of the individual treatments with respect to the best treatment are of primary interest we give an explicit formulation of this problem in the framework of randomized complete block designs a procedure based on sample means and two procedures based on signed ranks are proposed it is seen that for the problem considered these procedures have a substantial advantage over what can be deduced from all pairwise multiple comparisons procedures

information matrix and d optimal design with gaussian inputs for wiener model identification we present a closed form expression for the fischer s information matrix associated with the identification of wiener models in the derivation we assume that the input signal is gaussian the analysis allows the linear sub system in the wiener model to have a generic rational transfer function of arbitrary order it also allows the static nonlinearity of the wiener model to be a polynomial of arbitrary degree in addition we show how this analysis can be used to design tractable algorithms for d optimal input design the idea is further extended to design optimal inputs consisting of a sequence of gaussian signals with different mean values and variances by combining gaussian inputs with different means we can tune the amplitude distribution of the input to achieve the best identification accuracy in d optimal sense the analytical results are also illustrated with some numerical simulations

subgroup separability in integral group rings abstract we give a list of finite groups containing all finite groups g such that the group of units z g of the integral group ring z g is subgroup separable there are only two types of these groups g for which we cannot decide whether z g is subgroup separable namely the central product q 8 y d 8 and q 8 c p with p prime and p 1 mod 8

limit groups are subgroup conjugacy separable abstract a group g is called subgroup conjugacy separable if for every pair of non conjugate finitely generated subgroups of g there exists a finite quotient of g where the images of these subgroups are not conjugate we prove that limit groups are subgroup conjugacy separable we also prove this property for one relator groups of the form r a 1 a n w n with n w the property is also proved for infinite virtual retracts equivalently for infinite quasiconvex subgroups of hyperbolic virtually special groups

choosing between open and closed loop experiments in linear system identification this correspondence shows that open loop experiments are optimal for a broad class of systems when the system input is constrained in addition we show that for a general class of systems when the output power is constrained closed loop experiments are optimal both results use a strong notion of optimality and use expressions for estimation accuracy which are nonasymptotic in model order but asymptotic in data length

sequential multiple comparisons with the best abstract in this article we give a method of designing and analyzing an experiment for comparing k 2 treatments such that a a treatment is terminated as soon as there is statistical evidence that it is not the best treatment and b at the conclusion of the experiment one can assert at some prespecified confidence level simultaneously that those terminated treatments are not the best and those remaining treatments are respectively within certain small distances of the unknown best treatment the inference given by our method is stronger than existing sequential elimination selection inference

input design via lmis admitting frequency wise model specifications in confidence regions a framework for reformulating input design problems in prediction error identification as convex optimization problems is presented for linear time invariant single input single output systems this framework unifies and extends existing results on open loop input design that are based on the finite dimensional asymptotic covariance matrix of the parameter estimates basic methods for parametrizing the input spectrum are provided and conditions on these parametrizations that guarantee that all possible covariance matrices for the asymptotic distribution of the parameter estimates can be generated are provided a wide range of model quality constraints can be handled in particular different frequency by frequency constraints can be used this opens up new applications of input design in areas such as robust control furthermore quality specifications can be imposed on all models in a confidence region thus allowing for statements such as with at least 99 probability the model quality specifications will be satisfied

subgroups of graph groups given a graph x we define a group gx as follows gx is generated by the vertices of x with a defining relation xy jt for each pair y 2 of ver tices joined by an edge of x a group is called a graph group if it is isomorphic to gx for some graph x we will not distinguish by notation in what follows between a vertex of x and the corresponding element of gx we remark that the extreme cases of graphs namely the complete and the completely disconnected graphs correspond respectively to free abelian and free groups it is well known that any subgroup of a group of either of these types is again of the same type and it is thus natural to ask to what extent and in what form this is true of the graph groups that lie in between these extreme cases in this article we will prove the following

generalized kyp lemma unified frequency domain inequalities with design applications the celebrated kalman yakubovic spl caron popov kyp lemma establishes the equivalence between a frequency domain inequality fdi and a linear matrix inequality and has played one of the most fundamental roles in systems and control theory this paper first develops a necessary and sufficient condition for an s procedure to be lossless and uses the result to generalize the kyp lemma in two aspects the frequency range and the class of systems and to unify various existing versions by a single theorem in particular our result covers fdis in finite frequency intervals for both continuous discrete time settings as opposed to the standard infinite frequency range the class of systems for which fdis are considered is no longer constrained to be proper and nonproper transfer functions including polynomials can also be treated we study implications of this generalization and develop a proper interface between the basic result and various engineering applications specifically it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain phase properties in several frequency ranges the method is illustrated by numerical design examples of digital filters and proportional integral derivative controllers

asymptotic variance expressions for identified black box transfer function models identification of black box transfer function models is considered it is assumed that the transfer function models possess a certain shift property which is satisfied for example by all polynomial type models expressions for the variances of the transfer function estimates are derived that are asymptotic both in the number of observed data and in the model orders the result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance respectively is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise the factor of proportionality is the ratio of model order to number of data this result is independent of the particular model structure used the result is applied to evaluate the performance degradation due to variance for a number of typical model uses some consequences for input design are also drawn

testing for the supremacy of a multinomial cell probability tests for the supremacy of a multinomial cell probability are developed the tested null hypothesis states that a particular cell of interest is not more probable than all others rejection of this null leads to the conclusion that the cell of interest has a strictly greater probability than all other cells the null hypothesis constrains the multinomial probability vector to a nonconvex region that is a union of closed convex cones the likelihood ratio test for this problem is derived and shown to be equivalent to an intersection union test the least favorable configuration of the multinomial probability vector in the null parameter space is derived and the limiting null distribution of the test statistic that is stochastically greatest is shown to be a mixture of point mass at zero and a chi square distribution with a single degree of freedom asymptotic and valid finite sample testing procedures are proposed and examined via a simulation study and the analysis of two datasets the proposed procedure