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

strong consistency of the variance estimator in steady state simulation output analysis in this paper we study the problem of variance estimation in steady state simulation output analysis a confidence interval for the mean of an output sequence may be constructed using a weakly consistent estimator of the time average variance constant of the process moreover a strongly consistent estimator of the variance constant is required for fixed width confidence interval estimation procedures to be asymptotically valid here we establish sufficient conditions to ensure strong consistency of the estimator of the variance constant obtained by several widely used methods of steady state simulation output analysis namely batch means overlapping batch means spaced batch means and standardized time series area estimator we also introduce the overlapping area estimator of the variance constant the established sufficient conditions provide qualitative insight into the relation between the correlation of the process and certain parameters e g batch size of the output method used

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

mean square consistency of the variance estimator in steady state simulation output analysis in steady state simulation output analysis mean square consistency of the process variance estimator is important for a number of reasons one way to construct an asymptotically valid confidence interval around a sample mean is via construction of a consistent estimator of the process variance and a central limit theorem also if an estimator is consistent in the mean square sense a mean square error analysis is theoretically justified finally batch size selection is an open research problem in steady state output analysis and a mean square error analysis approach has been proposed in the literature to be valid the process variance estimators constructed must be consistent in the mean square sense in this paper we prove mean square consistency of the process variance estimator for the methods of batch means overlapping batch means standardized time series area and spaced batch means by rigorously computing the rate of decay of the variance of the process variance estimators asymptotic results for third and higher centered moments of the batch means and area variance estimators are also given along with central limit theorems

bootstrap prediction intervals for autoregression abstract the nonparametric bootstrap is applied to the problem of prediction in autoregression let y t t 0 1 2 be a stationary autoregressive process of known order p ar p given a realization of the series up to time t y 1 y 2 y t a 100 prediction interval for y t k is desired standard forecasting techniques which assume that the error sequence of the process y t is gaussian rely on the fact that the conditional distribution of y t k given the data is gaussian as well as a nonparametric alternative the bootstrap provides an estimate of the conditional distribution of y t k the method is similar to other applications of the bootstrap for linear models because the residuals are resampled the proposed methodology represents a different approach since an alternative representation for ar p series is used allowing for bootstrap replicates generated backward in time it follows that the resulting replicates all have the same conditionally fixed values at the end

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

a generalized omori yau maximum principle in finsler geometry abstract we obtain some new laplacian comparison theorems on finsler manifolds with the weighted ricci curvature bounded from above resp below by a smooth function then under some new sufficient conditions we generalize the omori yau type maximum principle in the finsler setting

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

batch size effects in the analysis of simulation output batching is a commonly used method for calculating confidence intervals on the mean of a sequence of correlated observations arising from a simulation experiment several recent papers have considered the effect of using batch sizes too small to satisfy assumptions of normality and or independence and the resulting incorrect probabilities of the confidence interval covering the mean this paper quantifies the effects of using batch sizes larger than necessary to satisfy normality and independence assumptions these effects include 1 correct probability of covering the mean 2 an increase in expected half length 3 an increase in the standard deviation and coefficient of variation of the half length and 4 an increase in the probability of covering points not equal to the mean for any sample size and independent and normal batch means the results are 1 the effects of less than 10 batches are large and the effects of more than 30 batches small and 2 additional batches have lesser effects on

the use of subseries values for estimating the variance of a general statistic from a stationary sequence let z i infty i infty be a strictly stationary infty mixing sequence without specifying the dependence model giving rise to z i and without specifying the marginal distribution of z i we address the question of variance estimation for a general statistic t n t n z 1 z n for estimating var t n from just the available data z 1 z n we propose computing subseries values t m z i 1 z i 2 z i m 0 leq i i m leq n these subseries values are used as replicates to model the sampling variability of t n in particular we use adjacent nonoverlapping subseries of length m m n with m rightarrow infty and m n n rigtharrow 0 our variance estimator is just the usual sample variance computed amongst these subseries values after appropriate standardization this estimator is shown to be consistent under mild integrability conditions we present optimal i e minimum m s e choices of m n for the special case where t n overset z n and z i is a normal ar 1 sequence a simulation study is conducted showing that those same choices of m n are effective when t n is a robust estimator of location and z i is subject to contamination

optimal mean squared error batch sizes when an estimator of the variance of the sample mean is parameterized by batch size one approach for selecting batch size is to pursue the minimal mean squared error mse we show that the convergence rate of the variance of the sample mean and the bias of estimators of the variance of the sample mean asymptotically depend on the data process only through its marginal variance and the sum of the autocorrelations weighted by their absolute lags combining these results with variance results of goldsman and meketon we obtain explicit asymptotic approximations for mse optimal batch size optimal mse and robustness for four quadratic form estimators of the variance of the sample mean our empirical results indicate that the asymptotic approximations are reasonably accurate for sample sizes seen in practice although we do not discuss batch size estimation procedures the empirical results suggest that the explicit asymptotic batch size approximation which depends only on a summary measure which we re

standardized time series l p norm variance estimators for simulations this paper studies a class of estimators for the variance parameter of a stationary stochastic process the estimators are based on lp norms of standardized time series and they generalize previously studied estimators due to schruben we show that the new estimators have some desirable properties they are asymptotically unbiased and have low asymptotic variance we also illustrate empirically the performance of the lp norm estimators on various stochastic processes

using standardized time series to estimate confidence intervals for the difference between two stationary stochastic processes this paper discusses confidence interval estimation for the difference between the means of two independent strictly stationary phi mixing stochastic processes the confidence intervals are based on batched subseries of the two time series and are obtained by using schruben s standardized time series method we compare these intervals with the classical result applied to the batch means and consider different assumptions on the variances and the number of observations the comparison results show that the four new estimators for each case have asymptotic properties that clearly dominate the classical estimator two applications of these intervals are 1 validating stationary discrete event simulation models and 2 comparing two alternative policies or system designs via simulation

nonparametric estimation of the moments of a general statistic computed from spatial data abstract a statistic s is computed on spatially indexed data x i i d where d is a finite subset of the integer lattice z2 we propose a simple nonparametric method for estimating the moments e g variance skewness of s d using only the observed data at hand the method uses replicates of s computed on smaller subsets of d no explicit knowledge of the underlying spatial dependence mechanism is needed and the marginal distribution of x i may also be unknown the shape of d can be quite irregular and s is allowed to be a general statistic the proposed estimator is shown to be consistent and asymptotically normal under mild conditions on s d and mixing conditions on the strength of spatial dependence as a numerical example the estimator is used in assessing the geographic clumping of cancer deaths in the united states

automatic optimal batch size selection for recursive estimators of time average covariance matrix abstractthe time average covariance matrix tacm k z k where k is the auto covariance function is an important quantity for the inference of the mean of an rd valued stationary process d 1 this article proposes two recursive estimators for with optimal asymptotic mean square error amse under different strengths of serial dependence the optimal estimator involves a batch size selection which requires knowledge of a smoothness parameter k z k k for some this article also develops recursive estimators for combining these two estimators we obtain a fully automatic procedure for optimal online estimation for consistency and convergence rates of the proposed estimators are derived applications to confidence region construction and markov chain monte carlo convergence diagnosis are discussed supplementary materials for this article are available online

subsampling for heteroskedastic time series abstract in this article a general theory for the construction of confidence intervals or regions in the context of heteroskedastic dependent data is presented the basic idea is to approximate the sampling distribution of a statistic based on the values of the statistic computed over smaller subsets of the data this method was first proposed by politis and romano 1994b for stationary observations we extend their results to heteroskedastic observations and prove a general asymptotic validity result under minimal conditions in contrast the usual bootstrap and moving blocks bootstrap are typically valid only for asymptotically linear statistics and their justification requires a case by case analysis our general asymptotic results are applied to a regression setting with dependent heteroskedastic errors

on the scalar curvature of constant mean curvature hypersurfaces in space forms abstract in this paper we study the behavior of the scalar curvature s of a complete hypersurface immersed with constant mean curvature into a riemannian space form of constant curvature deriving a sharp estimate for the infimum of s our results will be an application of a weak omori yau maximum principle due to pigola rigoli setti 2005 17

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

linear decision trees subspace arrangements and mobius functions let p be a set in rn given a point x we want to test if x e p our model of computation is a linear decision tree a rooted ternary tree t where with each interior node v is associated a linear function lv x l j ajxj b and the three edges connecting v to its descendants are labelled starting from the root we move down the tree at each internal node v we check whether iv x 0 and follow the appropriately labelled edge leaves are labelled yes and no and arriving at a leaf we read off the answer to the question is x e p linear decision trees are sometimes surprisingly powerful devices we mention here the result that some np complete problems like the knapsack problem have polynomial depth linear decision trees mh lower bound results on the size or depth of linear decision trees usually depend on counting the number of connected components of p or r n p this method was introduced by dobkin and lipton dl and further developed by steele and yao sy ben or bo and others in this paper we describe topological methods that can be applied to obtain lower bounds also if these sets are connected the basic idea of this paper was first explored in bly the euler characteristic of p or r n p was used to estimate the number of leaves in a linear decision tree for p here we improve and extend the topological methods of bly in particular we show that the euler characteristic can be replaced by the sum of the betti numbers of r n p in bl y the method was applied to the case when p is a subspace arrangement i e a union of a finite number of affine subspaces the euler characteristic of the union is essentially the mobius function of the intersection lattice of these subspaces in this paper using a formula of goresky and macpherson gm we work with the betti numbers of the complement of this union and thereby obtain better bounds the motivating problem in bly was the k equal problem given n real numbers xl xn decide if some k of them are equal it was shown that ev ry linear decision tree for the k equal problem has size at least 2njk 0 n and consequently depth at least q nlog 2njk which is best possible we

why the characteristic polynomial factors we survey three methods for proving that the characteristic polynomial of a finite ranked lattice factors over the nonnegative integers and indicate how they have evolved recently the first technique uses geometric ideas and is is based on zaslavsky s theory of signed graphs the second approach is algebraic and employs results of saito and terao about free hyperplane arrangements finally we consider a purely combinatorial theorem of stanley about supersolvable lattices and its generalizations

geometric analysis of lorentzian distance function on spacelike hypersurfaces some analysis on the lorentzian distance in a spacetime with controlled sectional or ricci curvatures is done in particular we focus on the study of the restriction of such distance to a spacelike hypersurface satisfying the omori yau maximum principle as a consequence and under appropriate hypotheses on the sectional or ricci curvatures of the ambient spacetime we obtain sharp estimates for the mean curvature of those hypersurfaces moreover we also give a sufficient condition for its hyperbolicity

estimating the steady state mean from short transient simulations steady state mean performance is a common basis for evaluating discrete event simulation models however analysis is complicated by autocorrelation and initial transients we present confidence interval procedures for estimating the steady state mean of a stochastic process from observed time series which may be short autocorrelated and transient we extend the generalized least squares estimator of snell and schruben iie trans 17 1985 354 and develop confidence interval procedures for single and multiple replication experiments the procedures are asymptotically valid and for short series with reasonable initializations e g empty and idle are comparable or superior to existing procedures further we demonstrate and explain the robustness of the weighted batch means procedure of bischak et al manage sci 39 1993 1002 to initialization bias the proposed confidence interval procedure requires neither truncation of initial observations nor choice of batch size and permits the existence of steady state mean to be inferred from the data

multiple comparisons for analyzing dichotomous response dichotomous response models are common in many experimental settings statistical parameters of interest are typically the probabilities pi that an experimental unit will respond at the various treatment levels herein simultaneous procedures are considered for multiple comparisons among these probabilities with attention directed at construction of simultaneous confidence intervals for various functions of the pi the inferences are based on the asymptotic normality of the maximum likelihood estimator of pi specific applications include all pairwise comparisons and comparisons with a fixed control treatment monte carlo evaluations are undertaken to examine the small sample properties of the various procedures it is seen that use of the usual estimates of variance consistently leads to less than nominal empirical coverage for most sample sizes examined for very large samples total size greater than about 300 nominal coverage is achieved a reformulation of the pairwise comparisons using a construction noted by beal 1987 biometrics 43 941 950 is shown to exhibit generally nominal empirical coverage characteristics and is recommended for use with small to moderate sample sizes

control variate models of common random numbers for multiple comparisons with the best using common random numbers crn in simulation experiment design is known to reduce the variance of estimators of differences in system performance however when more than two systems are compared exact simultaneous statistical inference in conjunction with crn is typically impossible we introduce control variate models of crn that permit exact statistical inference specifically multiple comparisons with the best these models explain the effect of crn via a linear regression of the simulation output on control variates that are functions of the simulation inputs we establish theoretically and illustrate empirically that the control variate models lead to sharper statistical inference in the sense that the probability of detecting differences in systems performance is increased

inference for non stationary time series regression with or without inequality constraints summary we consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non stationary behaviours over time meanwhile the regression parameters may be subject to linear inequality constraints a simple and unified procedure for structural stability checks and parameter inference is proposed in the case where the regression parameters are constrained the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones

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

the generalized dowling lattices in this paper we study a new class of lattices called the generalized dowling lattices these lattices are parametrized by a positive integer n a finite group g and a meet sublattice k of the lattice of subgroups of g for an appropriate choice of k the generalized dowling lattice d0 g k agrees with the ordinary dowling lattice dn g for a different choice of k the generalized dowling lattices are the lattice of intersections of a set of subspaces in complex space the set of subspaces defined in terms of a representation of g generalizes the thick diagonal in en we compute the mobius function and characteristic polynomial of the lattice dn g k along with the homology of dn g k in terms of the homology of k we go on to compute the character of g wr sn acting on the homology of d g k this computation provides a nontrivial generalization of a result due to stanley concerning the character of s acting on the top homology of the partition lattice

confidence intervals for steady state simulations i a survey of fixed sample size procedures we consider the problem of constructing a confidence interval for the steady state mean of a stochastic process by means of simulation and study the five main methods which have been proposed replication batch means autoregressive representation spectrum analysis and regeneration cycles for the case when the length of the simulation is fixed in advance comparing the performances of these methods on stochastic models with known steady state means we find that the simulator should exercise caution in interpreting the results from a simulation of fixed length and that the length of a simulation adequate for acceptable performance is highly model dependent we also investigate possible sources of error for the methods and conclude that variance estimator bias is more important than point estimator bias in confidence interval coverage degradation

shellable nonpure complexes and posets ii this is a direct continuation of shellable nonpure complexes and posets i which appeared in transactions of the american mathematical society 348 1996 1299 1327 8 interval generated lattices and dominance order in this section and the following one we will continue exemplifying the applicability of lexicographic shellability to nonpure posets let f i1 i2 in be a family of intervals of integers by which is meant sets of the form a b a a 1 b a b we assume that there are no containments among these intervals and that they are ordered so that their left and right endpoints are increasing let l f be the lattice of all sets that are unions of subfamilies of f ordered by inclusion such interval generated lattices l f were introduced and studied by greene g define an edge labeling of l f as follows if a b is a covering and a max b a then a b a if a 1 a and a is the left endpoint of some i f

eigenspace arrangements of reflection groups the lattice of intersections of reflecting hyperplanes of a complex reflection group w may be considered as the poset of 1 eigenspaces of the elements of w in this paper we replace 1 with an arbitrary eigenvalue and study the topology and homology representation of the resulting poset after posing the main question of whether this poset is shellable we show that all its upper intervals are geometric lattices and then answer the question in the affirmative for the infinite family g m p n of complex reflection groups and the first 31 of the 34 exceptional groups by constructing cl shellings in addition we completely determine when these eigenspaces of w form a k 1 resp free arrangement for the symmetric group we also extend the combinatorial model available for its intersection lattice to all other eigenvalues by introducing balanced partition posets presented as particular upper order ideals of dowling lattices study the representation afforded by the top co homology group and give a simple map to the posets of pointed d divisible partitions 1 main question and results let v denote an n dimensional c vector space a reflection in v is any nonidentity element r in gl v of finite order that fixes some hyperplane hr and a finite subgroup w of gl v is called a reflection group if it is generated by reflections example the action of the symmetric group sn on n 1 2 n gives rise to a faithful action on c via ei e i where e1 e2 en denote the standard basis vectors since the transpositions act as reflections and generate the group this representation realizes sn as a reflection group in gl c we shall refer to it as the defining representation for an element g w and root of unity let v g denote the eigenspace of g in v define e w to be the w poset partially ordered set of all such eigenspaces v g g w ordered by reverse inclusion with w action given by h v g v hgh the eigenvalue 1 gives the lattice lw of intersections of reflecting hyperplanes for w see 29 lemma 4 4 the minimal elements of e w i e the inclusion maximal eigenspaces forw are the focus of springer s theory of regular elements 35 and each has dimension equal to the number a d of degrees d1 d2 dn of w that are divisible by d the order of see proposition 3 7 below when w is crystallographic the poset e w itself appears in broue malle and michel s sylow theory 8 2010 mathematics subject classification primary 20f55 05e10 05e18 55p20 14n20

simulation output analysis using standardized time series the method of standardized time series sts was proposed by schruben as an approach for constructing asymptotic confidence intervals for the steady state mean from a single simulation run the sts method cancels out the variance constant while other methods attempt to consistently estimate the variance constant our goal in this paper is to generalize the sts method and to study some of its basic properties starting from a functional central limit theorem fclt for the sample mean of the simulated process a class of mappings of c 0 1 to is identified each of which leads to a sts confidence interval one of these mappings leads to the batch means method a lower bound is obtained for the expected length of the asymptotic as the run size becomes large sts confidence intervals this lower bound is not attained but can be approached arbitrarily closely by sts confidence intervals methods that consistently estimate the variance constant do realize this lower bound the variance of the length of a sts confidence interval is of larger order in the run length than is that for the regenerative method

simulation run length control in the presence of an initial transient this paper studies the estimation of the steady state mean of an output sequence from a discrete event simulation it considers the problem of the automatic generation of a confidence interval of prespecified width when there is an initial transient present it explores a procedure based on schruben s brownian bridge model for the detection of nonstationarity and a spectral method for estimating the variance of the sample mean the procedure is evaluated empirically for a variety of output sequences the performance measures considered are bias confidence interval coverage mean confidence interval width mean run length and mean amount of deleted data if the output sequence contains a strong transient then inclusion of a test for stationarity in the run length control procedure results in point estimates with lower bias narrower confidence intervals and shorter run lengths than when no check for stationarity is performed if the output sequence contains no initial transient then the performance measures of the procedure with a stationarity test are only slightly degraded from those of the procedure without such a test if the run length is short relative to the extent of the initial transient the stationarity tests may not be powerful enough to detect the transient resulting in a procedure with unreliable point and interval estimates

statistical inference for the difference between the best treatment mean and a control mean in many experiments researchers are interested in comparing several treatment means with a control mean when there are some treatments significantly better than the control it is often of interest to evaluate the difference between the best treatment mean and the control mean and to identify the best treatment in this article we derive lower confidence bounds for the aforementioned difference for the case that treatments are at least as effective as the control and for the case that no restriction is placed on the treatment means and the control mean the evaluation of the lower confidence bound for the difference between the best treatment mean and the control mean is a concave programming problem subject to homogeneous linear inequality constraints we propose two efficient computation algorithms and discuss the connection between our procedures and gupta s subset selection procedure we compare the expected lower confidence bounds of the two procedures with that of dunnett s procedure an applicati

an investigation of finite sample behavior of confidence interval estimators we investigate the small sample behavior and convergence properties of confidence interval estimators cies for the mean of a stationary discrete process we consider cies arising from nonoverlapping batch means overlapping batch means and standardized time series all of which are commonly used in discrete event simulation the performance measures of interest are the coverage probability and the expected value and variance of the half length we use empirical and analytical methods to make detailed comparisons regarding the behavior of the cies for a variety of stochastic processes all the cies under study are asymptotically valid however they are usually invalid for small sample sizes we find that for small samples the bias of the variance parameter estimator figures significantly in cie coverage performance the less bias the better a secondary role is played by the marginal distribution of the stationary process we also point out that some cies require fewer observations before manifesting

sieve bootstrap with variable length markov chains for stationary categorical time series a bootstrap for stationary categorical time series based on the method of sieves is studied here the data generating process is approximated by the so called variable length markov chain vlmc a flexible class of markov models that allows for parsimonious structure then the resampling is given by simulating from the fitted model it is shown that for a whole class of stationary categorical time series that is more general than vlmc the vlmc sieve has faster rate of convergence for variance estimation than the more general block bootstrap results are illustrated from a theoretical and empirical perspective for the latter a real data application about in homogeneity classification of a dna strand is also presented finally the vlmc sieve scheme enjoys an implementational advantage of using the plug in rule for bootstrapping a statistical procedure which generally is not the case for the block method

group actions on arrangements of linear subspaces and applications to configuration spaces for an arrangement of linear subspaces in ri that is invariant under a finite subgroup of the general linear group gin ir we develop a formula for the g module structure of the cohomology of the complement m a our formula specializes to the well known goresky macpherson theorem in case g 1 but for g 1 the formula shows that the g module structure of the complement is not a combinatorial invariant as an application we are able to describe the free part of the cohomology of the quotient space ma4ig our motivating examples are arrangements in cn that are invariant under the action of sn by permuting coordinates a particular case is the k equal arrangement first studied by bj6rner lovasz and yao motivated by questions in complexity theory in these cases ma4 and ma sn are spaces of ordered and unordered point configurations in cn many of whose properties are reduced by our formulas to combinatorial questions in partition lattices more generally we treat point configurations in rd and provide explicit results for the k equal and the k divisible cases

on δ equivalence with the best in k sample models in recent work we introduced a general a weak and a strong partitioning principles for the construction of multiple decision procedures as multiple testing or selection procedures partitioning principles can be viewed as natural extensions of the closure principle and sometimes yield more powerful decision procedures in this article we consider the problem of establishing equivalence with the best with respect to k treatment means where equivalence is defined in terms of a threshold value 0 we reformulate the original selection problem as a multiple testing problem and develop various step down and step up procedures by applying the closure principle and partitioning principles the new step down procedure is shown to provide a uniform improvement over procedures currently in use moreover we propose some projection methods that yield confidence intervals being compatible with stepwise tests and selection procedures

harmonic maps of bounded symmetric domains harmonic maps between complete and non compact manifolds have been studied by schoen yau li tam aviles choi micallef ding wang and others s y l t a c m and d w for further study it might be of interest to consider problems in various concrete manifolds which are more general than hyperbolic space bounded symmetric domains were introduced by e cartan c1 c2 and were systematically studied by hua look and siegel hi h2 l si those are specific cartan hadamard manifolds whose further geometrical and analytical properties should be explored such investigation might also imply more general results for complete and non compact manifolds the purpose of the present paper is to pursue this goal by the work done by y c wong w a bounded symmetric domain can be viewed as a pseudo grassmannian manifold of all the spacelike subspaces of dimension m in pseudo euclidean space r n of index n in sect 2 this interesting point of view is briefly introduced it is well known that the simplest bounded symmetric domain nm 2 can be identified with a product of two hyperbolic planes he in sect 3 we study harmonic maps into nn 2 via harmonic maps into hyperbolic space and obtain an interesting image shrinking property in the striking paper h o s the authors classified all complete constant mean curvature surfaces in r 3 and 4 with certain restricted gauss image one of the analogous properties in ambient minkowski space was already proved by a different approach in the author s previous paper xi also see a by ruh vilms theorem r v we can investigate submanifolds with parallel mean curvature in euclidean space via its harmonic gauss maps in the present

testing whether independent treatment groups have equal medians the paper suggests new methods for comparing the medians corresponding to independent treatment groups the procedures are based on the harrell davis estimator in conjunction with a slight modification and extension of the bootstrap calibration technique suggested by loh alternatives to the harrell davis estimator are briefly discussed for the special case of two treatment groups the proposed procedure always had more power than the fligner rust solution as well as the procedure examined by wilcox and charlin included is an illustration using real data that comparing medians rather than means can yield a substantially different conclusion as to whether two distributions differ in terms of some measure of central location

two stage stopping procedures based on standardized time series we propose some new two stage stopping procedures to construct absolute width and relative width confidence intervals for a simulation estimator of the steady state mean of a stochastic process the procedures are based on the method of standardized time series proposed by schruben and on stein s two stage sampling scheme we prove that our two stage procedures give rise to asymptotically valid confidence intervals as the prescribed length of the confidence interval approaches zero and the size of the first stage grows to infinity the sole assumption required is that the stochastic process satisfy a functional central limit theorem

confidence interval estimation using standardized time series observations of a stationary stochastic process can be transformed into a standardized time series this paper presents a lemma giving the asymptotic properties of this standardized series under quite general conditions in particular the conditions are satisfied by stationary discrete event simulations confidence intervals can be constructed using this lemma for illustration we develop two easily computed interval estimators for the process mean when independent replications of the series are available such as in computer simulation experiments these interval estimators may be combined with the classical confidence interval estimator these interval estimators also tend to compensate for simulation initialization bias if the sign of the bias is known in an empirical study using three elementary simulated processes the interval estimators presented here compare favorably with the classical interval estimator in a recent paper goldsman and schruben goldsman d l schruben 1982 asymptotic properties of some confidence interval estimators tech rep 544 school of o r i e cornell university ithaca ny show that the asymptotic properties of the confidence intervals presented in this paper strictly dominate those of classical confidence intervals

cramer von mises variance estimators for simulations we study estimators for the variance parameter 2 of a stationary process the estimators are based on weighted cramer von mises statistics and certain weightings yield estimators that are first order unbiased for 2 we derive an expression for the asymptotic variance of the new estimators this expression is then used to obtain the first order unbiased estimator having the smallest variance among fixed degree polynomial weighting functions our work is based on asymptotic theory however we present exact and empirical examples to demonstrate the new estimators small sample robustness we use a single batch of observations to derive the estimators asymptotic properties and then we compare the new estimators among one another in real life applications one would use more than one batch we indicate how this generalization can be carried out

homotopy types of subspace arrangements via diagrams of spaces we prove combinatorial formulas for the homotopy type of the union of the subspaces in an affine compactified affine spherical or projective subspace arrangement from these formulas we derive results of goresky macpherson on the homology of the arrangement and the cohomology of its complement the union of an arrangement can be interpreted as the direct limit of a diagram of spaces over the intersection poset a closely related space is obtained by taking the homotopy direct limit of this diagram our method consists in constructing a combinatorial model diagram over the same poset whose homotopy limit can be compared to the original one by usual homotopy comparison results for diagrams of spaces

large sample results for batch means in analyzing the output process generated by a steady state simulation we often seek to estimate the expected value of the output the sample mean based on a finite sample of size n is usually the estimator of choice for the steady state mean and a measure of the sample mean s precision is the variance parameter i e the limiting value of the sample size multiplied by the variance of the sample mean as n becomes large this paper establishes asymptotic properties of the conventional batch means bm estimator of the variance parameter as both the batch size and the number of batches become large in particular we show that the bm variance estimator is asymptotically unbiased and convergent in mean square we also provide asymptotic expressions for the variance of the bm variance estimator exact and empirical examples illustrate our findings

on the asymptotic validity of fully sequential selection procedures for steady state simulation we present fully sequential procedures for steady state simulation that are designed to select the best of a finite number of simulated systems when best is defined by the largest or smallest long run average performance we also provide a framework for establishing the asymptotic validity of such procedures and prove the validity of our procedures an example based on the m m 1 queue is given

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

planning queueing simulations simple heuristic formulas are developed to estimate the simulation run lengths required to achieve desired statistical precision in queueing simulations the formulas are intended to help in the early planning stages before any data have been collected the queueing simulations considered are single replications one long run conducted to estimate steady state characteristics such as expected equilibrium queue lengths the formulas can be applied to design simulation experiments to develop and evaluate queueing approximations in fact this work was motivated by efforts to develop approximations for packet communication networks with multiple classes of traffic having different service characteristics and bursty arrival processes in addition to indicating the approximate simulation run length required in each case of a designed experiment the formulas can help determine what cases to consider what statistical precision to aim for and even whether to conduct the experiment at all the formulas are bas

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

group actions on posets abstract in this paper we study quotients of posets by group actions in order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories categories without nontrivial automorphisms and inverses we view group actions as certain functors and define the quotients as colimits of these functors the advantage of this definition over studying the quotient poset which in our language is the colimit in the poset category is that the realization of the quotient loopfree category is more often homeomorphic to the quotient of the realization of the original poset we give conditions under which the quotient commutes with the nerve functor as well as conditions which guarantee that the quotient is again a poset

testing for structural change in conditional models in the past decade we have seen the development of a new set of tests for structural change of unknown timing in regression models most notably the supf statistic of andrews 1993 econometrica 61 825 856 the expf and avef statistics of andrewsploberger 1994 econometrica 62 1383 1414 and the statistic of nyblom 1989 journal of american statistical association 84 223 230 the distribution theory used for these tests is primarily asymptotic and has been derived under the maintained assumption that the regressors are stationary this excludes structural change in the marginal distribution of the regressors as a result these tests technically cannot discriminate between structural change in the conditional and marginal distributions this paper attempts to remedy this de ciency by deriving the large sample distributions of the test statistics allowing for structural change in the marginal distribution of the regressors we nd that the asymptotic distributions of the supf expf avef and statistics are not invariant to structural change in the regressors to solve the size problem we introduce a xed regressor bootstrap which achieves the rst order asymptotic distribution and appears to possess reasonable size properties in small samples our bootstrap theory allows for arbitrary structural change in the regressors including structural shifts polynomial trends and exogenous stochastic trends it allows for lagged dependent variables and heteroskedastic error processes 2000 elsevier science s a all rights reserved

partitions into even and odd block size and some unusual characters of the symmetric groups etude des partitions en blocs de taille paire et impaire et des caracteres insolites des groupes symetriques demonstration d une conjecture de r p stanley

some combinatorial and algebraic properties of coxeter complexes and tits buildings a des groupes de coxeter et des groupes a bn paire sont associes certaines structures combinatoires les complexes de coxeter et les constructions de tits on etudie ces structures du point de vue des complexes de cohen macaulay et des complexes decorticables

achieving a confidence interval for parameters estimated by simulation this paper presents a procedure for determining the number of simulation observations required to achieve a preassigned confidence interval for means estimated by simulation this procedure which is simple to implement and efficient to use is compared with two other methods for determining the required sample size in a simulation run the empirical results show that this procedure gives good results in the precision of estimated means and in sample size requirement

jackknife estimation of stationary autoregressive models abstract this paper explores the properties of jackknife methods of estimation in stationary autoregressive models some general results concerning the correct weights for bias reduction under various sampling schemes are provided and the asymptotic properties of a jackknife estimator based on non overlapping sub samples are derived for the case of a stationary autoregression of order p when the number of sub samples is either fixed or increases with the sample size at an appropriate rate the results of a detailed investigation into the finite sample properties of various jackknife and alternative estimators are reported and it is found that the jackknife can deliver substantial reductions in bias in autoregressive models this finding is robust to departures from normality arch effects and misspecification the median unbiasedness and mean squared error properties are also investigated and compared with alternative methods as are the coverage rates of jackknife based confidence intervals

an estimate for the sectional curvature of cylindricalli bounded submanifolds we give sharp sectional curvature estimates for complete immersed cylindrically bounded m submanifolds m n rl n l 2m 1 provided that either is proper with the second fundamental form with certain controlled growth or m has scalar curvature with strong quadratic decay this latter gives a non trivial extension of the jorge koutrofiotis theorem 8 mathematics subject classification 2000 53c42

the homology representations of the k equal partition lattice we determine the character of the action of the symmetric group on the homology of the induced subposet of the lattice of partitions of the set 1 2 nr obtained by restricting block sizes to the set 1 k k 1 a plethystic formula for the generating function of the frobenius characteristic of the representation is given we combine techniques from the theory of nonpure shellability recently developed by bj6rner and wachs with symmetric function techniques developed by sundaram for determining representations on the homology of subposets of the partition lattice

computational topology of equivariant maps from spheres to complements of arrangements the problem of the existence of an equivariant map is a classical topological problem ubiquitous in topology and its applications many problems in discrete geometry and combinatorics have been reduced to such a question and many of them resolved by the use of equivariant obstruction theory a variety of concrete techniques for evaluating equivariant obstruction classes are introduced discussed and illustrated by explicit calculations the emphasis is on d 2n equivariant maps from spheres to complements of arrangements motivated by the problem of finding a 4 fan partition of 2 spherical measures where d 2n is the dihedral group one of the technical highlights is the determination of the d 2n module structure of the homology of the complement of the appropriate subspace arrangement based on the geometric interpretation for the generators of the homology groups of arrangements

poset fiber theorems suppose that f p q is a poset map whose fibers f 1 qless than or equal to q are sufficiently well connected our main result is a formula expressing the homotopy type of p in terms of q and the fibers several fiber theorems from the literature due to babson baclawski and quillen are obtained as consequences or special cases homology cohen macaulay and equivariant versions are given and some applications are discussed

the moving blocks bootstrap and robust inference for linear least squares and quantile regressions abstract this paper presents the moving blocks bootstrap mbb as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms the mbb covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent hac standard errors for least squares ls and quantile regression qr coefficient estimators the mbb covariance estimator is shown to be asymptotically equivalent to the bartlett kernel estimator suggested by newey and west 1987 and the asymptotically optimal choice of the blocksize is discussed a monte carlo study is included showing that the mbb fares well in comparison to standard hac inference procedures considering strong mixing data generating processes the paper extends existing asymptotic results for the qr estimator the analogy to the ls case is stressed the paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new grenander like conditions for the latter case the use of the mbb approach is illustrated for a practical example using a standard econometric package

an inequality between the exterior diameter and the mean curvature of bounded immersions this paper is a natural outgrowth of 9 where the problem of studying the boundedness properties of complete minimal surfaces in 1r was approached via the consideration of a certain gradient flow after the completion of 9 it was soon realized that the basic technique lemma 3 below could be successfully employed to study boundedness of arbitrary complete submanifolds in this regard the method can be used to prove the following three theorems

an invariance principle for certain dependent sequences let x 1 x 2 cdots be a strictly stationary second order sequence which is associated i e is such that any two coordinatewise nondecreasing functions of the x i s of finite variance are nonnegatively correlated if sum j operatorname cov x 1 x j infty then the partial sum processes w n t defined in the usual way so that w n m n x 1 cdots x m me x 1 sqrt n for m 1 2 cdots converge in distribution on c lbrack 0 t rbrack to a wiener process this result is based on two general theorems concerning associated random variables which are of independent interest

asymptotic properties of some confidence interval estimators for simulation output the classical confidence interval estimator commonly used in simulation is compared with four new estimators based on standardization of a time series presented in a previous paper these new interval estimators are shown to have asymptotic properties that strictly dominate the classical estimator when used with data from independent simulation replications or means of batched observations from a single simulation run two of the new estimators also can be used with a single unbatched replication of a simulation program a situation where the classical estimator is not defined