on some characterisations of totally unimodular matrices a characterisation of totally unimodular matrices is derived from a result of hoffman and kruskal it is similar in spirit to a result of baum and trotter its relation with some other known characterisations is discussed and in the particular case where the matrices have 0 1 entries we derive some properties of the associated unimodular hypergraphs similar results for balanced and perfect matrices are also reviewed

a decomposition property of polyhedra a polyhedronp x n d ax e is said to have the real decomposition property rdp if for any positivet and any realx tp there are positive coefficients 1 r and integers1 sr p withx lsl rsr andt l r we give a constructive proof that this property holds for a polyhedronp iffp is integral this construction is used to show that some classes of polyhedra have an integral decomposition property furthemore the rdp provides a generalization of the theorem of birkhoff von neumann so rdp may be used in some scheduling problems on parallel processors with preemptions

a polynomial algorithm for multiprocessor scheduling with two job lengths the following multiprocessor scheduling problem was motivated by scheduling maintenance periods for aircraft each maintenance period is a job and the maintenance facilities are machines in this context there are very few different types of maintenances performed so it is natural to consider the problem with only a small fixed number c of different types of jobs each job type has a processing time and each machine is available for the same length of time a machine can handle at most one job at a time all jobs are released at time zero there are no due dates or precedence constraints and preemption is not allowed the question is whether it is possible to finish all jobs we call this problem the multiprocessor scheduling problem with c job lengths mspc scheduling problems such as mspc where we can partition the jobs into relatively few types such that all jobs of a certain type are identical are often called high multiplicity problems high multiplicity problems are interesting because their input is very compact the input to mspc consists of only 2c 2 numbers for the case c 2 we present a polynomial time algorithm we show that this algorithm guarantees a schedule that uses the minimum possible number of different one machine schedules namely three further we extend this algorithm to the case of machine dependent deadlines uniform parallel machines to a multi parametric case that contains the case of unrelated parallel machines and to some related covering problems finally we give some counterexamples showing why our results do not extend to the case c 2

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

a geometric framework for the numerical study of singular points while bifurcation theory has developed rapidly in recent years there appears to be a need for a tighter framework for the numerical analysis of bifurcation problems this paper presents such a mathematical framework for the numerical study of the bifurcation phenomena associated with a parameter dependent equation f z lambda 0 the presentation draws from differential geometry and singularity theory and provides a basis for various numerical methods used to detect and compute certain types of bifurcation points

bootstrapping realized volatility we propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases we consider the independent and identically distributed i i d bootstrap and the wild bootstrap wb and prove their first order asymptotic validity under general assumptions on the log price process that allow for drift and leverage effects we derive edgeworth expansions in a simpler model that rules out these effects the i i d bootstrap provides a second order asymptotic refinement when volatility is constant but not otherwise the wb yields a second order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the wb data appropriately none of these methods provides third order asymptotic refinements both methods improve upon the first order asymptotic theory in finite samples

on the computation of multi dimensional solution manifolds of parametrized equations a new algorithm is presented for computing vertices of a simplicial triangulation of thep dimensional solution manifold of a parametrized equationf x 0 wheref is a nonlinear mapping fromr n tor m p n m 1 an essential part of the method is a constructive algorithm for computing moving frames on the manifold that is of orthonormal bases of the tangent spaces that vary smoothly with their points of contact the triangulation algorithm uses these bases together with a chord form of the gauss newton process as corrector to compute the desired vertices the jacobian matrix of the mapping is not required at all the vertices but only at the centers of certain local triangulation patches several numerical examples show that the method is very efficient in computing triangulations even around singularities such as limit points and bifurcation points this opens up new possibilities for determining the form and special features of such solution manifolds

post critical analysis of structures with a nonlinear pre buckling state in the presence of imperfections in the context of the geometrically nonlinear analysis of structures by continuation methods a technique for the determination of the imperfection sensitivity is carried out the technique is based on galerkin s reduction of equilibrium equations in the subspace of extrapolation branches emanating from the bifurcation points the pre and post critical behaviour in the neighbourhood of bifurcation points however is well approximated provided that extrapolations have a large convergence domain to this end an efficient asymptotic representation of the primary and secondary equilibrium paths and procedures that overcome the ill conditioning of the systems defined in the critical points is used here

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

on a computational method for the second fundamental tensor and its application to bifurcation problems an algorithm is presented for the computation of the second fundamental tensorv of a riemannian submanifoldm ofr n fromv the riemann curvature tensor ofm is easily obtained moreover v has a close relation to the second derivative of certain functionals onm which in turn provides a powerful new tool for the computational determination of multiple bifurcation directions frequently in applications thed dimensional manifoldm is defined implicitly as the zero set of a submersionf onr n in this case the principal cost of the algorithm for computingv p at a given pointp m involves only the decomposition of the jacobiandf p off atp and the projection ofd d 1 neighboring points ontom by means of a local iterative process usingdf p several numerical examples are given which show the efficiency and dependability of the method

a polynomial algorithm for integer programming covering problems satisfying the integer round up property leta be a non negative matrix with integer entries and no zero column the integer round up property holds fora if for every integral vectorw the optimum objective value of the generalized covering problem min 1y ya w y 0 integer is obtained by rounding up to the nearest integer the optimum objective value of the corresponding linear program a polynomial time algorithm is presented that does the following given any generalized covering problem with constraint matrixa and right hand side vectorw the algorithm either finds an optimum solution vector for the covering problem or else it reveals that matrixa does not have the integer round up property

improvements of jackknife confidence limit methods summary edgeworth expansion is applied to studentized parameter estimates when the standard error has been computed by a jackknife method adjustments to the usual jackknife confidence limit formulae are obtained this approach is contrasted with a bootstrap approach in numerical illustrations for estimation of a ratio jackknife methods are nonparametric methods for estimating the bias and standard error of an estimate t approximate confidence limits for the estimand can be found by using a large sample normal approximation for t somewhat curiously little is known about possible improvements to the normal approximation in this context although improvements based on edgeworth expansions are familiar in other problems in this paper we show that edgeworth expansion methods can be applied in the jackknife context numerical results for a particular application raise the possibility that the resulting improvements of jackknife methods can be matched by a suitable use of bootstrap methods efron 1982

graph theoretic relaxations of set covering and set partitioning problems in this paper we review the graph theoretic relaxations of the set covering problem scp and the set partitioning problem ssp these are a network relaxation which can be solved by the greedy method a matching relaxation and a graph covering relaxation other relaxations such as assignment shortest route and minimum spanning tree are also presented

improved minimal augmentation procedure for the direct computation of critical points this paper presents a new numerical procedure for the direct computation of critical points for elastic beam structures undergoing large displacements and rotations compared to the approach described by wriggers et al comput methods appl mech engrg 70 1988 329 int j numer methods engrg 30 1990 155 two main modifications are introduced first following eriksson comput methods appl mech engrg 114 1994 77 comput methods appl mech engrg 156 1998 45 comput methods appl mech engrg 179 1999 265 int j struct stability dynam 1 1 2001 the condition of criticality is expressed by a scalar equation instead of a vectorial one next the present procedure does not use exclusively the extended system obtained from the equilibrium equations and the criticality condition but also introduces intermediate iterations based purely on equilibrium equations under load or displacement control eight numerical examples presenting bifurcation and limit points are used in order to compare the performances of this new method and the one presented in comput methods appl mech engrg 70 1988 329 int j numer methods engrg 30 1990 155

asymptotic expansions for sums of weakly dependent random vectors it is shown that formal edgeworth expansions are valid for sums of weakly dependent random vectors the error of approximation has ordero n s 2 2 if the strong mixing coefficients in iii are decreasing at an exponential rate the above conditions can easily be checked and are often satisfied when the sequence of random vectors is a gaussian or a markov or an autoregressive process explicit formulas are given for the distribution of finite fourier transforms of a strictly stationary time series

an extension of set partitioning with application to scheduling problems abstract the well known problems of set covering set partitioning and set packing are defined and their interrelationship is considered a natural generalisation called the extended set partitioning model is presented and the three standard models are shown to be special cases of this generalisation in addition the extended model includes another type of set problem which can be of greater use in certain applications the model forms the basis of a computer assisted bus crew scheduling system developed by the authors the system is in regular use by dublin city services in the republic of ireland finally the equivalence between a special case of the set partitioning problem and the shortest route problem is considered and it is shown that this equivalence also applies to the extended model

asymptotic distribution of statistics in time series veritable conditions are given for the validity of formal edgeworth expansions for the distribution of sums x 1 x n where x i f z i z i p 1 and z 1 z 2 is a strict sense stationary sequence that can be written as z j g e j k k 0 with an iid sequence e i of innovations these models include nonlinear functions of arma processes z i as well as certain nonlinear ar processes the results apply to many statistics in nonlinear time series models

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

second order correctness of the blockwise bootstrap for stationary observations we show that the blockwise bootstrap approximation for the distribution of a studentized statistic computed from dependent data is second order correct provided we choose an appropriate variance estimator we also show how to adapt the bc a confidence interval of efron to the dependent case for the proofs we extend the results of gotze and hipp on the validity of the formal edgeworth expansion for a sum to the studentized mean

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

bootstrap critical values for tests based on generalized method of moments estimators monte carlo experiments have shown that tests based on generalized method ofmoments estimators often have true levels that differ greatly from their nominal levels when asymptotic critical values are used this paper gives conditions under which the bootstrap provides asymptotic refinements to the critical values of t tests and the test of overidentifying restrictions particular attention is given to the case of dependent data it is shown that with such data the bootstrap must sample blocks of data and that the formulae for the bootstrap versions of test statistics differ from the formulae that apply with the original data the results of monte carlo experiments on the numerical performance of the bootstrap show that it usually reduces the errors in level that occur when critical values based on first order asymptotic theory are used the bootstrap also provides an indication of the accuracy of critical values obtained from first order asymptotic theory

on the computation of manifolds of foldpoints for parameter dependent problems for parameter dependent nonlinear equations in r n a new augmentation method for computing submanifolds of foldpoints is presented the underlying theory is based on a characterization developed earlier of foldpoints on solution manifolds of parameterized equations the method allows for a locally convergent iterative computation of foldpoints of a certain class for a continuation along paths of such foldpoints and for a computation of simplicial approximations of higher dimensional submanifolds of foldpoints of the same type

evaluation of simple bifurcation points and post critical path in large finite rotation problems the main aspects of an algorithm for the exact evaluation of single bifurcation points along the nonlinear equilibrium trajectory of flexible mechanisms with large 3 d rotations are discussed a first version of this algorithm was presented elsewhere 1 in this work we extend its range of application to problems involving large finite rotations several flexible mechanisms and structures presenting bifurcation points are analyzed solutions of perfect bifurcation cases are compared to solutions of the literature which were computed by geometric perturbation

higher order improvements of the parametric bootstrap for long memory gaussian processes abstract this paper determines coverage probability errors of both delta method and parametric bootstrap confidence intervals cis for the covariance parameters of stationary long memory gaussian time series cis for the long memory parameter d 0 are included the results establish that the bootstrap provides higher order improvements over the delta method analogous results are given for tests the cis and tests are based on one or other of two approximate maximum likelihood estimators the first estimator solves the first order conditions with respect to the covariance parameters of a plug in log likelihood function that has the unknown mean replaced by the sample mean the second estimator does likewise for a plug in whittle log likelihood the magnitudes of the coverage probability errors for one sided bootstrap cis for covariance parameters for long memory time series are shown to be essentially the same as they are with iid data this occurs even though the mean of the time series cannot be estimated at the usual n 1 2 rate

integral decomposition in polyhedra we say that a polyhedronp satisfies weak integral decomposition if whenever an integral vector is the sum ofk vectors inp it is also the sum ofk integral vectors inp this property is related to rounding results for packing and covering problems we study the property and two related properties and give results concerning integral polymatroids totally unimodular matrices and network flows pairs of strongly base orderable matroids and branchings in directed graphs

an optimal column generation with ranking algorithm for very large scale set partitioning problems in traffic assignment abstract we show in this paper how branch and bound and column generation techniques can be conbined very efficiently to solve to optimality some very large scale set partitioning problems with special structure such as the matrix decomposition problem arising in the context of satellite communication system optimization the main contribution of our approach is the use of column generation during the tree search procedure combined with a ranking procedure which ensures that the exact optimal integer solution is obtained extensive computational experiments are reported for the matrix decomposition problem encountered in the search for optimal schedules in satellite switching systems showing the effectiveness of this approach

a network relaxation based enumeration algorithm for set partitioning abstract hidden network structure in the element set incidence constraint matrix of a set partitioning problem can be identified by using procedures for testing when a binary matrix is transformable to a network the set partitioning problem is thus represented as a network with side constraints this paper reports the development of a new efficient solution procedure for the set partitioning problem facilitated by the new formulation and makes use of lagrangean duality modified subgradients efficient reoptimization and enumeration tree reduction

polynomial algorithms for a class of linear programs this paper describes several algorithms for solution of linear programs the algorithms are polynomial when the problem data satisfy certain conditions

optimal solution of set covering partitioning problems using dual heuristics we present an algorithm for a mixed set covering partitioning model that includes as special cases the well known set covering problem and set partitioning problem the novel feature of our algorithm is the use of continuous heuristics applied to the dual of the linear programming relaxation to provide lower bounds for a branch and bound algorithm the heuristics are continuous adaptations of the well known greedy and 3 opt methods that have been applied to a variety of combinatorial optimization problems our algorithm has outperformed the current best set covering algorithm of balas and ho 1980 by about a factor of 3 and appears to improve on the best existing set partitioning algorithm by more than an order of magnitude

computation and efficiency of potential function minimizers of combinatorial congestion games we study the computation and efficiency of pure nash equilibria in combinatorial congestion games where the strategies of each player i are given by the binary vectors of a polytope p i our main goal is to understand which structural properties of such polytopal congestion games enable us to derive an efficient equilibrium selection procedure to compute pure nash equilibria with attractive social cost approximation guarantees to this aim we identify two general properties of the underlying aggregation polytope p n sum i p i which are sufficient for our results to go through namely the integer decomposition property idp and the box totally dual integrality property box tdi our main results for polytopal congestion games satisfying idp and box tdi are as follows i we show that pure nash equilibria can be computed in polynomial time in fact we obtain this result through a general framework for separable convex function minimization which might be of independent interest ii we bound the inefficiency of these equilibria and show that this provides a tight bound on the price of stability iii we also prove that these results extend to strong equilibria for the bottleneck variant of polytopal congestion games examples of polytopal congestion games satisfying idp and box tdi include common source network congestion games symmetric totally unimodular congestion games non symmetric matroid congestion games and symmetric matroid intersection congestion games in particular r arborescences and strongly base orderable matroids

asymptotic refinements of a misspecification robust bootstrap for gel estimators abstract i propose a nonparametric iid bootstrap procedure for the empirical likelihood the exponential tilting and the exponentially tilted empirical likelihood estimators that achieves asymptotic refinements for t tests and confidence intervals and wald tests and confidence regions based on such estimators furthermore the proposed bootstrap is robust to model misspecification i e it achieves asymptotic refinements regardless of whether the assumed moment condition model is correctly specified or not this result is new because asymptotic refinements of the bootstrap based on these estimators have not been established in the literature even under correct model specification monte carlo experiments are conducted in dynamic panel data setting to support the theoretical finding as an application bootstrap confidence intervals for the returns to schooling of hellerstein and imbens 1999 are calculated the result suggests that the returns to schooling may be higher

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

numerical continuation methods a perspective in this historical perspective the principal numerical approaches to continuation methods are outlined in the framework of the mathematical sources that contributed to their development notably homotopy and degree theory simplicial complexes and mappings submanifolds defined by submersions and singularity and foldpoint theory

finite checkability for integer rounding properties in combinatorial programming problems leta be a nonnegative integral matrix with no zero columns theinteger round up property holds fora if for each nonnegative integral vectorw the solution value to the integer programming problem min 1 y ya w y 0 y integer is obtained by rounding up to the nearest integer the solution value to the corresponding linear programming problem min 1 y ya w y 0 theinteger round down property is similarly defined for a nonnegative integral matrixb with no zero rows by considering max 1 y yb w y 0 y integer and its linear programming correspondent it is shown that the integer round up and round down properties can be checked through a finite process the method of proof motivates a new and elementary proof of fulkerson s pluperfect graph theorem

on the bootstrap and confidence intervals we derive an explicit formula for the first term in an unconditional edgeworth type expansion of coverage probability for the nonparametric bootstrap technique applied to a very broad class of studentized statistics the class includes sample mean k sample mean sample correlation coefficient maximum likelihood estimators expressible as functions of vector means etc we suggest that the bootstrap is really an empiric one term edgeworth inversion with the bootstrap simulations implicitly estimating the first term in an edgeworth expansion this view of the bootstrap is reinforced by our discussion of the iterated bootstrap which inverts an edgeworth expansion to arbitrary order by simulating simulations

on the sensitivity of solutions of parameterized equations the sensitivity of a solution of a parameterized equation f z lambda 0 with respect to the parameter vector lambda is usually defined as the change of the state z in dependence of lambda in other words for any solution expressible in the form z lambda lambda with some smooth function z z lambda the sensitivity is the derivative dz lambda typically the solutions form a manifold m in the product of 1the state space and the parameter space and this sensitivity is available only at those points of m where the parameters can be used to define a local coordinate system this paper introduces a general sensitivity concept which applies at all solutions on m and which includes the earlier definition some general geometric interpretations of the new measure are presented and it is shown that the sensitivity analysis can be easily integrated into the solution process the theory also suggests the introduction of a readily computable second order sensitivity measure reflectin

prepivoting to reduce level error of confidence sets summary approximate confidence sets for a parameter 0 may be obtained by referring a function of 0 and of the sample to an estimated quantile of that function s sampling distribution we call this function the root of the confidence set either asymptotic theory or bootstrap methods can be used to estimate the desired quantile when the root is not a pivot in the sense of classical statistics the actual level of the approximate confidence set may differ substantially from the intended level prepivoting is the transformation of a confidence set root by its estimated bootstrap cumulative distribution function prepivoting can be iterated bootstrap confidence sets generated from a root prepivoted one or more times have smaller error in level than do confidence sets based on the original root the first prepivoting is nearly equivalent to studentizing when that operation is appropriate further iterations of prepivoting make higher order corrections automatically

the block block bootstrap improved asymptotic refinements the asymptotic refinements attributable to the block bootstrap for time series are not as large as those of the nonparametric iid bootstrap or the parametric bootstrap one reason is that the independence between the blocks in the block bootstrap sample does not mimic the dependence structure of the original sample this is the join point problem in this paper we propose a method of solving this problem the idea is not to alter the block bootstrap instead we alter the original sample statistics to which the block bootstrap is applied we introduce block statistics that possess join point features that are similar to those of the block bootstrap versions of these statistics we refer to the application of the block bootstrap to block statistics as the block block bootstrap the asymptotic refinements of the block block bootstrap are shown to be greater than those obtained with the block bootstrap and close to those obtained with the nonparametric iid bootstrap and parametric bootstrap

on the number of bootstrap simulations required to construct a confidence interval abstract the purpose of this document is to make two points about the effect of the number of bootstrap simulations b on percentile t bootstrap confidence intervals the first point concerns coverage probability the second distance of the simulated critical point form the true critical point derived with b infinity in both cases the author has in mind applications to smooth statistics such as the studentized mean of a sample drawn from a continuous distribution he indicates the change that have to be made if the distribution of the statistic is not smooth additional keywords exponentive functions

a new approach for crew pairing problems by column generation with an application to air transportation we propose a new approach to crew pairing problems arising in the context of airline companies the problem is first formulated as a large scale set covering problem with many colums each column representing a valid crew pairing we then suggest a solution procedure for the continuous relaxation of this large scale problem based on generalized linear programming in which the column generation subproblem is shown to be equivalent to a shortest path problem in an associated graph computational results obtained on a series of real problems involving up to 329 flight segments are reported confirming both computational efficiency and practical applicability of the new approach indeed not only were the resulting solutions observed to be integral for most test problems but average savings of about 4 to 5 over the best available hand built solutions were shown to be obtained

a note on ss tdma satellite communication abstract in a recent paper of lewandowski and liu a scheduling problem for a satellite switched time division multiple access scheme is discussed it consists in covering a traffic matrix t by a defined set of 0 1 matrices we show that the existence of optimal schedules is a consequence of known results on polyhedral decomposition furthermore a simple decomposition procedure is outlined for constructing schedules having special types of switching matrices

bootstrap methods for markov processes the block bootstrap is the best known bootstrap method for time series data when the analyst does not have a parametric model that reduces the data generation process to simple random sampling however the errors made by the block bootstrap converge to zero only slightly faster than those made by first order asymptotic approximations this paper describes a bootstrap procedure for data that are generated by a markov process or a process that can be approximated by a markov process with sufficient accuracy the procedure is based on estimating the markov transition density nonparametrically bootstrap samples are obtained by sampling the process implied by the estimated transition density conditions are given under which the errors made by the markov bootstrap converge to zero more rapidly than those made by the block bootstrap

characterization and computation of generalized turning points a minimal set of augmenting equations is given so that general parameter dependent problems together with these equations will be nonsingular at points of simple rank deficiency applications to de

double bootstrap methods that use a single double bootstrap simulation we show that when the double bootstrap is used to improve performance of bootstrap methods for bias correction techniques based on using a single double bootstrap sample for each single bootstrap sample can be particularly effective in particular they produce third order accuracy for much less computational expense than is required by conventional double bootstrap methods however this improved level of performance is not available for the single double bootstrap methods that have been suggested to construct confidence intervals or distribution estimators

asymptotic refinements of a misspecification robust bootstrap for generalized method of moments estimators i propose a nonparametric iid bootstrap that achieves asymptotic refinements for t tests and confidence intervals based on gmm estimators even when the model is misspecified in addition my bootstrap does not require recentering the moment function which has been considered as critical for gmm regardless of model misspecification the proposed bootstrap achieves the same sharp magnitude of refinements as the conventional bootstrap methods which establish asymptotic refinements by recentering in the absence of misspecification the key idea is to link the misspecified bootstrap moment condition to the large sample theory of gmm under misspecification of hall and inoue 2003 two examples are provided combining data sets and invalid instrumental variables

on symmetric bootstrap confidence intervals on montre que dans des circonstances generales les intervalles de confiance du bootstrap de percentile t symetrique ont une erreur de recouvrement o n 2 ou n denote la taille d echantillon

solution manifolds and submanifolds of parametrized equations and their discretization errors the paper concerns solution manifolds of nonlinear parameterdependent equations 1 f u y0 involving a fredholm operatorf between infinite dimensional banach spacesx z andy and a finitedimensional parameter space differntial geometric ideas are used to discuss the connection between augmented equations and certain onedimensional submanifolds produced by numerical path tracing procedures then for arbitrary finite dimension of estimates of the error between the solution manifold of 1 and its discretizations are developed these estimates are shown to be applicable to rather general nonlinear boundaryvalue problems for partial differential equations

on blocking rules for the bootstrap with dependent data summary we address the issue of optimal block choice in applications of the block bootstrap to dependent data it is shown that optimal block size depends significantly on context being equal to n 3 n 4 and nll5 in the cases of variance or bias estimation estimation of a onesided distribution function and estimation of a two sided distribution function respectively a clear intuitive explanation of this phenomenon is given together with outlines of theoretical arguments in specific cases it is shown that these orders of magnitude of block sizes can be used to produce a simple practical rule for selecting block size empirically that technique is explored numerically

an algorithm for set covering problem in this paper we present an algorithm for the set covering problem that combines problem reduction tests with dual ascent subgradient optimisation and linear programming computational results are presented for problems involving up to 400 rows and 4000 columns

superlinearly convergent algorithms for solving singular equations and smooth reformulations of complementarity problems we propose a new algorithm for solving smooth nonlinear equations in the case where their solutions can be singular compared to other techniques for computing singular solutions a distinctive feature of our approach is that we do not employ second derivatives of the equation mapping in the algorithm and we do not assume their existence in the convergence analysis important examples of once but not twice differentiable equations whose solutions are inherently singular are smooth equation based reformulations of the nonlinear complementarity problems reformulations of complementarity problems serve both as illustration of and motivation for our approach and one of them we consider in detail we show that the proposed method possesses local superlinear quadratic convergence under reasonable assumptions we further demonstrate that these assumptions are in general not weaker and not stronger than regularity conditions employed in the context of other superlinearly convergent newton type algorithms for solving complementarity problems which are typically based on nonsmooth reformulations therefore our approach appears to be an interesting complement to the existing ones

predictive density and conditional confidence interval accuracy tests abstract this paper outlines testing procedures for assessing the relative out of sample predictive accuracy of multiple conditional distribution models the tests that are discussed are based on either the comparison of entire conditional distributions or the comparison of predictive confidence intervals we also briefly survey existing related methods in the area of predictive density evaluation including methods based on the probability integral transform and the kullback leibler information criterion the procedures proposed in this paper are similar in many ways to andrews 1997 a conditional kolmogorov test econometrica 65 1097 1128 conditional kolmogorov test and to white s 2000 a reality check for data snooping econometrica 68 1097 1126 reality check in particular a predictive density test is outlined that involves comparing square approximation errors associated with models i i 1 n by constructing weighted averages over u of e f i u z t i f 0 u z t 0 2 where f 0 and f i are true and model i distributions u u and u is a possibly unbounded set on the real line a conditional confidence interval version of this test is also outlined and appropriate bootstrap procedures for obtaining critical values when predictions used in the formation of the test statistics are obtained via rolling and recursive estimation schemes are developed an empirical illustration comparing alternative predictive models for u s inflation is given for the predictive confidence interval test

higher order improvements of a computationally attractive k step bootstrap for extremum estimators this paper establishes the higher order equivalence of the k step bootstrap introduced recently by davidson and mackinnon 1999 and the standard bootstrap the k step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear extremum estimators such as generalized method of moment and maximum likelihood estimators the paper also extends results of hall and horowitz 1996 to provide new results regarding the higher order improvements of the standard bootstrap and the k step bootstrap for extremum estimators compared to procedures based on first order asymptotics the results of the paper apply to newton raphson nr default nr line search nr and gauss newton k step bootstrap procedures the results apply to the nonparametric iid bootstrap and nonoverlapping and overlapping block bootstraps the results cover symmetric and equal tailed two sided t tests and confidence intervals one sided t tests and confidence intervals wald tests and confidence regions and j tests of over identifying restrictions

applications of the blowing up construction and algebraic geometry to bifurcation problems a generalization of the morse lemma to vector valued functions is proved by a blowing up argument this is combined with a theorem from algebraic geometry on the number of real solutions of a system of homogeneous equations of even degree to yield a new bifurcation theorem bifurcation in a one or multi parameter problem is guaranteed if the leading term is of even degree it is often two and satisfies a regularity condition applications are given to nonlinear eigenvalue problems and to the hopf bifurcation

computation of cusp singularities for operator equations and their discretizations we discuss the direct calculation of cusp singularities as solutions of a minimally augmented defining system which is nonsingular under the canonical cusp conditions the underlying operator equation may have any finite fredholm index and bounds on the discretization error are derived for the case of projection methods

genetic clustering algorithms abstract this study employs genetic algorithms to solve clustering problems three models sicm stcm cspm are developed according to different coding decoding techniques the effectiveness and efficiency of these models under varying problem sizes are analyzed in comparison to a conventional statistics clustering method the agglomerative hierarchical clustering method the results for small scale problems 10 50 objects indicate that cspm is the most effective but least efficient method stcm is second most effective and efficient sicm is least effective because of its long chromosome the results for medium to large scale problems 50 200 objects indicate that cspm is still the most effective method furthermore we have applied cspm to solve an exemplified p median problem the good results demonstrate that cspm is usefully applicable

tapered block bootstrap summary we introduce and study tapered block bootstrap methodology that yields an improvement over the well known block bootstrap for time series of kiinsch 1989 the asymptotic validity and the favourable bias properties of the tapered block bootstrap are shown the important practical issues of optimally choosing the window shape and the block size are addressed in detail while some finite sample simulations are presented validating the good performance of the tapered block bootstrap