p value functions an underused method to present research results and to promote quantitative reasoning null hypothesis significance testing has received a great amount of attention in recent years in the light of the reproducibility crisis of science recently there have been calls to retire the dichotomization of study results into significant or not significant depending on whether the p value crosses some threshold or not ways of improving the interpretation of p values and confidence intervals are therefore needed we illustrate the use of p value functions which display confidence limits and p values for any confidence level for a parameter p value functions accessibly display a wealth of information point estimate for the parameter one sided and two sided confidence limits at any level and one sided and two sided p values for any null and non null value and the counternull value presenting several recent examples from the literature we show how p value functions can be applied to present evidence and to make informed statistical inferences without resorting to dichotomization we argue that p value functions are more informative than commonly used summaries of study results such as single p values or confidence intervals p value functions require minimal retraining are easily interpreted and show potential to fix many of the common misinterpretation of p values and confidence intervals to facilitate the adoption of p value functions we released an r package for creating p value functions for several commonly used estimates

efficient algorithms for the inverse spanning tree problem the inverse spanning tree problem is to modify edge weights in a graph so that a given treet is a minimum spanning tree the objective is to minimize the cost of the deviation the cost of deviation is typically a convex function we propose algorithms here that are faster than all known algorithms for the problem our algorithm s run time for any convex inverse spanning tree problem iso nm log 2n for a graph onn nodes andm edges plus the time required to find the minima of then convex deviation functions this not only improves on the complexity of previously known algorithms for the general problem but also for algorithms devised for special cases for the case when the objective is weighted absolute deviation sokkalingam et al 1999 devised an algorithm with run timeo n2m log nc forc the maximum edge weight for the sum of absolute deviations our algorithm runs in timeo n2 logn matching the run time of a recent ahuja and orlin 2000 improvement for this case a new algorithm for bipartite matching in path graphs is reported here with complexity ofo n1 5 logn this leads to a second algorithm for the sum of absolute deviations running ino n1 5 logn logc steps

using dual approximation algorithms for scheduling problems theoretical and practical results the problem of scheduling a set of n jobs on m identical machines so as to minimize the makespan time is perhaps the most well studied problem in the theory of approximation algorithms for np hard optimization problems in this paper the strongest possible type of result for this problem a polynomial approximation scheme is presented more precisely for each e an algorithm that runs in time o n e 1 e 2 and has relative error at most e is given in addition more practical algorithms for e 1 5 2 k and e 1 6 2 k which have running times o n k log n and o n km 4 log n are presented the techniques of analysis used in proving these results are extremely simple especially in comparison with the baroque weighting techniques used previously the scheme is based on a new approach to constructing approximation algorithms which is called dual approximation algorithms where the aim is to find superoptimal but infeasible solutions and the performance is measured by the degree of infeasibility allowed this notion should find wide applicability in its own right and should be considered for any optimization problem where traditional approximation algorithms have been particularly elusive

a technique for speeding up the solution of the lagrangian dual we propose techniques for the solution of the lp relaxation and the lagrangean dual in combinatorial optimization and nonlinear programming problems our techniques find the optimal solution value and the optimal dual multipliers of the lp relaxation and the lagrangean dual in polynomial time using as a subroutine either the ellipsoid algorithm or the recent algorithm of vaidya moreover in problems of a certain structure our techniques find not only the optimal solution value but the solution as well our techniques lead to significant improvements in the theoretical running time compared with previously known methods interior point methods ellipsoid algorithm vaidya s algorithm we use our method to the solution of the lp relaxation and the langrangean dual of several classical combinatorial problems like the traveling salesman problem the vehicle routing problem the steiner tree problem thek connected problem multicommodity flows network design problems network flow problems with side constraints facility location problems k polymatroid intersection multiple item capacitated lot sizing problem and stochastic programming in all these problems our techniques significantly improve the theoretical running time and yield the fastest way to solve them

a polynomial time approximation scheme for the two stage multiprocessor flow shop problem in this paper we investigate the two stage multiprocessor flow shop scheduling problem f2 p cmax where the numbers m1 and m2 of machines available in the two stages are part of the input we demonstrate the existence of a polynomial time approximation scheme for this problem this result solves the simplest case of an open problem that has been posed by leslie hall in a recent paper hall 1995 an extension of our algorithm yields an approximation scheme for the closely related two stage multiprocessor job shop problem

approximations of marginal tail probabilities and inference for scalar parameters summary in many situations inference for a scalar parameter in the presence of nuisance parameters requires integration of either a joint density of pivotal quantities or a joint posterior density for such inference accurate approximations of marginal tail probabilities are useful to avoid high dimensional integrals two tail probability approximations are developed in this paper numerical results given for conditional inference in location scale and linear regression models show the approximations to be generally accurate even for small sample sizes

nonnormal linear regression an example of significance levels in high dimensions summary analysis of nonnormal linear models leads to an initial conditioning on the standardized residuals giving an unnormed density on rk where k is the number of parameters to obtain an observed level of significance for a single parameter it is then necessary to calculate a marginal probability thus requiring integration in k dimensions in this paper a conditional approach to evaluating the observed level of significance is developed and an importance sampling technique is used to improve the approximation and assess the accuracy of the conditional approximation to the marginal observed level a further approximation based on the invariant version fraser 1990 of the lugannani rice 1980 formula is also proposed the approach extends to the evaluation of real pivots and to bayesian inference for a single parameter component

on holomorphic banach vector bundles over banach spaces let x be a banach space with a countable unconditional basis e g x l2 hilbert space x pseudoconvex open e a locally trivial holomorphic vector bundle with a banach space z for fiber type mathcal o e the sheaf of germs of holomorphic sections of e and z1 the banach space z 1 ell p z z z n z n in z z big sum n 1 infty z n p big 1 p infty 1 le p infty then e oplus omega times z 1 and z1 are holomorphically isomorphic mathcal o e is acyclic and e is so to speak stably trivial over in a generalized sense we also show that if e is continuously trivial over then e is holomorphically trivial over in particular if z l2 or is contractible then e is holomorphically trivial over some applications are also given

analytic cohomology groups of infinite dimensional complex manifolds abstract given a cohesive sheaf s over a complex banach manifold m we endow the cohomology groups h q m s of m and h q u s of open covers u of m with a locally convex topology under certain assumptions we prove that the canonical map h q u s h q m s is an isomorphism of topological vector spaces

approximation algorithms for scheduling unrelated parallel machines we consider the following scheduling problem there arem parallel machines andn independent jobs each job is to be assigned to one of the machines the processing of jobj on machinei requires timep ij the objective is to find a schedule that minimizes the makespan our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum we also present a polynomial approximation scheme for the case that the number of machines is fixed both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations in particular we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints in contrast to our main result we prove that no polynomial algorithm can achieve a worst case ratio less than 3 2 unlessp np we finally obtain a complexity classification for all special cases with a fixed number of processing times

exponential linear models a two pass procedure for saddlepoint approximation for an exponential linear model the saddlepoint method gives accurate approximations for the density of the minimal sufficient statistic or maximum likelihood estimate and for the corresponding distribution functions in this paper we describe a simple numerical procedure that constructs such approximations for a real parameter in an exponential linear model using only a two pass calculation on the observed likelihood function for the original data simple examples of the numerical procedure are discussed but we take the general accuracy of the saddlepoint procedure as given an immediate application of this is to exponential family models where inference for a component of the canonical parameter is to be based on the conditional density of the corresponding component of the sufficient statistic given the remaining components this conditional density is also of exponential family form but its functional form and cumulant generating function may not be accessible the procedure is applied to the corresponding likelihood approximated as the full likelihood divided by an approximate marginal likelihood obtained from barndorff nielsen s formula a double saddlepoint approximation provides another means of bypassing this difficulty the computational procedure is also examined as a numerical procedure for obtaining the saddlepoint approximation to the fourier inversion of a characteristic function as such it is a two pass calculation on a table of the cumulant generating function

practical use of higher order asymptotics for multiparameter exponential families recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families especially in generalized linear models the aim here is to clarify and explore these attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family excellent approximations to exact conditional inferences are often available in terms of simple adjustments to the signed square root of the likelihood ratio statistic

adjustments to profile likelihood summary conditional and marginal likelihoods constructed from parameter dependent functions of the data have an additional parameter dependence that changes with the choice of supporting metric for the corresponding densities we consider constructing marginal and conditional likelihoods by using densities expressed in terms of an intrinsic choice of support measure based on either euclidean metric or the constant information metric barndorff nielsen s 1983 approximation to the distribution of the maximum likelihood estimate is used to approximate these conditional and marginal likelihoods the resulting likelihoods are closely related to the modified profile likelihood of barndorff nielsen 1983 and the approximate conditional likelihood of cox reid 1987 the normal circle problem is examined in some detail

improved algorithms for bipartite network flow in this paper network flow algorithms for bipartite networks are studied a network g v e is called bipartite if its vertex set v can be partitioned into two subsets v 1 and v 2 such that all edges have one endpoint in v 1 and the other in v 2 let n v n 1 v 1 n 2 v 2 m e and assume without loss of generality that n 1 leq n 2 a bipartite network is called unbalanced if n 1 ll n 2 and balanced otherwise this notion is necessarily imprecise it is shown that several maximum flow algorithms can be substantially sped up when applied to unbalanced networks the basic idea in these improvements is a two edge push rule that allows one to charge most computation to vertices in v 1 and hence develop algorithms whose running times depend on n 1 rather than n for example it is shown that the two edge push version of goldberg and tarjan s fifo preflow push algorithm runs in o n 1 m n 1 3 time and that the analogous version of ahuja and orlin s excess scaling algorithm runs in o n 1 m n 1 2 log u time where u is the largest edge capacity these ideas are also extended to dynamic tree implementations parametric maximum flows and minimum cost flows

exact meta analysis approach for discrete data and its application to 2 2 tables with rare events this article proposes a general exact meta analysis approach for synthesizing inferences from multiple studies of discrete data the approach combines the p value functions also known as significance functions associated with the exact tests from individual studies it encompasses a broad class of exact meta analysis methods as it permits broad choices for the combining elements such as tests used in individual studies and any parameter of interest the approach yields statements that explicitly account for the impact of individual studies on the overall inference in terms of efficiency power and the type i error rate those statements also give rises to empirical methods for further enhancing the combined inference although the proposed approach is for general discrete settings for convenience it is illustrated throughout using the setting of meta analysis of multiple 2 2 tables in the context of rare events data such as observing few zero or zero total i e zero events in both arms out

structural and algorithmic properties for parametric minimum cuts we consider the minimum s t cut problem in a network with parametrized arc capacities following the seminal work of gallo et al siam j comput 18 1 30 55 1989 classes of this parametric problem have been shown to enjoy the nice structural property that minimum cuts are nested and the nice algorithmic property that all minimum cuts can be computed in the same asymptotic time as a single minimum cut by using a clever flow update step to move from one value of the parameter to the next we present a general framework for parametric minimum cuts that extends and unifies such results we define two conditions on parametrized arc capacities that are necessary and sufficient for strictly decreasing differences of the parametric cut function known results in parametric submodular optimization then imply the structural property we show how to construct appropriate flow updates in linear time under the above conditions implying that the algorithmic property also holds under these conditions we then consider other classes of parametric minimum cut problems without decreasing differences for which we establish the structural and or the algorithmic property as well as other cases where nested minimum cuts arise

a strongly polynomial algorithm for the transportation problem for the linear transportation problem withm supply nodes n demand nodes andk feasible arcs we describe an algorithm which runs in time proportional tom logm k n logn assuming w l o g m n the algorithm uses excess scaling the complexity bound is a slight improvement over the bound achieved by an application of a min cost flow algorithm of orlin to the transportation problem

online multiple strip packing we study an online multiple strip packing problem whose goal is to pack the given rectangles into m vertical strips of unit width such that the maximum height used among the strips is minimized rectangles arrive one by one the decision of delivering the rectangles to a strip as well as packing them into the strip must be done immediately and irrevocably without any information on the next rectangles both randomized and deterministic online algorithms are investigated all of which are guaranteed a constant competitive ratio

scheduling under linear constraints abstract we introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints the objective is to minimize the makespan i e the maximum job completion time among all feasible choices this novel problem is motivated by various real world application scenarios we discuss the computational complexity and algorithms for various settings of this problem in particular we show that if there is only one machine with an arbitrary number of linear constraints or there is an arbitrary number of machines with no more than two linear constraints or both the number of machines and the number of linear constraints are fixed constants then the problem is polynomial time solvable via solving a series of linear programming problems if both the number of machines and the number of constraints are inputs of the problem instance then the problem is np hard we further propose several approximation algorithms for the latter case

solving inverse spanning tree problems through network flow techniques given a solution x and an a priori estimated cost vector c the inverse optimization problem is to identify another cost vector d so that x is optimal with respect to the cost vector d and its deviation from c is minimum in this paper we consider the inverse spanning tree problem on an undirected graph g n a with n nodes and m arcs and where the deviation between c and d is defined by the rectilinear distance between the two vectors that is l1 norm we show that the inverse spanning tree problem can be formulated as the dual of an assignment problem on a bipartite network g0 n0 a0 with math not displayed and math not displayed the bipartite ne twork satisfies the property that n1 n 1 n2 m n 1 and a0 o nm in general n1 n2 using this special structure of the assignment problem we develop a specific implementation of the successive shortest path algorithm that runs in o n3 time we also consider the weighted version of the inverse spanning tree problem in which the objective function is to minimize the sum of the weighted deviations of arcs the weighted inverse spanning tree can be formulated as the dual of the transportation problem using a cost scaling algorithm this transportation problem can be solved in o n2m log nc time where c denotes the largest arc cost in the data finally we consider a minimax version of the inverse spanning tree problem and show that it can be solved in o n2 time

scheduling parallel machines with inclusive processing set restrictions and job release times we consider the problem of scheduling a set of jobs with different release times on parallel machines so as to minimize the makespan of the schedule the machines have the same processing speed but each job is compatible with only a subset of those machines the machines can be linearly ordered such that a higher indexed machine can process all those jobs that a lower indexed machine can process we present an efficient algorithm for this problem with a worst case performance ratio of 2 we also develop a polynomial time approximation scheme ptas for the problem as well as a fully polynomial time approximation scheme fptas for the case in which the number of machines is fixed

lower bounds for the earliness tardiness scheduling problem on parallel machines with distinct due dates this paper addresses the parallel machine scheduling problem in which the jobs have distinct due dates with earliness and tardiness costs new lower bounds are proposed for the problem they can be classed into two families first two assignment based lower bounds for the one machine problem are generalized for the parallel machine case second a time indexed formulation of the problem is investigated in order to derive efficient lower bounds throught column generation or lagrangean relaxation a simple local search algorithm is also presented in order to derive an upper bound computational experiments compare these bounds for both the one machine and parallel machine problems and show that the gap between upper and lower bounds is about 1 5

approximation algorithms for scheduling jobs with release times and arbitrary sizes on batch machines with non identical capacities abstract we consider the problem of scheduling jobs with release times and arbitrary sizes on batch machines with non identical capacities to minimize makespan a job can only be assigned to a machine whose capacity is not less than the size of the job a machine can process a group of jobs as a batch simultaneously as long as the total size of the jobs in this batch does not exceed the capacity of the machine the processing time of a batch is equal to the longest processing time of all the jobs in the batch for the case of equal release times we obtain a fast 5 approximation algorithm as well as an algorithm with approximation ratio arbitrarily close to 2 for the case of unequal release times and a fixed number of different batch capacities we obtain an algorithm with approximation ratio arbitrarily close to 2 we also study the problem of scheduling jobs with equal release times arbitrary sizes inclusive processing set restrictions and incompatible families on batch machines with identical capacities to minimize makespan we obtain a 8 3 approximation algorithm as well as an algorithm with approximation ratio arbitrarily close to 2 if only a single family is considered a 2 approximation algorithm is presented it is likely that these results cannot be too substantially improved upon since all of the problems studied cannot be approximated to within a ratio smaller than 2 unless p np

confidence distributions and a unifying framework for meta analysis this article develops a unifying framework as well as robust meta analysis approaches for combining studies from independent sources the device used in this combination is a confidence distribution cd which uses a distribution function instead of a point point estimator or an interval confidence interval to estimate a parameter of interest a cd function contains a wealth of information for inferences and it is a useful device for combining studies from different sources the proposed combining framework not only unifies most existing meta analysis approaches but also leads to development of new approaches we illustrate in this article that this combining framework can include both the classical methods of combining p values and modern model based meta analysis approaches we also develop under the unifying framework two new robust meta analysis approaches with supporting asymptotic theory in one approach each study size goes to infinity and in the other approach the number of studies

polynomial time algorithms for ratio regions and a variant of normalized cut in partitioning clustering and grouping problems a typical goal is to group together similar objects or pixels in the case of image processing at the same time another goal is to have each group distinctly dissimilar from the rest and possibly to have the group size fairly large these goals are often combined as a ratio optimization problem one example of such a problem is a variant of the normalized cut problem another is the ratio regions problem we devise here the first polynomial time algorithms solving optimally the ratio region problem and the variant of normalized cut as well as a few other ratio problems the algorithms are efficient and combinatorial in contrast with nonlinear continuous approaches used in the image segmentation literature which often employ spectral techniques such techniques deliver solutions in real numbers which are not feasible to the discrete partitioning problem furthermore these continuous approaches are computationally expensive compared to the algorithms proposed here the algorithms presented here use as a subroutine a minimum s t cut procedure on a related graph which is of polynomial size the output consists of the optimal solution to the respective ratio problem as well as a sequence of nested solutions with respect to any relative weighting of the objectives of the numerator and denominator

a dolbeault isomorphism theorem in infinite dimensions for a large class of separable banach spaces we prove the real analytic dolbeault isomorphism theorem for open subsets

plurisubharmonic domination in banach spaces abstract we show that if x is a banach space with a schauder basis x is a pseudoconvex open subset and u is a locally bounded function then there is a continuous plurisubharmonic function w with u x w x for all x this has many applications to analytic cohomology of complex banach manifolds

self adjusting binary search trees the splay tree a self adjusting form of binary search tree is developed and analyzed the binary search tree is a data structure for representing tables and lists so that accessing inserting and deleting items is easy on an n node splay tree all the standard search tree operations have an amortized time bound of o log n per operation where by amortized time is meant the time per operation averaged over a worst case sequence of operations thus splay trees are as efficient as balanced trees when total running time is the measure of interest in addition for sufficiently long access sequences splay trees are as efficient to within a constant factor as static optimum search trees the efficiency of splay trees comes not from an explicit structural constraint as with balanced trees but from applying a simple restructuring heuristic called splaying whenever the tree is accessed extensions of splaying give simplified forms of two other data structures lexicographic or multidimensional search trees and link cut trees

asymptotics and the theory of inference asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable more importantly asymptotic analysis can also provide insight into the inference process itself suggesting what information is available and how this information may be extracted the development of likelihood inference over the past twenty some years provides an illustration of the interplay between techniques of approximation and statistical theory

approximability issues for unconstrained and constrained maximization of half product related functions we address the boolean programming problem of maximizing a half product function with and without a linear knapsack constraint maximizing the half product can be done in polynomial time adding a knapsack constraint makes the problem non approximable within a constant factor provided that the coefficients in the linear part of the function are negative for maximizing a function with positive coefficients in the linear part we develop a fully polynomial time approximation scheme

a unified approach to truthful scheduling on related machines we present a unified framework for designing deterministic monotone polynomial time approximation schemes ptass for a wide class of scheduling problems on uniformly related machines this class includes among others minimizing the makespan maximizing the minimum load and minimizing the p norm of the machine loads vector previously this kind of result was only known for the makespan objective monotone algorithms have the property that an increase in the speed of a machine cannot decrease the amount of work assigned to it our results imply the existence of a truthful mechanism that can be implemented in polynomial time where the social goal is approximated within arbitrary precision

on the approximation property for banach spaces predual to h spaces abstract a major open problem asks about the grothendieck approximation property for the space h h d of bounded holomorphic functions in the unit disk d c motivated by this problem we establish approximation properties for banach spaces predual to the spaces h for being finite direct products of starlike domains and unbranched coverings of strongly pseudoconvex domains in stein manifolds

optimal attack and reinforcement of a network in a nonnegative edge weighted network the weight of an edge represents the effort required by an attacker to destroy the edge and the attacker derives a benefit for each new component created by destroying edges the attacker may want to minimize over subsets of edges the difference between or the ratio of the effort incurred and the benefit received this idea leads to the definition of the strength of the network a measure of the resistance of the network to such attacks efficient algorithms for the optimal attack problem the problem of computing the strength and the problem of finding a minimum cost reinforcement to achieve a desired strength are given these problems are also solved for a different model in which the attacker wants to separate vertices from a fixed central vertex

a general framework for designing approximation schemes for combinatorial optimization problems with many objectives combined into one in this paper we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination of more than one function examples of such problems include those in which the objective function is a product or ratio of two linear functions parallel machine scheduling problems with the makespan objective robust versions of weighted multiobjective optimization problems and assortment optimization problems with logit choice models the main idea behind our approximation schemes is the construction of an approximate pareto optimal frontier of the functions that constitute the given objective using this idea we give the first fully polynomial time approximation schemes for the max min resource allocation problem with a fixed number of agents combinatorial optimization problems in which the objective function is the sum of a fixed number of ratios of linear functions or the product of a fixed number of linear functions and assor

the highest confidence density region and its usage for joint inferences about constrained parameters suppose that we are interested in making joint inferences about a set of constrained parameters confidence regions for these parameters are often constructed via a normal approximation of the distribution of a consistent estimator for a transformation of the parameters in this article we utilize the confidence distribution a frequentist counterpart to the posterior distribution in bayesian statistics to obtain optimal confidence regions for the parameters members of such a region can be generated efficiently via a standard markov chain monte carlo algorithm we then apply this technique to draw inferences about the temporal profile of the survival function with censored observations we illustrate the new proposal with the survival data from the well known mayo primary biliary cirrhosis study and show that the volume of the new 0 95 confidence region is only one thirty fourth of that of the conventional confidence band

an efficient cost scaling algorithm for the assignment problem the cost scaling push relabel method has been shown to be efficient for solving minimum cost flow problems in this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment s special structure the results show that the method is very promising for practical use

algorithms for distributing telecommunication traffic on a multiple ring sonet based network abstract we examine a problem arising in the assignment of telecommunication traffic to a set of synchronous optical network sonet rings prior sonet design algorithms determine node to ring assignments while concurrently prescribing an assignment of traffic to the rings however due to uncertain voice and data demand among client nodes it may become necessary to revise the planned routing scheme once the true values of this data are realized we develop a minimum cost flow algorithm for the case in which demands may be split across multiple rings and provide a transformation to a maximum flow problem for specially structured data the case in which each demand pair may be routed on only one ring is proven to be np hard and we accordingly provide a powerful heuristic and an effective standard valid inequality generation scheme to optimally solve this problem within reasonable computational limits the effectiveness of our approach is demonstrated on a set of randomly generated test data

computing the strength of a graph the strength of a graph is a measure of its vulnerability strictly generalizing the edge connectivity of a weighted graph cunningham j assoc comput mach 32 1985 pp 549 562 showed how to compute the strength of a graph in o v 4 e time using ideas from polymatroids and network flow in this paper his polymatroid approach is modified a modified version of the goldberg tarjan network flow algorithm j assoc comput mach 4 1988 pp 136 146 is used then using ideas developed by gallo grigoriadis and tarjan siam j comput 18 1989 pp 30 55 and by gusfield martel and fernandez baca in siam j comput 16 1987 pp 237 251 it is shown that the solution runs in o v 3 e time analogous speedups for sparse case bounds are also obtainable

semiparametric analysis of heterogeneous data using varying scale generalized linear models this article describes a class of heteroscedastic generalized linear regression models in which a subset of the regression parameters are rescaled nonparametrically and develops efficient semiparametric inferences for the parametric components of the models such models provide a means to adapt for heterogeneity in the data due to varying exposures varying levels of aggregation and so on the class of models considered includes generalized partially linear models and nonparametrically scaled link function models as special cases we present an algorithm to estimate the scale function nonparametrically and obtain asymptotic distribution theory for regression parameter estimates in particular we establish that the asymptotic covariance of the semiparametric estimator for the parametric part of the model achieves the semiparametric lower bound we also describe bootstrap based goodness of scale test we illustrate the methodology with simulations published data and data from collaborative research on ultrasound safety

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

an efficient polynomial time approximation scheme for load balancing on uniformly related machines we consider basic problems of non preemptive scheduling on uniformly related machines for a given schedule defined by a partition of the jobs into m subsets corresponding to the m machines c i c i denotes the completion time of machine i our goal is to find a schedule that minimizes or maximizes sum i 1 m c i p i 1 m c i p for a fixed value of p such that 0 1 p 1 the minimization problem is equivalent to the well known problem of minimizing the ell p l p norm of the vector of the completion times of the machines and for 0 p 1 0 p 1 the maximization problem is of interest our main result is an efficient polynomial time approximation scheme eptas for each one of these problems our schemes use a non standard application of the so called shifting technique we focus on the work total size of jobs assigned to each machine and introduce intervals of work that are forbidden these intervals are defined so that the resulting effect on the goal function is sufficiently small this allows the partition of the problem into sub problems with subsets of machines and jobs whose solutions are combined into the final solution using dynamic programming our results are the first eptas s for this natural class of load balancing problems

tail probabilities from observed likelihoods summary an exponential model not in standard form is fully characterized by an observed likelihood function and its first sample space derivative up to one one transformations of the observable variable this property is used to modify the lugannani rice 1980 tail probability approximation to make it parameterization invariant then for general continuous models a version of tangent exponential model is defined and used to derive a general tail probability approximation that uses only the observed likelihood and its first sample space derivative the analysis extends from density functions to distribution functions the tangent exponential model methods of fraser 1988 a related tail probability approximation has been reported barndorff nielsen 1988b in the discussion to reid 1988

new algorithms for maximum weight matching and a decomposition theorem we revisit the classical maximum weight matching problem in general graphs with nonnegative integral edge weights we present an algorithm that operates by decomposing the problem into w unweighted versions of the problem where w is the largest edge weight our algorithm has running time as good as the current fastest algorithms for the maximum weight matching problem when w is small one of the highlights of our algorithm is that it also produces an integral optimal dual solution thus our algorithm also returns an integral certificate corresponding to the maximum weight matching that was computed our algorithm yields a new proof to the total dual integrality of edmonds matching polytope and it also gives rise to a decomposition theorem for the maximum weight of a matching in terms of the maximum size of a matching in certain subgraphs we also consider the maximum weight capacitated b matching problem in bipartite graphs with nonnegative integral edge weights and show that it can also be decomposed i

distributed asynchronous relaxation methods for convex network flow problems we consider the solution of the single commodity strictly convex network flow problem in a distributed asynchronous computation environment the dual of this problem is unconstrained differentiable and well suited for solution via gauss seidel relaxation we show that the structure of the dual allows the successful application of a distributed asynchronous method whereby relaxation iterations are carried out in parallel by several processors in arbitrary order and with arbitrarily large interprocessor communication delays

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

afptas results for common variants of bin packing a new method for handling the small items we consider two well known natural variants of bin packing and show that these packing problems admit asymptotic fully polynomial time approximation schemes afptass in bin packing problems a set of one dimensional items of size at most 1 is to be assigned packed to subsets of sum at most 1 bins it has been known for a while that the most basic problem admits an afptas in this paper we develop new methods that allow us to extend this result to other variants of bin packing consisting of a family of two parameter bin packing problems we demonstrate the use of our methods by designing afptass for the following problems the first problem is bin packing with cardinality constraints where a parameter k is given such that a bin may contain up to k items the goal is to minimize the number of bins used the second problem is bin packing with rejection where every item has a rejection penalty associated with it an item needs to be either packed to a bin or rejected and the goal is to minimize the number of bins used and the total rejection penalty of unpacked items this resolves the complexity of two important variants of the bin packing problem our approximation schemes use a novel method for packing the small items this new method is the core of the improved running times of our schemes over the running times of the previous results which are only asymptotic polynomial time approximationschemes

multiparameter testing in exponential models third order approximations from likelihood summary for composite testing of several canonical components in an exponential model a conical or directional test provides a one dimensional measure of departure we approximate the distribution of this test statistic to third order by numerical inversion of a profile likelihood the method extends the lugannani rice type formula to kernels other than the normal

meta analysis framework for exact inferences with application to the analysis of rare events the usefulness of meta analysis has been recognized in the evaluation of drug safety as a single trial usually yields few adverse events and offers limited information for rare events conventional meta analysis methods may yield an invalid inference as they often rely on large sample theories and require empirical corrections for zero events these problems motivate research in developing exact methods including tian et al s method of combining confidence intervals 2009 biostatistics 10 275 281 and liu et al s method of combining p value functions 2014 jasa 109 1450 1465 this article shows that these two exact methods can be unified under the framework of combining confidence distributions cds furthermore we show that the cd method generalizes tian et al s method in several aspects given that the cd framework also subsumes the mantel haenszel and peto methods we conclude that the cd method offers a general framework for meta analysis of rare events we illustrate the cd framework using two real data sets collected for the safety analysis of diabetes drugs

statistical inference likelihood to significance abstract the concepts of likelihood and significance were defined and initially developed by r a fisher but followed almost separate and distinct routes we suggest that a central function of statistical inference is in fact the conversion of the first likelihood into the second significance a linking of the fisher concepts a first order asymptotic route for this is incorporated into most statistical packages it uses the standardized maximum likelihood estimate the standardized score or the signed square root of the likelihood ratio statistic as arguments for the standard normal distribution function thus giving approximate tail probabilities or observed levels of significance recent third order asymptotic methods provide a substantial increase in accuracy but need the first derivative dependence of likelihood on the data value as an additional input this can be envisaged as the effect on the likelihood function of dithering the data point extensions to the multivariate multiparameter cont

on multidimensional packing problems we study the approximability of multidimensional generalizations of three classical packing problems multiprocessor scheduling bin packing and the knapsack problem specifically we study the vector scheduling problem its dual problem namely the vector bin packing problem and a class of packing integer programs the vector scheduling problem is to schedule n d dimensional tasks on m machines such that the maximum load over all dimensions and all machines is minimized the vector bin packing problem on the other hand seeks to minimize the number of bins needed to schedule all n tasks such that the maximum load on any dimension across all bins is bounded by a fixed quantity say 1 such problems naturally arise when scheduling tasks that have multiple resource requirements finally packing integer programs capture a core problem that directly relates to both vector scheduling and vector bin packing namely the problem of packing a maximum number of vectors in a single bin of unit height we obtain a variety of new algorithmic as well as inapproximability results for these three problems

the geometric maximum traveling salesman problem we consider the traveling salesman problem when the cities are points in n x211d d for some fixed d and distances are computed according to geometric distances determined by some norm we show that for any polyhedral norm the problem of finding a tour of maximum length can be solved in polynomial time if arithmetic operations are assumed to take unit time our algorithms run in time o nf 2 log n where f is the number of facets of the polyhedron determining the polyhedral norm thus for example we have o n2 log n algorithms for the cases of points in the plane under the rectilinear and sup norms this is in contrast to the fact that finding a minimum length tour in each case is np hard our approach can be extended to the more general case of quasi norms with a not necessarily symmetric unit ball where we get a complexity of o n2f 2 log n for the special case of two dimensional metrics with f 4 which includes the rectilinear and sup norms we present a simple algorithm with o n running time the algorithm does not use any indirect addressing so its running time remains valid even in comparison based models in which sorting requires n log n time the basic mechanism of the algorithm provides some intuition on why polyhedral norms allow fast algorithms complementing the results on simplicity for polyhedral norms we prove that for the case of euclidean distances in n x211d d for d 3 the maximum tsp is np hard this sheds new light on the well studied difficulties of euclidean distances

efficient algorithms for robustness in resource allocation and scheduling problems the robustness function of an optimization minimization problem measures the maximum increase in the value of its optimal solution that can be produced by spending a given amount of resources increasing the values of the elements in its input we present efficient algorithms for computing the robustness function of resource allocation and scheduling problems that can be modeled with partition and scheduling matroids for the case of scheduling matroids we give an o m2n2 time algorithm for computing a complete description of the robustness function where m is the number of elements in the matroid and n is its rank for partition matroids we give two algorithms one that computes the complete robustness function in o m log m time and other that optimally evaluates the robustness function at only a specified point