kernel weighted gmm estimators for linear time series models abstract this paper analyzes the higher order asymptotic properties of generalized method of moments gmm estimators for linear time series models using many lags as instruments a data dependent moment selection method based on minimizing the approximate mean squared error is developed in addition a new version of the gmm estimator based on kernel weighted moment conditions is proposed it is shown that kernel weighted gmm estimators can reduce the asymptotic bias compared to standard gmm estimators kernel weighting also helps to simplify the problem of selecting the optimal number of instruments a feasible procedure similar to optimal bandwidth selection is proposed for the kernel weighted gmm estimator

asymptotic optimality of cl and generalized cross validation in ridge regression with application to spline smoothing the asymptotic optimality of mallows c l and generalized cross validation is demonstrated in the setting of ridge regression an application is made to spline smoothing in nonparametric regression a counterexample is given to help understand why sometimes gcv may not be asymptotically optimal the coefficient of variation for the eigenvalues of the information matrix must be large in order to guarantee the optimality of gcv the proff is based on the connection between gcv and stein s unbiased risk estimate

milp formulations for the modularity density maximization problem abstract cluster analysis refers to finding subsets of vertices of a graph called clusters which are more likely to be joined pairwise than vertices in different clusters in the last years this topic has been studied by many researchers and several methods have been proposed one of the most popular is to maximize the modularity which represents the fraction of edges within clusters minus the expected fraction of such edges in a random graph with the same degree distribution however this criterion presents some issues for example the resolution limit i e the difficulty to detect clusters having small sizes in this paper we focus on a recent measure called modularity density which improves the resolution limit issue of modularity the problem of maximizing the modularity density can be described by means of a 0 1 nlp formulation we derive some properties of the optimal solution which will be used to tighten the formulation and we propose some milp reformulations which yield an improvement of the resolution time

efficient estimation of general dynamic models with a continuum of moment conditions there are two difficulties with the implementation of the characteristic function based estimators first the optimal instrument yielding the ml efficiency depends on the unknown probability density function second the need to use a large set of moment conditions leads to the singularity of the covariance matrix we resolve the two problems in the framework of gmm with a continuum of moment conditions a new optimal instrument relies on the double indexing and as a result has a simple exponential form the singularity problem is addressed via a penalization term we introduce hac type estimators for non markov models a simulated method of moments is proposed for non analytical cases

generating cuts in integer programming with families of special ordered sets abstract this paper describes families of cuts which can be added to integer programming formulations incorporating special ordered sets ways in which the cuts can be used are discussed and some computational experience is presented

the undirected m capacitated peripatetic salesman problem abstract in the m capacitated peripatetic salesman problem m cpsp the aim is to determine m hamiltonian cycles of minimal total cost on a graph such that all the edges are traversed less than the value of their capacity this article introduces three formulations for the m cpsp two branch and cut algorithms and one branch and price algorithm are developed tests performed on randomly generated and on tsplib euclidean instances indicate that the branch and price algorithm can solve instances with more than twice the size of what is achievable with the branch and cut algorithms

closest assignment constraints in discrete location problems the objective of this paper is to identify the most promising sets of closest assignment constraints in the literature of discrete location theory helping the authors in the field to model their problems when clients must be assigned to the closest plant inside an integer programming formulation in particular constraints leading to weak linear programming relaxations should be avoided if no other good property supports their use we also propose a new set of constraints with good theoretical properties

column generation algorithms for exact modularity maximization in networks finding modules or clusters in networks currently attracts much attention in several domains the most studied criterion for doing so due to newman and girvan phys rev e 69 026113 2004 is modularity maximization many heuristics have been proposed for maximizing modularity and yield rapidly near optimal solution or sometimes optimal ones but without a guarantee of optimality there are few exact algorithms prominent among which is a paper by xu et al eur phys j b 60 231 2007 modularity maximization can also be expressed as a clique partitioning problem and the row generation algorithm of grotschel and wakabayashi math program 45 59 1989 applied we propose to extend both of these algorithms using the powerful column generation methods for linear and non linear integer programming performance of the four resulting algorithms is compared on problems from the literature instances with up to 512 entities are solved exactly moreover the computing time of previously solved problems are reduced substantially

tools for reformulating logical forms into zero one mixed integer programs abstract a systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an integer linear programming ilp formulation or a mixed integer programming mip formulation is presented a reformulation procedure which uses the extended reverse polish notation to represent a compound logical form is then described the syntax of an lp modelling language is extended to incorporate statements in propositional logic forms with linear algebraic forms whereby 0 1 mip models can be automatically formulated a prototype user interface by which logical forms can be reformulated and the corresponding mip constructed and analysed within an existing mathematical programming modelling system is illustrated finally the steps to formulate a discrete optimisation model in this way are illustrated by means of an example

empirical likelihood estimation and consistent tests with conditional moment restrictions this paper is about efficient estimation and consistent tests of conditional moment restrictions we use unconditional moment restrictions based on splines or other approximating functions for this purpose empirical likelihood estimation is particularly appropriate for this setting because of its relatively low bias with many moment conditions we give conditions so that efficiency of estimators and consistency of tests is achieved as the number of restrictions grows with the sample size we also give results for generalized empirical likelihood generalized method of moments and nonlinear instrumental variable estimators

cluster analysis and mathematical programming given a set of entities cluster analysis aims at finding subsets called clusters which are homogeneous and or well separated as many types of clustering and criteria for homogeneity or separation are of interest this is a vast field a survey is given from a mathematical programming viewpoint steps of a clustering study types of clustering and criteria are discussed then algorithms for hierarchical partitioning sequential and additive clustering are studied emphasis is on solution methods i e dynamic programming graph theoretical algorithms branch and bound cutting planes column generation and heuristics

higher moment estimators for linear regression models with errors in the variables abstract this paper proposes consistent instrumental variable estimators for linear regression models with errors in the variables that require no extraneous information these estimators are based on sample moments of order higher than two while similar estimators proposed previously in the literature seem to be quite erratic our experimental f findings suggest that our estimators perform better than ordinary least squares estimators in terms of root mean squared errors and also in terms of size of type i errors of standard tests in many typical situations of economic analyses tests for the presence of errors in the variables are also described

gmm estimators with improved finite sample properties using principal components of the weighting matrix with an application to the dynamic panel data model gmm estimators have poor finite sample properties in highly overidentified models with many moment conditions the optimal weighting matrix is poorly estimated we suggest using principal components of the weighting matrix this effectively drops some of the moment conditions our simulations done in the context of the dynamic panel data model show that the resulting gmm estimator has better finite sample properties than the usual two step gmm estimator in the sense of smaller bias and more reliable standard errors

the boolean quadric polytope some characteristics facets and relatives we study unconstrained quadratic zero one programming problems havingn variables from a polyhedral point of view by considering the boolean quadric polytope qpn inn n 1 2 dimensions that results from the linearization of the quadratic form we show that qpn has a diameter of one descriptively identify three families of facets of qpn and show that qpn is symmetric in the sense that all facets of qpn can be obtained from those that contain the origin by way of a mapping the naive linear programming relaxation qpnlp of qpn is shown to possess the trubin property and its extreme points are shown to be 0 1 2 1 valued furthermore o n3 facet defining inequalities of qpn suffice to cut off all fractional vertices of qpnlp whereas the family of facets described by us has at least o 3n members the problem is also studied for sparse quadratic forms i e when several or many coefficients are zero and conditions are given for the previous results to carry over to this case polynomially solvable problem instances are discussed and it is shown that the known polynomiality result for the maximization of nonnegative quadratic forms can be obtained by simply rounding the solution to the linear programming relaxation in the case that the graph induced by the nonzero coefficients of the quadratic form is series parallel a complete linear description of the associated boolean quadric polytope is given the relationship of the boolean quadric polytope associated to sparse quadratic forms with the vertex packing polytope is discussed as well

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

a regularization approach to the many instruments problem abstract this paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite in order to improve the small sample properties of standard instrumental variable iv estimators we propose three modified iv estimators based on three different ways of inverting the covariance matrix of the instruments these inverses involve a regularization or smoothing parameter it should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation we show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound higher order analysis of the mse reveals that the bias of the modified estimators does not depend on the number of instruments finally we suggest a data driven method for selecting the regularization parameter interestingly our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument

simplifications in multidimensional stability margin computations previously published algorithms for the computation of multidimensional stability margins of discrete systems require a stability test of these systems before starting the computational algorithm in this correspondence it is shown that the multidimensional stability test may be replaced by single dimensional tests for one kind of stability margin and can be omitted completely for the second kind of stability margin

choosing the number of instruments properties of instrumental variable estimators are sensitive to the choice of valid instruments even in large cross section applications in this paper we address this problem by deriving simple mean square error criteria that can be minimized to choose the instrument set we develop these criteria for two stage least squares 2sls limited information maximum likelihood liml and a bias adjusted version of 2sls b2sls we give a theoretical derivation of the mean square error and show optimality in monte carlo experiments we find that the instrument choice generally yields an improvement in performance also in the angrist and krueger 1991 returns to education application when the instrument set is chosen in the way we consider it turns out that both 2sls and liml give similar large returns to education

formulating logical implications in combinatorial optimisation abstract when practical problems are formulated as combinatorial optimisation models one must often include logical implications between decisions it is useful to express these implications as linear constraints involving binary variables since linear constraints offer the possibility of using linear programming and branch and bound as an initial solution method often this formulation step of the modelling process seems far from evident to many practitioners students and researchers therefore it is of interest to make simple rules available to clarify and help in this process in this educationally oriented tutorial paper we introduce such a rule lip the logical implication principle it offers an easy and automatic way to translate elementary logical implications involving 0 1 variables into linear constraints based on an extremely simple cutting plane we demonstrate how the rule is extended using complementarity and implicit binary variables and leads to a simple but powerful instrument this is illustrated by several examples of applications in various fields of operational research the paper culminates in the description of a novel set of constraints which fully eliminate all permutation equivalent solutions to numbered clustering problems

tight representation of logical constraints as cardinality rules am are true then at least l of the propositions b1 bn are true the main result of the paper is that the procedure in fact provides a convex hull description

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail