empirical likelihood for regression discontinuity design this paper proposes empirical likelihood based inference methods for causal effects identified from regression discontinuity designs we consider both the sharp and fuzzy regression discontinuity designs and treat the regression functions as nonparametric the proposed inference procedures do not require asymptotic variance estimation and the confidence sets have natural shapes unlike the conventional wald type method these features are illustrated by simulations and an empirical example which evaluates the effect of class size on pupils scholastic achievements furthermore for the sharp regression discontinuity design we show that the empirical likelihood statistic admits a higher order refinement so called the bartlett correction bandwidth selection methods are also discussed

an exact confidence band for one dimensional polynomial regression summary an exact piecewise polynomial simultaneous confidence band is described for onedimensional p i th order polynomial regression the band is constructed by placing intervals around the estimated response at the zeros of the pth order orthogonal polynomial with respect to the design points since under the usual assumptions the response estimates are uncorrelated at these zeros the construction of the exact band in the normal case is made easy

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

reducing variance in univariate smoothing a variance reduction technique in nonparametric smoothing is proposed at each point of estimation form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged the nearby points are chosen to maximize the variance reduction we study in detail the case of univariate local linear regression while the new estimator retains many advantages of the local linear estimator it has appealing asymptotic relative efficiencies bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation a simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes this technique is very general and has a wide range of applications

a reexamination of diffusion estimators with applications to financial model validation time homogeneous diffusion models have been widely used for describing the stochastic dynamics of the underlying economic variables recently stanton proposed drift and diffusion estimators based on a higher order approximation scheme and kernel regression method he claimed that higher order approximations must outperform lower order approximations and concluded nonlinearity in the instantaneous return function of short term interest rates to examine the impact of higher order approximations we develop general and explicit formulas for the asymptotic behavior of both drift and diffusion estimators we show that these estimators will reduce the numerical approximation errors in asymptotic biases but their asymptotic variances escalate nearly exponentially with the order of approximation simulation studies also confirm our asymptotic results this variance inflation problem arises not only from nonparametric fitting but also from parametric fitting stanton s work also postulates the interesting qu

data driven confidence intervals for diffusion process using double smoothing empirical likelihood abstract in this paper we propose an innovative estimation method for the volatility function in diffusion process and construct the empirical likelihood confidence interval for it compared with double smoothing local constant estimator double smoothing local linear estimator proposed in this paper is an inventive estimation method moreover we find that the empirical likelihood confidence interval constructed with the approximate estimating equation is much better than the one based on the estimating equation since the latter undermines the predictability of the estimator accordingly new algorithm for simulation is proposed through monte carlo simulation and empirical analysis both these approaches are superior to traditional asymptotic normality confidence interval in terms of coverage rate etc

mixed integer bilinear programming problems this paper addresses a class of problems called mixed integer bilinear programming problems these problems are identical to the well known bilinear programming problems with the exception that one set of variables is restricted to be binary valued and they arise in various production location allocation and distribution application contexts we first identify some special cases of this problem which are relatively more readily solvable even though their continuous relaxations are still nonconvex for the more general case we employ a linearization technique and design a composite lagrangian relaxation implicit enumeration cutting plane algorithm extensive computational experience is provided to test the efficacy of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

nonparametric regression with predictors missing at random nonparametric regression with predictors missing at random mar where the probability of missing depends only on observed variables is considered univariate predictor is the primary case of interest a new adaptive orthogonal series estimator is developed large sample theory shows that the estimator is rate minimax and it is also sharp minimax whenever predictors are missing completely at random mcar furthermore confidence bands estimation of nuisance functions including conditional probability of observing the predictor design density and scale and multiple regression are also considered numerical study and a real example show feasibility of the proposed methodology for small samples supplementary materials containing results of the numerical study are available online

binary extended formulations of polyhedral mixed integer sets we analyze different ways of constructing binary extended formulations of polyhedral mixed integer sets with bounded integer variables and compare their relative strength with respect to split cuts we show that among all binary extended formulations where each bounded integer variable is represented by a distinct collection of binary variables what we call unimodular extended formulations are the strongest we also compare the strength of some binary extended formulations from the literature finally we study the behavior of branch and bound on such extended formulations and show that branching on the new binary variables leads to significantly smaller enumeration trees in some cases

nirs spm statistical parametric mapping for near infrared spectroscopy near infrared spectroscopy nirs is a non invasive method to measure brain activity via changes in the degree of hemoglobin oxygenation through the intact skull as optically measured hemoglobin signals strongly correlate with bold signals simultaneous measurement using nirs and fmri promises a significant mutual enhancement of temporal and spatial resolutions although there exists a powerful statistical parametric mapping tool in fmri current public domain statistical tools for nirs have several limitations related to the quantitative analysis of simultaneous recording studies with fmri in this paper a new public domain statistical toolbox known as nirs spm is described it enables the quantitative analysis of nirs signal more specifically nirs data are statistically analyzed based on the general linear model glm and sun s tube formula the p values are calculated as the excursion probability of an inhomogeneous random field on a representation manifold that is dependent on the structure of the error covariance matrix and the interpolating kernels nirs spm not only enables the calculation of activation maps of oxy deoxy hemoglobin and total hemoglobin but also allows for the super resolution localization which is not possible using conventional analysis tools extensive experimental results using finger tapping and memory tasks confirm the viability of the proposed method

empirical likelihood confidence intervals for nonparametric density estimation summary we suggest using empirical likelihood in conjunction with the kernel method to construct confidence intervals for the value of a probability density f at a point x this suggestion arises from a simulation study which shows that confidence intervals produced by the kernel based percentle t bootstrap do not have the coverage claimed by the theory this coverage discrepancy is due to a conflict between the prescribed undersmoothing and the explicit variance estimate needed by the percentile t method empirical likelihood avoids this conflict by studentising internally we show that the empirical likelihood produces confidence intervals having theoretical coverage accuracy of the same order of magnitude as the bootstrap and which are also empirically more accurate

on the value of binary expansions for general mixed integer linear programs we study the use of binary variables in reformulating general mixed integer linear programs we show that binary reformulations result in problems for which almost all the binary variables replacing a general integer variable need to be explored during branching we also give computational results on the performance of such reformulations in solving the mixed integer programs which support our theoretical results

simultaneous confidence bands for linear regression and smoothing suppose we observe y i f x i varepsilon i i 1 ldots n we wish to find approximate 1 alpha simultaneous confidence regions for f x x in mathscr x our regions will be centered around linear estimates hat f x of nonparametric or nonparametric f x there is a large amount of previous work on this subject substantial restrictions have been usually placed on some or all of the dimensionality of x the class of functions f that can be considered the class of linear estimates hat f and the region mathscr x the method we present is an approximation to the tube formula dn can be used for multidimensional x and a wide class of linear estimates by considering the effect of bias we are able to relax assumptions on the class of functions f which are considered simultaneous and numerical computations are used to illustrate the performance

pooling problem alternate formulations and solution methods the pooling problem which is fundamental to the petroleum industry describes a situation in which products possessing different attribute qualities are mixed in a series of pools in such a way that the attribute qualities of the blended products of the end pools must satisfy given requirements it is well known that the pooling problem can be modeled through bilinear and nonconvex quadratic programming in this paper we investigate how best to apply a new branch and cut quadratic programming algorithm to solve the pooling problem to this effect we consider two standard models one is based primarily on flow variables and the other relies on the proportion of flows entering pools a hybrid of these two models is proposed for general pooling problems comparison of the computational properties of flow and proportion models is made on several problem instances taken from the literature moreover a simple alternating procedure and a variable neighborhood search heuristic are developed to solve large instances and compared with the well known method of successive linear programming solution of difficult test problems from the literature is substantially accelerated and larger ones are solved exactly or approximately

confidence bands for regression functions abstract a method for obtaining conservative confidence bands for regression functions in low dimensions is given of particular importance is the applicability of the method to nonparametric regression computations examples and comparisons indicate the effectiveness of the method

the mathematics of playing golf or a new class of difficult non linear mixed integer programs we consider a class of non linear mixed integer programs with n integer variables and k continuous variables solving instances from this class to optimality is an np hard problem we show that for the cases with k 1 and k 2 every optimal solution is integral in contrast to this for every k 3 there exist instances where every optimal solution takes non integral values

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

bidimensional packing by bilinear programming we consider geometric problems in which rectangles have to be packed into identical squares these problems turn out to be very hard in practice and ilp formulations in which variables specify the coordinates in the packing perform very poorly while most methods developed so far are based on simple geometric considerations a recent landmark result of fekete and schepers suggests to put these geometric aspects aside and use the most advanced tools for the one dimensional case in this paper we make additional progress in this direction especially on the basic question does a given set of rectangles fit into a square which turns out to be the bottleneck of all the approaches known given a set of rectangles and the associated convex hull of rectangle subsets that fit into a square we derive a wide class of valid inequalities for this convex hull from a complete description of the two knapsack polytopes associated with the widths and the heights of the rectangles respectively in addition we illustrate how to solve the associated separation problem as a bilinear program for which we develop a solution method that turns out to be fast in practice and show that the integer solutions that satisfy all these constraints generally correspond to vertices of the original convex hull for the benchmark instances in the literature the same tools are used to derive lower bounds for the two dimensional bin packing problem corresponding to the determination of an optimal pair of so called dual feasible functions these lower bounds in many cases equal those obtained by the customary set covering formulation for which column generation is very hard but are computable within a time that is smaller by some orders of magnitude this allows us to close a few of the benchmark instances in the literature

hotelling s theorem on the volume of tubes some illustrations in simultaneous inference and data analysis we illustrate with contemporary examples hotelling s geometric approach to simultaneous probability calculations hotelling reduces the evaluation of certain normal theory significance probabilities to finding the volume of a tube about a curve in a hypersphere and shows that this volume is often exactly given by length times cross sectional area we review hotelling s result together with some recent complements and then use the approach to set simultaneous prediction regions for some data from gait analysis to study andrews plots in multivariate data analysis and to construct significance tests for projection pursuit regression a by product is a numerical criterion for tube self overlap relevant for example to uniqueness of certain nonlinear least squares estimates

inference of trends in time series summary we consider statistical inference of trends in mean non stationary models a test statistic is proposed for the existence of structural breaks in trends on the basis of a strong invariance principle of stationary processes we construct simultaneous confidence bands with asymptotically correct nominal coverage probabilities the results are applied to global warming temperature data and nile river flow data our confidence band of the trend of the global warming temperature series supports the claim that the trend is increasing over the last 150 years

simultaneous confidence bounds in multiple regression using predictor variable constraints abstract this article presents a method for approximating the coverage probability of simultaneous confidence bounds for multiple regression functions when the vector of predictor variables is constrained to lie in a polyhedral convex set the method is useful because it allows one to construct simultaneous confidence intervals with prescribed coverage probability for the regression function evaluated at various settings of the predictor variables which are narrower than bounds obtained without using the predictor variable constraints for a family of two sided simultaneous confidence bounds that includes scheffe type and constant width bounds the probability of coverage is related to the distribution of the maximum euclidean norm of the projection onto a polyhedral cone for a pair of random vectors with known joint distribution an analogous relation holds for one sided bounds if an algorithm for computing the projection onto the cone is available then these results enable one to use the monte carlo

on convex relaxations for quadratically constrained quadratic programming we consider convex relaxations for the problem of minimizing a possibly nonconvex quadratic objective subject to linear and possibly nonconvex quadratic constraints let mathcal f denote the feasible region for the linear constraints we first show that replacing the quadratic objective and constraint functions with their convex lower envelopes on mathcal f is dominated by an alternative methodology based on convexifying the range of the quadratic form genfrac 0 0pt 1 x genfrac 0 0pt 1 x t for x in mathcal f we next show that the use of alpha bb underestimators as computable estimates of convex lower envelopes is dominated by a relaxation of the convex hull of the quadratic form that imposes semidefiniteness and linear constraints on diagonal terms finally we show that the use of a large class of d c difference of convex underestimators is dominated by a relaxation that combines semidefiniteness with rlt constraints

conservative confidence bands in curvilinear regression this paper gives a method for constructing conservative scheffe type simultaneous confidence bands for curvilinear regression functions over finite intervals the method is based on the use of a geometric inequality giving an upper bound for the uniform measure of the set of points within a given distance from y an arbitrary piecewise differentiable path with finite length in s k 1 the unit sphere in r k the upper bound is obtained by straightening the path so that it lies in a great circle in s k 1

2 recognizeable classes of leibniz algebras abstract we show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5 that certain classes of leibniz algebras are 2 recognizeable these classes are solvable strongly solvable and supersolvable these same results hold in lie algebras and in general for groups

global minimization by reducing the duality gap we derive a general principle demonstrating that by partitioning the feasible set the duality gap existing between a nonconvex program and its lagrangian dual can be reduced and in important special cases even eliminated the principle can be implemented in a branch and bound algorithm which computes an approximate global solution and a corresponding lower bound on the global optimal value the algorithm involves decomposition and a nonsmooth local search numerical results for applying the algorithm to the pooling problem in oil refineries are given

nonparametric pricing of interest rate derivative securities we propose a nonparametric estimation procedure for continuous time stochastic models because prices of derivative securities depend crucially on the form of the instantaneous volatility of the underlying process we leave the volatility function unrestricted and estimate it nonparametrically only discrete data are used but the estimation procedure still does not rely on replacing the continuous time model by some discrete approximation instead the drift and volatility functions are forced to match the densities of the process we estimate the stochastic differential equation followed by the short term interest rate and compute nonparametric prices for bonds and bond options

strong valid inequalities for orthogonal disjunctions and bilinear covering sets in this paper we derive a closed form characterization of the convex hull of a generic nonlinear set when this convex hull is completely determined by orthogonal restrictions of the original set although the tools used in this construction include disjunctive programming and convex extensions our characterization does not introduce additional variables we develop and apply a toolbox of results to check the technical assumptions under which this convexification tool can be employed we demonstrate its applicability in integer programming by providing an alternate derivation of the split cut for mixed integer polyhedral sets and finding the convex hull of certain mixed pure integer bilinear sets we then extend the utility of the convexification tool to relaxing nonconvex inequalities which are not naturally disjunctive by providing sufficient conditions for establishing the convex extension property over the non negative orthant we illustrate the utility of this result by deriving the convex hull of a continuous bilinear covering set over the non negative orthant although we illustrate our results primarily on bilinear covering sets they also apply to more general polynomial covering sets for which they yield new tight relaxations

some finite varieties of lie algebras in the class whenever all n generated subalgebras of l are in the class thus the classes jv of nilpotent lie algebras and d of abelian lie algebras are 2 recognizable the problems are to find if a given class is n recognizable and to find the smallest n we consider the classes jv of lie algebras which have an abelian ideal with nilpotent quotient jv of lie algebras which have a nilpotent ideal with abelian quotient of supersolvable lie algebras and y of solvable lie algebras the same notation is used for the corresponding classes of finite groups most notation is standard except where indicated

jointly constrained biconvex programming this paper presents a branch and bound algorithm for minimizing the sum of a convex function in x a convex function in y and a bilinear term in x and y over a closed set such an objective function is called biconvex with biconcave functions similarly defined the feasible region of this model permits joint constraints in x and y to be expressed the bilinear programming problem becomes a special case of the problem addressed in this paper we prove that the minimum of a biconcave function over a nonempty compact set occurs at a boundary point of the set and not necessarily an extreme point the algorithm is proven to converge to a global solution of the nonconvex program we discuss extensions of the general model and computational experience in solving jointly constrained bilinear programs for which the algorithm has been implemented

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

a branch and cut algorithm for nonconvex quadratic programs with box constraints we present the implementation of a branch and cut algorithm for bound constrained nonconvex quadratic programs we use a class of inequalities developed in 12 as cutting planes we present various branching strategies and compare the algorithm to several other methods to demonstrate its effectiveness

a test for model specification of diffusion processes we propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process the empirical likelihood is used to formulate a statistic for each kernel smoothing bandwidth which is effectively a studentized l2 distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process to reduce the sensitivity of the test on smoothing bandwidth choice the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths to better capture the finite sample distribution of the test statistic and data dependence the critical value of the test is obtained by a parametric bootstrap procedure properties of the test are evaluated asymptotically and numerically by simulation and by a real data example

solving mixed integer bilinear problems using milp formulations in this paper we examine a mixed integer linear programming reformulation for mixed integer bilinear problems where each bilinearterm involves the product of a nonnegative integer variable and a nonnegative continuous variable this reformulation is obtained by first replacing a general integer variable with its binary expansion and then using mccormick envelopes to linearize the resulting product of continuous and binary variables we present the convex hull of the underlying mixed integer linear set the effectiveness of this reformulation and associated facet defining inequalities are computationally evaluated on five classes of instances

fully nonparametric estimation of scalar diffusion models we propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process we show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter the asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens we prove almost sure consistency and weak convergence to mixtures of normal laws where the mixing variates depend on the chronological local time of the underlying diffusion process that is the random time spent by the process in the vicinity of a generic spatial point the estimation method and asymptotic results apply to both stationary and nonstationary recurrent processes

different transformations for solving non convex trim loss problems by minlp in the present paper trim loss problems often named the cutting stock problem connected to the paper industry are considered the problem is to cut out a set of product paper rolls from raw paper rolls such that the cost function including the trim loss as well as the costs for the over production is minimized the problem is non convex due to certain bilinear constraints the problem can however be transformed into linear or convex form the resulting transformed problems can thereafter be solved as mixed integer linear programming problems or convex mixed integer non linear programming problems the linear and convex formulations are attractive from a formal point of view since global optimal solutions to the originally non convex problem can be obtained however as the examples considered will show the numerical efficiency of the solutions from the different transformed formulations varies considerably an example based on a trim optimization problem encountered daily at a finnish paper converting mill is finally presented in order to demonstrate differences in the numerical solutions

bootstrap simultaneous error bars for nonparametric regression simultaneous error bars are constructed for nonparametric kernel estimates of regression functions the method is based on the bootstrap where resampling is done from a suitably estimated residual distribution the error bars are seen to give asymptotically correct coverage probabilities uniformly over any number of gridpoints applications to an economic problem are given and comparison to both pointwise and bonferroni type bars is presented through a simulation study

adaptive confidence bands we show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions we propose instead to construct adaptive bands that cover a surrogate function f which is close to but simpler than f the surrogate captures the significant features in f we establish lower bounds on the width for any confidence band for f and construct a procedure that comes within a small constant factor of attaining the lower bound for finite samples

asymptotically optimal difference based estimation of variance in nonparametric regression summary we define and compute asymptotically optimal difference sequences for estimating error variance in homoscedastic nonparametric regression our optimal difference sequences do not depend on unknowns such as the mean function and provide substantial improvements over the suboptimal sequences commonly used in practice for example in the case of normal data the usual variance estimator based on symmetric second order differences is only 64 efficient relative to the estimator based on optimal second order differences the efficiency of an optimal mth order difference estimator relative to the error sample variance is 2m 2m 1 again this is for normal data and increases as the tails of the error distribution become heavier

simultaneous convexification of bilinear functions over polytopes with application to network interdiction we study the simultaneous convexification of graphs of bilinear functions g k x y y intercal a k x over x in ensuremath xi x in 0 1 n e x geq f and y in delta m y in r m 1 intercal y leq 1 we propose a constructive procedure to obtain a linear description of the convex hull of the resulting set this procedure can be applied to derive convex and concave envelopes of certain bilinear functions to study unary expansions of integer variables in mixed integer bilinear sets and to obtain convex hulls of sets with complementarity constraints exploiting the structure of xi the procedure naturally yields stronger linearizations for bilinear terms in a variety of practical settings in particular we demonstrate the effectiveness of the approach by strengthening the traditional dual formulation of network interdiction problems and report encouraging preliminary numerical results

exact confidence bands for linear regression over intervals abstract exact simultaneous confidence intervals and bands for the regression line on a set cx in simple linear regression have been known only when cx is a finite set with one or two points or when cx is a finite or infinite interval otherwise conservative bands have been used in this article we present a method for constructing exact confidence bands on an arbitrary finite union of intervals or points also tables are provided for cases of finite cx with three points and of cx an interval

the sequential knapsack polytope in this paper we describe the convex hull of all solutions of the integer bounded knapsack problem in the special case when the weights of the items are divisible the corresponding inequalities are defined via an inductive scheme that can also be used in a more general setting

on the functional estimation of jump diffusion models abstract we provide a general asymptotic theory for the fully functional estimates of the infinitesimal moments of continuous time models with discontinuous sample paths of the jump diffusion type minimal requirements are placed on the dynamic properties of the underlying jump diffusion process i e stationarity is not required our theoretical framework justifies consistent in a statistical sense nonparametric extraction of the parameters and functions that drive the dynamic evolution of the process of interest i e the potentially nonaffine and level dependent intensity of the jump arrival being an example from the estimated infinitesimal conditional moments as suggested in johannes 2003 the statistical and economic role of jumps in continuous time interest rate models journal of finance forthcoming

stochastic dual dynamic integer programming multistage stochastic integer programming msip combines the difficulty of uncertainty dynamics and non convexity and constitutes a class of extremely challenging problems a common formulation for these problems is a dynamic programming formulation involving nested cost to go functions in the linear setting the cost to go functions are convex polyhedral and decomposition algorithms such as nested benders decomposition and its stochastic variant stochastic dual dynamic programming sddp which proceed by iteratively approximating these functions by cuts or linear inequalities have been established as effective approaches however it is difficult to directly adapt these algorithms to msip due to the nonconvexity of integer programming value functions in this paper we propose an extension to sddp called stochastic dual dynamic integer programming sddip for solving msip problems with binary state variables the crucial component of the algorithm is a new reformulation of the subproblems in each stage and a new class of cuts termed lagrangian cuts derived from a lagrangian relaxation of a specific reformulation of the subproblems in each stage where local copies of state variables are introduced we show that the lagrangian cuts satisfy a tightness condition and provide a rigorous proof of the finite convergence of sddip with probability one we show that under fairly reasonable assumptions an msip problem with general state variables can be approximated by one with binary state variables to desired precision with only a modest increase in problem size thus our proposed sddip approach is applicable to very general classes of msip problems extensive computational experiments on three classes of real world problems namely electric generation expansion financial portfolio management and network revenue management show that the proposed methodology is very effective in solving large scale multistage stochastic integer optimization problems

confidence bands in nonparametric time series regression we consider nonparametric estimation of mean regression and conditional variance or volatility functions in nonlinear stochastic regression models simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct the imposed dependence structure allows applications in many linear and nonlinear auto regressive processes the results are applied to the s p 500 index data

generalized semiparametrically structured ordinal models motivated by recent work studying massive imaging data in the neuroimaging literature we propose multivariate varying coefficient models mvcm for modeling the relation between multiple functional responses and a set of covariates we develop several statistical inference procedures for mvcm and systematically study their theoretical properties we first establish the weak convergence of the local linear estimate of coefficient functions as well as its asymptotic bias and variance and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate we establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions we propose a global test for linear hypotheses of varying coefficient functions and derive its asymptotic distribution under the null hypothesis we also propose a simultaneous confidence band for each individual effect curve we conduct monte carlo simulation to examine the finite sample performance of the proposed procedures we apply mvcm to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment

empirical likelihood based inference for nonparametric recurrent diffusions this paper provides a new approach to constructing confidence intervals for nonparametric drift and diffusion functions in the continuous time diffusion model via empirical likelihood el the log el ratios are constructed through the estimating equations satisfied by the local linear estimators limit theories are developed by means of increasing time span and shrinking observational intervals the results apply to both stationary and nonstationary recurrent diffusion processes simulations show that for both drift and diffusion functions the new procedure performs remarkably well in finite samples and clearly dominates the conventional method in constructing confidence intervals based on asymptotic normality an empirical example is provided to illustrate the usefulness of the proposed method

empirical likelihood confidence intervals for local linear smoothers summary empirical likelihood is considered in conjunction with the local linear smoother to construct confidence intervals for a nonparametric regression function with bounded support the coverage error of the empirical likelihood confidence intervals is evaluated and is shown to be of the same order throughout the support of the regression function this is a significant improvement over confidence intervals based directly on the asymptotic normal distribution of the local linear estimator which have a larger order of coverage error near the boundary this improvement is attributable to the natural variance estimator that empirical likelihood implicitly chooses for the local linear smoother