density flow in dynamical networks via mean field games current distributed routing control algorithms for dynamic networks model networks using the time evolution of density at network edges while the routing control algorithm ensures edge density to converge to a wardrop equilibrium which was characterized by an equal traffic density on all used paths we rearrange the density model to recast the problem within the framework of mean field games in doing that we illustrate an extended state space solution approach and we study the stochastic case where the density evolution is driven by a brownian motion further we investigate the case where the density evolution is perturbed by a bounded adversarial disturbance for both the stochastic and the worst case scenarios we provide conditions for the density to converge to a pre assigned set moreover we analyze such conditions from two different perspectives repeated games with vector payoffs and inclusion theory

simple resampling methods for censored regression quantiles abstract powell journal of econometrics 25 1984 303 325 journal of econometrics 32 1986 143 155 considered censored regression quantile estimators the asymptotic covariance matrices of his estimators depend on the error densities and are therefore difficult to estimate reliably the difficulty may be avoided by applying the bootstrap method hahn econometric theory 11 1995 105 121 calculation of the estimators however requires solving a nonsmooth and nonconvex minimization problem resulting in high computational costs in implementing the bootstrap we propose in this paper computationally simple resampling methods by convexfying powell s approach in the resampling stage a major advantage of the new methods is that they can be implemented by efficient linear programming simulation studies show that the methods are reliable even with moderate sample sizes

censored regression quantiles using quantile regression to analyze survival times offers an valuable complement to traditional cox proportional hazards modelling unfortunately this approach has been hampered by the lack of a conditional quantile estimator for censored data that is directly analogous to the kaplan meier estimator and applies under standard assumptions for censored regression models here a recursively reweighted estimator of the regression quantile process is developed as a direct generalization of the kaplan meier estimator specifically the asymptotic behavior is directly analogous to that of the kaplan meier estimator and computation is essentially equivalent to current simplex methods for the quantile process in the uncensored case some preliminary examples suggest the strong potential of these methods as a complement to the use of cox models

exact computation of censored least absolute deviations estimator abstract we show that exact computation of the censored least absolute deviations clad estimator proposed by powell 1984 may be achieved by formulating the estimator as a linear mixed integer programming mip problem with disjunctive constraints we apply our approach to three previously studied datasets and find that widely used approximate optimization algorithms can lead to erroneous conclusions extensive simulations confirm that mip based computation using available solvers is effective for datasets typically encountered in econometric applications and that despite the proliferation of competitors clad remains a useful estimator

a resampling method based on pivotal estimating functions summary suppose that under a semiparametric model setting one is interested in drawing inferences about a finite dimensi onal parameter vector based on an estimating function generally a consistent point estimator j for 0 the true value for j can be easily obtained by finding a root of the corresponding estimating equation to estimate the variance of ft however may involve complicated and subjective nonparametric functional estimates in this paper a general and simple resampling method for inferences about js0 based on pivotal estimating functions is proposed the new procedure is illustrated with the quantile and rank regression models for both cases our proposal can be easily and efficiently implemented with existing statistical software

bayesian analysis of a tobit quantile regression model this paper develops a bayesian framework for tobit quantile regression our approach is organized around a likelihood function that is based on the asymmetric laplace distribution a choice that turns out to be natural in this context we discuss families of prior distributions on the quantile regression vector that lead to proper posterior distributions with finite moments we show how the posterior distribution can be sampled and summarized by markov chain monte carlo methods a method for comparing alternative quantile regression models is also developed and illustrated the techniques are illustrated with both simulated and real data in particular in an empirical comparison our approach out performed two other common classical estimators

the limiting distribution of the maximum rank correlation estimator han s maximum rank correlation mrc estimator is shown to be 4 consistent and asymptotically normal the proof rests on a general method for determining the asymptotic distribution of a maximization estimator a simple u statistic decomposition and a uniform bound for degenerate u processes a consistent estimator of the asymptotic covariance matrix is provided along with a result giving the explicit form of this matrix for any model within the scope of the mrc estimator the latter result is applied to the binary choice model and it is found that the mrc estimator does not achieve the semiparametric efficiency bound

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

inference for censored quantile regression models in longitudinal studies we develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants we consider a semi parametric quantile regression model that makes no distributional assumptions our research is motivated by the lack of proper inference procedures for data from biomedical studies where measurements are censored due to a fixed quantification limit in such studies the focus is often on testing hypotheses about treatment equality to this end we propose a rank score test for large sample inference on a subset of the covariates we demonstrate the importance of accounting for both censoring and intra subject dependency and evaluate the performance of our proposed methodology in a simulation study we then apply the proposed inference procedures to data from an aids related clinical trial we conclude that our framework and proposed methodology is very valuable for differentiating the influences of predictors at different locations in the conditional distribution of a response variable

fuzzy scheduling modelling flexible constraints vs coping with incomplete knowledge abstract an overview of some fuzzy set based approaches to scheduling is proposed emphasizing two distinct uses of fuzzy sets representing preference profiles and modelling uncertainty distributions the first setting leads to a valued non compensatory generalization of constraint directed scheduling the other setting yields a possibility theoretic counterpart of pert where probability distributions of activity durations are changed into possibility distributions for the purpose of modelling incomplete information it is pointed out that a special case of the latter interval valued pert is a difficult ill known problem regarding the determination of critical activities latest starting times and floats lastly when flexible constraints and uncertain processing times are to be jointly considered the use of possibilistic decision theory leads to the computation of robust schedules

bootstrapping general empirical measures it is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions mathscr f and based on a probability measure p holds a s if and only if mathscr f in mathrm clt p and int f 2 dp infty where f sup f in mathscr f f and it holds in probability if and only if mathscr f in mathrm clt p thus for a large class of statistics no local uniformity of the clt about p is needed for the bootstrap to work consistency of the bootstrap the bootstrapped law of large numbers is also characterized these results are proved under certain weak measurability assumptions on mathscr f

quantile regression under random censoring censored regression models have received a great deal of attention in both the theoretical and applied econometric literature most of the existing estimation procedures for either cross sectional or panel data models are designed only for models with fixed censoring in this paper a new procedure for adapting these estimators designed for fixed censoring to models with random censoring is proposed this procedure is then applied to the clad and quantile estimators of powell j econom 25 1984 303 32 1986a 143 to obtain an estimator of the coefficients under a mild conditional quantile restriction on the error term that is applicable to samples exhibiting fixed or random censoring the resulting estimator is shown to have desirable asymptotic properties and performs well in a small scale simulation study

estimation of censored quantile regression for panel data with fixed effects this article investigates estimation of censored quantile regression qr models with fixed effects standard available methods are not appropriate for estimation of a censored qr model with a large number of parameters or with covariates correlated with unobserved individual heterogeneity motivated by these limitations the article proposes estimators that are obtained by applying fixed effects qr to subsets of observations selected either parametrically or nonparametrically we derive the limiting distribution of the new estimators under joint limits and conduct monte carlo simulations to assess their small sample performance an empirical application of the method to study the impact of the 1964 civil rights act on the black white earnings gap is considered supplementary materials for this article are available online

specification analysis of linear quantile models this paper introduces a nonparametric test for the correct specification of a linear conditional quantile function over a continuum of quantile levels these tests may be applied to assess the validity of post estimation inferences regarding the effect of conditioning variables on the distribution of outcomes we show that the use of an orthogonal projection on the tangent space of nuisance parameters at each quantile index both improves power and facilitates the simulation of critical values via the application of a simple multiplier bootstrap procedure monte carlo evidence and an application to the empirical analysis of age earnings curves are included

specification tests of parametric dynamic conditional quantiles this article proposes omnibus specification tests of parametric dynamic quantile models in contrast to the existing procedures we allow for a flexible specification where a possible continuum of quantiles is simultaneously specified under fairly weak conditions on the serial dependence in the underlying data generating process since the null limit distribution of tests is not pivotal we propose a subsampling approximation of the asymptotic critical values a monte carlo study shows that the asymptotic results provide good approximations for small sample sizes finally an application suggests that our methodology is a powerful alternative to standard backtesting procedures in evaluating market risk

fuzzy dynamic timetable scheduling for public transit abstract timetable scheduling for public transit seeks to optimize service quality and utilization of limited resources a new method is proposed to find a sequence of time intervals adjusted to the dynamic passenger flow in a fuzzy environment with improved reverse flow the decision making is based on two fuzzy variables passenger satisfaction and vehicle capacity usage compared with the original timetable the optimized timetable can adjust to the varying passenger flow while balancing passenger satisfaction and vehicle load and it is optimized for any service time span a practical implementation is provided on a case study of three bus lines for which timetables are designed and discussed in varying situations

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

estimating the asymptotic covariance matrix for quantile regression models a monte carlo study abstract this monte carlo study examines several estimation procedures of the asymptotic covariance matrix in the quantile and censored quantile regression models design matrix bootstrap error bootstrapping order statistic sigma bootstrap homoskedastic kernel and heteroskedastic kernel the monte carlo samples are drawn from two alternative data sets 1 a the unaltered current population survey cps for 1987 and 2 b this cps data with independence between error term and regressors imposed this special setup allows one to evaluate the estimators under various realistic scenarios the results favor the design bootstrap for the general case but also support the order statistic when the error term is independent of the regressors

quantile regression models with multivariate failure time data en tant qu alternative a la classique modelisation de la moyenne par regression la modelisation des quantiles a ete largement etudiee surtout celle de la mediane dans le cas de donnees de survie independantes cependant les correlations naturelles ou artificielles entre donnees font qu il est courant de rencontrer en recherche biomedicale des donnees de survie multivariees pour lesquelles une correlation intra groupe doit etre ajustee pour des donnees de survie correlees et censurees a droite nous explorons ici la modelisation des quantiles et adaptons une approche par equations d estimation destinee a estimer les parametres sous hypothese d independance nous adaptons egalement une version ponderee de cette meme approche qui en ameliore l efficacite nous montrons que les estimateurs des parametres sont robustes et suivent asymptotiquement une distribution normale l estimation de la variance obtenue par approximation asymptotique utilise une estimation non parametrique de la densite cependant que la matrice de variance covariance est estimee par bootstrap et methodes de re echantillonnage perturbe des simulations montrent que l approche proposee convient aux echantillons de taille finie cette nouvelle demarche est appliquee pour illustration a des donnees issues d un essai clinique dans l otite

rough sets theory for multicriteria decision analysis the original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation it operates on a data table composed of a set u of objects actions described by a set q of attributes its basic notions are indiscernibility relation on u lower and upper approximation of either a subset or a partition of u dependence and reduction of attributes from q and decision rules derived from lower approximations and boundaries of subsets identified with decision classes the original rough set idea is failing however when preference orders of attribute domains criteria are to be taken into account precisely it cannot handle inconsistencies following from violation of the dominance principle this inconsistency is characteristic for preferential information used in multicriteria decision analysis mcda problems like sorting choice or ranking in order to deal with this kind of inconsistency a number of methodological changes to the original rough sets theory is necessary the main change is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered sets in multicriteria sorting to approximate preference relations in multicriteria choice and ranking problems another change is necessary substitution of the data table by a pairwise comparison table where each row corresponds to a pair of objects described by binary relations on particular criteria in all those mcda problems the new rough set approach ends with a set of decision rules playing the role of a comprehensive preference model it is more general than the classical functional or relational model and it is more understandable for the users because of its natural syntax in order to workout a recommendation in one of the mcda problems we propose exploitation procedures of the set of decision rules finally some other recently obtained results are given rough approximations by means of similarity relations rough set handling of missing data comparison of the rough set model with sugeno and choquet integrals and results on equivalence of a decision rule preference model and a conjoint measurement model which is neither additive nor transitive

simulation and the asymptotics of optimization estimators on demontre un theoreme de limite centrale general pour des estimateurs definis par minimisation de la longueur d une fonction de critere aleatoire a valeurs vectorielles aucune hypothese de regularite suffisante n est imposee sur la fonction de critere pour que les resultats puissent etre appliques a une classe d estimlateurs de simulation assez large des analyses completes de deux estimateurs de simulation l un introduit par pakes l autre par mcfadden illustrent l application des theoremes generaux

applications of fuzzy set theory to mathematical programming mathematical programming is one of the areas to which fuzzy set theory has been applied extensively primarily based on bellman and zadeh s model of decision in fuzzy environments models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming in integer and fractional programming and in dynamic programming these models in turn have been used to offer computationally efficient approaches for solving vector maximum problems this paper surveys major models and theories in this area and offers some indication on future developments which can be expected

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

an alternative estimator for the censored quantile regression model the paper introduces an alternative estimator for the linear censored quantile regression model the objective function is globally convex and the estimator is a solution to a linear programming problem hence a global minimizer is obtained in a finite number of simplex iterations the suggested estimator also applies to the case where the censoring point is an unknown function of a set of regressors it is shown that under fairly weak conditions the estimator has a n convergence rate and is asymptotically normal in the case of a fixed censoring point its asymptotic property is nearly equivalent to that of the estimator suggested by powell 1984 1986a a monte carlo study performed shows that the suggested estimator has very desirable small sample properties it precisely corrects for the bias induced by censoring even when there is a large amount of censoring and for relatively small sample sizes

an interior point algorithm for nonlinear quantile regression abstract a new algorithm for computing quantile regression estimates for problems in which the response function is nonlinear in parameters is described the nonlinear l 1 estimation problem is a special median case the algorithm is closely related to recent developments on interior point methods for solving linear programs performance of the algorithm on a variety of test problems including the censored linear quantile regression problem of powell 1986 is reported

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