kurzweil and mcshane product integration in banach algebras abstract we study product integrability of functions with values in unital banach algebras the product integrals are understood in the sense of kurzweil mcshane or riemann in particular we introduce new concepts of strong kurzweil and mcshane product integrals and investigate their properties we also provide necessary and sufficient conditions for product integrability of functions with countably many discontinuities

projection results for vehicle routing a variety of integer programming formulations have been proposed for vehicle routing problems vrps including the so called two and three index formulations the set partitioning formulation and various formulations based on extra variables representing the flow of one or more commodities until now there has not been a systematic study of how these formulations relate to each other an exception is a paper of luis gouveia which shows that a one commodity flow formulation of gavish and graves yields by projection certain multistar inequalities in the two index space we give a survey of formulations for the capacitated vrp and then present various results of a similar flavour to those of gouveia in particular we show that the three index formulation augmented by certain families of valid inequalities gives the same lower bound as the two index formulation augmented by certain simpler families of valid inequalities the two commodity flow formulation of baldacci et al gives the same lower bound and the same multistar inequalities as the one commodity gavish and graves formulation a certain non standard multi commodity flow formulation with one commodity per customer implies by projection certain hypotour like inequalities in the two index space the set partitioning formulation implies by projection both multistar and hypotour like inequalities in the two index space we also briefly look at some other variants of the vrp such as the vrp with time windows and derive multistar like inequalities for them we also present polynomial time separation algorithms for some of the new inequalities

bayesian approach with hidden markov modeling and mean field approximation for hyperspectral data analysis the main problems in hyperspectral image analysis are spectral classification segmentation and data reduction in this paper we propose a bayesian estimation approach which gives a joint solution for these problems the problem is modeled as a blind sources separation bss the data are m hyperspectral images and the sources are k m images which are composed of compact homogeneous regions and have mutually disjoint supports the set of all these regions cover the total surface of the observed scene to insure these properties we propose a hierarchical markov model for the sources with a common hidden classification field which is modeled via a potts markov field the joint bayesian estimation of the hidden variable sources and the mixing matrix of the bss gives a solution for all three problems spectra classification segmentation and data reduction of hyperspectral images the mean field approximation mfa algorithm for the posterior laws is proposed for the effective bayesian computation finally some results of the application of the proposed methods on simulated and real data are given to illustrate the performance of the proposed method compared to other classical methods such as pca and ica

generalized differential equations differentiability of solutions with respect to initial conditions and parameters abstract we show that under certain assumptions solutions of generalized ordinary differential equations are differentiable with respect to initial conditions and parameters this result unifies and extends several existing theorems for other types of equations such as impulsive differential equations or dynamic equations on time scales

an integer linear programming based heuristic for the capacitated m ring star problem abstract we address the capacitated m ring star problem in which the aim is to find m rings simple cycles visiting a central depot a subset of customers and a subset of potential steiner nodes while customers not belonging to any ring must be allocated to a visited customer or steiner node moreover the rings must be node disjoint and the number of customers allocated or visited in a ring cannot be greater than a given capacity q the objective is to minimize the total visiting and allocation costs the capacitated m ring star problem is np hard since it generalizes the traveling salesman problem in this paper we propose a new heuristic algorithm which combines both heuristic and exact ideas to solve the problem following the general variable neighborhood search scheme the algorithm incorporates an integer linear programming based improvement method which is applied whenever the heuristic algorithm is not able to improve the quality of the current solution extensive computational experiments on benchmark instances of the literature and on a new set of instances have been performed to compare the proposed algorithm with the most effective methods from the literature the results show that the proposed algorithm outperforms the other methods

semi supervised linear spectral unmixing using a hierarchical bayesian model for hyperspectral imagery this paper proposes a hierarchical bayesian model that can be used for semi supervised hyperspectral image unmixing the model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive gaussian noise the abundance parameters appearing in this model satisfy positivity and additivity constraints these constraints are naturally expressed in a bayesian context by using appropriate abundance prior distributions the posterior distributions of the unknown model parameters are then derived a gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances an extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library the performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data

an exact algorithm for the capacitated vehicle routing problem based on a two commodity network flow formulation the capacitated vehicle routing problem cvrp is the problem in which a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints in this paper we describe a new integer programming formulation for the cvrp based on a two commodity network flow approach we present a lower bound derived from the linear programming lp relaxation of the new formulation which is improved by adding valid inequalities in a cutting plane fashion moreover we present a comparison between the new lower bound and lower bounds derived from the lp relaxations of different cvrp formulations proposed in the literature a new branch and cut algorithm for the optimal solution of the cvrp is described computational results are reported for a set of test problems derived from the literature and for new randomly generated problems

hazard based nonparametric survivor function estimation summary a representation is developed that expresses the bivariate survivor function as a function of the hazard function for truncated failure time variables this leads to a class of nonparametric survivor function estimators that avoid negative mass the transformation from hazard function to survivor function is weakly continuous and compact differentiable so that such properties as strong consistency weak convergence to a gaussian process and bootstrap applicability for a hazard function estimator are inherited by the corresponding survivor function estimator the set of point mass assignments for a survivor function estimator is readily obtained by using a simple matrix calculation on the set of hazard rate estimators special cases arise from a simple empirical hazard rate estimator and from an empirical hazard rate estimator following the redistribution of singly censored observations within strips the latter is shown to equal van der laan s repaired nonparametric maximum likelihood estimator for which a greenwood like variance estimator is given simulation studies are presented to compare the moderate sample performance of various nonparametric survivor function estimators

a general class of parametric models for recurrent event data the general class of models proposed by pena and hollander for recurrent event data is considered under a fully parametric specification of the baseline hazard rate function and under the two cases where the model does and does not incorporate frailty components estimators of model parameters are presented and their finite and asymptotic properties are ascertained for the asymptotic properties the results of borgan concerning maximum likelihood estimators in counting process models are used to obtain weak convergence to gaussian distributions of estimators however the required regularity conditions are reformulated into conditions involving gap times which make it more feasible to obtain explicit theoretical expressions of asymptotic covariances the procedures are applied to fit the general class of models with a parametric baseline hazard rate function to a dataset on hydraulic subsystems of load haul dump machines in mining

beta stacy processes and a generalization of the polya urn scheme beta stacy process is dened it is shown to be neutral to the right and a generalization of the dirichlet process the posterior distribution is also a beta stacy process given independent and identically distributed iid observations possibly with right censoring from f a generalization of the p olya urn scheme is introduced which characterizes the discrete betastacy process 1 introduction let f be the space of cumulative distribution functions cdfs oni0 1e this paper considers placing a probability distribution on f by dening a stochastic process f onei0 1e ae where a is the borel eld of subsets such that fe0e d 0 a s f is a s nondecreasing a s right continuous and lim t 1 fete d 1 a s thus with probability 1 the sample paths of f are cdf s previous work includes the dirichlet process ferguson 1973 1974 neutral to the right processes doksum 1974 the extended gamma process dykstra and laud 1981 the beta process hjort 1990 and p olya trees lavine 1992 1994 mauldin sudderth and williams 1992 the purpose of this paper is twofold 1 to introduce a new stochastic process which generalizes the dirichlet process in that more exible prior beliefs are able to be represented and unlike the dirichlet process is conjugate to right censored observations and 2 to introduce a generalization of the p olyaurn scheme in order to characterize the discrete time version of the process the property of conjugacy to right censored observations is also a feature of the beta process however with the beta process the statistician is required to consider hazard rates and cumulative hazards when constructing the prior the beta stacy process only requires considerations on the distribution of the observations the process is shown to be neutral to the right the present paper is restricted to considering the estimation of an unknown cdf oni0 1e although it is trivially extended to includee1 1e finally for ease of notation f is written to mean either the cdf or the corresponding probability measure the organization of the paper is as follows in section 2 the process is dened and its connections with other processes given we also provide an

nonparametric methods for imperfect repair models in the age dependent minimal repair model of block borges and savits bbs a system failing at age t undergoes one of two types of repair with probability p t a perfect repair is performed and the system is returned to the good as new state while with probability 1 p t a minimal repair is performed and the system is repaired but is only as good as a working system of age t whitaker and samaniego propose an estimator for the system life distribution f when data are collected under this model in the present article an appropriate probability model for the bbs process is developed and a counting process approach is used to extend the large sample theorems of whitaker and samaniego to the whole line applications of these results to confidence bands and an extension of the wilcoxon two sample test are examined

strong approximations of some biometric estimates under random censorship the empirical distribution function has been widely used as an estimator for the distribution function of the elements of a random sample it is not however appropriate when the observations are incomplete this is the case for example when the observations have been randomly censored on the right in the latter case the so called product limit estimate of kaplan and meier 16 has been generally accepted as a substitute for the empirical distribution function and it possesses many of the same properties cf meier 19 developing the corresponding statement of efron 8 weak convergence over a finite interval of the kaplan meier product limit estimate to a gaussian process when there is censorship on the right has been obtained by breslow and crowley 3 cf also meier 19 breslow and crowley obtained their result via the limiting distribution of the closely related cumulative hazard process under random censorship a generalisation of the efron breslow crowley theorem was formulated by yang 24 for the case when censorship on the right is performed by more competing risks these results have numerous statistical applications in areas such as medical follow up studies life testing actuarial sciences and demography koziol and green 18 have computed tables for the limiting distribution of the cram6r von mises statistic based on the kaplan meier product limit estimate under a specific random censorship model a point will be stressed in this paper however that by a certain transformation which seems to have escaped many researchers attention and is due to efron 8 it is always possible to obtain the standard wiener process in the limit the distributions of many functionals of which are well known this transformation was only recently used in a stimulating note by gillespie and fisher 14 to construct asymptotic confidence bands for the unknown distribution function in the kaplan meier model a general scheme of random censorship can be defined in the following way let x be a real random variable with distribution function f t

collaborative sparse regression using spatially correlated supports application to hyperspectral unmixing this paper presents a new bayesian collaborative sparse regression method for linear unmixing of hyperspectral images our contribution is twofold first we propose a new bayesian model for structured sparse regression in which the supports of the sparse abundance vectors are a priori spatially correlated across pixels i e materials are spatially organized rather than randomly distributed at a pixel level this prior information is encoded in the model through a truncated multivariate ising markov random field which also takes into consideration the facts that pixels cannot be empty i e there is at least one material present in each pixel and that different materials may exhibit different degrees of spatial regularity second we propose an advanced markov chain monte carlo algorithm to estimate the posterior probabilities that materials are present or absent in each pixel and conditionally to the maximum marginal a posteriori configuration of the support compute the minimum mean squared error estimates of the abundance vectors a remarkable property of this algorithm is that it self adjusts the values of the parameters of the markov random field thus relieving practitioners from setting regularization parameters by cross validation the performance of the proposed methodology is finally demonstrated through a series of experiments with synthetic and real data and comparisons with other algorithms from the literature

the order of the remainder in derivatives of composition and inverse operators for p variation norms the theory of differentiable statisticals began with work of von mises e g von mises 1936 1947 and filippova 1961 a nonlinear funtional t is defined for examble on distribution functions von mises differentiated t at a distribution funtion f along lines for t to have a g teaux derivative at f means that in the direction of a function h t f th t f tt prime f h 0 t quad rm as t rightarrow 0 1 1 here t prime f is a bounded linear operator on funtions h for example of the form t prime f h int g quad dh hbox for some function g hbox depending on f 1 2

supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery this paper presents a nonlinear mixing model for hyperspectral image unmixing the proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white gaussian noise these nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model a bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model the performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data

a spatial compositional model for linear unmixing and endmember uncertainty estimation the normal compositional model ncm has been extensively used in hyperspectral unmixing however previous research has mostly focused on the estimation of endmembers and or their variability based on the assumption that the pixels are independent random variables in this paper we show that this assumption does not hold if all the pixels are generated by a fixed endmember set this introduces another concept endmember uncertainty which is related to whether the pixels fit into the endmember simplex to further develop this idea we derive the ncm from the ground up without the pixel independence assumption along with 1 using different noise levels at different wavelengths and 2 using a spatial and sparsity promoting prior for the abundances the resulting new formulation is called the spatial compositional model scm to better differentiate it from the ncm the scm maximum a posteriori objective leads to an optimization problem featuring noise weighted least squares minimization for unmixing the problem is solved by projected gradient descent resulting in an algorithm that estimates endmembers abundances noise variances and endmember uncertainty simultaneously we compared scm with current state of the art algorithms on synthetic and real images the results show that scm can in the main provide more accurate endmembers and abundances moreover the estimated uncertainty can serve as a prediction of endmember error under certain conditions

unsupervised post nonlinear unmixing of hyperspectral images using a hamiltonian monte carlo algorithm this paper presents a nonlinear mixing model for hyperspectral image unmixing the proposed model assumes that the pixel reflectances are post nonlinear functions of unknown pure spectral components contaminated by an additive white gaussian noise these nonlinear functions are approximated using second order polynomials leading to a polynomial post nonlinear mixing model a bayesian algorithm is proposed to estimate the parameters involved in the model yielding an unsupervised nonlinear unmixing algorithm due to the large number of parameters to be estimated an efficient hamiltonian monte carlo algorithm is investigated the classical leapfrog steps of this algorithm are modified to handle the parameter constraints the performance of the unmixing strategy including convergence and parameter tuning is first evaluated on synthetic data simulations conducted with real data finally show the accuracy of the proposed unmixing strategy for the analysis of hyperspectral images

large sample behaviour of the product limit estimator on the whole line weak convergence results are proved for the product limit estimator on the whole line applications are given to confidence band construction estimation of mean lifetime and to the theory of q functions the results are obtained using stochastic calculus and in probability linear bounds for empirical processes

a nonnegative pca algorithm for independent component analysis we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded so that they have a nonzero probability density function pdf in the region of zero we propose the use of a nonnegative principal component analysis nonnegative pca algorithm which is a special case of the nonlinear pca algorithm but with a rectification nonlinearity and we conjecture that this algorithm will find such nonnegative well grounded independent sources under reasonable initial conditions while the algorithm has proved difficult to analyze in the general case we give some analytical results that are consistent with this conjecture and some numerical simulations that illustrate its operation

joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a bayesian sampling approach we propose a joint segmentation algorithm for piecewise constant autoregressive ar processes recorded by several independent sensors the algorithm is based on a hierarchical bayesian model appropriate priors allow us to introduce correlations between the change locations of the observed signals numerical problems inherent to bayesian inference are solved by a gibbs sampling strategy the proposed joint segmentation methodology yields improved segmentation results when compared with parallel and independent individual signal segmentations the initial algorithm is derived for piecewise constant ar processes whose orders are fixed on each segment however an extension to models with unknown model orders is also discussed theoretical results are illustrated by many simulations conducted with synthetic signals and real arc tracking and speech signals

on posterior consistency of survival models ghosh and ramamoorthi studied posterior consistency for survival models and showed that the posterior was consistent when the prior on the distribution of survival times was the dirichlet process prior in this paper we study posterior consistency of survival models with neutral to the right process priors which include dirichlet process priors a set of sufficient conditions for posterior consistency with neutral to the right process priors are given interestingly not all the neutral to the right process priors have consistent posteriors but most of the popular priors such as dirichlet processes beta processes and gamma processes have consistent posteriors with a class of priors which includes beta processes a necessary and sufficient condition for the consistency is also established an interesting counter intuitive phenomenon is found suppose there are two priors centered at the true parameter value with finite variances surprisingly the posterior with smaller prior variance can be inconsistent while that with larger prior variance is consistent

efficient estimation from right censored data when failure indicators are missing at random the kaplan meier estimator of a survival function is well known to be asymptotically efficient when cause of failure is always observed it has been an open problem however to find an efficient estimator when failure indicators are missing at random lo showed that nonparametric maximum likelihood estimators are inconsistent and this has led to several proposals of ad hoc estimators none of which are efficient we now introduce a sieved nonparametric maximum likelihood estimator and show that it is efficient our approach is related to the estimation of a bivariate survival function from bivariate right censored data 1 introduction suppose that we wish to estimate a survival distribution based on right censored data when cause of failure is always observed the method of nonparametric maximum likelihood leads to the well studied kaplan meier 1958 estimator which has many desirable properties including asymptotic efficiency wellner 1982 in this paper we address the problem of finding an asymptotically efficient estimator when cause of failure information is missing for some individuals

locating median cycles in networks abstract in the median cycle problem the aim is to determine a simple cycle through a subset of vertices of a graph involving two types of costs a routing cost associated with the cycle itself and the cost of assigning vertices not on the cycle to visited vertices the objective is to minimize the routing cost subject to an upper bound on the total assignment cost this problem arises in the location of a circular shaped transportation and telecommunication infrastructure we present a mixed integer linear model and strengthen it with the introduction of additional classes of non trivial valid inequalities separation procedures are developed and an exact branch and cut algorithm is described computational results on instances from the classical tsp library and randomly generated ones confirm the efficiency of the proposed algorithm an application related to the city of milan italy is also solved within reasonable computation time

a heuristic procedure for the capacitated m ring star problem abstract in this paper we propose a heuristic method to solve the capacitated m ring star problem which has many practical applications in communication networks the problem consists of finding m rings simple cycles visiting a central depot a subset of customers and a subset of potential steiner nodes while customers not belonging to any ring must be allocated to a visited customer or steiner node moreover the rings must be node disjoint and the number of customers allocated or visited in a ring cannot be greater than the capacity q given as an input parameter the objective is to minimize the total visiting and allocation costs the problem is a generalization of the traveling salesman problem hence it is np hard in the proposed heuristic after the construction phase a series of different local search procedures are applied iteratively this method incorporates some random aspects by perturbing the current solution through a shaking procedure which is applied whenever the algorithm remains in a local optimum for a given number of iterations computational experiments on the benchmark instances of the literature show that the proposed heuristic is able to obtain within a short computing time most of the optimal solutions and can improve some of the best known results

separating capacity constraints in the cvrp using tabu search abstract branch and cut methods have shown to be very successful in the resolution of some hard combinatorial optimization problems the success has been remarkable for the symmetric traveling salesman problem tsp the crucial part in the method is the cutting plane algorithm the algorithm that looks for valid inequalities that cut off the current nonfeasible linear program lp solution in turn this part relies on a good knowledge of the corresponding polyhedron and our ability to design algorithms that can identify violated valid inequalities this paper deals with the separation of the capacity constraints for the capacitated vehicle routing problem cvrp three algorithms are presented a constructive algorithm a randomized greedy algorithm and a very simple tabu search procedure as far as we know this is the first time a metaheuristic is used in a separation procedure the aim of this paper is to present this application no advanced tabu technique is used we report computational results with these heuristics on difficult instances taken from the literature as well as on some randomly generated instances these algorithms were used in a branch and cut procedure that successfully solved to optimality large cvrp instances

a heavy censoring limit theorem for the product limit estimator a key identity for the product limit estimator due to aalen and johansen 1978 and gill 1980 is shown to be a consequence of the exponential formula of doleans dade 1970 the basic counting processes in the censored data problem are shown to converge jointly to poisson processes under heavy censoring g n rightarrow d delta 0 but n 1 g n rightarrow alpha where g n is the censoring distribution the poisson limit theorem for counting processes implies poisson type limit theorems under heavy censoring for the cumulative hazard function estimator and product limit estimator the latter in combination with the key identity of aalen johansen and gill and martingale properties of the limit processes yields a new approximate variance formula for the product limit estimator which is compared numerically with recent finite sample calculations for the case of proportional hazard censoring due to chen hollander and langberg 1982

a characterization of a neutral to the right prior via an extension of johnson s sufficientness postulate in this paper we present a new characterization and perspective on a neutral to the right prior this characterization is based on a sequence of predictive laws which provides explicitly the posterior parameters and bayes estimators for such a prior

survival analysis with temporal covariate effects summary we propose a natural generalization of the cox regression model in which the regression coefficients have direct interpretations as temporal covariate effects on the survival function under the conditionally independent censoring mechanism we develop a smoothing free estimation procedure with a set of martingale based equations our estimator is shown to be uniformly consistent and to converge weakly to a gaussian process a simple resampling method is proposed for approximating the limiting distribution of the estimated coefficients second stage inferences with time varying coefficients are developed accordingly simulations and a real example illustrate the practical utility of the proposed method finally we extend this proposal of temporal covariate effects to the general class of linear transformation models and also establish a connection with the additive hazards model

nonparametric estimation of component lifetime based on masked system life test data in this paper we study the model of masked data sets i e data sets consisting of failure times of a system and sets of failed components failing components can yield further failures the initially failed component is unknown initial failures and later failures are indistinguishable a nonparametric estimator of the component lifetime distribution is derived we prove weak convergence of the estimator to a gaussian process

the survival curve under monotone density constraints with applications to two dimensional line segment processes summary several situations involving survival data are examined in which the nonparametric maximum likelihood estimator is not the kaplan meier estimator cases covered are inclusion of initial observations in field studies estimation of the length distribution from convex window sampling of line segment processes in two dimensions and estimation of a survival curve with monotone density the first two cases are nonstandard because survival and censoring are not independent and thus form simple tractable variable sum models williams lagakos 1977

nonparametric estimation for right censored length biased data a pseudo partial likelihood approach to estimate the lifetime distribution of right censored length biased data we propose a pseudo partial likelihood approach that allows us to derive two nonparametric estimators with its closed form estimators and explicit limiting variances this approach retains the simplicity of conditional analysis and has only a small efficiency loss compared with the unconditional analysis under some regularity conditions we show that the two estimators are uniformly consistent and converge weakly to gaussian processes a simulation study demonstrates that the proposed estimators have satisfactory finite sample performance application to an alzheimer s disease study is reported

self consistent nonparametric maximum likelihood estimator of the bivariate survivor function summary as usually formulated the nonparametric likelihood for the bivariate survivor function is overparameterized resulting in uniqueness problems for the corresponding nonparametric maximum likelihood estimator here the estimation problem is redefined to include parameters for marginal hazard rates and for double failure hazard rates only at informative uncensored failure time grid points where there is pertinent empirical information double failure hazard rates at other grid points in the risk region are specified rather than estimated with this approach the nonparametric maximum likelihood estimator is unique and can be calculated using a two step procedure the first step involves setting aside all doubly censored observations that are interior to the risk region the nonparametric maximum likelihood estimator from the remaining data turns out to be the dabrowska 1988 estimator the omitted doubly censored observations are included in the procedure in the second stage using self consistency resulting in a noniterative nonparametric maximum likelihood estimator for the bivariate survivor function simulation evaluation and asymptotic distributional results are provided moderate sample size efficiency for the survivor function nonparametric maximum likelihood estimator is similar to that for the dabrowska estimator as applied to the entire dataset while some useful efficiency improvement arises for the corresponding distribution function estimator presumably due to the avoidance of negative mass assignments

nonlinearity detection in hyperspectral images using a polynomial post nonlinear mixing model this paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection the proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white gaussian noise these nonlinear functions are approximated by polynomials leading to a polynomial post nonlinear mixing model we have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods a generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model to compute the test statistic associated with the nonlinearity detection we propose to approximate the variance of the estimated nonlinearity parameter by its constrained cramer rao bound the performance of the detection strategy is evaluated via simulations conducted on synthetic and real data more precisely synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature the real data investigated in this study are extracted from the cuprite image which shows that some minerals seem to be nonlinearly mixed in this image finally it is interesting to note that the estimated abundance maps obtained with the post nonlinear mixing model are in good agreement with results obtained in previous studies

dynamic diffusion type equations on discrete space domains abstract we consider a class of partial dynamic equations on discrete space domains which includes as a special case the discrete space versions of the diffusion heat equation we focus on initial value problems and study the existence and uniqueness of forward and backward solutions moreover we discuss other topics such as sum and sign preservation maximum and minimum principles or symmetry of solutions

estimating the expected total number of events in a process we consider estimation of the cumulative mean function of a process recurring in time such as the numbers of arrests or migrations accrued by an individual as a function of their age we call this theage profile of a series of events in some situations we can expect a finite value for the total number of events experienced by an individual for example when the distribution of the interevent times is improper so that the process may cease at a finite time with positive probability we propose and analyze a new estimator constructed from kaplan meier km estimators of the interevent time distributions for such an age profile and compare it with the nelson aalen na estimator of the cumulative mean function of a process the km estimator is proved to be uniformly consistent for the age profile if and only if follow up in the sample is sufficient in a sense that is manifested in practice by the leveling off of the profiles at their right side ends and is asymptotically normally distributed around

assessment of uncertainty in high frequency data the observed asymptotic variance the availability of high frequency financial data has generated a series of estimators based on intra day data improving the quality of large areas of financial econometrics however estimating the standard error of these estimators is often challenging the root of the problem is that traditionally standard errors rely on estimating a theoretically derived asymptotic variance and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated standard errors are important they are used to assess the precision of estimators in the form of confidence intervals to create feasible statistics for testing to build forecasting models based on say daily estimates and also to optimize the tuning parameters the contribution of this paper is to provide an alternative and general solution to this problem which we call observed asymptotic variance it is a general nonparametric method for assessing asymptotic variance avar it provides consistent estimators of avar for a broad class of integrated parameters t dt where the spot parameter process can be a general semimartingale with continuous and jump components the observed avar is implemented with the help of a two scales method its construction works well in the presence of microstructure noise and when the observation times are irregular or asynchronous in the multivariate case the methodology is valid for a wide variety of estimators including the standard ones for variance and covariance and also for more complex estimators such as of leverage effects high frequency betas and semivariance

a result on projection for the vehicle routing ptoblem abstract in this paper we present a result on projection for the vehicle routing problem vrp the vrp is closely related to delivery type problems and appears in a large number of practical situations concerning the distribution of commodities the present work focuses on a commodity flow formulation presented by gavish and graves this formulation includes two sets of variables and hence it also must include coupling constraints between the two sets of variables these coupling constraints can be defined in several ways the main result of this work establishes that when the strongest form of the coupling constraints is used in the flow formulation the equivalent formulation using only the x ij variables satisfies the so called multistar constraints which for certain parameters induce facets of the non directed vrp polytope using an idea taken from gouveia we show how to derive a more compact representation in the number of constraints of the multistar constraints some consequences of our projection result are also discussed

functional censored quantile regression we propose a functional censored quantile regression model to describe the time varying relationship between time to event outcomes and corresponding functional covariates the time varying effect

hyperspectral unmixing in presence of endmember variability nonlinearity or mismodeling effects this paper presents three hyperspectral mixture models jointly with bayesian algorithms for supervised hyperspectral unmixing based on the residual component analysis model the proposed general formulation assumes the linear model to be corrupted by an additive term whose expression can be adapted to account for nonlinearities nls endmember variability ev or mismodeling effects mes the nl effect is introduced by considering a polynomial expression that is related to bilinear models the proposed new formulation of ev accounts for shape and scale endmember changes while enforcing a smooth spectral spatial variation the me formulation considers the effect of outliers and copes with some types of ev and nl the known constraints on the parameter of each observation model are modeled via suitable priors the posterior distribution associated with each bayesian model is optimized using a coordinate descent algorithm which allows the computation of the maximum a posteriori estimator of the unknown model parameters the proposed mixture and bayesian models and their estimation algorithms are validated on both synthetic and real images showing competitive results regarding the quality of the inferences and the computational complexity when compared with the state of the art algorithms

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

residual component analysis of hyperspectral images application to joint nonlinear unmixing and nonlinearity detection this paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection the proposed model assumes that the pixel reflectances are linear combinations of known pure spectral components corrupted by an additional nonlinear term affecting the end members and contaminated by an additive gaussian noise a markov random field is considered for nonlinearity detection based on the spatial structure of the nonlinear terms the observed image is segmented into regions where nonlinear terms if present share similar statistical properties a bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint nonlinear unmixing and nonlinearity detection algorithm the performance of the proposed strategy is first evaluated on synthetic data simulations conducted with real data show the accuracy of the proposed unmixing and nonlinearity detection strategy for the analysis of hyperspectral images

a flexible parametric approach for estimating continuous time inverse probability of treatment and censoring weights marginal structural cox models are used for quantifying marginal treatment effects on outcome event hazard function such models are estimated using inverse probability of treatment and censoring iptc weighting which properly accounts for the impact of time dependent confounders avoiding conditioning on factors on the causal pathway to estimate the iptc weights the treatment assignment mechanism is conventionally modeled in discrete time while this is natural in situations where treatment information is recorded at scheduled follow up visits in other contexts the events specifying the treatment history can be modeled in continuous time using the tools of event history analysis this is particularly the case for treatment procedures such as surgeries in this paper we propose a novel approach for flexible parametric estimation of continuous time iptc weights and illustrate it in assessing the relationship between metastasectomy and mortality in metastatic renal cell carcinoma patients copyright 2016 john wiley sons ltd

confidence bands for the median survival time as a function of the covariates in the cox model abstract let p x be the pth quantile of the distribution of the life length of an individual with covariate vector x in the cox model we introduce an estimator p x of p x and develop several families of confidence bands for x as a function of x to construct one type of band we proceed as follows we show that as n where n is the number of individuals in the study converges weakly to a gaussian process w x with a complicated covariance structure we then estimate this covariance structure from the data and simulate many gaussian processes with this estimated covariance structure the critical constants required for the construction of the confidence bands are obtained from the simulated processes another type of bands is obtained by bootstrapping we obtain an asymptotic theory for both types of bands simulation studies are used to compare the two types of bands the methods are illustrated on the stanford heart transplant data

the singularity of the information matrix of the mixed proportional hazard model this paper presents new identification conditions for the mixed proportional hazard model in particular the baseline hazard is assumed to be bounded away from 0 and near t 0 these conditions ensure that the information matrix is nonsingular the paper also presents an estimator for the mixed proportional hazard model that converges at rate n 1 2

dynamic equations on time scales and generalized ordinary differential equations abstract the aim of this paper is to show that dynamic equations on time scales can be treated in the framework of generalized ordinary differential equations as introduced by j kurzweil we also use some known results for generalized ordinary differential equations to obtain new theorems related to stability and continuous dependence on parameters for dynamic equations on time scales

fisher s information in terms of the hazard rate if g t is a regular family of probability densities on the real line with corresponding hazard rates h t then the fisher information for can be expressed in terms of the hazard rate as follows f g 2 g h h 2 g r where the dot denotes this identity shows that the hazard rate transform of a probability density has an unexpected length preserving property we explore this property is continuous and discrete settings some geometric consequences and curvature formulas its connection with martingale theory and its relation to statistical issues in the theory of life time distributions and censored data

pricing strategies for capacitated ring star problems based on dynamic programming algorithms abstract the capacitated m ring star problem crsp is the problem of designing a set of rings that pass through a central depot and through some transition points and or customers and then assigning each nonvisited customer to a visited point or customer the number of customers visited and connected to a ring is bounded by an upper limit the capacity of the ring the objective is to minimize the total routing cost plus assignment costs the problem has several applications in telecommunication network design and transportation planning in addition closely related versions to the crsp involving different graph topologies and objective functions have been recently studied by several authors the recent literature shows that effective methods for solving these class of difficult optimization problems are based on the combination of column and cut generation techniques in particular the effectiveness of these methods strongly depend on the qualities and complexities of the associated pricing problems in this paper we investigate different pricing strategies based on dynamic programming algorithms for the crsp that can also be adapted to deal with different graph topologies we describe a general bounding procedure based on column and cut generation that is used to test the effectiveness of the different pricing strategies we report an extensive computational analysis on crsp benchmark instances from the literature and on newly generated instances for its generalization to the multi depot case the multi depot ring star problem mdrsp the results obtained show the effectiveness of the pricing strategies proposed and that tight lower bounds can be computed for instances involving up to 431 nodes

quantile and probability curves without crossing this paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions also known as the quantile crossing problem bassett and koenker 1982 the method consists in sorting or monotone rearranging the original estimated non monotone curve into a monotone rearranged curve we show that the rearranged curve is closer to the true quantile curve than the original curve in finite samples establish a functional delta method for rearrangement related operators and derive functional limit theory for the entire rearranged curve and its functionals we also establish validity of the bootstrap for estimating the limit law of the entire rearranged curve and its functionals our limit results are generic in that they apply to every estimator of a monotone function provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions consequently our results apply to estimation of other econometric functions with monotonicity restrictions such as demand production distribution and structural distribution functions we illustrate the results with an application to estimation of structural distribution and quantile functions using data on vietnam veteran status and earnings

estimating regression parameters and degree of dependence for multivariate failure time data summary multivariate failure time data are frequently encountered in longitudinal studies when subjects may experience several events or when there is a grouping of individuals into a cluster to take into account the dependence of the failure times within the unit the individual or the cluster as well as censoring two multivariate generalizations of the cox proportional hazards model are commonly used the marginal hazard model is used when the purpose is to estimate mean regression parameters while the frailty model is retained when the purpose is to assess the degree of dependence within the unit we propose a new approach based on the combination of the two aforementioned models to estimate both these quantities this two step estimation procedure is quicker and more simple to implement than the em algorithm used in frailty models estimation simulation results are provided to illustrate robustness consistency and large sample properties of estimators finally this method is exemplified on a diabetic retinopathy study in order to assess the effect of photocoagulation in delaying the onset of blindness as well as the dependence between the two eyes blindness times of a patient

algebraic theory of product integrals in quantum stochastic calculus motivated by the search for solutions of the quantum yang baxter equation an algebraic theory of quantum stochastic product integrals is developed the product integrators are formal power series in an indeterminate h whose coefficients are elements of the lie algebra l labelling the usual integrators of a many dimensional quantum stochastic calculus the product integrals are also formal power series in h whose coefficients are finite iterated additive stochastic integrals which act on the exponential domain in the fock space of the calculus and which represent elements of the universal enveloping algebra u of l they obey a multiplication rule suggested by the quantum ito product formula and are characterized among all such formal power series by a grouplike property

nonparametric estimation for a general repair model the construction and analysis of repair models is an important area in reliability a commonly used model is the minimal repair model under this model repair restores the state of the system to its level prior to failure kijima introduced repair models that could be classified as better than minimal under kijima s models the system upon repair is functionally the same as a working system of lesser age which has never experienced failure in this paper we present a new approach to the modeling of better than minimal repair models using this approach we construct a general repair model that contains kijima s models as special cases we also study the problem of estimating the distribution of the time to first failure of a system maintained by general repair we make use of counting processes to show strong consistency of the estimator and prove results on weak convergence finally we derive a hall wellner type asymptotic confidence band for the distribution of the time to first failure of the system

bayesian estimation of linear mixtures using the normal compositional model application to hyperspectral imagery this paper studies a new bayesian unmixing algorithm for hyperspectral images each pixel of the image is modeled as a linear combination of so called endmembers these endmembers are supposed to be random in order to model uncertainties regarding their knowledge more precisely we model endmembers as gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous n finder n findr or vertex component analysis vca algorithms this paper proposes to estimate the mixture coefficients referred to as abundances using a bayesian algorithm suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters a hybrid gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances the performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images

censored regression with the multistate accelerated sojourn times model many disease processes are characterized by two or more successive health states and it is often of interest and importance to assess state specific covariate effects however with incomplete follow up data such inference has not been satisfactorily addressed in the literature we model the logarithm transformed sojourn time in each state as linearly related to the covariates however neither the distributional form of the error term nor the dependence structure of the states needs to be specified we propose a regression procedure to accommodate incomplete follow up data asymptotic theory is presented along with some tools for goodness of fit diagnostics simulation studies show that the proposal is reliable for practical use we illustrate it by application to a cancer clinical trial

efficient estimation of linear functionals of a probability measure p with known marginal distributions suppose that p is the distribution of a pair of random variables x y on a product space x x v with known marginal distributions px and py we study efficient estimation of functions 0 h fh dp for fixed h x x y r under iid sampling of x y pairs from p and a regularity condition on p our proposed estimator is based on partitions of both x and v and the modified minimum chi square estimates of deming and stephan 1940 the asymptotic behavior of our estimator is governed by the projection on a certain sum subspace of l2 p or equivalently by a pair of equations which we call the ace equations

hyperspectral image classification through bilayer graph based learning hyperspectral image classification with limited number of labeled pixels is a challenging task in this paper we propose a bilayer graph based learning framework to address this problem for graph based classification how to establish the neighboring relationship among the pixels from the high dimensional features is the key toward a successful classification our graph learning algorithm contains two layers the first layer constructs a simple graph where each vertex denotes one pixel and the edge weight encodes the similarity between two pixels unsupervised learning is then conducted to estimate the grouping relations among different pixels these relations are subsequently fed into the second layer to form a hypergraph structure on top of which semisupervised transductive learning is conducted to obtain the final classification results our experiments on three data sets demonstrate the merits of our proposed approach which compares favorably with state of the art

an efficient evolutionary algorithm for the ring star problem abstract this paper addresses the ring star problem rsp the goal is to locate a cycle through a subset of nodes of a network aiming to minimize the sum of the cost of installing facilities on the nodes on the cycle the cost of connecting them and the cost of assigning the nodes not on the cycle to their closest node on the cycle a fast and efficient evolutionary algorithm is developed which is based on a new formulation of the rsp as a bilevel programming problem with one leader and two independent followers the leader decides which nodes to include in the ring one follower decides about the connections of the cycle and the other follower decides about the assignment of the nodes not on the cycle the bilevel approach leads to a new form of chromosome encoding in which genes are associated to values of the upper level variables the quality of each chromosome is evaluated by its fitness by means of the objective function of the rsp hence in order to compute the value of the lower level variables two optimization problems are solved for each chromosome the computational results show the efficiency of the algorithm in terms of the quality of the solutions yielded and the computing time a study to select the best configuration of the algorithm is presented the algorithm is tested on a set of benchmark problems providing very accurate solutions within short computing times moreover for one of the problems a new best solution is found

product limit estimators of the survival function with twice censored data a model for competing resp complementary risks survival data where the failure time can be left resp right censored is proposed product limit estimators for the survival functions of the individual risks are derived we deduce the strong convergence of our estimators on the whole real half line without any additional assumptions and their asymptotic normality under conditions concerning only the observed distribution when the observations are generated according to the double censoring model introduced by turnbull the product limit estimators represent upper and lower bounds for turnbull s estimator

on summability multipliability product integrability and parallel translation abstract in this paper we provide necessary and sufficient conditions for the existence of the kurzweil mcshane and riemann product integrals of step mappings with well ordered steps and for right regulated mappings with values in banach algebras our basic tools are the concepts of summability and multipliability of families in normed algebras indexed by well ordered subsets of the real line these concepts also lead to the generalization of some results from the usual theory of infinite series and products finally we present two applications of product integrals first we describe the relation between stieltjes type product integrals haahti products and parallel translation operators second we provide a link between the theory of strong kurzweil product integrals and strong solutions of linear generalized differential equations

nonlinear unmixing of hyperspectral data based on a linear mixture nonlinear fluctuation model spectral unmixing is an important issue to analyze remotely sensed hyperspectral data although the linear mixture model has obvious practical advantages there are many situations in which it may not be appropriate and could be advantageously replaced by a nonlinear one in this paper we formulate a new kernel based paradigm that relies on the assumption that the mixing mechanism can be described by a linear mixture of endmember spectra with additive nonlinear fluctuations defined in a reproducing kernel hilbert space this family of models has clear interpretation and allows to take complex interactions of endmembers into account extensive experiment results with both synthetic and real images illustrate the generality and effectiveness of this scheme compared with state of the art methods

choosing the resampling scheme when bootstrapping a case study in reliability abstract often when dealing with complex data structures there is no unique way to bootstrap if the data can be viewed as u 1 u n iid from some distribution p then one can bootstrap by resampling the u s alternately one can resample in a more model based way that is by making use of the structure of the model p a typical example of this is linear regression in which the data is y i x i i 1 n one can resample the pairs y i x i or one can resample the residuals from a fitted model this phenomenon arises over quite a wide spectrum of problems and in many cases the different methods of bootstrapping can give substantially different results it seems hopeless to come up with a general theory that compares the different ways of bootstrapping in this article we study in some detail a certain model that arises in reliability theory in which there are two natural ways to bootstrap this model is described as follows available for testing is a sample of n iid systems each having t

additive hazards markov regression models illustrated with bone marrow transplant data summary when there are covariate effects to be considered multi state survival analysis is dominated either by parametric markov regression models or by semiparametric markov regression models using cox s 1972 proportional hazards models for transition intensities between the states the purpose of this research work is to study alternatives to cox s model in a general finite state markov process setting we shall look at two alternative models aalen s 1989 nonparametric additive hazards model and lin ying s 1994 semiparametric additive hazards model the former allows the effects of covariates to vary freely over time while the latter assumes that the regression coefficients are constant over time with the basic tools of the product integral and the functional delta method we present an estimator of the transition probability matrix and develop the large sample theory for the estimator under each of these two models data on 1459 hla identical sibling transplants for acute leukaemia from the international bone marrow transplant registry serve as illustration

multistars partial multistars and the capacitated vehicle routing problem in an unpublished paper araque hall and magnanti considered polyhedra associated with the capacitated vehicle routing problem cvrp in the special case of unit demands among the valid and facet inducing inequalities presented in that paper were the so called multistar and partial multistar inequalities each of which came in several versions some related inequalities for the case of general demands have appeared subsequently and the result is a rather bewildering array of apparently different classes of inequalities the main goal of the present paper is to present two relatively simple procedures that can be used to show the validity of all known and some new multistar and partial multistar inequalities in both the unit and general demand cases the procedures provide a unifying explanation of the inequalities and perhaps more importantly ideas that can be exploited in a cutting plane algorithm for the cvrp computational results show that the new inequalities can be useful as cutting planes for certain cvrp instances

nonparametric estimation of a bivariate survival function in the presence of censoring a new family of estimators of a bivariate survival function based on censored vectors is obtained from a decomposition of the bivariate survival function these estimators are uniformly consistent under bivariate censoring and are self consistent under univariate censoring

bayesian curve fitting using mcmc with applications to signal segmentation we propose some bayesian methods to address the problem of fitting a signal modeled by a sequence of piecewise constant linear in the parameters regression models for example autoregressive or volterra models a joint prior distribution is set up over the number of the changepoints knots their positions and over the orders of the linear regression models within each segment if these are unknown hierarchical priors are developed and as the resulting posterior probability distributions and bayesian estimators do not admit closed form analytical expressions reversible jump markov chain monte carlo mcmc methods are derived to estimate these quantities results are obtained for standard denoising and segmentation of speech data problems that have already been examined in the literature these results demonstrate the performance of our methods

nonlinear spectral unmixing of hyperspectral images using gaussian processes this paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images the proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components we assume that the spectral signatures of the pure components and the nonlinear function are unknown the first step of the proposed method estimates the abundance vectors for all the image pixels using a bayesian approach an a gaussian process latent variable model for the nonlinear function relating the abundance vectors to the observations the endmembers are subsequently estimated using gaussian process regression the performance of the unmixing strategy is first evaluated on synthetic data the proposed method provides accurate abundance and endmember estimations when compared to other linear and nonlinear unmixing strategies an interesting property is its robustness to the absence of pure pixels in the image the analysis of a real hyperspectral image shows results that are in good agreement with state of the art unmixing strategies and with a recent classification method

robust inference for event probabilities with non markov event data summary multistate event data in which a single subject is at risk for multiple events is common in biomedical applications this article considers nonparametric estimation of the vector of probabilities of state membership at time t estimators derived under the markov assumption have been shown datta and satten 2001 statistics and probability letters55 403 411 to be consistent for data that is non markov inference however must take into account possibly non markov transitions when constructing confidence bands for event curves we develop robust confidence bands for these curves evaluate them via simulation and illustrate the method on two datasets

on the capacitated vehicle routing problem we consider the vehicle routing problem in which a fixed fleet of delivery vehicles of uniform capacity must service known customer demands for a single commodity from a common depot at minimum transit cost this difficult combinatorial problem contains both the bin packing problem and the traveling salesman problem tsp as special cases and conceptually lies at the intersection of these two well studied problems the capacity constraints of the integer programming formulation of this routing model provide the link between the underlying routing and packing structures we describe a decomposition based separation methodology for the capacity constraints that takes advantage of our ability to solve small instances of the tsp efficiently specifically when standard procedures fail to separate a candidate point we attempt to decompose it into a convex combination of tsp tours if successful the tours present in this decomposition are examined for violated capacity constraints if not the farkas theorem provides a hyperplane separating the point from the tsp polytope we present some extensions of this basic concept and a general framework within which it can be applied to other combinatorial models computational results are given for an implementation within the parallel branch cut and price framework symphony

the capacitated m ring star problem the capacitated m ring star problem cmrsp is the problem of designing a set of rings that pass through a central depot and through some transition points and or customers and then assigning each nonvisited customer to a visited point or customer the number of customers visited and assigned to a ring is bounded by an upper limit the capacity of the ring the objective is to minimize the total routing cost plus assignment costs the problem has practical applications in the design of urban optical telecommunication networks this paper presents and discusses two integer programming formulations for the cmrsp valid inequalities are proposed to strengthen the linear programming relaxation and are used as cutting planes in a branch and cut approach the procedure is implemented and tested on a large family of instances including real world instances and the good performance of the proposed approach is demonstrated