an approach to parameter estimation and stochastic control in water resources with an application to reservoir operation this paper presents an algorithm for the estimation of parameters in state space models that represent hydrologic processes in which the state variables are observed with error the algorithm is based on the maximization of the conditional expectation of the likelihood function of the state equation the estimation algorithm is numerically stable and guarantees local convergence under mild conditions it is also shown that the estimation algorithm can be coupled with an optimal control method to yield a combined control estimation technique that can be easily implemented an application of the theory and methods developed herein is given for flood routing via reservoir operation

nonparametric estimation of successive duration times under dependent censoring summary this paper considers nonparametric inference for duration times of two successive events since the second duration process becomes observable only if the first event has occurred the length of the first duration affects the probability of the second duration being censored dependent censoring arises if the two duration times are correlated which is often the case standard approaches to this problem fail because of dependent censoring mechanism a new product limit estimator for the second duration variable and a pathdependent joint survival function estimator are proposed both modified for the dependent censoring properties of the estimators are discussed an example from lawless 1982 is studied for illustrative purposes as well as a simulation study

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

slab percolation for the ising model for the fk representation of the ising model we prove that the slab percolation threshold coincides with the critical temperature in any dimension d 3

improved dynamic programming methods for optimal control of lumped parameter stochastic systems new dynamic programming methods are developed to solve stochastic control problems with a larger number of state variables than previously possible these methods apply accurate interpolation to numerical approximation of continuous cost to go functions greatly reducing the number of discrete states that must be evaluated by efficiently incorporating information on first and second derivatives the approximation reduces computational effort by several orders of magnitude over traditional methods consequently it is practical to apply dynamic programming to complex stochastic problems with a larger number of state variables than traditionally possible results are presented for hypothetical reservoir control problems with up to seven state variables and two random inputs

an upper bound on the critical percolation probability for the three dimensional cubic lattice we prove that the critical probability for site percolation on the three dimensional cubic lattice satisfies the inequality p 3 c 1 2 an application to the three dimensional ising model is given

fitting continuous arma models to unequally spaced spatial data abstract methods for fitting continuous spatial autoregressive moving average arma models to unequally spaced observations in two dimensions are reviewed and extended these are models with rational two dimensional spectra assuming gaussian input noise and observational errors maximum likelihood methods are used to estimate the arma parameters and the regression coefficients of the deterministic trend when the number of observations is too large for exact maximum likelihood estimation approximate maximum likelihood estimation is used based on nearest neighbors comparisons of nearest neighbor methods with exact likelihood methods are presented predictions of the height of the field at unobserved points can be calculated with confidence intervals

semiparametric analysis of the additive risk model in contrast to the proportional hazards model the additive risk model specifies that the hazard function associated with a set of possibly time varying covariates is the sum of rather than the product of the baseline hazard function and the regression function of covariates this formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model and is more plausible than the latter for many applications in the present paper simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function

numerical solution of continuous state dynamic programs using linear and spline interpolation this paper demonstrates that the computational effort required to develop numerical solutions to continuous state dynamic programs can be reduced significantly when cubic piecewise polynomial functions rather than tensor product linear interpolants are used to approximate the value function tensor product cubic splines represented in either piecewise polynomial or b spline form and multivariate hermite polynomials are considered computational savings are possible because of the improved accuracy of higher order functions and because the smoothness of higher order functions allows efficient quasi newton methods to be used to compute optimal decisions the use of the more efficient piecewise polynomial form of the spline was slightly superior to the use of hermite polynomials for the test problem and easier to program in comparison to linear interpolation use of splines in piecewise polynomial form reduced the cpu time to obtain results of equivalent accuracy by a factor of 250 330 for a stochastic

locality of percolation for abelian cayley graphs we prove that the value of the critical probability for percolation on an abelian cayley graph is determined by its local structure this is a partial positive answer to a conjecture of schramm the function pcpc defined on the set of cayley graphs of abelian groups of rank at least 22 is continuous for the benjamini schramm topology the proof involves group theoretic tools and a new block argument

inferences on the association parameter in copula models for bivariate survival data we investigate two stage parametric and two stage semi parametric estimation procedures for the association parameter in copula models for bivariate survival data where censoring in either or both components is allowed we derive asymptotic properties of the estimators and compare their performance by simulations both parametric and semi parametric estimators of the association parameter are efficient at independence and the parameter estimates in the margins have high efficiency and are robust to misspecification of dependency structures in addition we propose a consistent variance estimator for the semi parametric estimator of the association parameter we apply the proposed methods to an aids data set for illustration

a nonparametric test for panel count data summary panel count data arise when a recurrent event is under investigation and each study subject is observed only at discrete time points in this situation observed data include only the numbers of occurrences of the event of interest between observation time points and no information is available on subjects between their observation time points we propose a nonparametric test for comparing the point processes characterising the recurrent event when only panel count data are available the asymptotic distribution of the test statistic is derived and a simulation study is conducted to evaluate its performance the method is illustrated using data from a medical follow up study

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

a semiparametric model for randomly truncated data abstract for randomly censored data it is known that the maximum likelihood estimate mle of the survival curve is not affected by parametric assumption on the censoring variable the kaplan meier 1958 estimate is the mle for both nonparametric and semiparametric models for randomly truncated data the truncation product limit estimate is the mle for nonparametric models this is not the case if the truncation mechanism is parameterized however specifically let x be a generic random variable and t be the truncation variable if the distribution of t is parameterized and the distribution of x is left unspecified it can be shown that the truncation product limit estimate is not the mle for this semiparametric model even though it is for the fully nonparametric model in this article the mle is characterized for the semiparametric model and the large sample properties of the estimate are established the results show that unlike censoring the parametric information from the truncation mechanism

nonparametric estimation of the gap time distributions for serial events with censored data summary in many follow up studies each subject can potentially experience a series of events which may be repetitions of essentially the same event or may be events of entirely diverent natures this paper provides a simple nonparametric estimator for the multivariate distribution function of the gap times between successive events when the follow up time is subject to right censoring the estimator is consistent and upon proper normalisation converges weakly to a zero mean gaussian process with an easily estimated covariance function numerical studies demonstrate that both the distribution function estimator and its covariance function estimator perform well for practical sample sizes an application to a colon cancer study is presented

real time forecasting and daily operation of a multireservoir system during floods by linear quadratic gaussian control the problem of short term daily operation of a multireservoir system during floods is examined the problem is how to use all available real time information to solve the tactical problem of regulating reservoirs to minimize the expected value of flood damage during a relatively short operating horizon and to do so consistently with the long term operating strategy a state space mathematical model is presented for short term forecasting of river flows and description of the dynamics of a multireservoir system the model includes reduced order state space unit hydrographs to forecast storm runoff from effective rainfall and state space representations of linear flood routing the optimization problem is solved in the framework of discrete time linear quadratic gaussian lqg control lqg control is a computationally efficient and flexible method of solving the large dimensional optimization problems associated with the solution of the tactical problem of short term operation of reservoirs for application of the lqg control methodology the system must be represented in state space form with quadratic cost functions subject to linear equality constraints given by the state transition equations the scheme was found to be suitable for operation under moderate flood conditions when capacity constraints are not likely to become binding the methodology has been applied and tested in a real world case

estimation and model selection of semiparametric multivariate survival functions under general censorship we study estimation and model selection of semiparametric models of multivariate survival functions for censored data which are characterized by possibly misspecified parametric copulas and nonparametric marginal survivals we obtain the consistency and root n asymptotic normality of a two step copula estimator to the pseudo true copula parameter value according to klic and provide a simple consistent estimator of its asymptotic variance allowing for a first step nonparametric estimation of the marginal survivals we establish the asymptotic distribution of the penalized pseudo likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship an empirical application is provided

the supercritical phase of percolation is well behaved we prove a general result concerning the critical probabilities of subsets of a lattice l it is a consequence of this result that the critical probability of a percolation process on l equals the limit of the critical probability of a slice of l as the thickness of the slice tends to infinity this verification of one of the standard hypotheses of the subject settles many questions concerning supercritical percolation

error analysis of conventional discrete and gradient dynamic programming an asymptotic error analysis of the conventional discrete dynamic programming ddp method is presented and upper bounds of the error in the control policy i e the difference of the estimated and true optimal control at each operation period are computed this error is shown to be of the order of the state discretization interval as a result with significant implications in the optimization of multistate systems where the curse of dimensionality restricts the number of states to a relatively small number the error in the optimal cost varies with as 2 the analysis provides useful insights into the effects of state discretization on calculated control and cost functions the comparability of results from different discretizations and criteria about the required number of nodes in an effort to reduce the discretization error in the case of smooth cost functions a new discrete dynamic programming method termed gradient dynamic programming gdp is proposed gdp uses a piecewise hermite interpolation of the cost to go function at each stage which preserves the values of the cost to go function and of its first derivatives at the discretization nodes the error in the control policy is shown to be of the order of as 3 and the error in the cost to vary with as thus as as decreases gdp converges to the true optimum much more rapidly than ddp another major advantage of the new methodology is that it facilitates the use of newton type iterative methods in the solution of the nonlinear optimization problems at each stage the linear convergence of ddp and the superlinear convergence of gdp are illustrated in an example

gradient dynamic programming for stochastic optimal control of multidimensional water resources systems a new computational algorithm is presented for the solution of discrete time linearly constrained stochastic optimal control problems decomposable in stages the algorithm designated gradient dynamic programming is a backward moving stagewise optimization the main innovations over conventional discrete dynamic programming ddp are in the functional representation of the cost to go function and the solution of the single stage problem the cost to go function assumed to be of requisite smoothness is approximated within each element defined by the discretization scheme by the lowest order polynomial which preserve its values and the values of its gradient with respect to the state variables at all nodes of the discretization grid the improved accuracy of this hermitian interpolation scheme reduces the effect of discretization error and allows the use of coarser grids which reduces the dimensionality of the problem at each stage the optimal control is determined on each node of the discretized state space using a constrained newton type optimization procedure which has quadratic rate of convergence the set of constraints which act as equalities is determined from an active set strategy which converges under lenient convexity requirements this method of solving the single stage optimization is much more efficient than the conventional way based on enumeration or iterative methods with linear rate of convergence once the optimal control is determined the cost to go function and its gradient with respect to the state variables is calculated to be used at the next stage the proposed technique permits the efficient optimization of stochastic systems whose high dimensionality does not permit solution under the conventional ddp framework and for which successive approximation methods are not directly applicable due to stochasticity results for a four reservoir example are presented the purpose of this paper is to present a new computational algorithm for the stochastic optimization of sequential decision problems one important and extensively studied class of such problems in the area of water resources is the discrete time optimal control of multireservoir systems under stochastic inflows other applications include the optimal design and operation of sewer systems e g mays and wenzel 1976 labadie et al 1980 the optimal conjunctive utilization of surface and groundwater resources e g buras 1972 and the minimum cost water quality maintenance in rivers e g dracup and fogarty 1974 chang and yeh 1973 to mention only a few of the water resources applications and pertinent references an extensive review of dynamic programming applications in water resources can be found in the works by yakowitz 1982 and yeh 1985 before we proceed with the

nonparametric inference on bivariate survival data with interval sampling association estimation and testing in many biomedical applications interest focuses on the occurrence of two or more consecutive failure events and the relationship between event times such as age of disease onset and residual lifetime bivariate survival data with interval sampling arise frequently when disease registries or surveillance systems collect data based on disease incidence occurring within a specific calendar time interval the initial event is then retrospectively confirmed and the subsequent failure event may be observed during follow up in life history studies the initial and two consecutive failure events could correspond to birth disease onset and death the statistical features and bias of observed data in relation to interval sampling were discussed by zhu wang 2012 here we propose nonparametric estimation of the association between bivariate failure times based on kendall s tau for data collected with interval sampling a nonparametric estimator is given where the contribution of each comparable and orderable pair is weighted by the inverse of the associated selection probability analysis methods for bivariate survival data with interval sampling rely on the assumption of quasi independence i e that bivariate failure times and the time of the initial event are independent in the observable region this paper develops a nonparametric test of quasi independence based on a bivariate conditional kendall s tau for such data simulation studies demonstrate that the association estimator and testing procedure perform well with moderate sample sizes illustrations with two real datasets are provided

extended linear quadratic gaussian control further extensions the extended linear quadratic gaussian elqg control method georgakakos and marks 1987 is a stochastic control algorithm for the optimal operation of multiobjective reservoirs mathematically this method optimizes a general functional of a stochastic system in state space form with upper and lower release constraints and probabilistic storage bounds elqg is a sequential algorithm which accounts for stochastic effects by preserving the first two statistical moments of the system s inputs and storages in this paper the method is first extended to handle nongaussian features which frequently characterize reservoir inputs second elqg s efficiency with respect to reliability storage constraints is discussed and a new barrier function method is researched these modifications are tested in case studies with the savannah river system

analysing bivariate survival data with interval sampling and application to cancer epidemiology in biomedical studies ordered bivariate survival data are frequently encountered when bivariate failure events are used as outcomes to identify the progression of a disease in cancer studies interest could be focused on bivariate failure times for example time from birth to cancer onset and time from cancer onset to death this paper considers a sampling scheme termed interval sampling in which the first failure event is identified within a calendar time interval the time of the initiating event can be retrospectively confirmed and the occurrence of the second failure event is observed subject to right censoring in a cancer data application the initiating first and second events could correspond to birth cancer onset and death the fact that the data are collected conditional on the first failure event occurring within a time interval induces bias interval sampling is widely used for collection of disease registry data by governments and medical institutions though the interval sampling bias is frequently overlooked by researchers this paper develops statistical methods for analysing such data semiparametric methods are proposed under semi stationarity and stationarity numerical studies demonstrate that the proposed estimation approaches perform well with moderate sample sizes we apply the proposed methods to ovarian cancer registry data

density and uniqueness in percolation two results on site percolation on thed dimensional lattice d 1 arbitrary are presented in the first theorem we show that for stationary underlying probability measures each infinite cluster has a well defined density with probability one the second theorem states that if in addition the probability measure satisfies the finite energy condition of newman and schulman then there can be at most one infinite cluster with probability one the simple arguments extend to a broad class of finite dimensional models including bond percolation and regular lattices

nonparametric methods for doubly truncated data abstract truncated data play an important role in the statistical analysis of astronomical observations as well as in survival analysis the motivating example for this article concerns a set of measurements on quasars in which there is double truncation that is the quasars are observed only if their luminosity occurs within a certain finite interval bounded at both ends with the interval varying for different observations nonparametric methods for the testing and estimation of doubly truncated data are developed these methods extend some known techniques for data that are truncated only on one side in particular lynden bell s estimator and the truncated version of kendall s tau statistic however the kind of hazard function arguments that underlie the one sided methods fail for two sided truncation bootstrap and markov chain monte carlo techniques are used here in their place finally we apply these techniques to the quasar data answering a question about their long term luminosity evolution

nonparametric estimation of the bivariate survival function with an application to vertically transmitted aids summary in this paper we propose a nonparametric estimator of the bivariate survival function when the two durations are subject to right censoring we consider the situation where the duration variables are successive and are always observed in a particular order and the censoring mechanism bears on their sum rather than on each separately thus if they are correlated the second duration is right censored by a dependent variable a nonparametric maximum likelihood estimator is derived that takes the dependent censoring into account we also derive the asymptotic variance of the estimator and show how it can be estimated the methods are applied on a vertically acquired mother to child transmission aids data set the first duration corresponds to the hiv incubation period and the second to the period of aids

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

convex interpolation for gradient dynamic programming local approximation of functions based on values and derivatives at the nodes of a discretized grid are often used in solving problems numerically for which analytical solutions do not exist in gradient dynamic programming foufoula georgiou and kitanidis 1988 the use of such functions for the approximation of the cost to go function alleviates the curse of dimensionality by reducing the number of discretization nodes per state while obtaining high accuracy solutions also efficient newton type schemes can be used for the stage wise optimization since now the approximation functions have continuous first derivatives our interest is in the case where the cost to go function is convex however the interpolants may not always be convex introducing numerical problems in this paper we address the problem of interpolating nodal values and derivatives of a one dimensional convex function with a convex interpolant so that potential computational difficulties due to approximation induced nonconvexity are avoided and an efficient convergence to global instead of local optimal controls is guaranteed at every single stage optimization

is the critical percolation probability local we show that the critical probability for percolation on a d regular non amenable graph of large girth is close to the critical probability for percolation on an infinite d regular tree we also prove a finite analogue of this statement valid for expander graphs without any girth assumption

mixture cure survival models with dependent censoring summary the paper is motivated by cure detection among the prostate cancer patients in the national institutes of health surveillance epidemiology and end results programme wherein the main end point e g deaths from prostate cancer and the censoring causes e g deaths from heart diseases may be dependent although many researchers have studied the mixture survival model to analyse survival data with non negligible cure fractions none has studied the mixture cure model in the presence of dependent censoring to account for such dependence we propose a more general cure model that allows for dependent censoring we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time by using a class of archimedean copula models within this framework we consider the parameter estimation the cure detection and the two sample comparison of latency distributions in the presence of dependent censoring when a proportion of patients is deemed cured large sample results by using martingale theory are obtained we examine the finite sample performance of the proposed methods via simulation and apply them to analyse the surveillance epidemiology and end results prostate cancer data