a size correction to the lagrange multiplier test for heteroskedasticity abstract making use by the recent work by harris this paper provides the formula for size correction to the lagrange multiplier test for heteroskedasticity monte carlo experiments indicate that our size correction is effective in improving the accuracy of the size of the test since the lagrange multiplier test tends to have a true size less than the nominal size in our experiments the application of the test at a higher true significance level tends to increase the power of the test as well reasonable results in our numerical experiments also give a partial check on the validity of the derived formula

modelling extreme multivariate events summary the classical treatment of multivariate extreme values is through componentwise ordering though in practice most interest is in actual extreme events here the point process of observations which are extreme in at least one component is considered parametric models for the dependence between components must satisfy certain constraints two new techniques for generating such models are presented aspects of the statistical estimation of the resulting models are discussed and are illustrated with an application to oceanographic data

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

fisher information for a bivariate extreme value distribution summary a representation of lee 1979 is used to give an explicit algebraic formula for the 5 x 5dimensional fisher information matrix for gumbel s 1960 bivariate type ii distribution of extreme values with weibull marginals numerical evaluations show that our parameterization makes the dependence parameter almost exactly orthogonal to the two marginal scale parameters

on site samples regression problems of non negative integers truncation and endogenous stratification abstract the paper corrects an estimation problem that has not yet been recognized in previous estimates of demand functions using on site samples there are three kinds of problems that one faces in on site samples namely non negative integers truncation and endogenous stratification two theoretically correct maximum likelihood methods are developed based on two different assumptions about the variable distribution the normal distribution and the poisson distribution a simulation is performed to compare the two methods using generated data sets of known models we should not use ols and instead should use the maximum likelihood methods developed here to estimate demand functions that use on site samples if forecasting is the purpose of estimation then the simulation indicates that the poisson ml method may be better

parallel depth first search in general directed graphs a directed cycle separator of an n vertex directed graph is a vertex simple directed cycle such that when the vertices of the cycle are deleted the resulting graph has no strongly connected component with more than n 2 vertices it is shown that the problem of finding a directed cycle separator is in randomized nc it is also proved that computing cycle separators and conducting depth first search in directed graphs are deterministically nc equivalent these two results together yield the first randomized nc algorithm for depth first search in general directed graphs

variance of the truncated negative binomial distribution abstract citations to formulas for the moments of the truncated negative binomial distribution usually reference the paper by gurmu and trivedi 1992 however their second moments of the truncated negative binomial are incorrect we derive the correct second moments for both the left and right truncated negative binomial distribution the second moments of the truncated distributions are written in a form that shows they will converge to the second moment of the un truncated distribution when the truncated first moment approaches the un truncated first moment

randomness optimal unique element isolation withapplications to perfect matching and related problems in this paper we precisely characterize the randomness complexity of the unique element isolation problem a crucial step in the rnc algorithm for perfect matching due to mulmuley vazirani and vazirani combinatorica 7 1987 pp 105 113 and in several other applications given a set s and an unknown family cal f subseteq 2 s with cal f leq z we present a scheme to assign polynomially bounded weights to the elements of s using only o log z log s random bits such that the minimum weight set in cal f is unique with high probability this generalizes the solution of mulmuley vazirani and vazirani who use o s log s bits independent of z we also provide a matching lower bound for the randomness complexity of this problem the new weight assignment scheme yields a randomness efficient rnc 2 algorithm for perfect matching which uses o log z log n random bits where z is any given upper bound on the number of perfect matchings in the input graph this generalizes the result of grigoriev and karpinski proc ieee symposium on foundations of computer science 1987 pp 166 172 who present an nc 3 algorithm when z is polynomial and also improves the running time in this case the worst case randomness complexity of our algorithm is o n log m n random bits improving on the previous bound of o m log n our scheme also gives randomness efficient solutions for several problems where unique element isolation is used such as rnc algorithms for variants of matching and basic problems on linear matroids we obtain a randomness efficient random reduction from sat to usat the language of uniquely satisfiable formulas which can be derandomized in the case of languages in fewp to yield new proofs of the results fewp subseteq oplus p and fewp subseteq c p

diagnostic testing and evaluation of maximum likelihood models abstract the paper develops a unified theory of likelihood specification testing based on m estimators of auxiliary parameters the theory is sufficiently general to encompass a wide class of specification tests including moment based tests pearson type goodness of fit tests the information matrix test and the cox test the paper also presents a framework based on frechet differentiation for determining the effects of misspecification on the almost sure limits of parameter estimates and specification test statistics

polylog time and near linear work approximation scheme for undirected shortest paths shortest paths computations constitute one of the most fundamental network problems nonetheless known parallel shortest paths algorithms are generally inefficient they perform significantly more work product of time and processors than their sequential counterparts this gap known in the literature as the transitive closure bottleneck poses a long standing open problem our main result is an o mn e 0 s m n1 e 0 work polylog time randomized algorithm that computes paths within 1 o 1 polylog n of shortest from s source nodes to all other nodes in weighted undirected networks with n nodes and m edges for any fixed e 0 0 this work bound nearly matches the o d sm sequential time in contrast previous polylog time algorithms required nearly min o d n3 o d m2 work even when s 1 and previous near linear work algorithms required near o n time we also present faster sequential algorithms that provide good approximate distances only between distant vertices we obtain an o m sn n e 0 time algorithm that computes paths of weight 1 o 1 polylog n dist o w max polylog n where dist is the corresponding distance and w max is the maximum edge weight our chief instrument which is of independent interest are efficient constructions of sparse hop sets a d e hop set of a network g v e is a set e of new weighted edges such that mimimum weight d edge paths in v e e have weight within 1 e of the respective distances in g we construct hop sets of size o n1 e 0 where e o 1 polylog n and d o polylog n

a count data model with unobserved heterogeneity abstract a count data model is defined via the distribution of the durations between successive events it is assumed that the durations follow independent exponential distributions conditionally to a set of variables the parameters of these distributions depend not only on observed and unobserved individual specific factors but also on unobserved spell specific factors the count data model is therefore a natural extension of the compound poisson model a local version of the count data model is used to analyse the effects of unobserved spell specific factors in particular it is shown that spell specific heterogeneity can induce not only overdispersion but also underdispersion the local model is also used to construct a score test for spell specific heterogeneity in the poisson model the results are applied on purchase data of a consumption good

specification and testing of some modified count data models abstract this paper explores the specification and testing of some modified count data models these alternatives permit more flexible specification of the data generating process dgp than do familiar count data models e g the poisson and provide a natural means for modeling data that are over or underdispersed by the standards of the basic models in the cases considered the familiar forms of the distributions result as parameter restricted versions of the proposed modified distributions accordingly score tests of the restrictions that use only the easily computed ml estimates of the standard models are proposed the tests proposed by hausman 1978 and white 1982 are also considered the tests are then applied to count data models estimated using survey microdata on beverage consumption

bipartite perfect matching is in quasi nc we show that the bipartite perfect matching problem is in quasi mathsf nc 2 that is it has uniform circuits of quasi polynomial size n o log n and o log 2 n depth previously only

parallel search algorithms for graphs and trees abstract this paper surveys parallel algorithms for tree traversal and graph search techniques the principal model of computation considered here is the parallel random access machine in this model each processor can access any cell of a shared memory in unit time thus the issue of interprocessor communication do not get intermixed with the logical structure of parallel algorithms the paper is organized into four major sections section 2 deals with tree traversals there are three main algorithms that differ completely from one another in approach in absolute terms however all require a specific input form or designed to preprocess the input in desired form section 3 presents parallel algorithms for breadth first search of general graphs there are two major techniques for developing efficient parallel algorithms for breadth first search of a graph one is based on computation of shortest paths in a uniformly positive edge weighted graph the other is based on tree merging technique section 4 is devoted to parallel algorithms for depth first search of graphs considering the importance of depth first search as a general paradigm for algorithmic solution of several graph problem there have been lot of efforts to design efficient parallel algorithms for depth first search but the success so far has been restricted to small classes of graphs like directed acyclic graphs dag or planar graphs for dags there are two different techniques to obtain depth first spanning trees or forests viz lexicographic sorting of paths and tree merging in the case of the planar graph the technique is to recursively divide the input graph into smaller graphs by path separators and then run the algorithm in parallel on smaller graphs produced by the separators section 5 talks about car decomposition search of graphs and efficient parallel algorithms for the problem in fact ear decomposition search is considered as an alternative to depth first search in designing parallel algorithms for complicated graph problems the strategy used for car decomposition of a graph is almost identical to that used for orientation of the edges of a connected bridgeless undirected graph so that the resultant graph is strongly connected

bivariate extreme value theory models and estimation summary bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima no natural parametric family exists for the dependence between the marginal distributions but there are considerable restrictions on the dependence structure we consider modelling the dependence function with parametric models for which two new models are presented tests for independence and discriminating between models are also given the estimation procedure and the flexibility of the new models are illustrated with an application to sea level data extreme value theory has recently been an area of much theoretical and practical work univariate theory is a well documented area whereas bivariate multivariate extreme value theory has until recently received surprisingly little attention in the multivariate case no natural parametric family exists for the dependence structure so this must be modelled in some way in the analysis of environmental extreme value data there is a need for models of dependence between extremes from different sources for example at various sea ports or at various points of a river in this paper we consider bivariate extreme value distributions we assume without loss of generality that we have exponential marginal distributions with unit means the class of bivariate exponential distributions in which we are interested satisfy a strong stability relation exponential variables x y satisfy the stability relation if and only if w min ax by is also exponentially distributed for all a b 0 pickands 1981 therefore the models we will consider have particular application in reliability and survival analysis one approach to modelling the dependence structure is via parametric models this requires a flexible family of models which satisfy certain constraints models are of two kinds either differentiable or nondifferentiable all nondifferentiable models give distri butions which are singular with nonzero probability concentrated on a certain subspace the differentiable models have densities but the existing models are symmetric which leads to the variables being exchangeable here we present two new asymmetric differenti able models which have increased flexibility properties of the differentiable models are examined estimation of the parametric models has previously been by ad hoc methods because there is a nonregular estimation problem when the margins are independent for the

fisher information for a multivariate extreme value distribution summary explicit algebraic formulae for the fisher information matrix of the multivariate extreme value distribution with generalised extreme value margins and logistic dependence structure are given

testing goodness of fit for the poisson assumption when observations are not identically distributed abstract tests for detecting negative binomial departures from a poisson model are studied for the one way layout and regression through the origin cases approximations to the null and alternative distributions of these test statistics are presented locally optimal tests and tests suggested in the literature are compared in terms of asymptotic relative efficiency small sample comparisons are included

econometric models for count data with an application to the patents r d relationship this paper focuses on developing and adapting statistical models of counts nonnegative integers in the context of panel data and using them to analyze the relationship between patents and r d expenditures since a variety of other economic data come in the form of repeated counts of some individual actions or events the methodology should have wide applications the statistical models we develop are applications and generalizations of the poisson distribution two important issues are i given the panel nature of our data how can we allow for separate persistent individual fixed or random effects ii how does one introduce the equivalent of disturbances in the equation into the analysis of poisson and other discrete probability functions the first problem is solved by conditioning on the total sum of outcomes over the observed years while the second problem is solved by introducing an additional source of randomness allowing the poisson parameter to be itself randomly distributed and compounding the two distributions lastly we develop a test statistic for the presence of serial correlation when fixed effects estimators are used in nonlinear conditional models

testing for overdispersion in poisson and binomial regression models abstract in this article a method for obtaining tests for overdispersion with respect to a natural exponential family is derived the tests are designed to be powerful against arbitrary alternative mixture models where only the first two moments of the mixed distribution are specified various tests for extra poisson and extra binomial variation are obtained as special cases the use of a particular test may be motivated by a consideration of the mechanism through which the overdispersion may arise the common occurrence of extra poisson and extra binomial variation has been noted by several authors however the poisson and binomial models remain valid in many instances and because of their simplicity and appeal it is of real interest to ascertain when they apply this paper develops a unifying theory for testing for overdispersion and generalizes tests previously derived including those by fisher 1950 collings and margolin 1985 and prentice 1986 it also shows the pearson statistic to be a sc

empirical evaluation of statistical models for counts or rates we consider methods for selecting the joint specification of the mean and variance functions in statistical models for rates or counts based on analyses of diagnosis specific hospital discharge rates in michigan we show that a poisson model with an extra variance component for the systematic variation is superior to several other probability models with regard to specification of the error structure further the deviance residual appears superior to the pearson residual the proper specification of such variation is crucial for many types of analyses such as identification of outliers and regression analyses designed to explain the systematic component of the variation

minimum hellinger distance estimation for the analysis of count data abstract minimum hellinger distance mhd estimation is studied in the context of discrete data the mhd estimator is shown to provide an effective treatment of anomalous data points and its properties are illustrated using short term mutagenicity test data asymptotic normality for a discrete distribution with countable support is derived under a readily verified condition on the model breakdown properties of the mhd estimator and an outlier screen are compared count data occur frequently in statistical applications for instance in chemical mutagenicity studies which comprise an important step in the identification of environmental carcinogens much of the resultant data are counts woodruff mason valencia and zimmering 1984 reported anomalous counts in the sex linked recessive lethal test in drosophila these outliers can have a substantial impact on the experimental conclusions mhd estimation provides a means for reliable inference when modeling count data that are prone to outliers the mh

pseudo maximum likelihood methods applications to poisson models pseudo maximum likelihood techniques are applied to basic poisson models and to poisson models with specification errors in the latter case it is shown that consistent and asymptotically normal estimators can be obtained without specifying the p d f of the disturbances these estimators are compared both from the finite sample and the asymptotic point of view quasi generalized pml estimators which asymptotically dominate all pml estimators are also proposed finally bivariate and panel data poisson models are discussed the analysis of economic behavior often leads to the study of characteristics taking a small number of positive values the classical linear model is not adapted to explain how such discrete variables depend on other quantitative or qualitative variables the reasons are similar to those usually given in the case of an endogenous qualitative variable the shape of the observation set does not correspond to a linear model the assumption of normality of the disturbances cannot be made since the endogenous variables take a small number of values with strictly positive probabilities and the prediction formulae which are deduced from a linear model give impossible values in the models considered in the literature to describe discrete variables cox and lewis 2 el sayyad 3 frome kutner and beauchamp 4 gilbert 5 hausman hall and griliches 8 see also lancaster 12 the endogenous variable is assumed to have a poisson distribution conditional upon the exogenous variables the parameter of this distribution is a function of the values of the exogenous variables the choice of such a model is justified if the dependent variable counts the occurrence of a given event during a fixed period and if the usual assumptions of the poisson process are satisfied for instance the model is adapted to describe daily numbers of oil tankers arrivals in a port the number of accidents at work by factory or the number of patents applied for and received by firms hausman hall and griliches 8

nc algorithms for computing the number of perfect matchings in k 3 3 free graph and related problems abstract we show that the problem of computing the number of perfect matchings in k3 3 free graphs is in nc this contrasts with the p completeness of counting the number of perfect matchings in arbitrary graphs as corollaries we obtain nc algorithms for checking if a given k3 3 free graph has a perfect matching and if it has an exact matching our result also opens up the possibility of obtaining an nc algorithm for finding a perfect matching in k3 3 free graphs

flow in planar graphs with multiple sources and sinks the problem of maximum flow in planar graphs has always been investigated under the assumption that there is only one source and one sink here we consider the case where there are many sources and sinks single commodity in a directed planar graph an algorithm for the case when the demands of the sources and sinks are fixed and given in advance is presented it can be implemented efficiently sequentially and in parallel and its complexity is dominated by the complexity of computing all shortest paths from a single source in a planar graph if the demands are not known an algorithm for computing the maximum flow is presented for the case where the number of faces that contain sources and sinks is bounded by a slowly growing function our result places the problem of computing a perfect matching in a planar bipartite graph in nc and it improves a previous parallel algorithm for the case of a single source single sink in a planar directed1nd undirected graph both in terms of processor bounds and in its simple presentation

the natural variability of vital rates and associated statistics the first concern of this work is the development of approximations to the distributions of crude mortality rates age specific mortality rates age standardized rates standardized mortality ratios and the like for the case of a closed population or period study it is found that assuming poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate poisson distribution it is suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic poisson distribution for the number of deaths with mean proportional to the population size and an exponential function of a linear combination of the explanatories such a model is fit to mortality data for canadian females classified by age and year a dynamic variant of the model is further fit to the time series of total female deaths alone by year the models with extra poisson variation are found to lead to substantially improved fits excerpt

modelling multivariate extreme value distributions summary multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima minima no parametric family exists for the depen dence between the margins this paper extends to more than two variables the models and results for the bivariate case obtained by tawn 1988 two new families of physically motivated parametric models for the dependence structure are presented and are illus trated with an application to trivariate extreme sea level data in the analysis of environmental extreme value data there is often need to study joint inter site extreme behaviour examples are joint flooding at various sea ports or at various rain gauges in this paper the class of multivariate extreme value distributions is considered the marginal distributions are all extreme value distributions without loss of generality we follow pickands s 1981 approach in transforming the margins to unit mean exponential distributions the resulting class of p variable multivariate exponential distributions satisfies a strong stability relation de haan resnick 1977 and pickands 1981 show that the resulting dependence structure is uniquely specified up to an arbitrary finite positive measure on p 1 variables therefore the bivariate dependence structure is univariate only when p 3 as considered here does the problem become really multivari ate in addition unlike in the multivariate normal distribution the multivariate depen dence structure is generally only restricted and not uniquely specified by the dependence structure of all possible pairs much has been written about the representations of multivariate extremes see resnick 1987 for a good review on the other hand models and estimation for such distributions have received little attention these aspects are considered here as no finite parametric family exists for the general dependence structure it must be modelled in some way thus true multivariate models are required using the most flexible bivariate model of tawn 1988 as a basis multivariate extensions are generated a model derived in the discrete choice literature will also be introduced and extended the resulting families of models are physically motivated flexible and possess hierarchical properties

utilizing concentration response data from individual components to detect statistically significant departures from additivity in chemical mixtures the classical approach for detecting interactions in a combination of drugs or chemicals is that of the isobologram quantified and generalized by berenbaum 1981 advances il cancer research 35 269 335 in this formulation it is assumed that contours of constant response of the dose response surface are planar if the compounds do not interact building upon this approach this paper develops methodology for detecting and characterizing departures from additivity reflecting the local rather than global nature of departure from additivity this methodology only requires doseresponse data for the individual components and the specific combinations s of interest this is in contrast to the larger experiments required to estimate the multidimensional dose response surface for the combination procedures for incorporating data from multiple control groups are developed for a fixed effects model a random effects model and through use of a generalized estimating equations approach an example is given that illustrates the application of these techniques to the analysis of a mixture of polycyclic aromatic hydrocarbons found in kerosene soot

testing hypotheses with estimated scores summary a method is proposed for testing hypotheses that is very much in the spirit of expected maximum log likelihood estimation and bears much the same relation to it as the likelihood ratio test methodology does to maximum likelihood estimation for a single test parameter the method amounts to basing critical regions on the difference between the estimated score and its expectation in some cases where a sufficient statistic independent of the test parameter exists for the nuisance parameter the test coincides with that based on the conditional distribution an approximate approach is described for complicated situations with algebraic examination of the scalar test and nuisance parameter case and examples of the vector parameter case

overdispersion tests for truncated poisson regression models abstract score tests of extra poisson variation in left or right truncated poisson regression models are derived for alternatives in the left or right truncated negative binomial family and for arbitrary truncation points using asymptotic expansions of the score function adjustment factors are derived for the tests which are expected to improve their small sample properties overdispersion tests for the untruncated poisson model in the econometric and statistical literature are special cases of the tests derived in this paper a monte carlo investigation of the new tests when data are truncated at zero show that the effect of truncation produces a significant size distortion and power reduction especially in small samples but also that the corrections suggested by asymptotic expansions improve the performance of the tests

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

log depth circuits for division and related problems we present optimal depth boolean circuits depth o log n for integer division powering and multiple products we also show that these three problems are of equivalent uniform depth and space complexity in addition we describe an algorithm for testing divisibility that is optimal for both depth and space

ozone concentrations a robust analysis of multivariate extremes data on ozone concentrations at four monitoring sites in central canada are examined univariate extreme value methods do not allow for the required inference and multivariate methods exploiting the joint dependence of the data are necessary families of multivariate extreme value copulas with a flexible dependence structure and closed form cumulative distribution functions have recently been derived this article shows that maximum likelihood estimates of these parametric models may be obtained numerically and that their use can lead to increased efficiency in the estimation of margins we do not however have any assurance that all data are well modeled by these distributions because the space of multivariate extreme value copulas is infinite dimensional and data on ozone levels are prone to outliers this article addresses the robust methods required for proper analysis

towards optimal parallel bucket sorting we present a simple deterministic parallel algorithm that runs on a crcw pram and sorts n integers of size polynomial in n in time o log n using o n log log nlog n processors it is closer to optimality than any previously known deterministic algorithm that solves the stated restricted sorting problem in polylog time

bivariate threshold methods for extremes summary an extension of the threshold method for extreme values is developed to consider the joint distribution of extremes of two variables the methodology is based on the point process representation of bivariate extremes both parametric and nonparametric models are considered the simplest case to handle is that in which both marginal distributions are known for the more realistic case in which the marginal distributions are unknown a mixed parametric nonparametric method is proposed the techniques are illustrated with data on sulphate and nitrate levels taken from a major study of acid rain

time work tradeoffs for parallel algorithms some parallel algorithms have the property that as they are allowed to take more time the total work that they do is reduced this paper describes several algorithms with this property these algorithms solve important problems on directed graphs including breadth first search topological sort strong connectivity and and the single source shorest path problem all of the algorithms run on the erew pram model of parallel computer except the algorithm for strong connectivity which runs on the probabilistic erew pram

regression based tests for overdispersion in the poisson model abstract a property of the poisson regression model is mean variance equality conditional on explanatory variables regression based tests for this property are proposed in a very general setting unlike classical statistical tests these tests require specification of only the mean variance relationship under the alternative rather than the complete distribution whose choice is usually arbitrary the optimal regression based test is easily computed as the t test from an auxiliary regression if a distribution under the alternative hypothesis is in fact specified and is in the katz system of distributions or is cox s local approximation to the poisson the score test for the poisson distribution is equivalent to the optimal regression based test

an nc algorithm for minimum cuts we show that the minimum cut problem for weighted undirected graphs can be solved in nc using three separate and independently interesting results the first is an m 2 n processor nc algorithm for finding a 2 epsilon approximation to the minimum cut the second is a randomized reduction from the minimum cut problem to the problem of obtaining a 2 epsilon approximation to the minimum cut this reduction involves a natural combinatorial set isolation problem that can be solved easily in rnc the third result is a derandomization of this rnc solution that requires a combination of two widely used tools pairwise independence and random walks on expanders we believe that the set isolation approach will prove useful in other derandomization problems the techniques extend to two related problems we describe nc algorithms finding minimum k way cuts for any constant k and finding all cuts of value within any constant factor of the minimum another application of these techniques yields an nc algorithm for finding a em sparse k connectivity certificate for all polynomially bounded values of k previously an nc construction was only known for polylogarithmic values of k

mixed poisson regression models with covariate dependent rates this paper studies a class of poisson mixture models that includes covariates in rates this model contains poisson regression and independent poisson mixtures as special cases estimation methods based on the em and quasi newton algorithms properties of these estimates a model selection procedure residual analysis and goodness of fit test are discussed a monte carlo study investigates implementation and model choice issues this methodology is used to analyze seizure frequency and ames salmonella assay data

semiparametric estimation of count regression models this paper develops a semiparametric estimation approach for mixed count regression models based on series expansion for the unknown density of the unobserved heterogeneity we use the generalized laguerre series expansion around a gamma baseline density to model unobserved heterogeneity in a poisson mixture model we establish the consistency of the estimator and present a computational strategy to implement the proposed estimation techniques in the standard count model as well as in truncated censored and zero inflated count regression models monte carlo evidence shows that the finite sample behavior of the estimator is quite good the paper applies the method to a model of individual shopping behavior

parallel matrix and graph algorithms matrix multiplication algorithms for cube connected and perfect shuffle computers are presented it is shown that in both these models two n times n matrices can be multiplied in o n m log m time when n 2 m 1 leqq m leqq n processing elements pes are available when only m 2 1 leqq m leqq n pes are available two n times n matrices can be multiplied in o n 2 m m n m 2 61 time it is shown that many graph problems can be solved efficiently using the matrix multiplication algorithms

efficient parallel algorithms for a class of graph theoretic problems in this paper we present efficient parallel algorithms for the following graph problems finding the lowest common ancestors for vertex pairs of a directed tree finding all fundamental cycles a directed spanning forest all bridges all bridge connected components all separation vertices all biconnected components and testing the biconnectivity of an undirected graph all these algorithms achieve the o lg 2 n time bound with the first two algorithms using n lceil n lg n rceil processors and the remaining algorithms using n lceil n lg 2 n rceil processors in all cases our algorithms are better than the previously known algorithms and in most cases reduce the number of processors used by a factor of n lg n moreover our algorithms are optimal with respect to the time processor product for dense graphs with the exception of the first two algorithms the machine model we use is the pram which is a simd model allowing simultaneous reads but not simultaneous writes to the same memory

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

new goodness of fit diagnostics for conditional discrete response models abstract this paper proposes new specification tests for conditional models with discrete responses which are key to apply efficient maximum likelihood methods to obtain consistent estimates of partial effects and to get appropriate predictions of the probability of future events in particular we test the static and dynamic ordered choice model specifications and can cover infinite support distributions for e g count data the traditional approach for specification testing of discrete response models is based on probability integral transforms of a jittered discrete data which leads to continuous uniform i i d series under the true conditional distribution then standard specification testing techniques for continuous variables could be applied to the transformed series but the extra randomness from jitters affects the power properties of these methods we investigate in this paper an alternative transformation based only on original discrete data that avoids any randomization we analyze the asymptotic properties of goodness of fit tests based on this new transformation and explore the properties in finite samples of a bootstrap algorithm to approximate the critical values of test statistics which are model and parameter dependent we show analytically and in simulations that our approach dominates the methods based on randomization in terms of power we apply the new tests to models of the monetary policy conducted by the federal reserve

testing goodness of fit of a multinomial model against overdispersed alternatives the problem of testing the goodness of fit of the multinomial sampling model against an overdispersed dirichlet multinomial alternative is studied and an improved approximate sampling distribution is presented for the corresponding c ca test statistic the elements of this improvement include better control of test size and increased power against overdispersion the pearson chi square test is also considered for the detection of this form of overdispersion and its asymptotic efficiency relative to the c a test is obtained and shown to be always less than or equal to 1 monte carlo investigations suggest that the gain in power of the c a test relative to the pearson chi square test is small unless there is substantial inequality among the dirichlet multinomial sample sizes

green s theorem and isolation in planar graphs we show a simple application of email protected s theorem from multivariable calculus to the isolation problem in planar graphs in particular we give a log space construction of a skew symmetric polynomially bounded edge weight function for directed planar graphs such that the weight of any simple cycle in the graph is non zero with respect to this weight function as a direct consequence of the above weight function we are able to isolate a directed path between two fixed vertices in a directed planar graph we also show that given a bipartite planar graph we can obtain an edge weight function using the above function in log space which isolates a perfect matching in the given graph earlier this was known to be true only for grid graphs which is a proper subclass of planar graphs we also look at the problem of obtaining a straight line embedding of a planar graph in log space although we do not quite achieve this goal we give a piecewise straight line embedding of the given planar graph in log space

truncated negative binomial mixed regression modelling of ischaemic stroke hospitalizations a zero truncated negative binomial mixed regression model is presented to analyse overdispersed positive count data the study is motivated by the determination of pertinent risk factors associated with ischaemic stroke hospitalizations random effects are incorporated in the linear predictor to adjust for inter hospital variations and the dependency of clustered observations using the generalized linear mixed model approach the method assists hospital administrators and clinicians to estimate the number of subsequent readmissions based on characteristics of the patient at the index stroke the findings have important implications on resource usage rehabilitation planning and management of acute stroke care copyright 2003 john wiley sons ltd

the value of water levels in water based recreation a pooled revealed preference contingent behavior model in this paper we present estimated recreation values for preventing a decline in water levels at and even the total loss of a large western lake that is drying up we use a poisson version of the count data travel cost model however in addition to and in combination with revealed preference rp data we employ contingent behavior cb responses to hypothetical questions on alternative water levels and number of trips the pooled model used allows for tests of differences between results using rp and cb data this particular pooled rp cb approach has not to our knowledge previously been applied to examine the values of alternative water quantities in water based recreation