system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

some aspects of polya tree distributions for statistical modelling the definition and elementary properties of polya tree distributions are reviewed two theorems are presented showing that polya trees can be constructed to concentrate arbitrarily closely about any desired pdf and that polya tree priors can put positive mass in every relative entropy neighborhood of every positive density with finite entropy thereby satisfying a consistency condition such theorems are false for dirichlet processes models are constructed combining partially specified polya trees with other information such as monotonicity or unimodality it is shown how to compute bounds on posterior expectations over the class of all priors with the given specifications a numerical example is given a theorem of diaconis and freedman about dirichlet processes is generalized to polya trees allowing polya trees to be the models for errors in regression problems finally empirical bayes models using dirichlet processes are generalized to polya trees an example from berry and christensen is reanalyzed with a polya tree model

conjugate priors for exponential families having quadratic variance functions abstract consider a natural exponential family parameterized by it is well known that the standard conjugate prior on is characterized by a condition of posterior linearity for the expectation of the model mean parameter often however this family is not parameterized in terms of but rather in terms of a more usual parameter such at the mean the main question we address is under what conditions does a standard conjugate prior on induce a linear posterior expectation on itself we prove that essentially this happens iff the exponential family has quadratic variance function a consequence of this result is that the standard conjugate on coincides with the prior on induced by the standard conjugate on iff the variance function is quadratic the rest of the article covers more specific issues related to conjugate priors for exponential families in particular we analyze the monotonicity of the expected posterior variance for with respect to the sample size and the hyperparameter

estimation in generalized mixed models regression models containing fixed and random effects may have a response variable which is not normally distributed the generalized mixed model includes both discrete and continuous response variables and is developed here for problems in which the regression variables enter linearly into the model best linear unbiased predictor methods are extended to maximum likelihood and residual maximum likelihood estimation procedures applications in modelling discrete response variables and in survival analysis are discussed

multilevel time series models with applications to repeated measures data the analysis of repeated measures data can be conducted efficiently using a two level random coefficients model a standard assumption is that the within individual level 1 residuals are uncorrelated in some cases especially where measurements are made close together in time this may not be reasonable and this additional correlation structure should also be modelled a time series model for such data is proposed which consists of a standard multilevel model for repeated measures data augmented by an autocorrelation model for the level 1 residuals first and second order autoregressive models are considered in detail together with a seasonal component both discrete and continuous time are considered and it is shown how the autocorrelation parameters can themselves be structured in terms of further explanatory variables the models are fitted to a data set consisting of repeated height measurements on children

hierarchical poisson regression modeling abstract the poisson model and analyses here feature nonexchangeable gamma distributions although exchangeable following a scale transformation for individual parameters with standard deviations proportional to means a relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components when tested in simulation studies the resulting procedure provides better coverage probabilities and smaller risk than several other published rules and thus works well from bayesian and frequentist perspectives alike the computations provide fast accurate density approximations to individual parameters and to structural regression coefficients the computer program is publicly available through statlib

necessary and sufficient conditions for optimal offers in electricity markets in this paper we consider the optimal policy for a generator offering power into a wholesale electricity market operating under a pool arrangement anderson and philpott math oper res 27 2002 pp 82 100 recently discussed necessary conditions for an optimal offer curve when there is uncertainty in the demand and in the behavior of other participants in the market they show that the objective function in these circumstances can be expressed as a line integral along the offer curve of a profit function integrated with respect to a market distribution function in this paper we prove the existence of an optimal offer stack and we extend the analysis of math oper res 27 2002 pp 82 100 to include necessary conditions of a higher order in the presence of horizontal and or vertical sections in an offer curve finally we establish sufficient conditions for an offer curve to be locally optimal

statistical analysis of field experiments using neighbouring plots the paper describes and provides examples of four different applications of the use of neighbouring plot values in the analysis of agricultural field experiments the topics include the use of check plots to control environmental variation in large unreplicated variety trials spatial models based on first differences to accommodate fertility effects in trials that have some degree of replication adjustment for interplot competition using a simultaneous equations formulation and the analysis of trials in which plot values are affected by the particular treatments on neighbouring plots

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

causal diagrams for empirical research summary the primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject matter information in particular the paper develops a principled nonparametric framework for causal inference in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data if so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions otherwise the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained

laplace s approximation for nonlinear mixed models summary an approximation to laplace s method for integrals is applied to marginal distributions of data arising from models in which both fixed and random effects enter nonlinearly the approach provides alternative derivations of some recent algorithms for fitting such models and it has direct ties with gaussian restricted maximum likelihood and the accompanying mixed model equations

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

maximum likelihood variance components estimation for binary data abstract we consider a class of probit normal models for binary data and describe ml and reml estimation of variance components for that class as well as best prediction for the realized values of the random effects ml estimates are calculated using an em algorithm for complicated models em includes a gibbs step the computations are illustrated through two examples

parameter estimation in longitudinal studies with outcome dependent follow up in many observational studies individuals are measured repeatedly over time although not necessarily at a set of prespecified occasions instead individuals may be measured at irregular intervals with those having a history of poorer health outcomes being measured with somewhat greater frequency and regularity i e those individuals with poorer health outcomes may have more frequent follow up measurements and the intervals between their repeated measurements may be shorter in this article we consider estimation of regression parameters in models for longitudinal data where the follow up times are not fixed by design but can depend on previous outcomes in particular we focus on general linear models for longitudinal data where the repeated measures are assumed to have a multivariate gaussian distribution we consider assumptions regarding the follow up time process that result in the likelihood function separating into two components one for the follow up time process the other for the outcome process the practical implication of this separation is that the former process can be ignored when making likelihood based inferences about the latter i e maximum likelihood ml estimation of the regression parameters relating the mean of the longitudinal outcomes to covariates does not require that a model for the distribution of follow up times be specified as a result standard statistical software e g sas proc mixed littell et al 1996 sas system for mixed models can be used to analyze the data however we also demonstrate that misspecification of the model for the covariance among the repeated measures will in general result in regression parameter estimates that are biased furthermore results of a simulation study indicate that the potential bias due to misspecification of the covariance can be quite considerable in this setting finally we illustrate these results using data from a longitudinal observational study lipshultz et al 1995 new england journal of medicine 332 1738 1743 that explored the cardiotoxic effects of doxorubicin chemotherapy for the treatment of acute lymphoblastic leukemia in children

robust empirical bayes analyses of event rates a collection of i similar items generates point event histories for example machines experience failures or operators make mistakes suppose the intervals between events are modeled as iid exponential i or the counts as poisson i t i for the ith item furthermore so as to represent between item variability each individual rate parameter i is presumed drawn from a fixed super population with density g being a vector parameter a parametric empirical bayes peb setup for g specified alternatively as log student t n or gamma we exhibit the results of numerical procedures for estimating superpopulation parameters ll and for describing pooled estimates of the individual rates i obtained via bayes s formula three data sets are analyzed and convenient explicit approximate formulas are furnished for i estimates in the student t case the individual estimates are seen to have a robust quality

on the generalization of the likelihood function and the likelihood principle abstract the parametric likelihood and likelihood principle lp play a central role in parametric methodology and in the foundations of statistics the main purpose of this article is to extend the concepts of likelihood and lp to general inferential aims and models covering for example prediction and empirical bayes models the likelihood function is the joint distribution of the data and the unobserved variables of inferential interest considered as a function of the parameters and these inferential variables lp is based on this likelihood and the principles of sufficiency sp and conditionality cp are modified such that the equivalence sp and cp lp is valid generalizing birnbaum s theorem

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

a scalable robust stability criterion for systems with heterogeneous lti components a scalable robust stability criterion for interconnected systems with heterogeneous linear time invariant components is presented in this paper the criterion involves only the properties of individual components and the spectrum of the interconnection matrix which can be verified with relatively low computational effort and more importantly maintains scalability of the analysis our main result shows that if the components are single input single output siso then the criterion has an appealing graphical interpretation which resembles the classical nyquist criterion

optimal offer construction in electricity markets in this paper we study strategies for generators making offers into electricity markets in circumstances where both the demand for electricity and the behaviour of competing generators is unknown but can be represented by a probability distribution given this probability distribution we derive necessary optimality conditions for a broad class of supply offer curves we show how these conditions can be used to construct an optimal solution for a simple example we also consider the case in which a generator is restricted in the number of prices at which power can be offered

non parametric tests for right censored data with biased sampling testing the equality of two survival distributions can be difficult in a prevalent cohort study when non random sampling of subjects is involved due to the biased sampling scheme independent censoring assumption is often violated although the issues about biased inference caused by length biased sampling have been widely recognized in statistical epidemiological and economical literature there is no satisfactory solution for efficient two sample testing we propose an asymptotic most efficient nonparametric test by properly adjusting for length biased sampling the test statistic is derived from a full likelihood function and can be generalized from the two sample test to a k sample test the asymptotic properties of the test statistic under the null hypothesis are derived using its asymptotic independent and identically distributed representation we conduct extensive monte carlo simulations to evaluate the performance of the proposed test statistics and compare them with the conditional test and the standard logrank test for different biased sampling schemes and right censoring mechanisms for length biased data empirical studies demonstrated that the proposed test is substantially more powerful than the existing methods for general left truncated data the proposed test is robust still maintains accurate control of type i error rate and is also more powerful than the existing methods if the truncation patterns and right censoring patterns are the same between the groups we illustrate the methods using two real data examples

regression analysis of longitudinal data in the presence of informative observation and censoring times longitudinal data frequently occur in many studies such as longitudinal follow up studies to develop statistical methods and theory for the analysis of these data independent or noninformative observation and censoring times are typically assumed which naturally leads to inference procedures conditional on observation and censoring times but in many situations this may not be true or realistic that is longitudinal responses may be correlated with observation times as well as censoring times this article considers the analysis of longitudinal data where these correlations may exist and proposes a joint modeling approach that uses some latent variables to characterize the correlations for inference about regression parameters estimating equation approaches are developed and both large sample and final sample properties of the proposed estimators are established in addition some graphical and numerical procedures are presented for model checking the methodology is applied to a bladder cancer stu

residuals in generalized linear models abstract generalized linear models are regression type models for data not normally distributed appropriately fitted by maximum likelihood rather than least squares typical examples are models for binomial or poisson data with a linear regression model for a given ordinarily nonlinear function of the expected values of the observations use of such models has become very common in recent years and there is a clear need to study the issue of appropriate residuals to be used for diagnostic purposes several definitions of residuals are possible for generalized linear models the statistical package glim baker and nelder 1978 routinely prints out residuals where v is the function relating the variance to the mean of y and is the maximum likelihood estimate of the ith mean as fitted to the regression model these residuals are the signed square roots of the contributions to the pearson goodness of fit statistic another choice of residual is the signed square root of the contribution to the devia

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

bias correction in generalised linear mixed models with a single component of dispersion summary general expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component for small values of the variance component in generalised linear mixed models with canonical link function and a single source of extraneous variation the estimators involve first and second order laplace expansions of the integrated likelihood and a related procedure known as penalised quasilikelihood numerical studies of a series of matched pairs of binary outcomes show that the first order estimators of the variance component are seriously biased easily computed correction factors produce satisfactory estimators of small variance components comparable to those obtained with a second order laplace expansion and markedly improve the asymptotic performance for larger values for a series of matched pairs of binomial observations the variance correction factors rapidly approach one as the binomial denominators increase these results greatly extend the range of parameter values for which the approximate estimation procedures have satisfactory asymptotic properties

marginalized models for moderate to long series of longitudinal binary response data marginalized models heagerty 1999 biometrics 55 688 698 permit likelihood based inference when interest lies in marginal regression models for longitudinal binary response data two such models are the marginalized transition and marginalized latent variable models the former captures within subject serial dependence among repeated measurements with transition model terms while the latter assumes exchangeable or nondiminishing response dependence using random intercepts in this article we extend the class of marginalized models by proposing a single unifying model that describes both serial and long range dependence this model will be particularly useful in longitudinal analyses with a moderate to large number of repeated measurements per subject where both serial and exchangeable forms of response correlation can be identified we describe maximum likelihood and bayesian approaches toward parameter estimation and inference and we study the large sample operating characteristics under two types of dependence model misspecification data from the madras longitudinal schizophrenia study thara et al 1994 acta psychiatrica scandinavica 90 329 336 are analyzed

ignorability for categorical data we study the problem of ignorability in likelihood based inference from incomplete categorical data two versions of the coarsened at random assumption car are distinguished their compatibility with the parameter distinctness assumption is investigated and several conditions for ignorability that do not require an extra parameter distinctness assumption are established it is shown that car assumptions have quite different implications depending on whether the underlying complete data model is saturated or parametric in the latter case car assumptions can become inconsistent with observed data

quasi likelihood for multiplicative random effects summary a quasi likelihood approach similar to that described by morton 1987 is found to be particularly simple in the case of measurements subject to two or more sources of multiplicative error still further simplification occurs when the effects of interest also are multiplicative the multiplicative analogue of the balanced split plot model is considered in detail an analysis of gamma deviance replaces the familiar analysis of variance the efficiency of the quasi likelihood method relative to a more conventional analysis of logarithms of the data is explored briefly

a popov criterion for networked systems abstract we consider robustness analysis of heterogeneous and homogeneous networked systems based on integral quadratic constraints iqcs first we show how the analysis decomposes into lower dimensional problems if the interconnection structure is exploited this generally leads to a significant reduction of the computational complexity secondly by considering a set of iqcs that characterizes the eigenvalues of the interconnection matrices of symmetrically networked systems we derive a popov like criterion for such systems in particular when the nodes of the networked system are single input single output linear time invariant operators the criterion can be illustrated using a generalized popov plot in such cases the popov criterion is also a necessary condition in the sense that if the criterion is violated then a destabilizing network with the specified eigenvalue distribution can be constructed

multivariate logistic models summary when data composed of several categorical responses together with categorical or continuous predictors are observed the multivariate logistic transform introduced by mccullagh and nelder can be used to define a class of regression models that is in many applications particularly suitable for relating the joint distribution of the responses to predictors in this paper we give a general definition of this class of models and study their properties a computational scheme for performing maximum likelihood estimation for data sets of moderate size is described and a system of model formulae that succinctly define particular models is introduced applications of these models to longitudinal problems are illustrated by numerical examples

coarsening at random in general sample spaces and random censoring in continuous time heitjan and rubin proposed a concept coarsening at random generalizing rubin s theory of missing at random their analysis was done in discrete sample spaces we propose a generalization to general sample spaces among heitjan and rubin s applications was right censoring in survival analysis we discuss the application of the generalized theory to various censoring patterns in continuous time and connect to the modern theory of random censoring

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

finding supply function equilibria with asymmetric firms firms compete in supply functions when they offer a schedule of prices and quantities into a market for example this occurs in many wholesale electricity markets we study the equilibrium behaviour when firms differ both with regard to their costs and their capacities we characterize strong equilibrium solutions in which given the other players supply functions optimal profits are achieved for every demand realisation if the demand can be low enough for it to be met economically with supply from just one firm then the supply function equilibria are ordered in a natural way we consider equilibria in which for the highest levels of demand all but one of the firms have reached their capacity limit we show that there can be at most one supply function equilibrium with this property we also propose a new numerical method to find asymmetric supply function equilibria using piecewise linear approximations and a discretization of the demand distribution we show that this approach has good theoretical convergence behaviour finally we present numerical results from an implementation using gams to demonstrate that the approach is effective in practice

the beta geometric distribution applied to comparative fecundability studies a convenient measure of fecundability is time number of menstrual cycles required to achieve pregnancy couples attempting pregnancy are heterogeneous in their per cycle probability of success if success probabilities vary among couples according to a beta distribution then cycles to pregnancy will have a beta geometric distribution the likelihood ratio test can thus be employed in studies of exposures that may impair fecundability covariates are incorporated in a natural way the model is illustrated by applying it to data on cycles to pregnancy in smokers and nonsmokers with adjustment for covariates summary in fre excerpt

methods for the analysis of sampled cohort data in the cox proportional hazards model methods are provided for regression parameter and cumulative baseline hazard estimation in the cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law the key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes leading to estimation methods parallel to those for full cohort data these techniques are illustrated for a number of sampling designs including three novel designs counter matching with additional randomly sampled controls quota sampling of controls and nested case control sampling with number of controls dependent on the failure s exposure status general asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs

posterior mode estimation by extended kalman filtering for multivariate dynamic generalized linear models abstract a family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family besides common conditionally gaussian models this article deals with univariate models for counted and binary data and as the most interesting multivariate case models for nonstationary multicategorical time series for univariate responses a related yet different class of models has been introduced in a bayesian setting by west harrison and migon assuming conjugate prior posterior distributions for the natural parameter of the exponential family they derive an approximate filter for estimation of time varying states or parameters however their method raises some problems in particular in extending it to the multivariate case a different approach to filtering and smoothing is chosen in this article to avoid a full bayesian analysis based on numerical integration which becomes computationally critical for higher

marginally specified logistic normal models for longitudinal binary data summary likelihood based inference for longitudinal binary data can be obtained using a generalized linear mixed model breslow n and clayton d g 1993 journal of the american statistical association88 9 25 wolfinger r and o connell m 1993 journal of statistical computation and simulation48 233 243 given the recent improvements in computational approaches alternatively fitzmaurice and laird 1993 biometrika80 141 151 molenberghs and lesaffre 1994 journal of the american statistical association89 633 644 and heagerty and zeger 1996 journal of the american statistical association91 1024 1036 have developed a likelihood based inference that adopts a marginal mean regression parameter and completes full specification of the joint multivariate distribution through either canonical and or marginal higher moment assumptions each of these marginal approaches is computationally intense and currently limited to small cluster sizes in this manuscript an alternative parameterization of the logistic normal random effects model is adopted and both likelihood and estimating equation approaches to parameter estimation are studied a key feature of the proposed approach is that marginal regression parameters are adopted that still permit individual level predictions or contrasts an example is presented where scientific interest is in both the mean response and the covariance among repeated measurements

asymptotic theory for nested case control sampling in the cox regression model by providing a probabilistic model for nested case control sampling in epidemiologic cohort studies consistency and asymptotic normality of the maximum partial likelihood estimator of regression parameters in a cox proportional hazards model can be derived using process and martingale theory as in andersen and gill a general expression for the asymptotic variance is given and used to calculate asymptotic relative efficiencies relative to the full cohort variance in some important special cases

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

delay robustness of interconnected passive systems an integral quadratic constraint approach we consider networks of passive systems with time delays in the interconnections and present a stability analysis technique with the help of the integral quadratic constraint iqc framework unlike the classical passivity approach that fails to characterize delay robustness and the small gain approach that conservatively accounts for arbitrarily large delays the new technique gives sharp stability estimates that depend on the duration of delay since the effect of delay depends on its duration relative to the time scales of the system we make use of a roll off iqc that captures magnitude roll off at high frequencies thus providing the critical time scale information we then combine this roll off iqc with an output strict passivity iqc that incorporates gain and phase information and demonstrate the benefit of this combined iqc approach on a cyclic interconnection structure with delay finally we develop a technique to verify these iqcs for classes of nonlinear state space models and present an example from internet congestion control

a comparison of gcv and gml for choosing the smoothing parameter in the generalized spline smoothing problem the partially improper prior behind the smoothing spline model is used to obtain a generalization of the maximum likelihood gml estimate for the smoothing parameter then this estimate is compared with the generalized cross validation gcv estimate both analytically and by monte carlo methods the comparison is based on a predictive mean square error criteria it is shown that if the true unknown function being estimated is smooth in a sense to be defined then the gml estimate undersmooths relative to the gcv estimate and the predictive mean square error using the gml estimate goes to zero at a slower rate than the mean square error using the gcv estimate if the true function is rough then the gcv and gml estimates have asymptotically similar behavior a monte carlo experiment was designed to see if the asymptotic results in the smooth case were evident in small sample sizes mixed results were obtained for n 32 gcv was somewhat better than gml for n 64 and gcv was decidedly superior for n 128 in the n 32 case gcv was better for smaller sigma 2 and the comparison close for larger sigma 2 the theoretical results are shown to extend to the generalized spline smoothing model which includes the estimate of functions given noisy values of various integrals of them

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

causal inference using potential outcomes design modeling decisions causal effects are defined as comparisons of potential outcomes under different treatments on a common set of units observed values of the potential outcomes are revealed by the assignment mechanism a probabilistic model for the treatment each unit receives as a function of covariates and potential outcomes fisher made tremendous contributions to causal inference through his work on the design of randomized experiments but the potential outcomes perspective applies to other complex experiments and nonrandomized studies as well as noted by kempthorne in his 1976 discussion of savage s fisher lecture fisher never bridged his work on experimental design and his work on parametric modeling a bridge that appears nearly automatic with an appropriate view of the potential outcomes framework where the potential outcomes and covariates are given a bayesian distribution to complete the model specification also this framework crisply separates scientific inference for causal effects and decisions based on s

varepsilon optimal bidding in an electricity market with discontinuous market distribution function this paper investigates the optimal bidding strategy supply function for a generator offering power into a wholesale electricity market the model has three characteristics the uncertainties facing the generator are described by a single probability function namely the market distribution function the supply function to be chosen is nondecreasing but need not be smooth the objective function is the expected profit which can be formulated as a stieltjes integral along the generator s supply curve in previous work the market distribution function has been assumed smooth but in practice this assumption may not be satisfied this paper focuses on the case that the market distribution function is not continuous and hence an optimal supply function may not exist we consider a modified optimization problem and show the existence of an optimal solution for this problem then we show constructively how such an optimum can be approximated with an varepsilon optimal supply function by undercutting when

robustness of network flow control against disturbances and time delay this paper studies robustness of kelly s source and link control laws in j oper res soc 49 1998 237 with respect to disturbances and time delays this problem is of practical importance because of unmodelled ows and propagation and queueing delays which are ubiquitous in networks we rst show lp stability for p 1 with respect to additive disturbances we pursue l stability within the input to state stability iss framework of sontag ieee trans automat control 34 1989 435 which makes explicit the vanishing eaect of initial conditions next using this iss property and a loop transformation we prove that global asymptotic stability is preserved for subciently small time delays in forward and return channels for larger delays we achieve global asymptotic stability by scaling down the control gains as in paganini et al proceedings of 2001 conference on decision and control orlando fl december 2001 pp 185 190 c

on the existence of supply function equilibria supply function equilibria are used in the analysis of divisible good auctions with a large number of identical objects to be sold or bought an important example occurs in wholesale electricity markets despite the substantial literature on supply function equilibria the existence of a pure strategy nash equilibria for a uniform price auction in asymmetric cases has not been established in a general setting in this paper we prove the existence of a supply function equilibrium for a duopoly with asymmetric firms having convex non decreasing marginal costs with decreasing concave demand subject to an additive demand shock provided that the second derivative of the demand function is small enough and not increasing the proof is constructive and also gives insight into the structure of the equilibrium solutions

the analysis of binomial data by a generalized linear mixed model summary methods for generalized linear models are extended to provide estimates of location and variance parameters for mixed models fitted to binomial data formed by classifying samples from an underlying normal distribution the method estimates the parameters directly on the underlying scale for a balanced one way random effects model the variance estimator simplifies to the usual analysis of variance one the estimation of variances and the prediction of random effects for binomial traits is required by animal breeders the predictors given are analogous to best linear unbiased predictors henderson 1973 but differ from those presented by harville mee 1984

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

two graphical displays for outlying and influential observations in regression summary the paper describes two procedures for detecting observations with outlying values either in the response variable or in the explanatory variables in multiple regression these procedures are presented as half normal plots with envelopes derived from simulation in order to avoid overinterpretation of the data analysis of a well known data set leads to the use of a data transformation a simple test for which is commended and to some comments on the relationship with robust regression the widespread availability of sophisticated computer software has made the fitting of multiple regression equations painless but the very ease of these procedures may cause insufficient care to be given to checking and scrutiny of the data transcription punching and data manipulation errors may lead to bad values both of the observations y and of the independent or explanatory variables x it is the purpose of the present paper to describe and exemplify two plots which provide checks against such bad values it is argued that these plots and a test for transformations should accompany any thorough regression analysis bad values of the response or outliers have long been detected by a variety of plots of residuals bad values of the explanatory variables are less easily detected even when they lead to an extreme point in the design space since the fitted equation will pass close to such an influential observation the residual may not be especially large even after allowance has been made for the small variance of the fitted value at such a point to detect such behaviour a quantity is needed which exhibits the dependence of the fitted model on each point or group of points discussions of such quantities are given by hoaglin welsch 1978 and more recently by belsley kuh welsch 1980 2 1 by cook weisberg 1980 and by pregibon 1981 the quantity used here is a modification of a statistic proposed by cook 1977 which is derived in 2 two half normal plots are presented in 3 as an aid to interpretation envelopes to the plots are generated by simulation examples of the plots are given in 4 both for simulated data and for the stack loss data given by brownlee 1965 p 454 transformations of this data set are discussed in 5 the paper concludes with some comments on the relationship with robust

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

unit commitment in electricity pool markets we consider an electricity generator making offers of energy into an electricity pool market over a horizon of several trading periods typically a single trading day the generator runs a set of generating units with given start up costs shut down costs and operating ranges at the start of each trading period the generator must submit to the pool system operator a new supply curve defining quantities of offered energy and the prices at which it wants these dispatched the amount of dispatch depends on the supply curve offered along with the offers of the other generators and market demand both of which are random but do not change in response to the actions of the generator we consider after dispatch the generator determines which units to run in the current trading period to meet the dispatch the generator seeks a supply function that maximizes its expected profit we describe an optimization procedure based on dynamic programming that can be used to construct optimal offers in successive time periods over a fixed planning horizon

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

brief paper structured semidefinite programs for the control of symmetric systems in this paper we show how the symmetry present in many linear systems can be exploited to significantly reduce the computational effort required for controller synthesis this approach may be applied when controller design specifications are expressible via semidefinite programming in particular when the overall system description is invariant under unitary coordinate transformations of the state space matrices synthesis semidefinite programs can be decomposed into a collection of smaller semidefinite programs

maximum likelihood algorithms for generalized linear mixed models abstract maximum likelihood algorithms are described for generalized linear mixed models i show how to construct a monte carlo version of the em algorithm propose a monte carlo newton raphson algorithm and evaluate and improve the use of importance sampling ideas calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously i also use the newton raphson algorithm as a framework to compare maximum likelihood to the joint maximization or penalized quasi likelihood methods and explain why the latter can perform poorly

score tests for association under response dependent sampling designs for expensive covariates this is a pre copyedited author produced pdf of an article accepted for publication in biometrika following peer review the version of record derkach a lawless j f and sun l 2015 score tests for association under response dependent sampling designs for expensive covariates biometrika 102 4 988 994 is available online at http biomet oxfordjournals org content 102 4 988 full pdf html doi 10 1093 biomet asv038

a generalized linear model with nested strata of extra poisson variation on etend la definition de quasivraisemblance pour tenir compte de plusieurs strates de variation emboitees dans un modele lineaire generalise

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

analysis of longitudinal data with irregular outcome dependent follow up summary a frequent problem in longitudinal studies is that subjects may miss scheduled visits or be assessed at self selected points in time as a result observed outcome data may be highly unbalanced and the availability of the data may be directly related to the outcome measure and or some auxiliary factors that are associated with the outcome if the follow up visit and outcome processes are correlated then marginal regression analyses will produce biased estimates building on the work of robins rotnitzky and zhao we propose a class of inverse intensity of visit process weighted estimators in marginal regression models for longitudinal responses that may be observed in continuous time this allows us to handle arbitrary patterns of missing data as embedded in a subject s visit process we derive the large sample distribution for our inverse visit intensity weighted estimators and investigate their finite sample behaviour by simulation our approach is illustrated with a data set from a health services research study in which homeless people with mental illness were randomized to three different treatments and measures of homelessness as percentage days homeless in the past 3 months and other auxiliary factors were recorded at follow up times that are not fixed by design

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

random point fields associated with certain fredholm determinants i fermion poisson and boson point processes we introduce certain classes of random point fields including fermion and boson point processes which are associated with fredholm determinants of certain integral operators and study some of their basic properties limit theorems correlation functions palm measures etc also we propose a conjecture on an analogue of the determinant and permanent

robust stability analysis of sparsely interconnected uncertain systems in this paper we consider robust stability analysis of large scale sparsely interconnected uncertain systems by modeling the interconnections among the subsystems with integral quadratic constraints we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities we also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness the sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

bias correction in generalized linear mixed models with multiple components of dispersion abstract general formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi likelihood pql in generalized linear mixed models with canonical link function and multiple sets of independent random effects easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values both first order and second order correction procedures are developed for regression coefficients estimated by pql the methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects and their properties are evaluated in a simulation study

the simulation smoother for time series models summary recently suggested procedures for simulating from the posterior density of states given a gaussian state space time series are refined and extended we introduce and study the simulation smoother which draws from the multivariate posterior distribution of the disturbances of the model so avoiding the degeneracies inherent in state samplers the technique is important in gibbs sampling with non gaussian time series models and for performing bayesian analysis of gaussian time series

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

dynamic linear model diagnostics summary in time series analysis using dynamic linear models retrospective analysis involves the calculation of filtered or smoothed distributions for state parameters in the past we develop and illustrate novel results that are useful in retrospective assessment of the influence of individual observations on such distributions in particular new and computationally simple filtering equations are derived for past state parameters based on leaving out one observation at a time providing dynamic model based versions of methods currently used in standard static regression diagnostics