covariate adjustment in randomized trials with binary outcomes targeted maximum likelihood estimation covariate adjustment using linear models for continuous outcomes in randomized trials has been shown to increase efficiency and power over the unadjusted method in estimating the marginal effect of treatment however for binary outcomes investigators generally rely on the unadjusted estimate as the literature indicates that covariate adjusted estimates based on the logistic regression models are less efficient the crucial step that has been missing when adjusting for covariates is that one must integrate average the adjusted estimate over those covariates in order to obtain the marginal effect we apply the method of targeted maximum likelihood estimation tmle to obtain estimators for the marginal effect using covariate adjustment for binary outcomes we show that the covariate adjustment in randomized trials using the logistic regression models can be mapped by averaging over the covariate s to obtain a fully robust and efficient estimator of the marginal effect which equals a targeted maximum likelihood estimator this tmle is obtained by simply adding a clever covariate to a fixed initial regression we present simulation studies that demonstrate that this tmle increases efficiency and power over the unadjusted method particularly for smaller sample sizes even when the regression model is mis specified

comparing markov chains aggregation and precedence relations applied to sets of states with applications to assemble to order systems solving markov chains is in general difficult if the state space of the chain is very large or infinite and lacking a simple repeating structure one alternative to solving such chains is to construct models that are simple to analyze and provide bounds for a reward function of interest we present a new bounding method for markov chains inspired by markov reward theory our method constructs bounds by redirecting selected sets of transitions facilitating an intuitive interpretation of the modifications of the original system we show that our method is compatible with strong aggregation of markov chains thus we can obtain bounds for an initial chain by analyzing a much smaller chain we illustrate our method by using it to prove monotonicity results and bounds for assemble to order systems

a new approach to weighting and inference in sample surveys the validity of design based inference is not dependent on any model assumption however it is well known that estimators derived through design based theory may be inefficient for the estimation of population totals when the design weights are weakly related to the variables of interest and have widely dispersed values we propose estimators that have the potential to improve the efficiency of any estimator derived under the design based theory our main focus is limited to the improvement of the horvitz thompson estimator but we also discuss the extension to calibration estimators the new estimators are obtained by smoothing design or calibration weights using an appropriate model our approach to inference requires the modelling of only one variable the weight and it leads to a single set of smoothed weights in multipurpose surveys this is to be contrasted with other model based approaches such as the prediction approach in which it is necessary to postulate and validate a model for each variable of interest leading potentially to variable specific sets of weights our proposed approach is first justified theoretically and then evaluated through a simulation study

accounting for parameter uncertainty in large scale stochastic simulations with correlated inputs this paper considers large scale stochastic simulations with correlated inputs having normal to anything norta distributions with arbitrary continuous marginal distributions examples of correlated inputs include processing times of workpieces across several workcenters in manufacturing facilities and product demands and exchange rates in global supply chains our goal is to obtain mean performance measures and confidence intervals for simulations with such correlated inputs by accounting for the uncertainty around the norta distribution parameters estimated from finite historical input data this type of uncertainty is known as the parameter uncertainty in the discrete event stochastic simulation literature we demonstrate how to capture parameter uncertainty with a bayesian model that uses sklar s marginal copula representation and cooke s copula vine specification for sampling the parameters of the norta distribution the development of such a bayesian model well suited for handling many correlated inputs is the primary contribution of this paper we incorporate the bayesian model into the simulation replication algorithm for the joint representation of stochastic uncertainty and parameter uncertainty in the mean performance estimate and the confidence interval we show that our model improves both the consistency of the mean line item fill rate estimates and the coverage of the confidence intervals in multiproduct inventory simulations with correlated demands

survey design under the regression superpopulation model abstract the construction of sample designs and estimators under a linear regression superpopulation model is considered the anticipated variance the variance of the predictor computed with respect to the sampling design and the superpopulation model is used as a criterion for evaluating probability designs and model unbiased predictors regression predictors that are model unbiased and design consistent are constructed

a unified approach to robust estimation in finite population sampling we argue that the conditional bias associated with a sample unit can be a useful measure of influence in finite population sampling we use the conditional bias to derive robust estimators that are obtained by downweighting the most influential sample units under the model based approach to inference our proposed robust estimator is closely related to the well known estimator of chambers 1986 under the design based approach it possesses the desirable feature of being applicable with most sampling designs used in practice for stratified simple random sampling it is essentially equivalent to the estimator of kokic bell 1994 the proposed robust estimator depends on a tuning constant in this paper we propose a method for determining the tuning constant and show that the resulting estimator is consistent results from a simulation study suggest that our approach improves the efficiency of standard nonrobust estimators when the population contains units that may be influential if selected in the sample

inference under covariate adaptive randomization this article studies inference for the average treatment effect in randomized controlled trials with covariate adaptive randomization here by covariate adaptive randomization we mean randomizati

analysis of covariance in randomized trials more precision and valid confidence intervals without model assumptions covariate adjustment in the randomized trial context refers to an estimator of the average treatment effect that adjusts for chance imbalances between study arms in baseline variables called covariates the baseline variables could include for example age sex disease severity and biomarkers according to two surveys of clinical trial reports there is confusion about the statistical properties of covariate adjustment we focus on the analysis of covariance ancova estimator which involves fitting a linear model for the outcome given the treatment arm and baseline variables and trials that use simple randomization with equal probability of assignment to treatment and control we prove the following new to the best of our knowledge robustness property of ancova to arbitrary model misspecification not only is the ancova point estimate consistent as proved by yang and tsiatis 2001 but so is its standard error this implies that confidence intervals and hypothesis tests conducted as if the linear model were correct are still asymptotically valid even when the linear model is arbitrarily misspecified for example when the baseline variables are nonlinearly related to the outcome or there is treatment effect heterogeneity we also give a simple robust formula for the variance reduction equivalently sample size reduction from using ancova by reanalyzing completed randomized trials for mild cognitive impairment schizophrenia and depression we demonstrate how ancova can achieve variance reductions of 4 to 32

on the asymptotic distribution of ratio and regression estimators we give a formal derivation of the asymptotic normality of ratio and regression estimators of a finite population total for simple random sampling and for sampling with probability proportional to aggregate size the results are all well known and widely used of course but a rigorous development spelling out relatively simple sufficient conditions under which the standard results are valid does not seem to be available at present

robustness of ancova in randomized trials with unequal randomization randomized trials with continuous outcomes are often analyzed using analysis of covariance ancova with adjustment for prognostic baseline covariates the ancova estimator of the treatment effect is consistent under arbitrary model misspecification in an article recently published in the journal wang et al proved the model based variance estimator for the treatment effect is also consistent under outcome model misspecification assuming the probability of randomization to each treatment is 1 2 in this reader reaction we derive explicit expressions which show that when randomization is unequal the model based variance estimator can be biased upwards or downwards in contrast robust sandwich variance estimators can provide asymptotically valid inferences under arbitrary misspecification even when randomization probabilities are not equal

structural analysis of a queueing system with multiclasses of correlated arrivals and blocking in assemble to order production systems and others of a similar flavor it is often the case that orders for components of various types are placed simultaneously but that these components are manufactured or assembled at separate facilities t he order process introduces correlation among the jobs at separate facilities the purpose of this paper is to study the effect of this correlation on a variety of system performance measures consider a system that consists of s parallel servers where e ach server has a finite buffer and is dedicated to a separate job type multiple classes of customer orders arrive to the system where each class is composed of one or more unique job types upon the arrival of an order each job in the order is separately routed to its designated buffer if the buffer is full that job is blocked and lost otherwise it enters the buffer and is served according to the fcfs discipline under markovian assumptions we systematically examine the impact of arrival correlati ons on system based performance measures such as the queue length vector and the workload vector and class based performance measures such as the waiting time vector and the order response time among other things we establish several stochastic orders between performance vectors with different degrees of arrival correlations we also show that greater arrival correlation can stochastically improve the worst component in a performance vector e g the longest queue the heaviest workload reduce the expected sum of the j longest queues 1 j s and for any given order type increase its entering probability and reduce its order response time our results can also be extended to the compound poisson arrival process where each order contains multiple units of several job types

multidimensional stochastic ordering and associated random variables this paper presents several relationships between the concept of associated random variables rvs and notions of stochastic ordering the question that provides the impetus for this work is whether the association of the valued rvs x1 xn implies a possible stochastic ordering between the n valued rv x x1 xn and its independent version xi xi 1 xi n this leads to results on how multidimensional probability distributions are determined by conditions on their one dimensional marginal distributions in the event of comparison under the stochastic orderings st c1 cv d and k such results have direct implications for the comparison of bounds for fork join queues and for the structure of monotone functions of several variables

majorization of weighted trees a new tool to study correlated stochastic systems stochastic models with simultaneous arrivals arise naturally in the areas such as synchronized communication networks flexible manufacturing systems production inventory systems reliability modeling in random environment etc with a wide variety of interpretations simultaneous arrivals introduce dependence among various components of the system and make the explicit solutions of joint system performance measures either computationally intensive or intractable this calls for structural analysis of dependence natures of such systems so that the insight gained from the analysis can suggest plausible approaches to develop tight bounds and efficient approximations to key system performance measures the usual majorization order on a totally ordered index set and schur convexity are powerful tools for establishing inequalities in particular for stochastic systems however the investigation on stochastic systems with simultaneous arrivals leads naturally to the comparison of distributions of parameter values on a tree structured index set in this paper we introduce the notion ofmajorization with respect to weighted trees the fundamental strength of tree majorization lies in its ability to make versatile comparisons over two parameter sets defined on a partially ordered index set we identify several classes of transformations that provide simple characterizations of tree majorization orders finally we apply the new notion to an assemble to order system and to a shock model with simultaneous subsystem failures and study the dependence structure of these systems our results show that tree majorization and its interplay with various notions of stochastic orders are useful tools to study the dependency of stochastic systems with multivariate synchronized input processes

outlier robust finite population estimation abstract outliers in sample data are a perennial problem for applied survey statisticians moreover it is a problem for which traditional sample survey theory offers no real solution beyond the sensible advice that such sample elements should not be weighted to their fullest extent in estimation sample outliers can be identified as of two basic types here we are concerned with the first type which may conveniently be termed representative outliers these are sample elements with values that have been correctly recorded and that cannot be assumed to be unique that is there is no good reason to assume there are no more similar outliers in the nonsampled part of the target population the remaining sample outliers which by default are termed nonrepresentative are sample elements whose data values are incorrect or unique in some sense methods for dealing with these nonrepresentative outliers lie basically within the scope of survey editing and imputation theory and are therefore not considered in

miscellanea influence diagnostic in survey sampling conditional bias we propose a diagnostic to assess the influence of a unit u i in the sample s selected from a finite population u u 1 u n using a sampling design d on s as an estimator of a population parameter 0 y 1 y n we adjust the definition of conditional bias munoz pichardo et al 1995 in order to obtain an influence diagnostic in survey sampling conditional bias as an influence measure of unit u i u i s on s depends on y i and on the sampling design d this is a distinctive feature of sample surveys only in particular cases is the proposed influence measure a case deletion diagnostic

approximate analysis of fork join synchronization in parallel queues an approximation technique called scaling approximation is introduced and applied to the analysis of homogeneous fork join queuing systems consisting of k or 2 servers the development of the scaling approximation technique is guided by both experimental and theoretical considerations the approximation is based on the observation that there exist upper and lower bounds on the mean response time that grow at the same rate as a function of k simple closed form approximate expressions for the mean response time are derived and compared to simulation results the relative error in the approximation is less than 5 for k

bias calibrated estimation from sample surveys containing outliers we discuss the problem of estimating finite population parameters on the basis of a sample containing representative outliers we clarify the motivation for chambers s bias calibrated estimator of the population total and show that bias calibration is a key idea in constructing estimators of finite population parameters we then link the problem of estimating the population total to distribution function or quantile estimation and explore a methodology based on the use of chambers s estimator we also propose methodology based on the use of robust estimates and a bias calibrated form of the chambers and dunstan estimator of the population distribution function this proposal leads to a bias calibrated estimator of the population total which is an alternative to that of chambers we present a small simulation study to illustrate the utility of these estimators

upper bounds for single server queues with doubly stochastic poisson arrivals consider the following type of single server queues arrivals are according to a doubly stochastic poisson process with a stationary ergodic random intensity t service times are independent identically distributed also independent from arrivals it is proven that the mean stationary work load is not greater than e 0 where a denotes the mean stationary work load in the m gi 1 queue with arrival intensity a and the same service process similar results are given for the mean stationary queue size and the mean stationary delay

finite population sampling with multivariate auxiliary information abstract this article examines strategies that are approximately design unbiased and nearly optimal assuming a large sample survey and a regression superpopulation model a new class of predictors is proposed to link certain features of optimal design unbiased and model unbiased predictors generalized regression predictors are shown to pervade the subclass of asymptotically design unbiased adu predictors generalized regression predictors are combined with model based stratification to construct highly efficient adu strategies

downweighting influential clusters in surveys certain clusters may be extremely influential on survey estimates and consequently contribute disproportionately to their variance we propose a general approach to estimation that downweights highly influential clusters with the amount of downweighting based on m estimation applied to the empirical influence of the clusters the method is motivated by a problem in census coverage estimation and we illustrate it by using data from the 1990 post enumeration survey pes in this context an objective prespecified methodology for handling influential observations is essential to avoid having to justify judgmental post hoc adjustment of weights in 1990 both extreme weights and large errors in the census led to extreme influence we estimated influence by taylor linearization of the survey estimator and we applied m estimators based on the t distribution and the huber function as predicted by theory the robust procedures greatly reduced the estimated variance of estimated coverage rates more so tha

rearrangement majorization and stochastic scheduling rearrangement inequalities such as the classical hardy littlewood polya inequality and the more general day s inequality and related majorization results are often useful in solving scheduling problems among other things they are essential for pairwise interchange arguments motivated by solving stochastic scheduling problems we develop stochastic versions of day s inequality over both unrestricted and restricted specifically one cycle permutations these lead to a general and unified approach which we apply to solve the stochastic versions of several classical deterministic scheduling problems in most cases the approach leads to new or stronger results in other cases it recovers known results with new insight the approach is built upon recent developments in stochastic majorization and multivariate characterization of stochastic order relations

local influence on the ratio and horvitz thompson estimators through the second order approach abstract since cook introduced the notion of local influence in 1986 a great number of papers have appeared in statistics handling this topic in a wide variety of areas however until we know there is no paper focussed on local influence in survey sampling this paper assesses the local influence through the curvature of the perturbation formed surface of the ratio estimator in a simple random sampling without replacement and the horvitz thompson estimator in an inclusion proportional to size sampling design both estimators use auxiliary information x and can be obtained through a model assisted reasoning where the ratio model with variance proportional to x plays an important role two perturbation schemes are considered a model perturbation and an auxiliary variable perturbation we illustrate the effectiveness of the method in order to identify influential points with two real examples

influence functions and robust bayes and empirical bayes small area estimation we introduce new robust small area estimation procedures based on area level models we first find influence functions corresponding to each individual area level observation by measuring the divergence between the posterior density functions of regression coefficients with and without that observation next based on these influence functions properly standardized we propose some new robust bayes and empirical bayes small area estimators the mean squared errors and estimated mean squared errors of these estimators are also found a small simulation study compares the performance of the robust and the regular empirical bayes estimators when the model variance is larger than the sample variance the proposed robust empirical bayes estimators are superior

robust alternatives to ancova for estimating the treatment effect via a randomized comparative study in comparing two treatments via a randomized clinical trial the analysis of covariance ancova technique is often utilized to estimate an overall treatment effect the ancova is generally perceiv

moving beyond the conventional stratified analysis to estimate an overall treatment efficacy with the data from a comparative randomized clinical study for a two group comparative study a stratified inference procedure is routinely used to estimate an overall group contrast to increase the precision of the simple two sample estimator unfortunately most commonly used methods including the cochran mantel haenszel statistic for a binary outcome and the stratified cox procedure for the event time endpoint do not serve this purpose well in fact these procedures may be worse than their two sample counterparts even when the observed treatment allocations are imbalanced across strata various procedures beyond the conventional stratified methods have been proposed to increase the precision of estimation when the naive estimator is consistent in this paper we are interested in the case when the treatment allocation proportions vary markedly across strata we study the stochastic properties of the two sample naive estimator conditional on the ancillary statistics the observed treatment allocation proportions and or the stratum sizes and present a biased adjusted estimator this adjusted estimator is asymptotically equivalent to the augmentation estimators proposed under the unconditional setting moreover this consistent estimation procedure is also equivalent to a rather simple procedure which estimates the mean response of each treatment group first via a stratum size weighted average and then constructs the group contrast estimate this simple procedure is flexible and readily applicable to any target patient population by choosing appropriate stratum weights all the proposals are illustrated with the data from a cardiovascular clinical trial whose treatment allocations are imbalanced

outlier resistant alternatives to the ratio estimator abstract many techniques have been suggested to lower the impact of outliers on sample survey estimates outliers can be downweighted by winsorization that is by replacing extreme data points by a data dependent or a predetermined value before calculating estimates another approach is to reduce the weight of outliers from the inverse sampling fraction to 1 in the estimation of population characteristics in this article the problem of estimating the population mean using auxiliary information in the presence of outliers is considered a resistant version of the ratio estimator is introduced it is constructed with a m or a gm estimator of the slope of the regression model through the origin which is implicitly called on when considering the ratio estimator the asymptotic biases and asymptotic variances of the proposed alternatives to the ratio estimator are calculated with respect to the randomization of the sampling plan the selection of a resistant estimator is seen to involve a trade off betwee

some estimators of a population total from simple random samples containing large units abstract the problem considered is the estimation of the population total of some characteristic from a simple random sample containing a few large or extreme observations the effect of these large units in the sample is to distort the estimate of the population total it is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units in this paper three estimators that alter the usual sampling weights have been considered the efficiencies of these estimators have been worked out in terms of the ratio of the mean squared error of the usual estimator of the population total to the mean squared error of these estimators a numerical study of these estimators is also discussed

an empirical study of the ratio estimator and estimators of its variance abstract this paper reports results from an empirical study of the ratio estimator for a finite population total from each of six real populations 1 000 simple random samples 1 000 restricted random samples and three nonrandom samples of size 32 are drawn performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using a prediction superpopulation models and b probability sampling distributions the results presented graphically show that theory based on prediction models can reveal relationships that are essential in making inferences but that are concealed in probability sampling analyses