regression models for longitudinal binary responses with informative drop outs this paper reviews both likelihood based and non likelihood generalized estimating equations regression models for longitudinal binary responses when there are drop outs throughout it is assumed that the regression parameters for the marginal expectations of the binary responses are of primary scientific interest the association or time dependence between the responses is largely regarded as a nuisance characteristic of the data the performance of the methods is compared in terms of asymptotic bias under mis specification of the association between the responses and the missing data mechanism or drop out process

fitting regression models to case control data by maximum likelihood summary we consider fitting categorical regression models to data obtained by either stratified or nonstratified case control or response selective sampling from a finite population with known population totals in each response category with certain models such as the logistic with appropriate constant terms a method variously known as conditional maximum likelihood breslow cain 1988 or pseudo conditional likelihood wild 1991 which involves the prospective fitting of a pseudo model results in maximum likelihood estimates of case control data we extend these results by showing the maximum likelihood estimates for any model can be found by iterating this process with a simple updating of offset parameters attention is also paid to estimation of the asymptotic covariance matrix one benefit of the results of this paper is the ability to obtain maximum likelihood estimates of the parameters of logistic models for stratified case control studies compare breslow cain 1988 scott wild 1991 using an ordinary logistic regression program even when the stratum constants are modelled

properties of estimators of the finite population distribution function two leading estimators of the finite population distribution function are studied their large sample mean squared errors are compared under a given model neither estimator is universally better circumstances are identified where the model based estimator would do poorly despite employing the correct model

local multiple imputation dealing with missing data via parametric multiple imputation methods usually implies stating several strong assumptions both about the distribution of the data and about underlying regression relationships if such parametric assumptions do not hold the multiply imputed data are not appropriate and might produce inconsistent estimators and thus misleading results in this paper a fully nonparametric and a semiparametric imputation method are studied both based on local resampling principles it is shown that the final estimator based on these local imputations is consistent under fewer or no parametric assumptions asymptotic expressions for bias variance and mean squared error are derived showing the theoretical impact of the different smoothing parameters simulations illustrate the usefulness and applicability of the method

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

a note about models for selectivity bias on decrit une representation tabulaire simplifiee qui fait ressortir une hypothese structurale implicite importante dans des modeles de selection bases sur la censure

nonparametric estimation of mean functionals with data missing at random abstract this article considers a distribution free estimation procedure for a basic pattern of missing data that often arises from the wellknown double sampling in survey methodology without parametric modeling of the missing mechanism or the joint distribution kernel regression estimators are used to estimate mean functionals through empirical estimation of the missing pattern a generalization of the method of cheng and wei is verified under the assumption of missing at random asymptotic distributions are derived for estimating the mean of the incomplete data and for estimating the mean treatment difference in a nonrandomized observational study the nonparametric method is compared with a naive pairwise deletion method and a linear regression method via the asymptotic relative efficiencies and a simulation study the comparison shows that the proposed nonparametric estimators attain reliable performances in general

an alternative empirical likelihood method in missing response problems and causal inference missing responses are common problems in medical social and economic studies when responses are missing at random a complete case data analysis may result in biases a popular debias method is inverse probability weighting proposed by horvitz and thompson to improve efficiency robins et al proposed an augmented inverse probability weighting method the augmented inverse probability weighting estimator has a double robustness property and achieves the semiparametric efficiency lower bound when the regression model and propensity score model are both correctly specified in this paper we introduce an empirical likelihood based estimator as an alternative to qin and zhang 2007 our proposed estimator is also doubly robust and locally efficient simulation results show that the proposed estimator has better performance when the propensity score is correctly modeled moreover the proposed method can be applied in the estimation of average treatment effect in observational causal inferences finally we apply our method to an observational study of smoking using data from the cardiovascular outcomes in renal atherosclerotic lesions clinical trial copyright 2016 john wiley sons ltd

semiparametric regression analysis with missing response at random we develop inference tools in a semiparametric partially linear regression model with missing response data a class of estimators is defined that includes as special cases a semiparametric regression imputation estimator a marginal average estimator and a marginal propensity score weighted estimator we show that any of our class of estimators is asymptotically normal the three special estimators have the same asymptotic variance they achieve the semiparametric efficiency bound in the homoscedastic gaussian case we show that the jackknife method can be used to consistently estimate the asymptotic variance our model and estimators are defined with a view to avoid the curse of dimensionality which severely limits the applicability of existing methods the empirical likelihood method is developed it is shown that when missing responses are imputed using the semiparametric regression method the empirical log likelihood is asymptotically a scaled chi squared variable an adjusted empirical log likel

on estimating distribution functions and quantiles from survey data using auxiliary information summary ratio and difference estimators of a population distribution function under a general sampling design are obtained using auxiliary population information the relative mean errors and relative mean square errors of these estimators and a model based estimator of chambers dunstan 1986 are compared through a simulation study the advantages of the design based estimators over the model based estimator under model misspecifications especially for large samples are demonstrated ratio and difference estimators of a population quantile are also studied

fuzzy color spaces a conceptual approach to color vision in this paper we introduce formal definitions of the concepts of fuzzy color and fuzzy color space first we formalize the notion of fuzzy color for representing the correspondence between computational representation of colors and perceptual color categories identified by a color name second we propose a methodology for learning fuzzy colors based on the paradigm of conceptual spaces where prototypes are used for each category to be learnt since the conceptual space approach yields crisp categorizations we introduce a novel methodology for defining fuzzy boundaries of color categories on the basis of a voronoi tessellation of a color space finally we also formalize the notion of fuzzy color space as the collection of fuzzy colors corresponding to the color categories employed in a certain context application and or for a specific user different typologies of fuzzy color spaces are proposed in order to be consistent with the nature of the categories we want to model our approach is illustrated by defining fuzzy color spaces using rgb with the euclidean distance examples based on the well known iscc nbs color naming system are presented as well as others based on collections of color names and prototypes provided by users the proposal is evaluated and compared with the most used approaches for color modeling additionally a website located at http www jfcssoftware com including all experimentation data software implementing our models and additional materials is available to researchers in color modeling

estimating equations with nonignorably missing response data troxel lipsitz and brennan 1997 biometrics 53 857 869 considered parameter estimation from survey data with nonignorable nonresponse and proposed weighted estimating equations to remove the biases in the complete case analysis that ignores missing observations this paper suggests two alternative modifications for unbiased estimation of regression parameters when a binary outcome is potentially observed at successive time points the weighting approach of robins rotnitzky and zhao 1995 journal of the american statistical association 90 106 121 is also modified to obtain unbiased estimating functions the suggested estimating functions are unbiased only when the missingness probability is correctly specified and misspecification of the missingness model will result in biases in the estimates simulation studies are carried out to assess the performance of different methods when the covariate is binary or normal for the simulation models used the relative efficiency of the two new methods to the weighting methods is about 3 0 for the slope parameter and about 2 0 for the intercept parameter when the covariate is continuous and the missingness probability is correctly specified all methods produce substantial biases in the estimates when the missingness model is misspecified or underspecified analysis of data from a medical survey illustrates the use and possible differences of these estimating functions

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

toward a curse of dimensionality appropriate coda asymptotic theory for semi parametric models we argue that due to the curse of dimensionality there are major difficulties with any pure or smoothed likelihood based method of inference in designed studies with randomly missing data when missingness depends on a high dimensional vector of variables we study in detail a semi parametric superpopulation version of continuously stratified random sampling we show that all estimators of the population mean that are uniformly consistent or that achieve an algebraic rate of convergence no matter how slow require the use of the selection randomization probabilities we argue that in contrast to likelihood methods which ignore these probabilities inverse selection probability weighted estimators continue to perform well achieving uniform n 1 2 rates of convergence we propose a curse of dimensionality appropriate coda asymptotic theory for inference in non and semi parametric models in an attempt to formalize our arguments we discuss whether our results constitute a fatal blow to the likelihood principle and study the attitude toward these that a committed subjective bayesian would adopt finally we apply our coda theory to analyse the effect of the curse of dimensionality in several interesting semi parametric models including a model for a two armed randomized trial with randomization probabilities depending on a vector of continuous pretreatment covariates x we provide substantive settings under which a subjective bayesian would ignore the randomization probabilities in analysing the trial data we then show that any statistician who ignores the randomization probabilities is unable to construct nominal 95 per cent confidence intervals for the true treatment effect that have both i an expected length which goes to zero with increasing sample size and ii a guaranteed expected actual coverage rate of at least 95 per cent over the ensemble of trials analysed by the statistician during his or her lifetime however we derive a new interval estimator depending on the randomization probabilities that satisfies i and ii

a semiparametric estimation of mean functionals with nonignorable missing data parameter estimation with nonignorable missing data is a challenging problem in statistics the fully parametric approach for joint modeling of the response model and the population model can produce results that are quite sensitive to the failure of the assumed model we propose a more robust modeling approach by considering the model for the nonresponding part as an exponential tilting of the model for the responding part the exponential tilting model can be justified under the assumption that the response probability can be expressed as a semiparametric logistic regression model in this paper based on the exponential tilting model we propose a semiparametric estimation method of mean functionals with nonignorable missing data a semiparametric logistic regression model is assumed for the response probability and a nonparametric regression approach for missing data discussed in cheng 1994 is used in the estimator by adopting nonparametric components for the model the estimation method can be mad

multiply robust estimation in regression analysis with missing data doubly robust estimators are widely used in missing data analysis they provide double protection on estimation consistency against model misspecifications however they allow only a single model for the missingness mechanism and a single model for the data distribution and the assumption that one of these two models is correctly specified is restrictive in practice for regression analysis with possibly missing outcome we propose an estimation method that allows multiple models for both the missingness mechanism and the data distribution the resulting estimator is consistent if any one of those multiple models is correctly specified and thus provides multiple protection on consistency this estimator is also robust against extreme values of the fitted missingness probability which for most doubly robust estimators can lead to erroneously large inverse probability weights that may jeopardize the numerical performance the numerical implementation of the proposed method through a modified newton ra

a general framework for quantile estimation with incomplete data quantile estimation has attracted significant research interests in recent years however there has been only a limited literature on quantile estimation in the presence of incomplete data in this paper we propose a general framework to address this problem our framework combines the two widely adopted approaches for missing data analysis the imputation approach and the inverse probability weighting approach via the empirical likelihood method the proposed method is capable of dealing with many different missingness settings we mainly study three of them i estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates ii estimating the conditional quantile of a fully observed response while the covariates are partially available and iii estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables the proposed method allows multiple models for both the missingness probability and the data distribution the resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified the asymptotic distributions are established using the empirical process theory

missing covariates in generalized linear models when the missing data mechanism is non ignorable we propose a method for estimating parameters in generalized linear models with missing covariates and a non ignorable missing data mechanism we use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one dimensional conditional distributions with each one dimensional conditional distribution consisting of a logistic regression we allow the covariates to be either categorical or continuous the joint covariate distribution is also modelled via a sequence of one dimensional conditional distributions and the response variable is assumed to be completely observed we derive the e and m steps of the em algorithm with non ignorable missing covariate data for categorical covariates we derive a closed form expression for the e and m steps of the em algorithm for obtaining the maximum likelihood estimates mles for continuous covariates we use a monte carlo version of the em algorithm to obtain the mles via the gibbs sampler computational techniques for gibbs sampling are proposed and implemented the parametric form of the assumed missing data mechanism itself is not testable from the data and thus the non ignorable modelling considered here can be viewed as a sensitivity analysis concerning a more complicated model therefore although a model may have passed the tests for a certain missing data mechanism this does not mean that we have captured even approximately the correct missing data mechanism hence model checking for the missing data mechanism and sensitivity analyses play an important role in this problem and are discussed in detail several simulations are given to demonstrate the methodology in addition a real data set from a melanoma cancer clinical trial is presented to illustrate the methods proposed

mann whitney test with adjustments to pretreatment variables for missing values and observational study the conventional wilcoxon mann whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies this is because the missingness of the outcomes or the participation in the treatments may depend on certain pre treatment variables we propose an approach to adjust the mann whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the pre treatment variables we also propose semiparametric extensions of the adjusted mann whitney test which leads to dimension reduction for high dimensional covariate a novel bootstrap procedure is devised to approximate the null distribution of the test statistics for practical implementations results from simulation studies and an economic observational study data analysis are presented to demonstrate the performance of the proposed approach

a munsell colour based approach for soil classification using fuzzy logic and artificial neural networks abstract munsell soil colour charts are widely used for soil classification these charts contain 238 standardised colours in small rectangular chips arranged in seven charts and encoded in the munsell system each chart uses three coordinates well correlated with the visual colour attributes hue value and chroma the colour of a soil sample is commonly estimated by visual comparison between the actual soil colour and the munsell chips looking for the closest one and taking its munsell notation consequently the visual determination of soil colour with munsell charts is a difficult task due to the subjectivity of the observer to match the colour of a soil sample with a single standard munsell chip for this reason to avoid misclassification caused by subjective coincidence we propose an intelligent method to provide the closest values of the munsell chips to an unknown colour of a soil sample by using artificial neural networks and fuzzy logic

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

limits and colimits of hopf algebras abstract it is shown that for any commutative unital ring r the category hopf r of r hopf algebras is locally presentable and a coreflective subcategory of the category bialg r of r bialgebras admitting cofree hopf algebras over arbitrary r algebras the proofs are based on an explicit analysis of the construction of colimits of hopf algebras which generalizes an observation of takeuchi essentially be a duality argument also the dual statement namely that hopf r is closed in bialg r under limits is shown to hold provided that the ring r is von neumann regular it then follows that hopf r is reflective in bialg r and admits free hopf algebras over arbitrary r coalgebras for any von neumann regular ring r finally takeuchi s free hopf algebra construction is analysed and shown to be simply a composition of standard categorical constructions by simple dualization also a construction of the hopf coreflection is provided

fuzzy colour category map for the measurement of colour similarity and dissimilarity a new colour space for representing colour based upon psychophysical research into human perception is presented it provides both the ability to measure similarity and determine dissimilarity using the combination of fuzzy logic and psychologically based set theoretic similarity measurement these abilities are shown to enable it to be equal or superior to conventional colour spaces in measuring the similarity and dissimilarity of colours in addition to being able to saliently label colours for accurate chromatic linguistic description

robust estimation for finite populations based on a working model a common scenario in finite population inference is that it is possible to find a working superpopulation model which explains the main features of the population but which may not capture all the fine details in addition there are often outliers in the population which do not follow the assumed superpopulation model in situations like these it is still advantageous to make use of the working model to estimate finite population quantities provided that we do it in a robust manner the approach that we suggest is first to fit the working model to the sample and then to fine tune for departures from the model assumed by estimating the conditional distribution of the residuals as a function of the auxiliary variable this is a more direct approach to handling outliers and model misspecification than the huber approach that is currently being used two simple methods stratification and nearest neighbour smoothing are used to estimate the conditional distributions of the residuals which result in two modifications to the standard model based estimator of the population distribution function the estimators suggested perform very well in simulation studies involving two types of model departure and have small variances due to their model based construction as well as acceptable bias the potential advantage of the proposed robustified model based approach over direct nonparametric regression is also demonstrated

pattern mixture models for multivariate incomplete data consider a random sample on variables x1 xv with some values of xv missing selection models specify the distribution of x1 xv over respondents and nonrespondents to xv and the conditional distribution that xv is missing given x1 xv in contrast pattern mixture models specify the conditional distribution of x 1 xv given that xv is observed or missing respectively and the marginal distribution of the binary indicator for whether or not xv is missing for multivariate data with a general pattern of missing values the literature has tended to adopt the selection modeling approach see for example little and rubin here pattern mixture models are proposed for this more general problem pattern mixture models are chronically underidentified in particular for the case of univariate nonresponse mentioned above there are no data on the distribution of xv given x1 xv 1 in the stratum with xv missing thus the models require restrictions or prior information to identify the paramet

estimating equations inference with missing data there is a large and growing body of literature on estimating equation ee as an estimation approach one basic property of ee that has been universally adopted in practice is that of unbiasedness and there are deep conceptual reasons why unbiasedness is a desirable ee characteristic this article deals with inference from ees when data are missing at random the investigation is motivated by the observation that direct imputation of missing data in ees generally leads to ees that are biased and thus violates a basic assumption of the ee approach the main contribution of this article is that it goes beyond existing imputation methods and proposes a procedure whereby one mitigates the effects of missing data through a reformulation of ees imputed through a kernel regression method these modified ees then constitute a basis for inference by the generalized method of moments gmm and empirical likelihood el asymptotic properties of the gmm and el estimators of the unknown parameters are derived a

efficient and doubly robust imputation for covariate dependent missing responses in this article we study a well known response missing data problem missing data is an ubiquitous problem in medical and social science studies imputation is one of the most popular methods for dealing with missing data the most commonly used imputation that makes use of covariates is regression imputation in which the regression model can be parametric semiparametric or nonparametric parametric regression imputation is efficient but is not robust against misspecification of the regression model although nonparametric regression imputation such as nearest neighbor imputation and kernel regression imputation is model free it is not efficient especially if the dimension of covariate vector is high the well known problem of curse of dimensionality semiparametric regression imputation such as partially linear regression imputation can reduce the dimension of the covariate in nonparametric regression fitting but is not robust against misspecification of the linear component in the regression

on tree coalgebras and coalgebra presentations for deterministic systems expressed as coalgebras over polynomial functors every tree t an element of the final coalgebra turns out to represent a new coalgebra at the universal property of this family of coalgebras resembling freeness is that for every state s of every system s there exists a unique coalgebra homomorphism from a unique at which takes the root of t to s consequently the tree coalgebras are finitely presentable and form a strong generator thus these categories of coalgebras are locally finitely presentable in particular every system is a filtered colimit of finitely presentable systems in contrast for transition systems expressed as coalgebras over the finite power set functor we show that there are systems which fail to be filtered colimits of finitely presentable finite ones surprisingly if is an uncountable cardinal then presentation is always well behaved whenever an endofunctor f preserves filtered colimits i e is accessible then presentable coalgebras are precisely those whose underlying objects are presentable consequently every f coalgebra is a filtered colimit of presentable coalgebras thus coalg f is a locally presentable category this holds for all endofunctors of accessible categories with colimits of chains corollary a set functor is bounded at in the sense of kawahara and mori iff it is accessible

handling estimating equation with nonignorably missing data based on sir algorithm abstract in this paper the estimation of parameters in estimating equation with nonignorably missing data is considered based on a logistic regression model for the response mechanism and an assumed parametric model for the distribution of respondents we propose to use the sampling importance resampling sir algorithm to calculate the conditional expectation for non respondents the proposed method can avoid the difficulty of high dimensional kernel smoothing on calculating the conditional expectation under nonignorably missing data based on the sir algorithm we derive a modified estimating equation to facilitate comparison we apply the empirical likelihood method to derive the parameters estimator some numerical simulation results based on linear and nonlinear models show that the proposed method is robust and performs the best among the compared existing methods so we extend the estimation method of e g y using sir algorithm with nonignorably missing response to the estimation of parameters in generalized estimating equation and obtain a new and more robust estimation method

use of regression functions for improved estimation of means summary suppose one has a random sample from a distribution fy x the goal being to estimate u4 the unconditional mean of y if the regression function of y on x is of a known parametric form one might consider estimating u by the average of the estimated regression function values at the sample points it is shown here that such an estimator can offer substantial improvement over the sample mean of y and that in no case does the former estimator have larger asymptotic variance than the latter estimator applications of this asymptotic distribution theory to the double sampling setting are also given

multiply robust estimation of causal quantile treatment effects in causal inference often the interest lies in the estimation of the average causal effect other quantities such as the quantile treatment effect may be of interest as well in this article we propose a multiply robust method for estimating the marginal quantiles of potential outcomes by achieving mean balance in a the propensity score and b the conditional distributions of potential outcomes an empirical likelihood or entropy measure approach can be utilized for estimation instead of inverse probability weighting which is known to be sensitive to the misspecification of the propensity score model simulation studies are conducted across different scenarios of correctness in both the propensity score models and the outcome models both simulation results and theoretical development indicate that our proposed estimator is consistent if any of the models are correctly specified in the data analysis we investigate the quantile treatment effect of mothers smoking status on infants birthweight

empirical likelihood based inference under imputation for missing response data inference under kernel regression imputation for missing response data is considered an adjusted empirical likelihood approach to inference for the mean of the response variable is developed a nonparametric version of wilks theorem is proved for the adjusted empirical log likelihood ratio by showing that it has an asymptotic standard chi squared distribution and the corresponding empirical likelihood confidence interval for the mean is constructed with auxiliary information an empirical likelihood based estimator is defined and an adjusted empirical log likelihood ratio is derived asymptotic normality of the estimator is proved also it is shown that the adjusted empirical log likelihood ratio obeys wilks theorem a simulation study is conducted to compare the adjusted empirical likelihood and the normal approximation methods in terms of coverage accuracies and average lengths of confidence intervals based on biases and standard errors a comparision is also made by simulation between the empirical likelihood based estimator and related estimators our simulation indicates that the adjusted empirical likelihood method performs competitively and that the use of auxiliary information provides improved inferences

estimation with missing data beyond double robustness summary we propose an estimator that is more robust than doubly robust estimators based on weighting completecasesusingweightsotherthaninverseprobabilitywhenestimatingthepopulationmean of a response variable subject to ignorable missingness we allow multiple models for both the propensity score and the outcome regression our estimator is consistent if any of the multiple models is correctly specified such multiple robustness against model misspecification is a significant improvement over double robustness which allows only one propensity score model and one outcome regression model our estimator attains the semiparametric efficiency bound when one propensity score model and one outcome regression model are correctly specified without requiring knowledge of which models are correct

application of empirical bayes inference to estimation of rate of change in the presence of informative right censoring we apply parametric empirical bayes inference of morris7 to the estimation of rate of change from incomplete longitudinal studies where the right censoring process is considered informative that is the length of time the subjects participate in the study is associated with level of the study variable ignoring such an association can result in a biased estimate of rate of change the proposed method provides estimates of rate of change for individual subjects as well as for the entire group adjusted for informative right censoring the method is considered more robust than those based on a specific parametric model for the censoring distribution under non informative right censoring these estimators of slopes are equivalent to the bayes estimators derived by fearn 11 we illustrate the method with an example involving renal transplant data we evaluate the method s performance through a simulation study

estimation with survey data under nonignorable nonresponse or informative sampling nonresponse is a very common phenomenon in survey sampling nonignorable nonresponse that is a response mechanism that depends on the values of the variable having nonresponse is the most difficult type of nonresponse to handle this article studies a likelihood based estimation method for data with nonignorable nonresponse the likelihood is semiparametric in the sense that it consists of a parametric component for the response mechanism such as a logistic model and a nonparametric component for the distribution of the variable of interest and the covariates we show how auxiliary information can be augmented to improve the efficiency of estimators asymptotic distributions for the resulting parameter estimates are derived a simulation study shows that the proposed method gives promising results the method can also be applied to problems with two phase sampling in which the second phase sampling is informative

weighted estimating equations with nonignorably missing response data we propose weighted estimating equations for data with nonignorable nonresponse in order to reduce the bias that can occur with a complete case analysis a survey concerning medical practice guidelines malpractice litigation and settlement provides the framework the survey was sent to recipients in two waves those who responded on the first or second wave are used to estimate a nonignorable nonresponse model while the fraction of recipients who never responded is used to allow the percentage of missing data to change with each wave we use the structure of the gee of liang and zeger 1986 biometrika 73 13 22 adding weights equal to the inverse probability of being observed we present simulations demonstrating the bias that can occur with an unweighted analysis and use the survey data to illustrate the methods

on epimorphisms and monomorphisms of hopf algebras abstract we provide examples of non surjective epimorphisms h k in the category of hopf algebras over a field even with the additional requirement that k have bijective antipode by showing that the universal map from a hopf algebra to its enveloping hopf algebra with bijective antipode is an epimorphism in hopfalg although it is known that it need not be surjective dual results are obtained for the problem of whether monomorphisms in the category of hopf algebras are necessarily injective we also notice that these are automatically examples of non faithfully flat and respectively non faithfully coflat maps of hopf algebras

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

a kernel method for estimating finite population distribution functions using auxiliary information summary this paper considers the use of auxiliary information to improve the estimation of the distribution function of a finite population a method is proposed which combines the known distribution of the auxiliary variable with a kernel estimate of the conditional distribution of the survey variable given the value of the auxiliary variable the resulting estimator compares favourably with existing estimators in terms of efficiency conditional behaviour and robustness the proposed method also has the advantage of producing estimates which are bona fide distribution functions this is not the case for many calibration type estimators suggested in the literature finally the proposed method is applicable under any probability sampling scheme