over dispersed age period cohort models summarywe consider inference and forecasting for aggregate data organised in a two way table with age and cohort as indices but without measures of exposure this is modelled using a poisson likelihood with an age period cohort structure for the mean while allowing for over dispersion we propose a repetitive structure that keeps the dimension of table fixed while increasing the latent exposure for this we use a class of infinitely divisible distributions which include a variety of compound poisson models and poisson mixture models this results in asymptotic f inference and t forecast distributions

score tests in generalized linear measurement error models summary hypothesis tests in generalized linear models are studied under the condition that a surrogate w is observed in place of the true predictor x the efficient score test for the hypothesis of no association depends on the conditional expectation e xi w which is generally unknown the usual test substitutes w for e xi w and is asymptotically valid but not efficient we investigate two new test statistics appropriate when w x z where z is an independent measurement error the first is a wald test based on estimators corrected for measurement error despite the correction for attenuation in the estimator this test has the same local power as the usual test the second test employs an estimator of e x i w and is both asymptotically efficient for normal errors and approximately efficient when the measurement error variance is small

beta binomial poisson regression models for repeated bivariate counts we analyze data obtained from a study designed to evaluate training effects on the performance of certain motor activities of parkinson s disease patients maximum likelihood methods were used to fit beta binomial poisson regression models tailored to evaluate the effects of training on the numbers of attempted and successful specified manual movements in 1 min periods controlling for disease stage and use of the preferred hand we extend models previously considered by other authors in univariate settings to account for the repeated measures nature of the data the results suggest that the expected number of attempts and successes increase with training except for patients with advanced stages of the disease using the non preferred hand

tests for no treatment effect in randomized clinical trials summary we propose a test of the null hypothesis of no treatment effect in a randomized clinical trial that is based on the randomization distribution of residuals these residuals result from regressing the response on covariates but not treatment in contrast to model based score tests this procedure maintains nominal size when the model is misspecified and in particular when relevant covariates are omitted from the regression the efficiency of the procedure is evaluated for regressions with some but not all required covariates for many generalized linear models and survival models conventional model based score tests are shown to have supranominal size when relevant covariates are omitted but logistic regression and the proportional hazards model are robust

estimating a population of parameter values using bayes and empirical bayes methods abstract in standard bayes and empirical bayes component decision problems estimating inidividual parameters is the primary goal in multiple comparison problems and in comparisons of histograms of estimates however the primary goal is to produce parameter estimates that can be considered as an ensemble for example the histogram of estimates should be a good estimate of the histogram of parameters standard methods of estimating by the posterior expectation do minimize symmetric componentwise losses such as squared error but they produce ensembles of estimates with a sample variance smaller than the posterior expected sample variance for parameters in this article we propose new bayes and empirical bayes estimates that minimize a distance function between the empirical cdf of the estimates and the true parameters these estimators are weighted averages of the prior mean and the data with weight on the data being approximately the square root of that for the posterior expectation we give theoreti

l measure of non exchangeability for bivariate extreme value and archimax copulas in the class of bivariate extreme value copulas an upper bound is calculated for the measure of non exchangeability based on the l norm distance between a copula c and its transpose ct x y c y x copulas that are maximally non exchangeable with respect to are also determined moreover similar upper bounds are given respectively for the class of all ev copulas having a fixed upper tail dependence coefficient and for the larger class of archimax copulas

transitivity bounds in additive fuzzy preference structures transitivity plays a crucial role in preference modeling and related fields in this paper we discuss this property in the general context of additive fuzzy preference structures of particular interest is the decomposition of a large preference relation r in its symmetric part i indifference relation and its asymmetric part p strict preference relation by means of a so called indifference generator i given the type of transitivity of a large preference relation r w r t a conjunctor and a generator we establish basic lower bounds and general upper bounds on the transitivity of p and i these bounds are due to the careful design of generic counterexamples moreover we identify the situations in which these bounds are effectively reached thereby establishing connections with interesting properties such as dominance bisymmetry the 1 lipschitz property and rotation invariance

on the insensitivity of the score test for heterogeneity to omitted covariates in multivariate failure time models the multivariate weibull distribution often provides a point of departure for modelling repeated or a sequence of failure times for a particular individual it is then natural to want to test the implied assumption of homogeneity and a number of authors have derived a score test for this purpose see for example kimber 1996 in the present paper it is shown that the proposed score test for neglected heterogeneity can be insensitive to specification error in the implied log linear regression structure

reducing measurement error in student achievement estimation the achievement level is a variable measured with error that can be estimated by means of the rasch model teacher grades also measure the achievement level but they are expressed on a different scale this paper proposes a method for combining these two scores to obtain a synthetic measure of the achievement level based on the theory developed for regression with covariate measurement error in particular the focus is on ordinal scaled grades using the simex method for measurement error correction the result is a measure comparable across subjects with smaller measurement error variance an empirical application illustrates the method

a disaggregate negative binomial regression procedure for count data analysis various research areas face the methodological problems presented by nonnegative integer count data drawn from heterogeneous populations we present a disaggregate negative binomial regression procedure for analysis of count data observed for a heterogeneous sample of cross sections possibly over some fixed time periods this procedure simultaneously pools or groups cross sections while estimating a separate negative binomial regression model for each group an e m algorithm is described within a maximum likelihood framework to estimate the group proportions the group specific regression coefficients and the degree of overdispersion in event rates within each derived group the proposed procedure is illustrated with count data entailing nonnegative integer counts of purchases events for a frequently bought consumer good

estimation of additive regression models with known links summary we consider estimation of an additive nonparametric regression model with known link function the asymptotic distribution of this regression estimate is given the practical performance is investigated via an application to the study of migration between east and west germany

meta theorems on inequalities for scalar fuzzy set cardinalities we present meta theorems stating general conditions ensuring that certain inequalities for cardinalities of ordinary sets are preserved under fuzzification when adopting a scalar approach to fuzzy set cardinality the conditions pertain to the commutative conjunctor used for modelling fuzzy set intersection in particular this conjunctor should fulfil a number of bell type inequalities the advantage of these meta theorems is that repetitious calculations can be avoided this is illustrated in the demonstration of the lukasiewicz transitivity of fuzzified versions of the simple matching coefficient and the jaccard coefficient or equivalently the triangle inequality of the corresponding dissimilarity measures

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

on degrees of asymmetry of a copula with respect to a track abstract in this paper we provide lower and upper bounds on the degree of asymmetry of a copula with respect to a track a continuous and strictly increasing curve in the unit square generalizing the problem with respect to the main diagonal we also study an average asymmetry in sections for given tracks finally we also give an asymmetry map with respect to the opposite diagonal

using the overdispersed exponential family to estimate the distribution of usual daily intakes of people aged between 18 and 28 in taiwan assessment of usual dietary intake of a population is essential to understand the nutrition status of the population methods like 24 hour dietary recall and food records are commonly used for this task however within individual variation exists in the food record data methods considering measurement errors have been used to evaluate the association between nutrient intakes and diseases few have been devoted to estimating the distribution of usual daily intakes this paper proposes applying the formulation of the overdispersed exponential family to estimate the distribution of usual nutrient intake and applies the adjustments developed by liu to reduce the variance of the distribution the proposed method has the advantages of working on the original scale of data and implementation convenience the adjustment of the variance is carried out by dividing the variance into within individual variance and among individual variance the adjusted variance then is used to estimate the distribution of the usual daily intake sampling weights are considered in all the steps except the estimation of the ratio of within to among variance the data for this study are from the nutritional and health survey in taiwan conducted between 1993 and 1996 nahsit 1993 1996 an independent external set of data for people aged between 18 and 28 years 49 males and 20 females is used to estimate the ratio of within to among individual variance due to the availability of data in estimating the ratio of within to among individual variance 430 males and 422 females in the nahsit sample are used to estimate the distribution of usual daily intakes for people aged between 18 and 28 in taiwan the distribution also allows us to estimate the proportion of people who do not meet the recommended daily nutrient allowance rdna the results show that the intakes of calcium and vitamin e of this group of people fall far below rdna

tests for homogeneity of odds ratio when the data are sparse summary three tests for homogeneity of odds ratio for a series of 2 x 2 tables when the data are sparse are studied by means of monte carlo experiments a score test based on the assumption that the log odds ratios are generated from some unknown distribution is shown to be more powerful than the other two the original test of zelen 1971 later corrected by halperin ware byar et al 1977 is also examined it tends to be too liberal under the sparse data situation however it has approximately the nominal size when there are as many as ten tables with as few as ten observations per table

the effect of measurement error summary measurement error causes the distribution generating data to differ from the distribution that is of substantive interest to understand the effect of measurement error on the information produced by statistical procedures it is thus necessary to understand the distortions induced by measurement error this paper sheds light on this by providing small error variance approximations to the distribution of variates subject to contamination by measurement error these provide the basis for the analysis of the properties of estimators and tests and less formal procedures when measurement error is present and the basis for the development of tests to detect measurement error and of models which incorporate its influence

spatial classification using fuzzy membership models in the usual statistical approach to spatial classification it is assumed that each pixel belongs to precisely one of a small number of known groups this framework is extended to include mixed pixel data then only a proportion of each pixel belongs to each group two models based on multivariate gaussian random fields are proposed to model this fuzzy membership process the problems of predicting the group membership and estimating the parameters are discussed some simulations are presented to study the properties of this approach and an example is given using landsat remote sensing data

semiparametric regression models for repeated events with random effects and measurement error abstract statistical methodology is presented for the regression analysis of multiple events in the presence of random effects and measurement error omitted covariates are modeled as random effects our approach to parameter estimation and significance testing is to start with a naive model of semiparametric poisson process regression and then to adjust for random effects and any possible covariate measurement error we illustrate the techniques with data from a randomized clinical trial for the prevention of recurrent skin tumors

tests of homogeneity for generalized linear models abstract we propose two tests for testing homogeneity among clustered data adjusting for the effects of covariates the first is a score test for a generalized linear model with random effect in which the distribution of the response variable given the random effect is entirely defined in contrast to the likelihood ratio test however the score test does not require estimation of the parameters of a mixed effects model nor specification of the mixing distribution the second test is proposed in the framework of the generalized estimating equation gee approach in deriving this test we need only the specification of the marginal expectation and variance of the response variable and the fourth moment for the overdispersion term whereas for deriving the score test for mixed effects models the entire conditional distribution must be specified we demonstrate that the two tests are identical when the covariance matrix assumed in the gee approach is that of the random effects model in both approaches

relation between non exchangeability and measures of concordance of copulas abstract an investigation is presented of how a comprehensive choice of five most important measures of concordance namely spearman s rho kendall s tau gini s gamma blomqvist s beta and their weaker counterpart spearman s footrule relate to non exchangeability i e asymmetry on copulas besides these results the method proposed also seems to be new and may serve as a raw model for exploration of the relationship between a specific property of a copula and some of its measures of dependence structure or perhaps the relationship between various measures of dependence structure themselves

analysis of two way layout of count data involving multiple counts in each cell abstract multiple counts may occur in each cell of an a b two way layout balanced or unbalanced of two fixed factors a and b standard log linear model analysis based on a poisson distribution assumption of the cell counts is not applicable here because of the unbalanced nature of the table or because the poisson distribution assumption is not valid we develop c tests for interaction and main effects assuming data to be poisson distributed and also assuming that data within the cells have extra over under dispersion beyond that explained by a poisson distribution for this we consider an extended negative binominal distribution and a semiparametric model using the quasi likelihood we show that in all situations the c tests for interaction are of very simple forms for c tests for the main effect in presence of no interaction such simplification is possible only under certain conditions a score test for detecting extra dispersion in presence of interaction is also obtained and is of sim

computer assisted analysis of mixtures c a man statistical algorithms summary this paper presents various algorithmic approaches for computing the maximum likelihood estimator of the mixing distribution of a one parameter family of densities and provides a unifying computeroriented concept for the statistical analysis of unobserved heterogeneity i e observations stemming from different subpopulations in a univariate sample the case with unknown number of population subgroups as well as the case with known number of population subgroups with emphasis on the first is considered in the computer package c a man computer assisted mixture analysis it includes an algorithmic menu with choices of the em algorithm the vertex exchange algorithm a combination of both as well as the vertex direction method to ensure reliable convergence a steplength menu is provided for the three latter methods each achieving monotonicity for the direction of choice c a man has the option to work with restricted support size that is the case when the number of components is known a priori in the latter case the em algorithm is used applications of mixture modelling in medical problems are discussed

a simple method for analysing overdispersion in clustered poisson data a simple method is proposed for analysing grouped count data exhibiting overdispersion relative to a poisson model the method is similar to the approach suggested for the analysis of clustered binary data in rao and scott 1992 it requires no specific model for the overdispersion and it can be implemented easily using standard programs designed to handle independent poisson counts after a small amount of preprocessing

bayesian semiparametric analysis of developmental toxicology data modeling of developmental toxicity studies often requires simple parametric analyses of the dose response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure this article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations we approach our analysis using a bayesian semiparametric model that we tailored specifically to developmental toxicology studies it combines parametric dose response relationships with a flexible nonparametric specification of the distribution of the response obtained via a product of dirichlet process mixtures approach pdpm our formulation achieves three goals 1 the distribution of the response is modeled in a general way 2 the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data and 3 the marginal posterior distribution of the parameters of interest is available in closed form the logistic regression model as well as many of its extensions such as the beta binomial model and finite mixture models are special cases in the context of the two motivating examples and a simulated example we provide model comparisons illustrate overdispersion diagnostics that can assist model specification show how to derive posterior distributions of the effective dose parameters and predictive distributions of response and discuss the sensitivity of the results to the choice of the prior distribution

zero linear copulas abstract we introduce a new method for constructing copulas c a special type of aggregation functions based on the idea that c u v 0 if u g v for any continuous and decreasing function g 0 1 0 1 such that g 1 0 and c is linear if u g v 1 we also study the relationship between these copulas and other known families of copulas we provide some salient properties and measure the dependence and asymmetry in this class of copulas

hierarchical models a current computational perspective 2000 hierarchical models a current computational perspective journal of the american statistical association vol 95 no 452 pp 1312 1316

local model uncertainty and incomplete data bias with discussion problems of the analysis of data with incomplete observations are all too familiar in statistics they are doubly difficult if we are also uncertain about the choice of model we propose a general formulation for the discussion of such problems and develop approximations to the resulting bias of maximum likelihood estimates on the assumption that model departures are small loss of efficiency in parameter estimation due to incompleteness in the data has a dual interpretation the increase in variance when an assumed model is correct the bias in estimation when the model is incorrect examples include non ignorable missing data hidden confounders in observational studies and publication bias in meta analysis doubling variances before calculating confidence intervals or test statistics is suggested as a crude way of addressing the possibility of undetectably small departures from the model the problem of assessing the risk of lung cancer from passive smoking is used as a motivating example

estimation for the nonlinear functional relationship on etudie les proprietes asymptotiques de l estimateur du maximum de vraisemblance pour le modele fonctionnel implicite

understanding the effect of measurement error on quantile regressions the impact of measurement error in explanatory variables on quantile regression functions is investigated using a small variance approximation the approximation shows how the error contaminated and error free quantile regression functions are related a key factor is the distribution of the error free explanatory variable exact calculations probe the accuracy of the approximation the order of the approximation error is unchanged if the density of the error free explanatory variable is replaced by the density of the error contaminated explanatory variable which is easily estimated it is then possible to use the approximation to investigate the sensitivity of estimates to varying amounts of measurement error

a score test for testing a zero inflated poisson regression model against zero inflated negative binomial alternatives count data often show a higher incidence of zero counts than would be expected if the data were poisson distributed zero inflated poisson regression models are a useful class of models for such data but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the poisson distribution we therefore provide a score test for testing zero inflated poisson regression models against zero inflated negative binomial alternatives

models for zero inflated correlated count data with extra heterogeneity when is it too complex statistical analysis of count data typically starts with a poisson regression however in many real life applications it is observed that the variation in the counts is larger than the mean and one needs to deal with the problem of overdispersion in the counts several factors may contribute to overdispersion 1 unobserved heterogeneity due to missing covariates 2 correlation between observations such as in longitudinal studies and 3 the occurrence of many zeros more than expected from the poisson distribution in this paper we discuss a model that allows one to explicitly take each of these factors into consideration the aim of this paper is twofold 1 investigate whether we can identify the cause of overdispersion via model selection and 2 investigate the impact of a misspecification of the model on the power of a covariate the paper is motivated by a study of the occurrence of drug induced arrhythmia in beagle dogs based on electrocardiogram recordings with the objective to evaluate the effect of potential drugs on the heartbeat irregularities copyright 2016 john wiley sons ltd

instrumental variable treatment of nonclassical measurement error models while the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors in variables models with continuously distributed variables our main identifying assumption is that conditional on the value of the true regressors some measure of location of the distribution of the measurement error e g its mean mode or median is equal to zero the proposed approach relies on the eigenvalue eigenfunction decomposition of an integral operator associated with specific joint probability densities the main identifying assumption is used to index the eigenfunctions so that the decomposition is unique we propose a convenient sieve based estimator derive its asymptotic properties and investigate its finite sample behavior through monte carlo simulations

heterogeneous treatment effects instrumental variables without monotonicity imbens and angrist 1994 were the first to exploit a monotonicity condition in order to identify a local average treatment effect parameter using instrumental variables more recently heckman and vytlacil 1999 suggested the estimation of a variety of treatment effect parameters using a local version of their approach we investigate the sensitivity of the respective estimates to random departures from monotonicity approximations to the respective bias terms are derived in an empirical application the bias is calculated and bias corrected estimates are obtained the accuracy of the approximation is investigated in a monte carlo study

odds ratio inference with dependent data summary when data can be presented as a series of k 2 x 2 tables with cell counts xi ni xi yi mi yi it is often assumed that xi and yi are binomially distributed this paper deals with inference for the common odds ratio i l when the binomial assumption is invalid when k increases the consistency and asymptotic normality of the mantel haenszel 1959 estimator is derived the conditional maximum likelihood estimator is shown to be inconsistent and the asymptotic bias is computed when either the first order markov chain or beta binomial model is assumed the mantel haenszel test for testing f 1 is also shown to be inappropriate through some simulation studies two consistent test statistics are proposed and shown to be comparable to each other in terms of size and efficiency some possible further work is described

best possible bounds on the set of copulas with a given value of spearman s footrule abstract in this paper we find pointwise best possible bounds on the set of copulas with a given value of the spearman s footrule coefficient we show that the lower bound is always a copula but unlike the bounds on sets of copulas with a given value of other measures such as kendall s tau spearman s rho and blonqvist s beta the upper bound can be a copula or a proper quasi copula we characterised both of these cases

nonparametric identification and semiparametric estimation of classical measurement error models without side information virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information e g validation data known error distributions repeated measurements or instruments in contrast we establish that the fully nonparametric classical errors in variables model is identifiable from data on the regressor and the dependent variable alone unless the model takes a very specific parametric form this parametric family includes but is not limited to the linear specification with normally distributed variables as a well known special case this result relies on standard primitive regularity conditions taking the form of smoothness constraints and nonvanishing characteristic functions assumptions our approach can handle both monotone and nonmonotone specifications provided the latter oscillate a finite number of times given that the very specific unidentified parametric functional form is arguably the exception rather than the rule this identification r

generalised residuals and heterogeneous duration models with applications to the weilbull model this paper deals with models for the duration of an event that are misspecified by the neglect of random multiplicative heterogeneity in the hazard function this type of misspecification has been widely discussed in the literature e g heckman and singer 1982 lancaster and nickell 1980 but no study of its effect on maximum likelihood estimators has been given this paper aims to provide such a study with particular reference to the weibull regression model which is by far the most frequently used parametric model e g heckman and borjas 1980 lancaster 1979 in this paper we define generalised errors and residuals in the sense of cox and snell 1968 1971 and show how their use materially simplifies the analysis of both true and misspecified duration models we show that multiplicative heterogeneity in the hazard of the weibull model has two errors in variables interpretations we give the exact asymptotic inconsistency of m l estimation in the weibull model and give a general expression for the inconsistency of m l estimators due to neglected heterogeneity for any duration model to o 2 where 2 is the variance of the error term we also discuss the information matrix test for neglected heterogeneity in duration models and consider its behaviour when 2 0

on a simple test for neglected heterogeneity in panel studies summary this paper deals with the performance of a simple test for the detection of unmeasured heterogeneity in regression models for panel data it is assumed that the unmeasured heterogeneity can be modeled by an individual specific random variable that does not vary over time conditionally on the individual specific effects and the regressor variables the distribution of the dependent variable is assumed to belong to a linear exponential family this class of distributions includes linear models for continuous dependent variables as well as nonlinear models for discrete outcomes the proposed test does not assume a special form of the distribution of the heterogeneity and the test statistic can be calculated with available computer programs the performance of the test is investigated in a simulation experiment

best possible bounds on the set of copulas with given degree of non exchangeability abstract we establish best possible bounds on the set of quasi copulas with given degree of non exchangeability these bounds are shown to be best possible bounds as well for the set of copulas with given degree of non exchangeability and consequently also on the set of bivariate distribution functions of continuous random variables with given margins and given degree of non exchangeability non exchangeability of a quasi copula is measured in the sense of nelsen i e proportional to the maximal absolute difference between this quasi copula and its transpose

tests for detecting overdispersion in models with measurement error in covariates measurement error in covariates can affect the accuracy in count data modeling and analysis in overdispersion identification the true mean variance relationship can be obscured under the influence of measurement error in covariates in this paper we propose three tests for detecting overdispersion when covariates are measured with error a modified score test and two score tests based on the proposed approximate likelihood and quasi likelihood respectively the proposed approximate likelihood is derived under the classical measurement error model and the resulting approximate maximum likelihood estimator is shown to have superior efficiency simulation results also show that the score test based on approximate likelihood outperforms the test based on quasi likelihood and other alternatives in terms of empirical power by analyzing a real dataset containing the health related quality of life measurements of a particular group of patients we demonstrate the importance of the proposed methods by showing that the analyses with and without measurement error correction yield significantly different results copyright 2015 john wiley sons ltd

conditional independence models for epidemiological studies with covariate measurement error we construct a unifying representation of the structure of measurement error problems with particular reference to situations commonly encountered in epidemiological studies and outline how estimation of the parameters of interest can be carried out in a bayesian framework using gibbs sampling we show how this approach can be implemented for designs involving continuous measurement errors assessed through a validation substudy and discuss our results on simulated data

instrumental variable estimation of nonlinear errors in variables models this paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of fourier transforms of conditional expectations of observable variables for parametrically specified regression functions we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged in nonparametric kernel density estimate both the identification and the estimation methodologies rely on fourier analysis and on the theory of generalized functions the finite sample properties of the estimator are investigated through monte carlo simulations

diagnostics for overdispersion abstract diagnostic tools are proposed for assessing the dependence of extrabinomial or extra poisson variation on explanatory variables and for comparing several common models for overdispersion these tools are based on tests for regression terms in the dispersion parameter of a generalized linear model using double exponential family and pseudolikelihood formulations score tests do not require the full fitting of models for variation and lead to easy graphical and numerical procedures based on squared residuals deviance or pearson robust modifications of these are motivated by levene s test in linear models the diagnostic tools are intended primarily to ensure prudent modeling of the variance to make correct inferences about parameters in the mean

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

duration response measurement error the impact of response measurement error in duration data is investigated using small parameter asymptotic approximations and compared with the effect of hazard function heterogeneity the approximations lead to a specification test to detect measurement error which is shown to be related to the class of information matrix tests it is shown that in a commonly used class of models the test statistic is exactly pivotal the second order asymptotic properties of the alternative forms of the test statistic are derived and the quality of the approximations and the performance of the test are investigated via monte carlo experimentation

estimating prevalence by group testing using generalized linear models a method is described for estimating prevalence by group testing using generalized linear models this provides a simple way of analysing such data using widely available software existing methodology to correct for overdispersion using quasi likelihoods is applied to the group testing model the methods are illustrated by an estimation of salmonella contamination in eggs and of yellow fever virus infection in a mosquito population

bell type inequalities for quasi copulas we present all bell type inequalities regarding at most four random events of which not more than two are intersected at the same time reformulating these inequalities in the context of fuzzy probability calculus leads to related inequalities on commutative conjunctors we prove that some of these inequalities hold for quasi copulas or copulas additionally for the important parametric family of frank t norms which are also copulas we identify for each of the inequalities the parameter values for which it is fulfilled thereby completing the results of pykacz and d hooghe

generalized score test of homogeneity based on correlated random effects models summary we present a family of tests based on correlated random effects models which provides a synthesis and a generalization of recent work on homogeneity testing in these models each subject has a particular random effect but the random effects between subjects are correlated we derive the general form of the score statistic for testing that the random effects have a variance equal to 0 we apply this result to both parametric and semiparametric models in both cases we show that under certain conditions the score statistic has an asymptotic normal distribution we consider several applications of this theory including overdispersion heterogeneity between groups spatial correlations and genetic linkage

individual tree based species classification in high spatial resolution aerial images of forests using fuzzy sets this paper presents an application of fuzzy set theory for classification of individual tree crowns into species groups in high spatial resolution colour infrared aerial photographs in this type of digital image the trees are visible as individual objects the number of individuals to classify might be very large in the acquired set of photographs but the applied grade of membership gom model which this paper focuses on is suitable for dealing with large datasets the extent of each tree crown in the image is defined using a previously published procedure based on colour information hue an optimal fuzzy thresholding technique divides the tree crown universal set into a dominant set and its minor complement nine different features of each image object are estimated and transformed using principal component analysis pca the first three or four pcs are subsequently used in the gom model furthermore the concept of fuzzy relation is applied to one of the descriptors to predict a centroid of the star shaped pattern of norway spruce the gom model needs initial membership values which are estimated using an unsupervised fuzzy clustering approach of small subareas branches in the tree crowns and their corresponding digital numbers in each colour band rgb images the complete classification system comprises three independent components decisions on coniferous deciduous scots pine norway spruce and birch aspen the accuracies ground patches excluded using the supervised gom model with crossvalidation are 87 76 and 79 respectively the accuracy for the compounded system is 67

on the efficiency of quasi likelihood estimation summary a quasi likelihood method has been proposed by wedderburn 1974 for the estimation of parameters in regression models when there is some assumed relationship between the mean and variance of each observation but not necessarily a fully specified likelihood if the underlying distribution comes from a natural exponential family the quasi likelihood estimates maximize the likelihood and so have full asymptotic efficiency under more general distributions there is some loss of efficiency which is investigated here three types of model are discussed in detail models with constant variance models with constant coefficient of variation and models with overdispersion relative to some exponential family the asymptotic efficiency of quasi likelihood estimation is calculated under some particular distributions and then more generally via an approximation for small departures from the corresponding natural exponential family the possibility of refinement of the quasi likelihood approach to incorporate additional information about the underlying distribution is considered

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors abstract this paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes which is of empirical importance we show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of interest which has been observed in linear parametric models two step consistent estimators of the parameters of interest are proposed we also show that the proposed estimators are consistent with a rate faster than n 1 4 under a certain metric and the proposed estimators of the finite dimensional unknown parameters obtain root n asymptotic normality monte carlo evidences show that the proposed estimators perform well under a variety of identification conditions an application to instrumental variables estimation of engel curves illustrates the usefulness of our method it supports that correcting for both endogeneity and measurement errors on total expenditure is substantial in estimating economically meaningful engel curves

on the degree of asymmetry of a quasi copula with respect to a curve abstract the geometrical interpretation of symmetry of a function on the unit square is that it takes the same value in mirror images w r t the main diagonal here this concept is generalized by considering the reflection w r t a curve representing the graph of an automorphism of the unit interval a function on the unit square that takes the same value in mirror images w r t such a curve is called symmetric w r t that curve moreover a measure is proposed for quantifying to what extent a quasi copula can be regarded as being asymmetric w r t a given curve the major part of the paper is concerned with establishing lower and upper bounds on this degree of asymmetry finally it is shown that these bounds are sharp within the class of copulas

robust and consistent estimation of nonlinear errors in variables models this paper considers the consistent estimation of nonlinear errors in variables models it adopts the functional modeling approach by assuming that the true but unobserved regressors are random variables but making no parametric assumption on the distribution from which the latent variables are drawn this paper shows how the information extracted from the replicate measurements can be used to identify and consistently estimate a general nonlinear errors in variables model the identification is established through characteristic functions the estimation procedure involves nonparametric estimation of the conditional density of the latent variables given the measurements using the identification results at the first stage and at the second stage a semiparametric nonlinear least squares estimator is proposed the consistency of the proposed estimator is also established finite sample performance of the estimator is investigated through a monte carlo study

local polynomial regression and simulation extrapolation summary the paper introduces a new local polynomial estimator and develops supporting asymptotic theory for nonparametric regression in the presence of covariate measurement error we address the measurement error with cook and stefanski s simulation extrapolation simex algorithm our method improves on previous local polynomial estimators for this problem by using a bandwidth selection procedure that addresses simex s particular estimation method and considers higher degree local polynomial estimators we illustrate the accuracy of our asymptotic expressions with a monte carlo study compare our method with other estimators with a second set of monte carlo simulations and apply our method to a data set from nutritional epidemiology simex was originally developed for parametric models although simex is in principle applicable to nonparametric models a serious problem arises with simex in nonparametric situations the problem is that smoothing parameter selectors that are developed for data without measurement error are no longer appropriate and can result in considerable undersmoothing we believe that this is the first paper to address this difficulty

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

overdispersion diagnostics for generalized linear models abstract generalized linear models glm s are simple convenient models for count data but they assume that the variance is a specified function of the mean although overdispersed glm s allow more flexible mean variance relationships they are often not as simple to interpret nor as easy to fit as standard glm s this article introduces a convexity plot or c plot for short that detects overdispersion and relative variance curves and relative variance tests that help to understand the nature of the overdispersion convexity plots sometimes detect overdispersion better than score tests and relative variance curves and tests sometimes distinguish the source of the overdispersion better than score tests

a mixed effects model for overdispersed count data in animal breeding count data models are developed for animal breeding applications to account for more variability than in a poisson mixed effects model a gamma distribution is assigned to poisson parameters thereby leading to a negative binomial model the natural log of the expected value of the poisson parameter is expressed as a linear function of fixed and random polygenic effects the negative binomial and poisson mixed models were compared in two simulations in the first marginal maximum likelihood mml estimates of genetic variances obtained under a poisson sire model psm and under a poisson animal model pam accounting for half sib relationships were different contrary to what occurs in a gaussian mixed linear model mml estimates of genetic variance under a negative binomial sire model were less biased than estimates under a psm and had a slightly smaller mean squared error mse the second simulation compared animal models in which the variance of the residuals was larger than the genetic variance empirical relative bias and mse of mml estimates of genetic variance were larger under a pam that ignored the residuals than under a negative binomial animal model differences in performance widened as genetic variance increased an application to the analysis of number of artificial inseminations until conception in dairy heifers is presented to illustrate potential differences in genetic variance estimates under the two animal models

density estimation in the presence of heteroscedastic measurement error we consider density estimation when the variable of interest is subject to heteroscedastic measurement error the density is assumed to have a smooth but unknown functional form that we model with a penalized mixture of b splines we treat the situation in which multiple mismeasured observations of each variable of interest are observed for at least some of the subjects and the measurement error is assumed to be additive and normal the measurement error variance function is modeled with a second penalized mixture of b splines the article s main contributions are to address the effects of heteroscedastic measurement error effectively explain the biases caused by ignoring heteroscedasticity and present an equivalent kernel for a spline based density estimator derivation of the equivalent kernel may be of independent interest we use small sigma asymptotics to approximate the biases incurred by assuming that the measurement error is homoscedastic when it actually is heteroscedastic the biases incurred

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

estimation of nonlinear models with measurement error this paper presents a solution to an important econometric problem namely the root n consistent estimation of nonlinear models with measurement errors in the explanatory variables when one repeated observation of each mismeasured regressor is available while a root n consistent estimator has been derived for polynomial specifications see hausman ichimura newey and powell 1991 such an estimator for general nonlinear specifications has so far not been available using the additional information provided by the repeated observation the suggested estimator separates the measurement error from the true value of the regressors thanks to a useful property of the fourier transform the fourier transform converts the integral equations that relate the distribution of the unobserved true variables to the observed variables measured with error into algebraic equations the solution to these equations yields enough information to identify arbitrary moments of the true unobserved variables the value of these moments can then be used to construct any estimator that can be written in terms of moments including traditional linear and nonlinear least squares estimators or general extremum estimators the proposed estimator is shown to admit a representation in terms of an influence function thus establishing its root n consistency and asymptotic normality monte carlo evidence and an application to engel curve estimation illustrate the usefulness of this new approach

a fuzzy k partitions model for categorical data and its comparison to the gom model the grade of membership gom model uses fuzzy sets as memberships of each individual to extreme profiles or classes on the likelihood function of multivariate multinomial distributions the gom clustering algorithm derived from the gom model is used in cluster analysis for categorical data but it is iterated with complicated calculations in this paper we create another approach termed a fuzzy k partitions fkp model which is also based on the likelihood function of multivariate multinomial distributions however the calculations of the fkp algorithm for clustering categorical data derived from the proposed fkp model are simpler the proposed fkp clustering algorithm is not only easier in calculation than the gom but also has more accuracy and computation efficiency to verify it we employ real empirical data and also some simulation data we find that fkp has superior results to gom we then apply these two algorithms to classification of pathology the results show the superiority of the fkp clustering algorithm moreover the proposed fkp algorithm can be used as a fuzzy clustering algorithm for categorical data some comparisons between fkp and two popular algorithms fuzzy k modes and fuzzy centroids are made these results show that the fkp clustering algorithm can be another useful tool in analyzing categorical data

regression methods for poisson process data abstract this article is directed toward situations where individuals can experience repeated events and data on an individual consist of the number and occurrence times of events along with concomitant variables methods of regression analysis are presented based on poisson process and proportional intensity assumptions these include parametric and semi parametric approaches to model fitting model assessment and the treatment of random effects in addition insight is gained as to the central role of poisson and mixed poisson regression analysis of counts in these methods and as to the effects of unobserved heterogeneity on semi parametric analyses the methods in the article are based on the proportional intensity poisson process model for which an individual with given fixed covariate vector x has repeated events occur according to a nonhomogeneous poisson process with intensity function x t 0 t exp x estimation of and the baseline intensity 0 t are considered when 0 t is specifi

transform both sides approach for overdispersed binomial data when n is unobserved abstract a common complication in analyzing binomial data is overdispersion where the observed variation exceeds that predicted from the binomial distribution with parameters n and p we consider the situation where n is not observed and variable to estimate the regression parameters associated with covariates we apply the transform both sides method based on the first order asymptotic variance stabilizing transformation we develop the arcsine transformation family indexed by a single parameter this family includes the square root and the arcsine transformations as special cases asymptotic properties of the transformation methods are obtained simulation study indicates that the arcsine transformation family is more efficient than the square root and arcsine transformations when there is moderate overdispersion these approaches are applied to a data set from radiobiology

tests for variation over groups in survival data abstract when survival data can be divided into natural groups such as in a clinical trial with patients from a number of different institutions the question arises whether effects are different for the different groups for situations where one is concerned with a random pattern of variation over groups this article proposes testing the null hypothesis of no variation using statistics based on the sums of martingale residuals over subjects within groups these tests are closely related to the locally most powerful tests of liang for testing for variation across a large number of strata the tests are applied to data from a lung cancer trial conducted by the eastern cooperative oncology group

treatment effect estimation with covariate measurement error this paper investigates the effect that covariate measurement error has on a treatment effect analysis built on an unconfoundedness restriction in which there is conditioning on error free covariates the approach uses small parameter asymptotic methods to obtain the approximate effects of measurement error for estimators of average treatment effects the approximations can be estimated using data on observed outcomes the treatment indicator and error contaminated covariates without employing additional information from validation data or instrumental variables the results can be used in a sensitivity analysis to probe the potential effects of measurement error on the evaluation of treatment effects

analyzing repeated measures on generalized linear models via the bootstrap the analysis of longitudinal data for which the response variables have nonnormal error distributions previously has been complex and or dependent on restrictive assumptions in this paper simple methods are introduced for the class of generalized linear models glms regressions are fit to the data at each observation time functions of the resulting coefficients may be bootstrapped or the coefficients combined through closed form estimation of their covariances application is made to a data set on xerophthalmia in indonesian children