robust models in probability sampling in the estimation of a population mean or total from a random sample certain methods based on linear models are known to be automatically design consistent regardless of how well the underlying model describes the population a sufficient condition is identified for this type of robustness to model failure the condition which we call internal bias calibration relates to the combination of a model and the method used to fit it included among the internally bias calibrated models in addition to the aforementioned linear models are certain canonical link generalized linear models and nonparametric regressions constructed from them by a particular style of local likelihood fitting other models can often be made robust by using a suboptimal fitting method thus the class of model based but design consistent analyses is enlarged to include more realistic models for certain types of survey variable such as binary indicators and counts particular applications discussed are the estimation of the size of a population subdomain as arises in tax auditing for example and the estimation of a bootstrap tail probability

graph based change point detection we consider the testing and estimation of change points locations where the distribution abruptly changes in a data sequence a new approach based on scan statistics utilizing graphs representing the similarity between observations is proposed the graph based approach is nonparametric and can be applied to any data set as long as an informative similarity measure on the sample space can be defined accurate analytic approximations to the significance of graph based scan statistics for both the single change point and the changed interval alternatives are provided simulations reveal that the new approach has better power than existing approaches when the dimension of the data is moderate to high the new approach is illustrated on two applications the determination of authorship of a classic novel and the detection of change in a network over time

a predictive estimator of finite population proportion despite missing data abstract this paper considers the problem of estimating a finite population proportion when there are missing values the prediction approach is used to define a new estimator that presents desirable efficiency properties simulation studies are considered to evaluate the performance of the proposed estimator via empirical relative bias and empirical relative efficiency and favourable results are achieved

estimating a weighted average of stratum specific parameters this article investigates estimators of a weighted average of stratum specific univariate parameters and compares them in terms of a design based estimate of mean squared error mse the research is motivated by a stratified survey sample of florida medicaid beneficiaries in which the parameters are population stratum means and the weights are known and determined by the population sampling frame assuming heterogeneous parameters it is common to estimate the weighted average with the weighted sum of sample stratum means under homogeneity one ignores the known weights in favor of precision weighting adaptive estimators arise from random effects models for the parameters we propose adaptive estimators motivated from these random effects models but we compare their design based performance we further propose selecting the tuning parameter to minimize a design based estimate of mean squared error this differs from the model based approach of selecting the tuning parameter to accurately represent the heterogeneity of stratum means our design based approach effectively downweights strata with small weights in the assessment of homogeneity which can lead to a smaller mse we compare the standard random effects model with identically distributed parameters to a novel alternative which models the variances of the parameters as inversely proportional to the known weights we also present theoretical and computational details for estimators based on a general class of random effects models the methods are applied to estimate average satisfaction with health plan and care among florida beneficiaries just prior to medicaid reform

multilevel covariance component models summary a straightforward extension to the multilevel linear model with nested covariance components is described this allows the specification and efficient estimation of a very general mixed linear model with both crossed and nested covariance components goldstein 1986 describes the analysis of the multilevel mixed effects linear model with random coefficients where the variance and covariance components have a nested structure across levels the purpose of the present note is to show how a simple extension to the formulae in that paper can accommodate cross classifications of the components within any level of the nesting thus enabling quite general covariance component models to be specified and efficient parameter estimates obtained for simplicity the 3 level model is used with the extension to 4 or more levels being straightforward we write the random part of the 3 level model as

using sample survey weights in multiple regression analyses of stratified samples abstract the rationale for the use of sample survey weights in a least squares regression analysis is examined with respect to four increasingly general specifications of the population regression model the appropriateness of the weighted regression estimate depends on which model is chosen a proposal is made to use the difference between the weighted and unweighted estimates as an aid in choosing the appropriate model and hence the appropriate estimator when applied to an analysis of the familial and environmental determinants of the educational level attained by a sample of young adults the methods lead to a revision of the initial additive model in which interaction terms between county unemployment and race as well as between sex and mother s education are included

latent variable modeling in heterogeneous populations common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values this article describes the problem and gives an overview of methodology that can address heterogeneity artificial examples of mixtures are given where if the mixture is not recognized strongly distorted results occur mimic structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple group analysis other useful methods instead take a random effects approach describing heterogeneity in terms of random parameter variation across groups these random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data examples are drawn from educational achievement testing psychopathology and sociology of education estimation is carried out by the liscomp program

in praise of simplicity not mathematistry ten simple powerful ideas for the statistical scientist ronald fisher was by all accounts a first rate mathematician but he saw himself as a scientist not a mathematician and he railed against what george box called in his fisher lecture mathematistry mathematics is the indispensable foundation of statistics but for me the real excitement and value of our subject lies in its application to other disciplines we should not view statistics as another branch of mathematics and favor mathematical complexity over clarifying formulating and solving real world problems valuing simplicity i describe 10 simple and powerful ideas that have influenced my thinking about statistics in my areas of research interest missing data causal inference survey sampling and statistical modeling in general the overarching theme is that statistics is a missing data problem and the goal is to predict unknowns with appropriate measures of uncertainty

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

the method of lines and invariant imbedding for elliptic and parabolic free boundary problems a combination of the method of lines and invariant imbedding is suggested as a general purpose numerical algorithm for free boundary problems its effectiveness is illustrated by computing the solidification of a binary alloy in one dimension electrochemical machining and hele shaw flow in two dimensions and a stefan and ablation problem in three dimensions

bayesian approach for addressing differential covariate measurement error in propensity score methods propensity score methods are an important tool to help reduce confounding in non experimental studies and produce more accurate causal effect estimates most propensity score methods assume that covariates are measured without error however covariates are often measured with error recent work has shown that ignoring such error could lead to bias in treatment effect estimates in this paper we consider an additional complication that of differential measurement error across treatment groups such as can occur if a covariate is measured differently in the treatment and control groups we propose two flexible bayesian approaches for handling differential measurement error when estimating average causal effects using propensity score methods we consider three scenarios systematic i e a location shift heteroscedastic i e different variances and mixed both systematic and heteroscedastic measurement errors we also explore various prior choices i e weakly informative or point mass on the sensitivity parameters related to the differential measurement error we present results from simulation studies evaluating the performance of the proposed methods and apply these approaches to an example estimating the effect of neighborhood disadvantage on adolescent drug use disorders

relative efficiencies of two stage sampling schemes for mean estimation in multilevel populations when cluster size is informative in multilevel populations there are two types of population means of an outcome variable ie the average of all individual outcomes ignoring cluster membership and the average of cluster specific means to estimate the first mean individuals can be sampled directly with simple random sampling or with two stage sampling tss that is sampling clusters first and then individuals within the sampled clusters when cluster size varies in the population three tss schemes can be considered ie sampling clusters with probability proportional to cluster size and then sampling the same number of individuals per cluster sampling clusters with equal probability and then sampling the same percentage of individuals per cluster and sampling clusters with equal probability and then sampling the same number of individuals per cluster unbiased estimation of the average of all individual outcomes is discussed under each sampling scheme assuming cluster size to be informative furthermore the three tss schemes are compared in terms of efficiency with each other and with simple random sampling under the constraint of a fixed total sample size the relative efficiency of the sampling schemes is shown to vary across different cluster size distributions however sampling clusters with probability proportional to size is the most efficient tss scheme for many cluster size distributions model based and design based inference are compared and are shown to give similar results the results are applied to the distribution of high school size in italy and the distribution of patient list size for general practices in england

illustration of bayesian inference in normal data models using gibbs sampling abstract the use of the gibbs sampler as a method for calculating bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models including variance components unordered and ordered means hierarchical growth curves and missing data in a crossover trial in all cases the approach is straightforward to specify distributionally and to implement computationally with output readily adapted for required inference summaries

a two step semiparametric method to accommodate sampling weights in multiple imputation multiple imputation mi is a well established method to handle item nonresponse in sample surveys survey data obtained from complex sampling designs often involve features that include unequal probability of selection mi requires imputation to be congenial that is for the imputations to come from a bayesian predictive distribution and for the observed and complete data estimator to equal the posterior mean given the observed or complete data and similarly for the observed and complete variance estimator to equal the posterior variance given the observed or complete data more colloquially the analyst and imputer make similar modeling assumptions yet multiply imputed data sets from complex sample designs with unequal sampling weights are typically imputed under simple random sampling assumptions and then analyzed using methods that account for the sampling weights this is a setting in which the analyst assumes more than the imputer which can led to biased estimates and anti conservative inference less commonly used alternatives such as including case weights as predictors in the imputation model typically require interaction terms for more complex estimators such as regression coefficients and can be vulnerable to model misspecification and difficult to implement we develop a simple two step mi framework that accounts for sampling weights using a weighted finite population bayesian bootstrap method to validly impute the whole population including item nonresponse from the observed data in the second step having generated posterior predictive distributions of the entire population we use standard iid imputation to handle the item nonresponse simulation results show that the proposed method has good frequentist properties and is robust to model misspecification compared to alternative approaches we apply the proposed method to accommodate missing data in the behavioral risk factor surveillance system when estimating means and parameters of regression models

design based maps for finite populations of spatial units abstractthe estimation of the values of a survey variable in finite populations of spatial units is considered for making maps when samples of spatial units are selected by probabilistic sampling schemes the single values are estimated by means of an inverse distance weighting predictor the design based asymptotic properties of the resulting maps referred to as the design based maps are considered when the study area remains fixed and the sizes of the spatial units tend to zero conditions ensuring design based asymptotic unbiasedness and consistency are derived they essentially require the existence of a pointwise or uniformly continuous density function of the survey variable onto the study area some regularities in the size and shape of the units and the use of spatially balanced designs to select units the continuity assumption can be relaxed into a riemann integrability assumption when estimation is performed at a sufficiently small spatial grain and the estimates are subsequently aggregated

inference of nested variance components in a longitudinal myopia intervention trial this paper was motivated by a double blind randomized clinical trial of myopia intervention in addition to the primary goal of comparing treatment effects we are concerned with the modelling of correlation that may come from two possible sources one among the longitudinal observations and the other between measurements taken from both eyes per subject the data are nested repeated measurements we suggest three models for analysis each one expresses the correlation differently in various covariance structures we articulate their differences and describe the implementations in estimation using commercial statistical software the computer output can be further utilized to perform model selection with schwarz criterion simulation studies are conducted to evaluate the performance under each model data of the myopia intervention trial are reanalysed with these models for illustration the results indicate that atropine is more effective in reducing the progression rate the rates are homogeneous across subjects and among the suggested models the one with independent random effects of two eyes fits best we conclude that model selection is a crucial step before making inference with estimates otherwise the correlation may be attributed incorrectly to a different mechanism the same conclusion applies to other variance components as well copyright 2005 john wiley sons ltd

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

restricted unbiased iterative generalized least squares estimation summary it is shown that the iterative least squares procedure for estimating the parameters in a general multilevel random coefficients linear model can be modified to produce unbiased estimates of the random parameters in the multivariate normal case these are equivalent to restricted maximum likelihood estimates

multilevel mixed linear model analysis using iterative generalized least squares summary models for the analysis of hierarchically structured data are discussed an iterative generalized least squares estimation procedure is given and shown to be equivalent to maximum likelihood in the normal case there is a discussion of applications to complex surveys longitudinal data and estimation in multivariate models with missing responses an example is given using educational data

consistent and powerful graph based change point test for high dimensional data a change point detection is proposed by using a bayesian type statistic based on the shortest hamiltonian path and the change point is estimated by using ratio cut a permutation procedure is applied to approximate the significance of bayesian type statistics the change point test is proven to be consistent and an error probability in change point estimation is provided the test is very powerful against alternatives with a shift in variance and is accurate in change point estimation as shown in simulation studies its applicability in tracking cell division is illustrated

describing the elephant structure and function in multivariate data there is a unity underlying the diversity of models for the analysis of multivariate data essentially they constitute a family models most generally nonlinear for structural functional relations between variables drawn from a behavior domain

multilevel analysis of structural equation models summary this paper considers the multilevel analysis of structural equation models with unbalanced sampling designs the analysis is based on the maximum likelihood and the generalized least squares approaches basic statistical results for inference such as the asymptotic distribution of the estimators goodness of fit test statistics for the validity of the model and functional constraints are developed computationally the applications of the scoring algorithm and the gauss newton algorithm are discussed

a general model for two level data with responses missing at random a general model for two level multivariate data with responses possibly missing at random is described the model combines regressions on fixed explanatory variables with structured residual covariance matrices the likelihood function is reduced to a form enabling computational methods for estimating the model to be devised

an evaluation of model dependent and probability sampling inferences in sample surveys abstract in this paper we are concerned with inferences from a sample survey to a finite population we contrast inferences that are dependent on an assumed model with inferences based on the randomization induced by the sample selection plan randomization consistency for finite population estimators is defined and adopted as a requirement of probability sampling a numerical example is examined to illustrate the dangers in the use of model dependent estimators even when the model is apparently consonant with the sample data the paper concludes with a summary of principles that we believe should guide the practitioner of sample surveys of finite populations

to model or not to model competing modes of inference for finite population sampling finite population sampling is perhaps the only area of statistics in which the primary mode of analysis is based on the randomization distribution rather than on statistical models for the measured variables this article reviews the debate between design based and model based inference the basic features of the two approaches are illustrated using the case of inference about the mean from stratified random samples strengths and weakness of design based and model based inference for surveys are discussed it is suggested that models that take into account the sample design and make weak parametric assumptions can produce reliable and efficient inferences in surveys settings these ideas are illustrated using the problem of inference from unequal probability samples a model based regression analysis that leads to a combination of design based and model based weighting is described

generalized multilevel structural equation modeling a unifying framework for generalized multilevel structural equation modeling is introduced the models in the framework called generalized linear latent and mixed models gllamm combine features of generalized linear mixed models glmm and structural equation models sem and consist of a response model and a structural model for the latent variables the response model generalizes glmms to incorporate factor structures in addition to random intercepts and coefficients as in glmms the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower level units in the higher level units and missing data a wide range of response processes can be modeled including ordered and unordered categorical responses counts and responses of mixed types the structural model is similar to the structural part of a sem except that it may include latent and observed variables varying at different levels for example unit level latent variables factors or random coefficients can be regressed on cluster level latent variables special cases of this framework are explored and data from the british social attitudes survey are used for illustration maximum likelihood estimation and empirical bayes latent score prediction within the gllamm framework can be performed using adaptive quadrature in gllamm a freely available program running in stata

some mathematical models for deciding the number of examination questions on computerized adaptive tests abstract the computerized adaptive test cat was developed to obtain an efficient estimate of an examinee s ability in traditional paper and pencil tests all examinees had to answer the same number of questions this kind of test was not fair for every examinee consequently the cat plays an important role in fair and adaptive examinations however the basic and necessary requirements in the cat are the databases and computer operation rules of the examination system this paper presents some mathematical algorithms dealing with the number of questions for the examination system the algorithms are feasible and can determine the reasonable number of questions for a cat system

multiplicative effects in mixed model analysis of variance summary a class of two way mixed analysis of variance models is proposed in which the fixed and random effects enter multiplicatively equations are developed for iterative computation of maximum likelihood estimates via a scoring algorithm parameter estimation and hypothesis testing are illustrated on a set of plant genetics data

small area estimation under informative probability sampling of areas and within the selected areas in this article we show how to predict small area means and obtain valid mean squared error estimators and confidence intervals when the areas represented in the sample are sampled with unequal probabilities possibly related to the true unknown area means and the sampling of units within the selected areas is with probabilities possibly related to the outcome values ignoring the effects of the sampling process on the distribution of the observed outcomes in such cases may bias the inference very severely classical design based inference that uses the randomization distribution of probability weighted estimators cannot be applied for predicting the means of nonsampled areas we propose simple test statistics for testing the informativeness of the selection of areas and sampling of units within the selected areas we illustrate the proposed procedures by a simulation study and a real application of estimating mean body mass index in u s counties using data from the third national health and nutrition

local polynomial regresssion estimators in survey sampling estimation of finite population totals in the presence of auxiliary information is considered a class of estimators based on local polynomial regression is proposed like generalized regression estimators these estimators are weighted linear combinations of study variables in which the weights are calibrated to known control totals but the assumptions on the superpopulation model are considerably weaker the estimators are shown to be asymptotically design unbiased and consistent under mild assumptions a variance approximation based on taylor linearization is suggested and shown to be consistent for the design mean squared error of the estimators the estimators are robust in the sense of asymptotically attaining the godambe joshi lower bound to the anticipated variance simulation experiments indicate that the estimators are more efficient than regression estimators when the model regression function is incorrectly specified while being approximately as efficient when the parametric specification is correct

uniform change point tests in high dimension consider d dependent change point tests each based on a cusum statistic we provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both the sample size n and d tend to infinity we achieve this either by a consistent bootstrap or an appropriate limit distribution this allows for the construction of simultaneous confidence bands for dependent change point tests and explicitly allows us to determine the location of the change both in time and coordinates in high dimensional time series if the underlying data has sample size greater or equal n for each test our conditions explicitly allow for the large d small n situation that is where n d to0 the setup for the high dimensional time series is based on a general weak dependence concept the conditions are very flexible and include many popular multivariate linear and nonlinear models from the literature such as arma garch and related models the construction of the tests is completely nonparametric difficulties associated with parametric model selection model fitting and parameter estimation are avoided among other things the limit distribution for max 1 leq h leq d sup 0 leq t leq1 vert mathcal w t h t mathcal w 1 h vert is established where mathcal w t h 1 leq h leq d denotes a sequence of dependent brownian motions as an application we analyze all s p 500 companies over a period of one year

non parametric bayesian models for samples from finite populations summary using ferguson s 1973 non parametric priors in a bayesian analysis of finite popula tions we show that asymptotically at least the usual estimates and confidence intervals for the population mean in simple and stratified random samples can be justified in bayesian terms we then apply these models for estimating population percentiles and a new procedure for interval estimates in stratified sampling is developed at present there are a number of general approaches in the statistical literature for making inferences based on data selected from a finite population many of these are summarized in smith 1976 probably the most widely used methodology in practice is the design based inference from random samples where criteria such as bias and mean squared error derived from the sampling distribution of the data are used this methodology does not preclude the possibility that the estimator may be based on an inherent superpopulation model however confidence intervals and mean squared errors are based only on the probability distribution of the design and ignore the model one of the reasons for the popularity of this approach may be that it is non parametric in nature and sample sizes tend to be large for many applications so that the loss of efficiency compared with parametric superpopulation approaches is considered less important than the robustness of the design based approach with respect to a wide class of models

multiple change point detection for high dimensional time series via sparsified binary segmentation time series segmentation a k a multiple change point detection is a well established problem however few solutions are designed specifically for high dimensional situations in this paper our interest is in segmenting the second order structure of a high dimensional time series in a generic step of a binary segmentation algorithm for multivariate time series one natural solution is to combine cusum statistics obtained from local periodograms and cross periodograms of the components of the input time series however the standard maximum and average methods for doing so often fail in high dimensions when for example the change points are sparse across the panel or the cusum statistics are spuriously large in this paper we propose the sparsified binary segmentation sbs algorithm which aggregates the cusum statistics by adding only those that pass a certain threshold this sparsifying step reduces the impact of irrelevant noisy contributions which is particularly beneficial in high dimensions in order to show the consistency of sbs we introduce the multivariate locally stationary wavelet model for time series which is a separate contribution of this work

models for nonresponse in sample surveys abstract the literature on the analysis of incomplete data using models is reviewed in the context of nonresponse in sample surveys the modeling approach provides a large body of methods for handling unit and item nonresponse some of which cannot be derived from the randomization theory of inference for surveys key concepts from the literature on incomplete data such as factorizations of the likelihood for special data patterns the em algorithm for general data patterns and ignorability of the response mechanism are discussed within the survey context model based procedures are related to common methods for handling nonresponse in surveys such as weighting or imputation of means within subclasses of the population

weighting for unequal selection probabilities in multilevel models when multilevel models are estimated from survey data derived using multistage sampling unequal selection probabilities at any stage of sampling may induce bias in standard estimators unless the sources of the unequal probabilities are fully controlled for in the covariates this paper proposes alternative ways of weighting the estimation of a two level model by using the reciprocals of the selection probabilities at each stage of sampling consistent estimators are obtained when both the sample number of level 2 units and the sample number of level 1 units within sampled level 2 units increase scaling of the weights is proposed to improve the properties of the estimators and to simplify computation variance estimators are also proposed in a limited simulation study the scaled weighted estimators are found to perform well although non negligible bias starts to arise for informative designs when the sample number of level 1 units becomes small the variance estimators perform extremely well the procedures are illustrated using data from the survey of psychiatric morbidity

multi level modelling under informative sampling we consider a model dependent approach for multi level modelling that accounts for informative probability sampling of first and lower level population units the proposed approach consists of first extracting the hierarchical model holding for the sample data given the selected sample as a function of the corresponding population model and the first and lower level sample selection probabilities and then fitting the resulting sample model using bayesian methods an important implication of the use of the model holding for the sample is that the sample selection probabilities feature in the analysis as additional data that possibly strengthen the estimators a simulation experiment is carried out in order to study the performance of this approach and compare it to the use of design based methods the simulation study indicates that both approaches perform in general equally well in terms of point estimation but the model dependent approach yields confidence credibility intervals with better coverage properties another simulation study assesses the impact of misspecification of the models assumed for the sample selection probabilities the use of maximum likelihood estimation is also considered

approximate bayesian inference under informative sampling summary statistical inference with complex survey data is challenging because the sampling design can be informative and ignoring it can produce misleading results current methods of bayesian inference under complex sampling assume that the sampling design is noninformative for the specified model in this paper we propose a bayesian approach which uses the sampling distribution of a summary statistic to derive the posterior distribution of the parameters of interest asymptotic properties of the method are investigated it is directly applicable to combining information from two independent surveys and to calibration estimation in survey sampling a simulation study confirms that it can provide valid estimation under informative sampling we apply it to a measurement error problem using data from the korean longitudinal study of aging

numerical length estimation for tubular flow reactors abstract this work was motivated by the engineering problem of determining the optimal length for tubular flow reactors we considered an isothermal nth order chemical reaction occuring in a tubular flow reactor with axial missing the mathematical model describing the problem was a free boundary value one the free boundary represented the reactor length in this context we proved a theorem characterizing an upper bound for the free boundary in order to solve the problem in point we introduced two different numerical methods first a noniterative method was considered in order to obtain an upper bound of the free boundary then we used this upper bound in order to start an iterative method that allowed us to find an approximation of the free boundary in closing we obtained numerical results either for an even or an odd order reaction

estimating variance components by using survey data summary inflation type weighted estimators for variance components can be badly biased modified weighted estimators suggested in the literature are also badly biased for certain sampling designs we propose new estimators for variance components some of which are approximately unbiased regardless of the sampling design these estimators require knowledge of the joint inclusion probabilities of the observations the small sample properties of the estimators are studied via simulation for the simple one way random effects model an application is given by using data from the us hispanic health and nutrition examination survey

some contributions to efficient statistics in structural models specification and estimation of moment structures current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments e g means and covariances and to distribution theory based on multivariate normality in psychometrics the multinormality assumption is often incorrect so that statistical tests on parameters or model goodness of fit will frequently be incorrect as well it is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary structural representations are developed for generalizations of the bentler weeks joreskog keesling wiley and factor analytic models some asymptotically distribution free efficient estimators for such arbitrary structural models are developed limited information estimators are obtained as well the special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail the argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds many open research areas are described

a distribution free two sample run test applicable to high dimensional data we propose a multivariate generalization of the univariate two sample run test based on the shortest hamiltonian path the proposed test is distribution free in finite samples while most existing two sample tests perform poorly or are even inapplicable to high dimensional data our test can be conveniently used in high dimension low sample size situations we investigate its power when the sample size remains fixed and the dimension of the data grows to infinity simulated and real datasets demonstrate our method s superiority over existing nonparametric two sample tests

application of invariant imbedding to the estimation of process duration abstract this work deals with the application of invariant imbedding to solve a particularly important design problem namely the duration of the process a numerical example is used to illustrate the approach the advantage of this approach is its straightforward nature and uses only the usual design data it avoids any iterations and thus no convergence problems need to be considered

post stratification a modeler s perspective abstract post stratification is a common technique in survey analysis for incorporating population distributions of variables into survey estimates the basic technique divides the sample into post strata and computes a post stratification weight w ih rp h r h for each sample case in post stratum h where r h is the number of survey respondents in post stratum h p h is the population proportion from a census and r is the respondent sample size survey estimates such as functions of means and totals then weight cases by w h variants and extensions of the method include truncation of the weights to avoid excessive variability and raking to a set of two or more univariate marginal distributions literature on post stratification is limited and has mainly taken the randomization or design based perspective where inference is based on the sampling distribution with population values held fixed this article develops bayesian model based theory for the method a basic normal post stratification mod

calculation of unconditional and conditional reference intervals for foetal size and growth from longitudinal measurements methods for estimating unconditional and conditional reference intervals for foetal size and growth based on longitudinal observations are presented the methods are based on simple random effects regression models and involve transforming both the response and the covariate timepoint a dataset from a designed longitudinal study of foetal size is analysed in detail as a motivating example

conditionally consistent estimators using only probabilities of selection in complex sample surveys abstract predictive regression estimators using functions of the probability of selection i as covariates are studied as an alternative to classical p weighting estimators for the finite population mean in complex sample surveys variance estimators are developed based on the relationship var y i i where y is the response and i is the probability of selection extensions to cluster sample designs are outlined and an example is given from the national educational longitudinal survey of 1988

a general model for the analysis of multilevel data a general model is developed for the analysis of multivariate multilevel data structures special cases of the model include repeated measures designs multiple matrix samples multilevel latent variable models multiple time series and variance and covariance component models

limited information likelihood analysis of survey data analysts of survey data are often interested in modelling the population process or superpopulation that gave rise to a target set of survey variables an important tool for this is maximum likelihood estimation a survey is said to provide limited information for such inference if data used in the design of the survey are unavailable to the analyst in this circumstance sample inclusion probabilities which are typically available provide information which needs to be incorporated into the analysis we consider the case where these inclusion probabilities can be modelled in terms of a linear combination of the design and target variables and only sample values of these are available strict maximum likelihood estimation of the underlying superpopulation means of these variables appears to be analytically impossible in this case but an analysis based on approximations to the inclusion probabilities leads to a simple estimator which is a close approximation to the maximum likelihood estimator in a simulation study this estimator outperformed several other estimators that are based on approaches suggested in the sampling literature

on normal theory based inference for multilevel models with distributional violations data in social and behavioral sciences are often hierarchically organized though seldom normal yet normal theory based inference procedures are routinely used for analyzing multilevel models based on this observation simple adjustments to normal theory based results are proposed to minimize the consequences of violating normality assumptions for characterizing the distribution of parameter estimates sandwich type covariance matrices are derived standard errors based on these covariance matrices remain consistent under distributional violations implications of various covariance estimators are also discussed for evaluating the quality of a multilevel model a rescaled statistic is given for both the hierarchical linear model and the hierarchical structural equation model the rescaled statistic improving the likelihood ratio statistic by estimating one extra parameter approaches the same mean as its reference distribution a simulation study with a 2 level factor model implies that the rescaled statistic is preferable

efficient parametrisations for normal linear mixed models summary the generality and easy programmability of modern sampling based methods for maximisation of likelihoods and summarisation of posterior distributions have led to a tremendous increase in the complexity and dimensionality of the statistical models used in practice however these methods can often be extremely slow to converge due to high correlations between or weak identifiability of certain model parameters we present simple hierarchical centring reparametrisations that often give improved convergence for a broad class of normal linear mixed models in particular we study the two stage hierarchical normal linear model the laird ware model for longitudinal data and a general structure for hierarchically nested linear models using analytical arguments simulation studies and an example involving clinical markers of acquired immune deficiency syndrome aids we indicate when reparametrisation is likely to provide substantial gains in efficiency

model based multiplicity estimation of population size a survey is conducted at w of k selection units or lists e g health care institutions or weeks in a year to estimate n the total number of individuals with particular characteristics our estimator utilizes two items determined for each survey participant the number u among the w lists in s and the number j among all k lists on which each survey participant appears in its traditional form selection units are chosen using probability sampling and the statistical properties of the estimator derive from the sampling mechanism here selection units are purposively chosen to maximize the chance that they are typical and a model based analysis is used for inference if the sample is typical the ml estimators of n and e j are unbiased if a condition on the second moment of u j is satisfied the model based variance of the estimator of n based on a purposively chosen typical sample is smaller than one based on a randomly chosen sample methods to test whether the typical assumption is valid using data from the survey are not yet available the importance of proper selection of the sample to maximize the chance that it is typical and model breakdown does not occur must be emphasized

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