a geometric characterization of c optimal designs for heteroscedastic regression we consider the common nonlinear regression model where the variance as well as the mean is a parametric function of the explanatory variables the c optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest a geometric characterization of c optimal designs in this context is presented which generalizes the classical result of elfving 1952 for c optimal designs as in elfving s famous characterization c optimal designs can be described as representations of boundary points of a convex set however in the case where there appear parameters of interest in the variance the structure of the elfving set is dierent roughly speaking the elfving set corresponding to a heteroscedastic regression model is the convex hull of a set of ellipsoids induced by the underlying model and indexed by the design space the c optimal designs are characterized as representations of the points where the line in direction of the vector c intersects the boundary of the new elfving set the theory is illustrated in several examples including pharmacokinetic models with random eects

direct method for yau filtering system with nonlinear observations for all known finite dimensional filters one always assumes that the observation terms be degree one polynomials however in practice the observation terms may be nonlinear e g tracking proble

composite linear models for incomplete multinomial data a composite linear model clm is a matrix model for incomplete multinomial data a clm provides a unified approach for maximum likelihood inference which is applicable to a wide variety of problems involving incomplete multinomial data by formulating a model as a clm one can simplify computation of maximum likelihood estimates and asymptotic standard errors as an example we use clm to test marginal homogeneity for ordered categories subject to both ignorable and non ignorable missing data mechanisms

on a necessary and sufficient condition for finite dimensionality of estimation ever since the technique of the kalman bucy filter was popularized there has been an intense interest in finding new classes of finite dimensional recursive filters in the late seventies the concept of the estimation algebra of a filtering system was introduced it has proven to be an invaluable tool in the study of nonlinear filtering problems in this paper a simple algebraic necessary and sufficient condition is established for an estimation algebra of a special class of filtering systems to be finite dimensional also presented is a rigorous proof of the wei norman program which allows one to construct finite dimensional recursive filters from finite dimensional estimation algebras

adjustment for non differential misclassification error in the generalized linear model it is well known that estimates of association between an outcome variable and a set of categorical covariates some of which are measured with misclassification tend to be biased upon application of the usual methods of estimation that ignore the classification error we propose a method to adjust for misclassification in covariates when one applies the generalized linear model in the case where one can observe some true covariates only through surrogates we combine a latent class analysis with the approach to incorporate multiple surrogates into the model we include discussion on the efficacy of repeated measurements which one can view as a special case of multiple surrogates with identical distribution we provide two examples to demonstrate the applicability of the method and the efficacy of multiple replicates for a covariate subject to misclassification in a regression framework

the use of a canonical form in the construction of locally optimal designs for non linear problems optimal experimental designs for non linear problems depend on the values of the underlying undknown parameters in the model for various reasons there is interest in providing explicit formulae for the optimal designs as a function of the unknown parameters this paper shows that for a certain class of generalized linear models the problem can be reduced to a canonical form this simplifies the underlying problem and designs are constructed for several contexts with a single variable using geometric and other arguments

finite dimensional filters with nonlinear drift ii brockett s problem on classification of finite dimensional estimation algebras the idea of using estimation algebras to construct finite dimensional nonlinear filters was first proposed by brockett and mitter independently it turns out that the concept of estimation algebra plays a crucial role in the investigation of finite dimensional nonlinear filters in his talk at the international congress of mathematics in 1983 brockett proposed classifying all finite dimensional estimation algebras in this paper all finite dimensional algebras with maximal rank are classified if the dimension of the state space is less than or equal to two therefore from the lie algebraic point of view all finite dimensional filters are understood generically in the case where the dimension of state space is less than three

small sample inference for fixed effects from restricted maximum likelihood restricted maximum likelihood reml is now well established as a method for estimating the parameters of the general gaussian linear model with a structured covariance matrix in particular for mixed linear models conventionally estimates of precision and inference for fixed effects are based on their asymptotic distribution which is known to be inadequate for some small sample problems in this paper we present a scaled wald statistic together with an f approximation to its sampling distribution that is shown to perform well in a range of small sample settings the statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias this approach has the advantage that it reproduces both the statistics and f distributions in those settings where the latter is exact namely for hotelling t2 type statistics and for analysis of variance f ratios the performance of the modified statistics is assessed through simulation studies of four different reml analyses and the methods are illustrated using three examples

nonparametric regression estimates using misclassified binary responses summary for random design nonparametric regression in the case that the responses are binary and subject to misclassification the performance of the kernel estimator is investigated the kernel estimator is generally biased for the local proportion to adjust for the bias the double sampling scheme of tenenbein 1970 1971 is considered a plugged in kernel estimator and an imputed kernel estimator which adjust for the effect of misclassification on the kernel estimator are proposed and their asymptotic mean squared errors are analysed the plugged in kernel estimator is better than the simple kernel estimator which uses only the data without misclassification in the validation subsample in the sense of having smaller asymptotic mean squared error however the imputed kernel estimator has smaller asymptotic variance if the misclassification probabilities are constant then the two proposed estimators have the same asymptotic bias in this case the imputed kernel estimator is always better than the plugged in kernel estimator for general misclassification probabilities the asymptotic biases of the two proposed estimators are not comparable in magnitude however our simulation results demonstrate that even when the misclassification probabilities are not constant the imputed kernel estimator is still better for reasonable sample sizes

bayesian analysis of multivariate probit models with surrogate outcome data a new class of parametric models that generalize the multivariate probit model and the errors in variables model is developed to model and analyze ordinal data a general model structure is assumed to accommodate the information that is obtained via surrogate variables a hybrid gibbs sampler is developed to estimate the model parameters to obtain a rapidly converged algorithm the parameter expansion technique is applied to the correlation structure of the multivariate probit models the proposed model and method of analysis are demonstrated with real data examples and simulation studies

construction of some balanced incomplete block designs with nested rows and columns par i j qac ij as j j a 1 where a a constant integer independent of the pair i j chosen satisfies the relationship a v 1 r p 1 q 1 ar ij ac ij and a i j denote respectively the numbers of rows within sets columns within sets and sets in which the pair occurs together these variance balanced binary designs introduced and discussed by singh dey 1979 with parameters v b r p q and a are abbreviated as bibrc v b r p q a note that 1 1 is an alternative version of their condition 4 3 agarwal prasad 1982 1983 and cheng 1986 gave further methods of construction of these designs cheng 1986 considered the case of k v in these designs and called them balanced complete block designs with nested rows and columns with parameters v b r p q and a and abbreviated as bcbrc v b r p q a he has equivalently used the condition

asymptotically good quantum codes exceeding the ashikhmin litsyn tsfasman bound it is known that quantum error correction can be achieved using classical binary codes or additive codes over f sub 4 asymptotically good quantum codes have been constructed from algebraic geometry codes and a bound on spl delta r was computed from the tsfasman vladut zink bound of the theory of classical algebraic geometry codes in this correspondence by the use of a concatenation technique we construct a family of asymptotically good quantum codes exceeding the bound in a small interval

optimality criteria in survey sampling summary this paper attempts to fill the gap between some different and conflicting approaches in survey sampling based on a fixed population regression type model a class of optimality criteria similar to those well accepted in optimal experimental design theory is introduced the minimax and superpopulation approaches in survey sampling turn out to correspond to two extreme criteria in the proposed class this helps understand the role of randomization the strategy of simple random sampling with sample mean and the rao hartley cochran strategy are shown to be criterion robust

approximation of the zakai equation by the splitting up method the objective of this article is to apply an operator splitting method to the time integration of zakai equation using this approach one can decompose the numerical integration into a stochastic step and a deterministic one both of them much simpler to handle than the original problem a strong convergence theorem is given in the spirit of existing results for deterministic problems

on the design of experiments under spatial correlation on considere tout d abord le cas ou les effets du traitement sont estimes par les moindres carres on considere ensuite le cas ou l analyse a utiliser est les moindres carres generalises utilisant une matrice de correlation connue

binary regression models for contaminated data on etudie la nature des observations aberrantes dans le contexte des donnees de regression binaires on propose un modele simple qui permet qu un petit nombre de reponses binaires soit mal enregistre

the construction of exact d optimum experimental designs with application to blocking response surface designs summary the properties of optimum designs are investigated when there are both qualitative and quantitative factors algorithms for the construction of exact designs are described which are of general applicability the case when the qualitative factors represent blocking variables is given special treatment a modified algorithm provides the opportunity to divide the experimental trials into blocks of specified sizes examples are given of second order models in the quantitative factors divided into two or three blocks of a variety of sizes use of the adjustment algorithm to improve such designs generated from a list of candidate points is demonstrated

new quantum mds codes from negacyclic codes let q be an odd prime power based on classical negacyclic codes we construct two classes of quantum maximum distance separable mds codes with parameters q2 1 q2 2d 3 d q where q 1 mod 4 and 2 d q 1 is even and q2 1 2 q2 1 2 2d 2 d q where 3 d q is odd some of these quantum mds codes are new in the sense that their parameters are different from all the previously known ones

nested generalized cyclic row column designs summary a nested row column design has v treatments arranged in b blocks each comprising pq units grouped into p rows and q columns a class of designs based on a cyclical method of construction is defined the canonical efficiency factors of such nested generalized cyclic row column designs are examined efficient designs are tabulated for 5 v 15 p 3 q 7 and r v where r bpq v is the number of replications of each treatment row column designs are used to eliminate heterogeneity in two directions more generally an experiment may have several blocks each containing pq plots arranged in p rows and q columns where the blocks may represent a further blocking factor or provide replications of the basic row column design these designs are called nested row column designs since rows and columns are nested within blocks the lattice square designs introduced by yates 1940 are examples of such designs a general analysis and the concept of balance have been considered by singh dey 1979 several series of balanced nested row column designs have been given by singh dey 1979 street 1981 and agrawal prasad 1982a preece 1967 provides a table of nested balanced incomplete block designs and a number of these designs can also be used as balanced nested row column designs other series based on partially balanced designs have been given by street 1981 and agrawal prasad 1982b jarrett hall 1982 gave some examples of small designs based on cyclic and generalized cyclic methods of con struction which they suggested could provide useful alternatives to nearest neighbour designs and methods as an example of a balanced nested row column design consider the following design given by singh dey 1979 for five treatments 0 1 2 3 4 arranged in five blocks of two rows and two columns

a note on design when response has an exponential family distribution summary some simple design problems are considered when responses have an exponential family distribution with the difference between treatment groups in the canonical parameter being the objective of study it is shown that normal theory conclusions apply to a possibly surprising extent the loss from randomizing followed by subsequent stratification is the equivalent of one observation per stratum for binary data heterogeneity has to be quite large before failure to stratify induces serious loss whereas unnecessary use of a matched pair design is fully efficient asymptotically

double sampling for exact values in some multivariate measurement error problems abstract increasing attention is being given to measurement error models in which the dimension of the proxy or surrogate values is different from that of the missing true values even if they are of the same dimension the error model may not be the simple additive one of observed true error where the error has mean 0 the use of broader models relating true and observed values requires the use of external or internal data containing some true values to calibrate validate the measurement error model this article considers a multivariate normal framework in which measurement error is allowed in any subset of the variables with a broad class of multivariate regression models relating true and observed values the classical additive model is a special case multiple regression with random regressors the structural case is treated within this framework correcting for measurement error is made possible through double sampling in which true values are obtained for a randomly chosen subset of the main

optimum biased coin designs for sequential treatment allocation with covariate information randomized optimum designs of biased coin type are compared with other strategies for the sequential allocation of two or more treatments in a clinical trial the emphasis is on the variance of estimated treatment contrasts this variance which depends on the design strategy employed may be interpreted as the number of patients on whom information is lost simulations provide clear plots of the evolution of this loss during the course of the clinical trial

a general approach to analyzing epidemiologic data that contain misclassification errors misclassification is a common source of bias and reduced efficiency in the analysis of discrete data several methods have been proposed to adjust for misclassification using information on error rates i gathered by resampling the study population ii gathered by sampling a separate population or iii assumed a priori we present unified methods for incorporating these types of information into analyses based on log linear models and maximum likelihood estimation general variance expressions are developed examples from epidemiologic studies are used to demonstrate the proposed methodology

classification of finite dimensional estimation algebras of maximal rank with arbitrary state space dimension and mitter conjecture in the late seventies the concept of the estimation algebra of a filtering system was introduced it was proven to be an invaluable tool in the study of non linear filtering problems in the early eighties brockett proposed to classify finite dimensional estimation algebras and mitter conjectured that all functions in finite dimensional estimation algebras are necessarily polynomials of total degree at most one despite the massive effort in understanding the finite dimensional estimation algebras the 20 year old problem of brockett and mitter conjecture remains open in this paper we give a classification of finite dimensional estimation algebras of maximal rank and solve the mitter conjecture affirmatively for finite dimensional estimation algebras of maximal rank in particular for an estimation algebra e of maximal rank we give a necessary and sufficient conditions for e to be finite dimensional in terms of the drift fi x and observation hj x as an important corollary we show that the numb

nonbinary quantum stabilizer codes we define and show how to construct nonbinary quantum stabilizer codes our approach is based on nonbinary error bases it generalizes the relationship between self orthogonal codes over f sub 4 and binary quantum codes to one between self orthogonal codes over f q sup 2 and q ary quantum codes for any prime power q

optimality criteria for regression models based on predicted variance in the context of nonlinear regression models a new class of optimum design criteria is developed and illustrated this new class termed i l optimality is analogous to kiefer s k criterion but is based on predicted variance whereas kiefer s class is based on the eigenvalues of the information matrix i l optimal designs are invariant with respect to different parameterisations of the model and contain g and d optimality as special cases we provide a general equivalence theorem which is used to obtain and verify i l optimal designs the method is illustrated by various examples

enlargement of calderbank shor steane quantum codes it is shown that a classical error correcting code c n k d which contains its dual c sup spl perp spl sube c and which can be enlarged to c n k k 1 d can be converted into a quantum code of parameters n k k n min d 3d 2 this is a generalization of a previous construction it enables many new codes of good efficiency to be discovered examples based on classical bose chaudhuri hocquenghem bch codes are discussed

optimal two period repeated measurement designs with two or more treatments summary for two period repeated measurement designs for comparing t 2 treatments we discuss universally optimal designs when the number of subjects n is a multiple of t2 and some cases when n is a multiple of t we examine efficiencies of balanced designs and other symmetric designs relative to strongly balanced designs in addition efficiencies of the universally optimal designs obtained by hedayat zhao 1990 are examined under both fixed subject and random subject effect model assumptions

bayesian sample size determination for inference on two binomial populations with no gold standard classifier we consider the impact of test properties on the required sample size for the bayesian design problem for comparing two proportions with error prone data specifically we examine four cases a single diagnostic test and two independent diagnostic tests both when the test properties are identical across populations and when they differ interval based and moment based sample size determination criteria are contrasted using monte carlo simulation methods we consider an application in which strongyloides infections are compared in two populations

neighbour balanced block designs for correlated errors summary the paper considers a simple block model and assumes that the errors within the blocks are correlated following a stationary first order autoregressive process gill shukla 1985 consider this model but they restrict the set of the competing designs to a small subset of the possible designs the binary and equireplicate designs in the present paper we show that the designs determined by gill shukla are optimal over all possible designs for positive correlations and that neighbour balanced designs in general are highly efficient

conditional resampling for misclassified multinomial data with applications to sampling inspection a conditional resampling methodology is proposed for improving the estimators of multinomial classification probabilities in the presence of a fallible classifier the unbiased estimator requires knowledge of the misclassification error rates which are obtained by resampling from the initial sample and applying an infallible classifier tenenbein s double sampling methodology resamples randomly from the initial sample we show that substantial gains in efficiency are obtainable if instead of simple random resampling different resampling rates are allowed for the fallibly determined classes in the initial sample in most situations this resampling methodology is neither more difficult nor more expensive than the double sampling methodology a very promising area of application of the proposed methodology is sampling inspection in quality control where products can either be classified quickly by inspectors or by a more thorough perhaps destructive inspection

determining the value of additional surrogate exposure data for improving the estimate of an odds ratio we consider the design of both cohort and case control studies in which an initial stage 1 sample of complete data on an error free disease indicator d a correct gold standard dichotomous exposure measurement x and an error prone exposure measurement z are available we calculate the amount of additional information on the odds ratio relating d to x that one can obtain from a second stage 2 sample of measurements only on d and z if one allows for differential measurement error in z there is often little advantage in having more than four times as much data in stage 2 data as in stage 1 with the assumption that a non differential measurement error model is reasonable larger amounts of stage 2 data can be useful simulations indicate that stage 1 samples of modest size 50 cases in case control studies and 50 failures in cohort studies yield sufficiently reliable estimates of needed parameters to assist in determining an appropriate size for the stage 2 sample these ideas apply in settings either where the amount of stage 1 data is limited and fixed by external constraints or where one has gathered stage 1 data in advance to avoid collecting superfluous stage 2 data

some optimal designs for repeated measurements with autoregressive errors summary a number of individuals are observed at equally spaced time points different individuals behave independently but the observations on the same individual have the autocorrelation structure of a first order autoregressive process we are concerned with the optimal allocation of treatments assuming that at each time point a new selection must be made conditions for optimality are given for models without nuisance parameters and also with covariates and with block effects

optimal partial diallel crosses even in the absence of blocks each cross in a partial diallel cross design can be formally identified with a block of size two and thus the design itself can be identified with a binary block design we show that unblocked partial diallel crosses so linked with a certain class of group divisible designs are uniquely e optimal in general and also uniquely d and a optimal in the saturated case further results on e optimality applicable even when the number of parental lines does not admit a factorisation are also derived the issue of optimal or efficient blocking of partial diallel crosses is discussed

testing hypotheses with binary data subject to misclassification errors analysis and experimental design summary consider a binary random variable having outcomes subject to misclassification errors where the probabilities of misclassification errors depend on outcome the asymptotic relative efficiencies are derived for comparing two binomial populations comparing stratified binomial populations and for paired comparisons the probabilities of misclassification can vary with strata or be different for each pair the criterion for optimum experimental designs is shown to be the ratio of the asymptotic relative efficiency to expected cost per observation this criterion implies that mixtures of different experiments can never be optimal a number of experimental strategies is discussed

nested youden square designs summary youden square designs nested in two or three blocks are discussed these designs are useful in experimental settings with scarce materials involving many treatments

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

asymptotic bounds on quantum codes from algebraic geometry codes we generalize a characterization of p ary p is a prime quantum codes given by feng and xing to q ary q is a prime power quantum codes this characterization makes it possible to convert an asymptotic bound of stichtenoth and xing for nonlinear algebraic geometry codes to a quantum asymptotic bound besides we also investigate the asymptotic behavior of quantum codes

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

transitive and self dual codes attaining the tsfasman vla spl breve dut 80 zink bound a major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good in this correspondence as a generalization of cyclic codes the notion of transitive codes is introduced see definition 1 4 in section i and it is shown that the class of transitive codes is asymptotically good even more transitive codes attain the tsfasman vlabrevedut 80 zink bound over fq for all squares q l2 it is also shown that self orthogonal and self dual codes attain the tsfasman vlabrevedut 80 zink bound thus improving previous results about self dual codes attaining the gilbert varshamov bound the main tool is a new asymptotically optimal tower e0subee1 subee2sube middotmiddotmiddot of function fields over fq with q lscr2 where all extensions en e0 are galois

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

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

the fisher information matrix for log linear models arguing conditionally on observed explanatory variable summary for poisson or multinomial contingency table data the conditional distribution is product multinomial when conditioning on observed values of explanatory variables birch 1963 showed that under the restriction formed by keeping the marginal totals of one margin fixed at their observed values the poisson multinomial and product multinomial likelihoods are proportional and give the same estimates for common parameters in the log linear model here the inverses of the fisher information matrices are shown to be identical over common parameters so that the asymptotic covariance matrices of the estimates correspond

a mean squared error criterion for the design of experiments in estimating a response surface over a design region of interest mean squared error can arise both from sampling variance and bias introduced by model inadequacy the criterion adopted here for experimental design attempts to protect against bias resulting from a large class of deviations from the assumed model two algorithms are proposed for the construction of either approximate or exact designs and an example is given

a unified approach to the construction of minimax designs summary we present a unified approach for constructing large sample optimal designs when the optimality criterion is of the minimax type the assumed model is a general linear regression model with a known efficiency function defined on a closed and bounded space an equivalence theorem is formulated and computer algorithms for generating minimax optimal designs are proposed it is shown that this methodology is simple and rather general it can be used to construct for example minimax variance optimal designs minimax with respect to the single parameters designs and e optimal designs an application of this procedure to find an optimal design for minimizing the maximum predictive variance over a compact region in a heteroscedastic design problem is included

a predictive approach to the bayesian design problem with application to normal regression models a predictive decision theoretic approach is developed for the bayesian design problem the loss functions used are fair bayes or proper scoring rules and are quadratic measures of distance between probability measures optimal bayesian designs are those which minimise the preposterior risk for the decision problem such designs typically depend on both the prior distribution and the loss function the results are applied to certain normal regression models where explicit optimal designs are constructed

finite dimensional filters with nonlinear drift x explicit solution of dmz equation in this note we consider the explicit solution of duncan mortensen zakai dmz equation for the finite dimensional filtering system we show that yau s 1990 1994 filtering system spl delta f sub j spl delta x sub i spl delta f sub i spl delta x sub i c sub ij constant for all i j can be solved explicitly with an arbitrary initial condition by solving a system of ordinary differential equations and a kolmogorov type equation let n be the dimension of state space we show that we need only n sufficient statistics in order to solve the dmz equation

a general approach to categorical data analysis with missing data using generalized linear models with composite links a general approach for analyzing categorical data when there are missing data is described and illustrated the method is based on generalized linear models with composite links the approach can be used among other applications to fill in contingency tables with supplementary margins fit loglinear models when data are missing fit latent class models without or with missing data on observed variables fit models with fused cells including many models from genetics and to fill in tables or fit models to data when variables are more finely categorized for some cases than others both newton like and em methods are easy to implement for parameter estimation

robust designs for serially correlated observations summary the presence of serial correlation affects the design strategy of a statistical experiment it is the object of this paper to construct robust and efficient designs under such conditions special consideration is given to the two level factorial designs and weighing designs

algorithms versus models for analyzing data that contain misclassification errors espeland and hui 1987 biometrics 43 1001 1012 propose a methodology for analysing epidemiologic data contaminated by misclassification they explicate their algorithm by a data set concerning cervical cancer and circumcision we reanalyse these data using a conditional independence assumption different from theirs and reach radically different conclusions espeland and hui s methodology is a form of correlation analysis we propose an alternative methodology based on the logic of regression analysis

optimal bayesian design of experiments for the one way random effects model summary since variance components are nonlinear parameters in a linear model classical optimal designs for estimating variance components in the one way random effects model depend on the values of the parameters optimal bayesian designs are derived for the more realistic situation of unknown parameters using the fisher information of the variance components as a basis for comparing the designs balanced designs in which the same number of measurements are taken on each unit are shown to be optimal under various criteria for wide classes of priors in the one way random effects model in contrast to other nonlinear design problems the number of support points for the design does not necessarily increase with increasingly vague prior information some design criteria that work well for other nonlinear design problems such as d optimality do not give intuitively appealing designs for estimating variance components

solution of filtering problem with nonlinear observations for all known finite dimensional filters one always needs the conditon that the observation terms are degree one polynomial on the other hand in many practical examples e g tracking problem the observation terms may be nonlinear our new method in this paper can treat filtering problems with nonlinear observation terms in the first time which includes kalman bucy filter as a special case

locally optimal design for comparing two probabilities from binomial data subject to misclassification optimal experimental designs are found for estimating the difference 1 2 of two population probabilities using measuring instruments possibly subject to known error rates the available experiments considered are to measure for i 1 or 2 the outcome of a trial on the population i without error or with error or with error with the possibility of checking either positive or negative responses given that the cost per observation depends on which experiment is carried out an asymptotically locally optimal allocation is derived in terms of results of elfving which provide a simple geometrical solution

design of validation studies for estimating the odds ratio of exposure disease relationships when exposure is misclassified summary we compared several validation study designs for estimating the odds ratio of disease with misclassified exposure we assumed that the outcome and misclassified binary covariate are available and that the error free binary covariate is measured in a subsample the validation sample we considered designs in which the total size of the validation sample is fixed and the probability of selection into the validation sample may depend on outcome and misclassified covariate values design comparisons were conducted for rare and common disease scenarios where the optimal design is the one that minimizes the variance of the maximum likelihood estimator of the true log odds ratio relating the outcome to the exposure of interest misclassification rates were assumed to be independent of the outcome we used a sensitivity analysis to assess the effect of misspecifying the misclassification rates under the scenarios considered our results suggested that a balanced design which allocates equal numbers of validation subjects into each of the four outcome mismeasured covariate categories is preferable for its simplicity and good performance a user friendly fortran program is available from the second author which calculates the optimal sampling fractions for all designs considered and the efficiencies of these designs relative to the optimal hybrid design for any scenario of interest

projective properties of certain orthogonal arrays summary a question of importance in factor screening is when a two level orthogonal design for a multifactor experiment can be projected into lower dimension typically p 2 or 3 new results relate to the projectivity p of saturated designs in which n 1 factors are tested in n runs it is shown that a design obtained by doubling an n x n orthogonal array is always of projectivity p 2 a twolevel cyclic design is either a factorial array and hence has p 2 or it has p 3 a two level orthogonal design with 4m runs m odd has p 3 in particular these results allow the designs derived by plackett burman 1946 to be categorised in terms of these projective properties

model robust response surface designs scaling two level factorials summary response surface methods use simple graduating functions to study the relationship between an experimental response variable and a set of continuous explanatory variables in designing a response surface study an experimenter must decide how far apart to set the levels of each factor i e how to scale the design a good choice should be sensitive to the fact that the graduating function is only an approximation to the true response function a bayesian model is proposed that makes explicit assumptions about the inadequacy of an assumed model and a design criterion based on the model leads to reasonable choices of scale for two level factorial designs the choice of scale is found to be insensitive to the prior distributions in the model

constacyclic codes and some new quantum mds codes one central theme in quantum error correction is to construct quantum codes that have a large minimum distance quantum maximal distance separable mds codes are optimal in the sense they attain maximal minimum distance recently constructing quantum mds codes has received much attention and seems to become more and more difficult in this paper based on classical constacyclic codes we construct some new quantum mds codes by employing the hermitian construction compared with the known quantum mds codes these quantum mds codes have much larger minimum distance

case control studies with errors in covariates we devise methods for estimating the parameters of a prospective logistic model with dichotomous response d and arbitrary covariates x from case control data when these covariates are measured with error we suppose that some fraction of the cases and controls provide only the error prone covariate measurements w the incomplete or reduced data whereas some of the cases and controls provide measurements on x and w the complete data we assume a measurement error density with a finite set of parameters namely fw xd w x d and nondifferential error is treated as a special case of this model fw x w x our algorithm estimates both the logistic parameters and from a pseudolikelihood because empirical distribution functions are used in place of needed distributions in the pseudolikelihoods the required asymptotic theory is more elaborate than for pseudolikelihoods based on substitution for a finite number of nuisance parameters we also examine computationally simpler methods under t

a note on optimality in lattice square designs summary this note demonstrates that lattice square designs are a optimal within the class of lattice square designs if and only if they are m s optimal certain restricted lattice square designs are shown to be a optimal

on quantum and classical bch codes classical bose chaudhuri hocquenghem bch codes that contain their euclidean or hermitian dual codes can be used to construct quantum stabilizer codes this correspondence studies the properties of such codes it is shown that a bch code of length n can contain its dual code only if its designed distance delta o radicn and the converse is proved in the case of narrow sense codes furthermore the dimension of narrow sense bch codes with small design distance is completely determined and consequently the bounds on their minimum distance are improved these results make it possible to determine the parameters of quantum bch codes in terms of their design parameters

incomplete block designs for comparing treatments wth a control general theory in this paper we develop a theory of optimal incomplete block designs for comparing several treatments with a control this class of designs is appropriate for comparing simultaneously p 2 test treatments with a control treatment the so called multiple comparisons with a control mcc problem when the observations are taken in incomplete blocks of common size k p 1 for this problem we propose a new general class of incomplete block designs that are balanced with respect to wrt test treatments we shall use the abbreviation btib to refer to such designs we study their structure and give some methods of construction a procedure for making exact joint confidence statements for this multiple comparisons problem is described by using a new concept of admissibility of designs it is shown how inferior designs can be eliminated from consideration and attention limited to a small class of btib designs that can be constructed from so called generator designs in the minimal complete class of such d

hierarchical log linear models not preserved by classification error abstract a model of bross 1954 for classification error in 2 2 contingency tables is extended to higher dimensional tables it is known mote and anderson 1965 that the usual hypothesis tests of independence for a sampled two dimensional table have the nominal significance level in the presence of misclassification a simple criterion is given to determine which hierarchical log linear models in higher dimensional tables do not share this property that is are not preserved by classification error

effects of exposure misclassification on regression analyses of epidemiologic follow up study data in epidemiologic studies subjects are often misclassified as to their level of exposure ignoring this misclassification error in the analysis introduces bias in the estimates of certain parameters and invalidates many hypothesis tests for situations in which there is misclassification of exposure in a follow up study with categorical data we have developed a model that permits consideration of any number of exposure categories and any number of multiple category covariates when used with logistic and poisson regression procedures this model helps assess the potential for bias when misclassification is ignored when reliable ancillary information is available the model can be used to correct for misclassification bias in the estimates produced by these regression procedures

regression models for choice based samples with misclassification in the response variable abstract in this paper we provide a general framework to deal with the presence of misclassification in the response variable in choice based samples the contaminated data sampling distribution is written as a function of the error free conditional distribution of the dependent variable given the covariates and the conditional misclassification probabilities of the observable variable of interest given its latent values we propose an extension of imbens econometrica 60 1992 1187 efficient generalized method of moments to estimate this model and outline a specification test to detect the presence of this sort of measurement error the performance of both the estimators and the test is investigated in a monte carlo simulation study which shows very encouraging results

generalization of steane s enlargement construction of quantum codes and applications we generalize steane s enlargement construction of binary quantum codes to q ary quantum codes we then apply this result to bch codes and the study of asymptotic bounds and obtain improvements to the quantum bch codes constructed by aly and klappenecker and the quantum asymptotic bounds from algebraic geometry codes obtained by feng ling and xing

precision of double sampling estimators for comparing two probabilities summary it is assumed that both error prone and error free observations can be made on a binary response the second type being more expensive in double sampling error prone observations are made on all sample units and for a random subsample error free observations are made as well tenenbein 1970 studied allocation of units in double sampling for estimating a single probability we consider double sampling for comparing two probabilities for different cost ratios for error prone versus error free observations and for fixed total cost we assess how the large sample variance of the log odds ratio estimator varies with the proportion of units subject to both error prone and error free observation we determine the optimal double sampling proportion and the possible gain from using double sampling versus single sampling in which only error free observations are made

application of constacyclic codes to quantum mds codes quantum maximum distance separable mds codes form an important class of quantum codes to get q ary quantum mds codes one of the effective ways is to find linear mds codes c over f q2 satisfying c h c where c h denotes the hermitian dual code of c for a linear code c of length n over f q2 we say that c is a dual containing code if c h c and c f q2 n several classes of new quantum mds codes with relatively large minimum distance have been produced through dual containing constacyclic mds codes these works motivate us to make a careful study on the existence conditions for dual containing constacyclic codes we obtain necessary and sufficient conditions for the existence of dual containing constacyclic codes four classes of dual containing constacyclic mds codes are constructed and their parameters are computed consequently the quantum mds codes are derived from these parameters the quantum mds codes exhibited here have minimum distance bigger than the ones available in the literature

optimality and efficiency of two treatment repeated measurements designs for an arbitrary covariance matrix and any number of treatments and periods necessary and sufficient conditions for the optimality of a repeated measurements i e crossover or changeover design were given in the as yet unpublished report by h b kushner optimal repeated measurements designs the linear optimality equations kushner report here we specialise the results to the two treatment case we give linear equations whose solutions are the proportions of subjects allocated to each treatment sequence in the most general optimal design the treatment effects information matrix of an optimal design is also presented the results are applied to several situations for arbitrary covariance matrices we show that designs consisting of at most two treatment sequences and their duals must necessarily be dual balanced to be optimal for autoregressive covariance matrices we confirm that designs of matthews 1987 for three and four periods are optimal and we derive new optimal designs for five and six periods some optimality results of laska meisner 1985 are extended a simple formula for the efficiency of a dual balanced nonoptimal design is provided and used to compute the exact efficiencies of some of kunert s 1991 designs

log linear models for doubly sampled categorical data fitted by the em algorithm abstract double sampling experiments can be expressed as incomplete multiway contingency tables and analyzed by using techniques appropriate for fitting log linear models the framework described can be applied to experiments with any number of factors and measurement devices maximum likelihood estimation via the em algorithm leads to straightforward expressions for covariances of estimates of the parameters and functions of the parameters

optimal two stage screening designs for survival comparisons summary a two stage design is presented which enables the screening at the first stage of several new experimental treatments for survival improvement over a standard regimen only promising treatments are carried forward to the second stage for definitive evaluation our procedure is to minimize the number of patients expected to be accrued to new regimens which do not offer a survival benefit over the standard regimen subject to constraints of specified alpha error power and a stopping rule wlhich allows specification of the magnitude of the hazards ratio which would warrant accrual beyond the first stage we explore the savings in patient accrual by comparing our design with a single stage design for a variety of situations our design may offer a substantial saving when the hazard rate is large relative to the patient accrual rate a situation often encountered in clinical trials in advanced cancer although computations are based on asymptotic results simulations verify that the approximations are adequate for most trials of interest in the development of treatments for advanced cancer a standard regimen with limited survival benefit may be available as well as several new promising regimens which have not been evaluated in a comparative trial to determine their possible survival benefit we offer an efficient two stage design which allows survival comparisons of the new regimens with a standard regimen but which permits early termination of accrual onto those new regimens which do not demonstrate a minimum prespecified survival advantage over the standard regimen in this way we hope to minimize the number of patients assigned to new regimens which are not promising the design also permits early accrual termination if a new treatment offers an early substantial survival advantage over the standard regimen 2 the design we propose a two stage screening design so that survival times of each of k experimental regimens will be compared to the survival of the standard treatment at possibly two time points t1 and t2 furthermore we assume proportional hazards such that

computer aided blocking of factorial and response surface designs we consider the problem of blocking response surface and factorial designs when block sizes are prespecified often rendering standard approaches inapplicable a generalization of harville s 1974

optimal block designs for diallel crosses summary optimal block designs for a type of diallel cross experiment are proposed these incomplete block designs are derived by using triangular partially balanced designs with two associate classes some efficient incomplete block designs for diallel crosses are also reported

a class of e optimal proper efficiency balanced designs summary proper efficiency balanced designs are considered upper bounds are given for the efficiency factor of proper efficiency balanced designs a class of e optimal efficiency balanced designs is observed as designs which attain such an upper bound

some universally optimal row column designs with empty nodes summary general forms of the reduced coefficient matrix for estimation of treatment effects and the intrablock analysis of variance of row column designs with n experimental units and v treatments are obtained from earlier work by the authors these results are used to identify desirable properties for row column designs with empty nodes a need for such designs is apparent when the blocking criteria are implemented in sequence and empty nodes do not represent wasted experimental units the construction and properties of three special classes of row column designs with some empty nodes are discussed and examples given in particular it is shown that if a row column design belongs to one of these classes then it is universally optimal for specified design parameters where universally optimal designs are designs that maximize a generalized optimality criterion as defined by kiefer

exact two sample permutation tests based on the randomized play the winner rule in comparing two treatments in a clinical trial the randomized play the winner rule tends to assign more study subjects to the better treatment it is applicable when patients have delayed responses to treatments it is not deterministic and is less vulnerable to experimental bias than other adaptive designs in this paper an efficient algorithm is provided to construct exact permutation tests for testing the equality of the two treatments with the randomized play the winner rule the test procedure is illustrated with a real life example the example shows that the design used in the trial should not be ignored in the analysis