external boundary conditions for three dimensional problems of computational aerodynamics we consider an unbounded steady state flow of viscous fluid over a three dimensional finite body or configuration of bodies for the purpose of solving this flow numerically we discretize the governing equations navier stokes on a finite difference grid prior to the discretization we obviously need to truncate the original unbounded domain by introducing an artificial computational boundary at a finite distance from the body otherwise the number of discrete variables will not be finite this artificial boundary is typically the external boundary of the domain covered by the grid the flow problem both continuous and discretized formulated on the finite computational domain is clearly subdefinite unless supplemented by some artificial boundary conditions abcs at the external computational boundary in this paper we present an innovative approach to constructing highly accurate abcs for three dimensional flow computations the approach extends our previous technique developed for the two dimensional case it employs the finite difference counterparts to calderon s pseudodifferential boundary projections calculated in the framework of the difference potentials method dpm of ryaben kii the resulting abcs appear spatially nonlocal but are particularly easy to implement along with the existing flow solvers the new boundary conditions have been successfully combined with the nasa developed production code tlns3d and used for the analysis of wing shaped configurations in subsonic and transonic flow regimes as demonstrated by the computational experiments and comparison with the standard local methods the dpm based abcs allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution moreover they may provide for a noticeable speedup of multigrid convergence

β expectation and β content tolerance limits for balanced one way anova random model this article discusses procedures for computing tolerance limits for a population consisting of many batches the results of mee and owen 1983 for one sided content tolerance limits are extended to the two sided case in addition expectation tolerance limit procedures are presented the procedures given for the case in which the ratio of the between and within variances is known are exact whereas the procedures derived for settings in which the ratio is unknown involve an approximation

computing gaussian likelihoods and their derivatives for general linear mixed models algorithms are described for computing the gaussian likelihood or restricted likelihood corresponding to a general linear mixed model included are arbitrary covariance structures for both the random effects and errors formulas are also given for the first and second derivatives of the likelihoods thus enabling a newton raphson implementation the algorithms make heavy use of the cholesky decomposition the sweep operator and the w transformation also described are the modifications needed for variance profiling fisher scoring and mivque 0 as well as the computational order of the procedures

recovery of inter block information in cross over trials for cross over designs we show that one can recover information on direct and or residual treatment effects from an inter block patients as blocks analysis as is done in an incomplete block design 1 by combining the intra and inter block estimates we obtain the generalized least squares estimate in analysing cross over trials we recommended this approach provided the between patient variance component can be estimated efficiently

one sided tolerance limits for balanced and unbalanced random effects models a simple analytical approach for constructing one sided content confidence tolerance limits is proposed for general random effects models with normal data in both balanced and unbalanced data scenarios the approach is based on an approximation to the noncentral t distribution and modified large sample methods for constructing confidence bounds on functions of variance components an alternative bootstrap adjusted limit is also proposed the performance of the analytical and bootstrap adjusted limits is assessed via simulation techniques the results indicate that the analytical limit is generally somewhat conservative but is often less conservative than an existing analytical approach and may provide substantially shorter interval lengths particularly for smaller sample sizes and larger values of the bootstrap adjusted limit generally maintains the nominal confidence level and yields shorter interval lengths though it can be anticonservative for small sample sizes this article has supplementa

the estimation of the mean squared error of small area estimators abstract small area estimation has received considerable attention in recent years because of a growing demand for reliable small area statistics the direct survey estimators based only on the data from a given small area or small domain are likely to yield unacceptably large standard errors because of small sample size in the domain therefore alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency these estimators use models either implicitly or explicitly that connect the small areas through supplementary e g census and administrative data for example simple synthetic estimators are based on implicit modeling in this article three small area models of battese harter and fuller 1988 dempster rubin and tsutakawa 1981 and fay and herriot 1979 are investigated these models are all special cases of a general mixed linear model involving fixed and random effects and a small area mean can be expr

the subgraph isomorphism problem for outerplanar graphs this paper deals with the subgraph isomorphism problem for outerplanar graphs suboutisom in general since trees and forests are outerplanar suboutisom is np complete we show that suboutisom remains np complete even when the strongest connectivity requirements are imposed on both graphs the same results holds for the induced subgraph isomorphism problem for outerplanar graphs except the case when both graphs are 2 connected for such graphs we give a polynomial algorithm which verifies whether a 2 connected outerplanar graph is an induced subgraph of another 2 connected outerplanar graph

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

variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

two dimensional transonic aerodynamic design method this paper demonstrates the capabilities of a new transonic two dimensional design method based on the simultaneous solution of multiple streamtubes coupled through the position of and pressure at the streamline interfaces this allows the specification of either the airfoil shape direct analysis mode or the airfoil surface pressure distribution inverse design mode the nonlinear system of equations is formulated in a conservative manner which guarantees the correct treatment of shocks and is solved by a rapid newton solution method viscous effects can also be included through a coupled integral boundary layer analysis the first set of results shows the effect of different far field treatments demonstrating the improvement in accuracy obtained by including the second order doublet terms in addition to the usual first order vortex term the results are also compared to those obtained by specifying straight far field streamlines corresponding to solid wall wind tunnel experiments or constant far field pressure corresponding to freejet experiments to show the sensitivity to the farfield distance in the second set of results the design method is used to design a transonic airfoil with c 1 000 at a oo 0 70 it is shown that the off design performance is improved by specifying a surface pressure distribution with a very weak shock

on the complexity of submap isomorphism and maximum common submap problems generalized maps describe the subdivision of objects in cells and are widely used to model 2d and 3d images in this context several pattern recognition tasks involve solving submap isomorphism problems to decide if a map is included in another map or more generally computing maximum common submaps to measure the distance between two maps recently we have described a polynomial time algorithm for solving the submap isomorphism problem when the pattern map is connected in this paper we show that submap isomorphism is np complete when the pattern map is not connected then we characterize the inherent difficulty of submap isomorphism with respect to the number of connected components we show that it is fixed parameter tractable fpt and we give an fpt algorithm for submap isomorphism we experimentally compare this algorithm with a state of the art subgraph isomorphism algorithm for searching for patterns in an image and we show that it is both more accurate and more efficient finally we study the complexity of the maximum common submap problem and we show that it is np hard even though we restrict the problem to the search of common connected submaps highlightswe show that submap isomorphism is np complete we give a fixed parameter tractable algorithm for submap isomorphism we experimentally evaluate it to search for patterns in segmented images we show that maximum common connected submap is np hard

the complexity of subgraph isomorphism for classes of partial k trees we present a clear demarcation between classes of bounded tree width graphs for which the subgraph isomorphism problem is np complete and those for which it can be solved in polynomial time in previous work it has been shown that this problem is solvable in polynomial time if the source graph either has bounded degree or is k connected for k the tree width of the two graphs as well it has also been shown that for certain specific connectivity or degree conditions the problem becomes np complete here we give a complete characterization of the complexity of this problem on bounded tree width graphs for all possible connectivity conditions of the two input graphs specifically we show that when the source graph is not k connected or has more than k vertices of unbounded degree the problem is np complete this answers an open question of matousek and thomas many of our reductions are restricted to using a subset of graphs of bounded tree width namely graphs of bounded path width as a direct result of our constructions we also show that when the source and target graphs have connectivity less than k or at least one has k vertices of unbounded degree the subgraph isomorphism problem for bounded path width graphs is np complete

exploring the information in p values for the analysis and planning of multiple test experiments a new methodology is proposed for estimating the proportion of true null hypotheses in a large collection of tests each test concerns a single parameter delta whose value is specified by the null hypothesis we combine a parametric model for the conditional cumulative distribution function cdf of the p value given delta with a nonparametric spline model for the density g delta of delta under the alternative hypothesis the proportion of true null hypotheses and the coefficients in the spline model are estimated by penalized least squares subject to constraints that guarantee that the spline is a density the estimator is computed efficiently using quadratic programming our methodology produces an estimate g delta of the density of delta when the null is false and can address such questions as when the null is false is the parameter usually close to the null or far away this leads us to define a falsely interesting discovery rate fidr a generalization of the false discovery rate we contrast the fidr approach to efron s 2004 journal of the american statistical association 99 96 104 empirical null hypothesis technique we discuss the use of g in sample size calculations based on the expected discovery rate edr our recommended estimator of the proportion of true nulls has less bias compared to estimators based upon the marginal density of the p values at 1 in a simulation study we compare our estimators to the convex decreasing estimator of langaas lindqvist and ferkingstad 2005 journal of the royal statistical society series b 67 555 572 the most biased of our estimators is very similar in performance to the convex decreasing estimator as an illustration we analyze differences in gene expression between resistant and susceptible strains of barley

mean squared error of estimation or prediction under a general linear model abstract the problem considered is that of predicting a linear combination of the fixed and random effects of a mixed effects linear model more generally the problem considered is that of predicting an unobservable random variable from a set of observable random variables the best linear unbiased predictor depends on parameters which generally are unknown various exact or approximate expressions are given for the mean squared error mse of the predictor obtained by replacing the unknown parameters with estimates several estimators of the mse are investigated

average information reml an efficient algorithm for variance parameter estimation in linear mixed models a strategy of using an average information matrix is shown to be computationally convenient and efficient for estimating variance components by restricted maximum likelihood reml in the mixed linear model three applications are described the motivation for the algorithm was the estimation of variance components in the analysis of wheat variety means from 1 071 experiments representing 10 years and 60 locations in new south wales we also apply the algorithm to the analysis of designed experiments by incomplete block analysis and spatial analysis of field experiments

multiple imputation approaches for the analysis of dichotomized responses in longitudinal studies with missing data often a binary variable is generated by dichotomizing an underlying continuous variable measured at a specific time point according to a prespecified threshold value in the event that the underlying continuous measurements are from a longitudinal study one can use the repeated measures model to impute missing data on responder status as a result of subject dropout and apply the logistic regression model on the observed or otherwise imputed responder status standard bayesian multiple imputation techniques rubin 1987 in multiple imputation for nonresponse in surveys that draw the parameters for the imputation model from the posterior distribution and construct the variance of parameter estimates for the analysis model as a combination of within and between imputation variances are found to be conservative the frequentist multiple imputation approach that fixes the parameters for the imputation model at the maximum likelihood estimates and construct the variance of parameter estimates for the analysis model using the results of robins and wang 2000 biometrika 87 113 124 is shown to be more efficient we propose to apply kenward and roger 1997 biometrics 53 983 997 degrees of freedom to account for the uncertainty associated with variance covariance parameter estimates for the repeated measures model

design of supercritical cascades with high solidity the method of complex characteristics of garabedian and korn has been used successfully to design shockless cascades with solidities of up to one a new code has been developed using this method and a new hodograph transformation of the flow onto an ellipse this new code allows the design of cascades with solidities of up to two and larger turning angles the equations of potential flow are solved in a complex hodograph like domain by setting a characteristic initial value problem and integrating along suitable paths the topology that the new mapping introduces permits a simpler construction of these paths of integration

subgraph isomorphism for biconnected outerplanar graphs in cubic time abstract a dynamic programming algorithm for determining whether a biconnected outerplanar graph is isomorphic to a subgraph of another biconnected outerplanar graph is presented the algorithm runs in cubic time

row column α designs in row column designs the experimental units are grouped in two directions i e two blocking factors are used with one factor representing the rows of the design and the other factor representing columns for instance in an agricultural experiment the rows and columns of a design might represent different times and method of application of fertilizers in a preference testing experiment the columns might represent different subjects and the rows the order in which different products are presented to the subjects in an insulin response experiment the rows columns and treatments may represent respectively individual animals date of injection and levels of insulin in all these experiments it is hoped that there will be a gain in the accuracy of estimating treatment comparisons resulting from eliminating the effects of the row and column factors

induced subgraph isomorphism on proper interval and bipartite permutation graphs given two graphs g and h as input the induced subgraph isomorphism isi problem is to decide whether g has an induced subgraph that is isomorphic to h this problem is np complete already when g and h are restricted to disjoint unions of paths and consequently also np complete on proper interval graphs and on bipartite permutation graphs we show that isi can be solved in polynomial time on proper interval graphs and on bipartite permutation graphs provided that h is connected as a consequence we obtain that isi is fixed parameter tractable on these two graph classes when parametrised by the number of connected components of h our results contrast and complement the following known results w 1 hardness of isi on interval graphs when parametrised by the number of vertices of h np completeness of isi on connected interval graphs and on connected permutation graphs and np completeness of subgraph isomorphism on connected proper interval graphs and connected bipartite permutation graphs

semiparametric regression of multidimensional genetic pathway data least squares kernel machines and linear mixed models we consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least squares kernel machines lskms this unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way this semiparametric model also makes it possible to test for the overall genetic pathway effect we show that the lskm semiparametric regression can be formulated using a linear mixed model estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software both the regression coefficients of the covariate effects and the lskm estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation the smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood a score test is developed to test for the genetic pathway effect model variable selection within the lskm framework is discussed the methods are illustrated using a prostate cancer data set and evaluated using simulations

coupled problem of the inverse design and constraint optimization two dimensional inviscid compressible flow solver has been implemented validated and extended for completing inverse design based optimization problems euler equations are used for modelling basic physics the standard cell centred finite volume method has been applied with roe s approximated riemann solver muscl monotone upstream schemes for conservation laws approach and mulder limiter stratford s separation prediction method with constrained sqp sequential quadratic programming optimization is implemented to evaluate the optimum pressure distribution at strong adverse pressure gradient flow conditions a particular inverse design method is developed to complete wall surface modification till the optimum target pressure distribution is reached by means of inverse wall modification and direct algorithms the direct solver is validated and the coupled system of the inverse design method with constraint optimization is tested over the naca 65 410 airfoil

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

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

on parallel complexity of the subgraph homeomorphism and the subgraph isomorphism problem for classes of planar graphs abstract we consider the problems of subgraph homeomorphism with fixed pattern disjoint connecting paths with bounded number of terminal pairs recognition and subgraph isomorphism for some classes of planar graphs following the results of robertson and seymour on forbidden minor characterization we show that the first three of the above problems for any family of planar graphs closed under minor taking are in nc 3 i e they can be solved by an algorithm running in time o log 3 n using polynomial number of processors we also show that the related subgraph isomorphism problem for two connected outerplanar graphs is in nc 3 this is the first example of a restriction of subgraph isomorphism to a non trivial graph family admitting an nc algorithm

a general strategy for analyzing data from split plot and multistratum experimental designs increasingly industrial experiments use multistratum designs such as split plot and strip plot designs often these experiments span more than one processing stage the challenge is to identify an appropriate multistratum design along with an appropriate statistical model in this article we introduce hasse diagrams in the response surface context as a tool to visualize the unit structure of the experimental design the randomization and sampling approaches used the stratum in which each experimental factor is applied and the degrees of freedom available in each stratum to estimate main effects interactions and variance components we illustrate their use on several responses measured in a large study of the adhesion properties of coatings to polypropylene we discuss quantitative binary and ordered categorical responses for designs ranging from a simple split plot to a strip plot that involves repeated measurements of the response the datasets discussed in this article are available online a

multistratum response surface designs response surface designs are usually described as if the treatments have been completely randomized to the experimental units however in practice there is often a structure to the units implying the need for blocking if in addition some factors are more difficult to vary between units than others a multistratum structure arises naturally we present a general strategy for constructing response surface designs in multistratum unit structures designs are constructed stratum by stratum starting in the highest stratum in each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata allowing for all the effects that have to be estimated three examples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment set finally some practical considerations in randomization are discussed

classical and bayesian prediction as applied to an unbalanced mixed linear model unbalanced mixed linear models that contain a single set of random effects are frequently employed in animal breeding applications in small area estimation and in the analysis of comparative experiments the problem considered is that of the point or interval prediction of the value of a linear combination of the fixed and random effects or the value of a future data point a common approach is empirical blup best linear unbiased prediction in which an estimate of the variance ratio is regarded as the true value empirical blup is satisfactory or can be made satisfactory by introducing appropriate modifications unless the estimate of the variance ratio is imprecise and is close to zero in which case more sensible point and interval predictions can be obtained by adopting a bayesian approach two animal breeding examples are used to illustrate the similarities and differences between the bayesian and empirical blup approaches

the application of reml in clinical trials residual maximum likelihood reml is a technique for estimating variance components in multi classified data in contrast to analysis of variance it can be routinely applied to unbalanced data and avoids some of the problems of biased variance estimates found with standard maximum likelihood estimation the full reml method is of particular value for the analysis of unbalanced clinical trials as it allows recovery of all the available information on treatment effects which can lead to significant improvements in their precision the use of reml has until recently been limited by heavy computational requirements and lack of readily available software this is no longer such a restriction however as reml procedures are now available in several widely used statistical packages including bmdp genstat and sas this paper describes the reml technique and discusses its application to three common types of clinical trial crossover repeated measures and multicentre

the influence of design on validity and efficiency of neighbour methods summary neighbour methods have often been shown to be apparently more efficient than analysis of variance for the analysis of field experiments this means that the precision of the analysis estimated by the statistical method itself is smaller for the neighbour method than for the classical one this comparison is meaningful only if the analysis is valid in the sense that it estimates its own precision without bias although precise validity properties are known for the analysis of variance of randomized designs no analogous properties are known for neighbour analyses in this paper we investigate the validity and efficiency of some neighbour methods and their relations with the design first we give precise definitions of the desirable properties of the combination of design including randomization and method of analysis then we report on a simulation study we show that neighbour methods are often valid or conservative with higher efficiency than classical ones to better ensure these properties we advocate the use of randomized neighbour designs and corrections to degrees of freedom finally we discuss how these results can be used to assess neighbour methods for routine trials

decomposition of prediction error abstract the problem considered is that of predicting the value of an unobservable random variable w from the value of an observable random vector y this problem is considered under each of four states of knowledge about the joint distribution of w and y ranging from complete knowledge to no knowledge a point predictor or predictors are presented for each case prediction error is decomposed so that each component reflects an absence of information under certain conditions these components are uncorrelated and have zero means an exact or approximate expression is given for the variance of each component

linear score tests for variance components in linear mixed models and applications to genetic association studies summary following the rapid development of genome scale genotyping technologies genetic association mapping has become a popular tool to detect genomic regions responsible for certain disease phenotypes especially in early phase pharmacogenomic studies with limited sample size in response to such applications a good association test needs to be 1 applicable to a wide range of possible genetic models including but not limited to the presence of gene by environment or gene by gene interactions and non linearity of a group of marker effects 2 accurate in small samples fast to compute on the genomic scale and amenable to large scale multiple testing corrections and 3 reasonably powerful to locate causal genomic regions the kernel machine method represented in linear mixed models provides a viable solution by transforming the problem into testing the nullity of variance components in this study we consider score based tests by choosing a statistic linear in the score function when the model under the null hypothesis has only one error variance parameter our test is exact in finite samples when the null model has more than one variance parameter we develop a new moment based approximation that performs well in simulations through simulations and analysis of real data we demonstrate that the new test possesses most of the aforementioned characteristics especially when compared to existing quadratic score tests or restricted likelihood ratio tests

one and two sided tolerance intervals for general balanced mixed models and unbalanced one way random models in this article we develop procedures for one and two sided tolerance intervals for normal general linear models in which there exists a set of independent scaled chi squared random variables the proposed procedures are based on the concept of generalized pivotal quantities and are applicable to general mixed models provided that balanced data are available however this study focuses on situations involving unbalanced data specific attention is given to the unbalanced one way random model it is shown that the use of generalized pivotal quantities allows the construction of the tolerance intervals of interest fairly straightforward some practical examples are given to illustrate the proposed procedures furthermore detailed statistical simulation studies are conducted to evaluate their performance showing that the proposed procedures can be recommended for practical use

on efficiency of constrained longitudinal data analysis versus longitudinal analysis of covariance in randomized clinical trials measurements are often collected on each subject at a baseline visit and several post randomization time points the longitudinal analysis of covariance in which the postbaseline values form the response vector and the baseline value is treated as a covariate can be used to evaluate the treatment differences at the postbaseline time points liang and zeger 2000 sankhy the indian journal of statistics series b 62 134 148 propose a constrained longitudinal data analysis in which the baseline value is included in the response vector together with the postbaseline values and a constraint of a common baseline mean across treatment groups is imposed on the model as a result of randomization if the baseline value is subject to missingness the constrained longitudinal data analysis is shown to be more efficient for estimating the treatment differences at postbaseline time points than the longitudinal analysis of covariance the efficiency gain increases with the number of subjects missing baseline and the number of subjects missing all postbaseline values and for the pre post design decreases with the absolute correlation between baseline and postbaseline values

delta method and bootstrap in linear mixed models to estimate a proportion when no event is observed application to intralesional resection in bone tumor surgery resecting bone tumors requires good cutting accuracy to reduce the occurrence of local recurrence this issue is considerably reduced with a navigated technology the estimation of extreme proportions is challenging especially with small or moderate sample sizes when no success is observed the commonly used binomial proportion confidence interval is not suitable while the rule of three provides a simple solution unfortunately these approaches are unable to differentiate between different unobserved events different delta methods and bootstrap procedures are compared in univariate and linear mixed models with simulations and real data by assuming the normality the delta method on the z score and parametric bootstrap provide similar results but the delta method requires the estimation of the covariance matrix of the estimates in mixed models the observed fisher information matrix with unbounded variance components should be preferred the parametric bootstrap easier to apply outperforms the delta method for larger sample sizes but it may be time costly copyright 2016 john wiley sons ltd

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

some alternatives to asymptotic tests for the analysis of pharmacogenetic data using nonlinear mixed effects models nonlinear mixed effects models allow investigating individual differences in drug concentration profiles pharmacokinetics and responses pharmacogenetics focuses on the genetic component of this variability two tests often used to detect a gene effect on a pharmacokinetic parameter are 1 the wald test assessing whether estimates for the gene effect are significantly different from 0 and 2 the likelihood ratio test comparing models with and without the genetic effect because those asymptotic tests show inflated type i error on small sample size and or with unevenly distributed genotypes we develop two alternatives and evaluate them by means of a simulation study first we assess the performance of the permutation test using the wald and the likelihood ratio statistics second for the wald test we propose the use of the f distribution with four different values for the denominator degrees of freedom we also explore the influence of the estimation algorithm using both the first order conditional estimation with interaction linearization based algorithm and the stochastic approximation expectation maximization algorithm we apply these methods to the analysis of the pharmacogenetics of indinavir in hiv patients recruited in the cophar2 anrs 111 trial results of the simulation study show that the permutation test seems appropriate but at the cost of an additional computational burden one of the four f distribution based approaches provides a correct type i error estimate for the wald test and should be further investigated

a score test against one sided alternatives abstract a score type statistic t s is introduced for testing h 0 against k 0 and more general one sided hypotheses when nuisance parameters may be present is a vector parameter the main advantages of t s are that it requires estimation of the model only under the null hypothesis and that it is asymptotically equivalent to the likelihood ratio statistic these are precisely the reasons for the popularity of the score tests for testing against two sided alternatives in this sense t s preserves the main attractive features of the classical two sided score test the theoretical results are presented in a general framework where the likelihood based score function is replaced by an estimating function so that the test is applicable even if the exact population distribution is unknown computation of t s is simplified by the fact that it can be computed easily once the corresponding two sided statistic has been computed the relevance and simplicity of t s are illustrated by discussing

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

exact tests for variance components ofversten 1993 presented methods for obtaining exact f tests of variance components in three unbalanced mixed linear models he developed methods for models with one random factor models with nested classifications and models with interaction between two random factors in section 2 we review and extend wald s test which is a generalization of one of ofversten s methods ofversten s other method is a generalization of khuri 1987 1990 and khuri and littell 1987 it does not apply to the one random factor model in section 3 we present a unified treatment of ofversten s second method this treats all of ofversten s examples and gives a formal justification to ofversten s claim that the method extends quite generally section 3 also gives a formal condition for when the method does not require resampling from the residuals the unified treatment is conceptually simpler than ofversten s treatment in that it uses a single orthonormal basis rather than a series of matrix decompositions that change slightly from example to example there do not seem to be any particular computational advantages to the unified treatment the unified treatment also appears to generalize ofversten s method in that it applies in some cases where wald s test also applies section 4 compares the two tests when both apply all of the arguments are given in terms of vector space ideas cf christensen 1987

some bayesian and non bayesian procedures for the analysis of comparative experiments and for small area estimation computational aspects frequentist properties and relationships abstract the estimation of a treatment contrast from experimental data and the estimation of a small area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two part mixed linear model in this article a bayesian approach to point and interval prediction is presented and its computational requirements are examined differences between the bayesian approach and the traditional classical approach are discussed in general terms and in addition in terms of two examples taken from the literature 1 the comparison of drug formulations in a bioavailability trial westlake and 2 the estimation of corn crop areas using satellite data battese harter and fuller some deficiencies in the classical approach are pointed out and the bayesian approach is considered from a frequentist perspective it is shown via a monte carlo study that for certain noninformative choices of the prior distribution the frequentist prop

confidence prediction and tolerance in linear mixed models the literature about prediction interval pi and tolerance interval ti in linear mixed models is usually developed for specific designs which is a main limitation to their use this paper proposes to reformulate the two sided pi to be generalizable under a wide variety of designs one random factor nested and crossed designs for multiple random factors and balanced or unbalanced designs this new methodology is based on the hessian matrix namely the inverse of observed fisher information matrix and is built with a cell mean model the degrees of freedom for the total variance are calculated with the generalized satterthwaite method and compared to the kenward roger s degrees of freedom for fixed effects construction of two sided tis are also detailed with one random factor and two nested and two crossed random variables an extensive simulation study is carried out to compare the widths and coverage probabilities of confidence intervals ci pis and tis to their nominal levels it shows excellent coverage whatever the design and the sample size are finally these cis pis and tis are applied to two real data sets one from orthopedic surgery study intralesional resection risk and the other from assay validation study during vaccine development

one sided tolerance limits in balanced and unbalanced one way random models based on generalized confidence intervals we consider the problem of deriving one sided tolerance intervals in the one way random model with balanced as well as unbalanced data under the usual normality assumptions the problems investigated deal with the computation of such intervals for the observable random variable as well as the unobservable random effect in the one way random model the tolerance limits are derived using the concept of a generalized confidence interval some approximations are derived for the tolerance limits and their performance is investigated by simulation the simulation results show that the proposed tolerance limits are quite satisfactory for practical use

sensitivity analysis of unsteady aerodynamic loads in cascades a method for computing the effect perturbations in the shape of airfoils in a cascade have on the steady and unsteady flow through the cascade is presented first the full potential equation is used to describe the behavior of the nonlinear steady flow and the small disturbance unsteady flow through the cascade the steady flow and small disturbance unsteady flow versions of the full potential equation are then discretized on a computational grid of quadrilateral cells using a variational finite element technique the resulting discretized equations describing the nonlinear steady flow are solved using newton iteration with lower upper decomposition at each iteration similarly the discretized unsteady small disturbance equations which are linear are solved using a single lower upper decomposition next a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the steady and unsteady flowfields the sensitivity analysis makes use of the nominal steady and unsteady flow lower upper decompositions so that no additional matrices need to be factored hence the present method is computationally very efficient

euler based inverse method for turbomachine blades part 2 three dimensional flows the aerodynamic design method for turbomachine blades reported in part 1 is extended to three dimensions in this inverse method the blade pressure loading i e pressure difference between blade upper and lower surfaces and the blade thickness distributions are prescribed and the corresponding blade camber surface is sought the inverse problem is formulated using a pressure loading boundary condition across the blade surfaces and modification of the blade geometry is achieved using the flow tangency conditions along the blade surfaces the method is demonstrated for the design of axial flow machines ranging from the subsonic to the supersonic flow regimes

testing against a high dimensional alternative summary as the dimensionality of the alternative hypothesis increases the power of classical tests tends to diminish quite rapidly this is especially true for high dimensional data in which there are more parameters than observations we discuss a score test on a hyperparameter in an empirical bayesian model as an alternative to classical tests it gives a general test statistic which can be used to test a point null hypothesis against a high dimensional alternative even when the number of parameters exceeds the number of samples this test will be shown to have optimal power on average in a neighbourhood of the null hypothesis which makes it a proper generalization of the locally most powerful test to multiple dimensions to illustrate this new locally most powerful test we investigate the case of testing the global null hypothesis in a linear regression model in more detail the score test is shown to have significantly more power than the f test whenever under the alternative the large variance principal components of the design matrix explain substantially more of the variance of the outcome than do the small variance principal components the score test is also useful for detecting sparse alternatives in truly high dimensional data where its power is comparable with the test based on the maximum absolute t statistic

testing against a high dimensional alternative in the generalized linear model asymptotic type i error control summary testing a low dimensional null hypothesis against a high dimensional alternative in a generalized linear model may lead to a test statistic that is a quadratic form in the residuals under the null model using asymptotic arguments we show that the distribution of such a test statistic can be approximated by a ratio of quadratic forms in normal variables for which algorithms are readily available for generalized linear models the asymptotic distribution shows good control of type i error for moderate to small samples even when the number of covariates in the model far exceeds the sample size

improved design of subcritical and supercritical cascades using complex characteristics and boundary layer correction the method of complex characteristics and hodograph transformation for the design of shockless airfoils was extended to design supercritical cascades with high solidities and large inlet angles this capability was achieved by introducing a conformal mapping of the hodograph domain onto an ellipse and expanding the solution in terms of tchebycheff polynomials a computer code was developed based on this idea a number of airfoils designed with the code are presented various supercritical and subcritical compressor turbine and propeller sections are shown the lag entrainment method for the calculation of a turbulent boundary layer was incorporated to the inviscid design code the results of this calculation are shown for the airfoils described the elliptic conformal transformation developed to map the hodograph domain onto an ellipse can be used to generate a conformal grid in the physical domain of a cascade of airfoils with open trailing edges with a single transformation a grid generated with this transformation is shown for the korn airfoil previously announced in star as n83 24474

one sided and two sided tolerance intervals in general mixed and random effects models using small sample asymptotics the computation of tolerance intervals in mixed and random effects models has not been satisfactorily addressed in a general setting when the data are unbalanced and or when covariates are present this article derives satisfactory one sided and two sided tolerance intervals in such a general scenario by applying small sample asymptotic procedures in the case of one sided tolerance limits the problem reduces to the interval estimation of a percentile and accurate confidence limits are derived using small sample asymptotics in the case of a two sided tolerance interval the problem does not reduce to an interval estimation problem however it is possible to derive an approximate margin of error statistic that is an upper confidence limit for a linear combination of the variance components for the latter problem small sample asymptotic procedures can once again be used to arrive at an accurate upper confidence limit in the article balanced and unbalanced data situations are treated separately and

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

order restricted score tests for homogeneity in generalised linear and nonlinear mixed models lin 1997 building on work by solomon cox 1992 and lin breslow 1996 introduced a score test for homogeneity in the generalised linear mixed model in this paper we propose an improvement to lin s test that exploits the fact that covariance parameters associated with random effects in the model are constrained so as to form a positive semidefinite covariance matrix therefore an omnibus score test will have power against alternatives that are known never to occur our improvement works by concentrating the score test into directions given by the positive semidefiniteness constraint we apply the same sort of modification to the bias corrected version of her score test in the generalised linear mixed model context and in a nonlinear mixed model context to a score test analogous to hers we show how to obtain the limiting distribution of our proposed test statistic we also argue via simulations and local alternative power calculations that the restricted test has better power than the unrestricted one

viscous inviscid analysis of transonic and low reynolds number airfoils a method of accurately calculating transonic and low reynolds number airfoil flows implemented in the viscous inviscid design analysis code ises is presented the euler equations are discretized on a conservative streamline grid and are strongly coupled to a two equation integral boundary layer formulation using the displacement thickness concept a transition prediction formulation of the e type is derived and incorporated into the viscous formulation the entire discrete equation set including the viscous and transition formulations is solved as a fully coupled nonlinear system by a global newton method this is a rapid and reliable method for dealing with strong viscous inviscid interactions which invariably occur in transonic and low reynolds number airfoil flows the results presented demonstrate the ability of the ises code to predict transitioning separation bubbles and their associated losses the rapid airfoil performance degradation with decreasing reynolds number is thus accurately predicted also presented is a transonic airfoil calculation involving shock induced separation showing the robustness of the global newton solution procedure good agreement with experiment is obtained further demonstrating the performance of the present integral boundary layer formulation

euler based inverse method for turbomachine blades i two dimensional cascades a three dimensio nal inverse method for the aerodynamic design of turbomachine blades using robust timemarching algorithms for the numerical solutions of the euler equations is proposed in this inverse method the circumferential mass averaged tangential velocity or the blade loading is the primary specified flow quantity and the corresponding blade geometry is sought after the presence of the blades is represented by a periodic array of discrete body forces which is included in the equations of motion a four stage runge kutta time stepping scheme is used to march a finite volume formulation of the unsteady euler equations to a steady state solution modification of the blade geometry during this time marching process is achieved using the flow tangency conditions along the blade surfaces in this paper the method is demonstrated for the design of two dimensional infinitely thin cascaded blades ranging from the subsonic to the supersonic flow regimes including cases with rotational flows and complex shock structures in the flow passage

exact tests for variance components in unbalanced mixed linear models a method for deriving exact tests for variance components in some unbalanced mixed linear models is presented the derivation is based on a new kind of preliminary orthogonal transformation and a subsequent resampling procedure the resulting tests are based on mutually independent sums of squares which under the null hypothesis are distributed as scalar multiples of chi square variates for balanced data the tests are identical to the traditional f tests

handling of baseline measurements in the analysis of crossover trials different analytic approaches for modeling baseline data in crossover trials were compared based on the efficiency in estimating treatment effects jointly modeling baseline and post baseline data is recommended to best utilize baseline data it results in the most significant gain in efficiency when data are strongly correlated within the same period but weakly correlated between different periods its performance remains comparable to the best of various other modeling methods under small within period correlation or large between period correlation we also examined the use of baseline data in modeling carryover effect we noted that to model carryover effect in crossover trial generally would lead to a much less efficient estimator and much more sensitive inference copyright 2012 john wiley sons ltd

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures