a posteriori error estimates for mixed finite element approximations of elliptic problems we derive residual based a posteriori error estimates of the flux in l 2 norm for a general class of mixed methods for elliptic problems the estimate is applicable to standard mixed methods such as the raviart thomas nedelec and brezzi douglas marini elements as well as stabilized methods such as the galerkin least squares method the element residual in the estimate employs an elementwise computable postprocessed approximation of the displacement which gives optimal order

inferences on multivariate measures of interclass and intraclass correlations in familial data summary multivariate measures of interclass and intraclass correlations are introduced to assess the degree of resemblance between family members with respect to more than one characteristic unified estimators for the multivariate measures are proposed as the eigenvalues of certain random matrices constructed by the matrices of the weighted sums of squares and products of observations asymptotic distributions of the proposed estimators are derived under the assumption of multivariate normality the asymptotic results produce approximate confidence intervals and test procedures in a simple way

on the well posedness of weakly hyperbolic equations with time dependent coefficients in this paper we analyse the gevrey well posedness of the cauchy problem for weakly hyperbolic equations of general form with time dependent coefficients the results involve the order of lower order terms and the number of multiple roots we also derive the corresponding well posedness results in the space of gevrey beurling ultradistributions

parent offspring and sibling correlation estimation based on minque theory summary we derive easily computable expressions for minque estimators of covariance parameters in an unbalanced family data structure used to study traits these estimators are strongly consistent and asymptotically normal simple expressions for limiting sample variances and covariances of minque estimators are provided

limiting the effects of single member families in the estimation of the intraclass correlation summary because the maximum likelihood estimator for the intraclass correlation p does not exist in closed form for the unbalanced one way random effects model several noniterative estimators have been proposed for p in normal populations estimators that exclude all families of only one member have been recommended in the literature of familial correlations however these estimators lose efficiency appreciably for certain ranges of values of p indeed no single estimator can have the highest efficiency along the full range of the intraclass correlation coefficient three proposed estimators each formed by combining a pair of noniterative estimators of which one constituent estimator excludes families having only one member are shown by simulation to be nearly fully efficient for the full range of values of p a mathematical expression is given that can be used to calculate the large sample standard errors of all known noniterative estimators of the intraclass correlation

using a dpg method to validate dma experimental calibration of viscoelastic materials abstract a discontinuous petrov galerkin dpg method is used to solve the time harmonic equations of linear viscoelasticity it is based on a broken primal variational formulation which is very similar to the classical primal variational formulation used in galerkin methods but has additional interface variables at the boundaries of the mesh elements both the classical and broken formulations are proved to be well posed in the infinite dimensional setting and the resulting discretization is proved to be stable a full h p convergence analysis is also included and the analysis is verified using computational simulations the method is particularly useful as it carries its own natural arbitrary p a posteriori error estimator which is fundamental for solving problems with localized solution features this proves to be useful when validating calibration models of dynamic mechanical analysis dma experiments indeed different dma experiments of epoxy and silicone resins were successfully validated to within 5 of the quantity of interest using the numerical method

test for equality of intraclass correlation coefficients under unequal family sizes the likelihood ratio test the large sample z test and the large sample z test have been proposed to test for the equality of two intraclass correlation coefficients under unequal family sizes based on two independent multinomial samples it has been found on the basis of simulation studies that the likelihood ratio test consistently and reliably produces results superior to those of the large sample z test and large sample z test in terms of power for various combinations of intraclass correlation coefficient values

confidence interval construction for parent offspring correlations summary a method is proposed for constructing a confidence interval about an interclass correlation between a parent score and one or more offspring scores in the analysis of family data the method is based on a modification of fisher s z transformation for the case of dependent observations a monte carlo study is performed comparing the effectiveness of the method to several other procedures that could be adopted

association arrays in assessing forms of dependencies between bivariate random variables abstract the bivariate distribution of pairs of random variables x y is said to be associated with respect to the classes of functions unk and unk if the product moment correlation r x y 0 for all unk and unk in the case in which both unk unk unk consist of all increasing functions then the bivariate distribution of x y is said to be positive quadrant dependent to apply the concept to data i examine the correlations for classes of extremal functions that span by positive combinations the totality of functions unk and unk to investigate whether the pair of random variables x y are associated with respect to unk and unk and to assess the relative degree or strength of association when comparing two sets of random variables x y and z w

estimation of interclass correlations in familial data summary the maximum likelihood estimates of the parent child interclass correlation and other parameters from familial data when the families have unequal numbers of offspring is given also given are two alternative sets of estimates which are easier to compute than the maximum likelihood estimates using these estimates a test for the interclass correlation to be zero requires only the ordinary student s t distribution similarly other tests use only known distributions in the analysis of familial data the degree of mother sib resemblance is measured by the interclass correlation the correlation between two different types of family member several estimates of this correlation have been proposed in the literature see rosner donner hennekens 1977 for details and their monte carlo comparisons of mean squared errors in particular they gave maximum likelihood estimates when the sib sizes are equal however when the sib sizes are not equal rosner 1979 proposed an algorithm for finding the maximum likelihood estimates which involves iterative maximization of an implicit function of two parameters this algorithm is difficult to implement and may not even converge for some sets of data recently mak ng 1981 used the linear model approach of kempthorne tandan 1953 to obtain the maximum likelihood estimates this reduces the problem to iterative maximization of a function of one parameter however nothing is known about the convergence of the procedure another iterative method of finding the maximum likelihood estimates has been given by smith 1980 in this paper an alternative approach is given which requires solving only one equation also two alternative sets of estimates are given these estimates are easier to compute than the maximum likelihood estimates using these estimates a test for the interclass correlation to be zero is given it requires only the ordinary student s t distribution similarly other tests use only known results

on the implementation of mixed methods as nonconforming methods for second order elliptic problems in this paper we show that mixed finite element methods for a fairly general second order elliptic problem with variable coefficients can be given a nonmixed formulation lower order terms are treated so our results apply also to parabolic equations we define an approximation method by incorporating some projection operators within a standard galerkin method which we call a projection finite element method it is shown that for a given mixed method if the projection method s finite element space m h satisfies three conditions then the two approximation methods are equivalent these three conditions can be simplified for a single element in the case of mixed spaces possessing the usual vector projection operator we then construct appropriate nonconforming spaces m h for the known triangular and rectangular elements the lowest order raviart thomas mixed solution on rectangular finite elements in r 2 and r 3 on simplices or on prisms is then implemented as a nonconforming method modified in a simple and computationally trivial manner this new nonconforming solution is actually equivalent to a postprocessed version of the mixed solution a rearrangement of the computation of the mixed method solution through this equivalence allows us to design simple and optimal order multigrid methods for the solution of the linear system

robust a posteriori error control and adaptivity for multiscale multinumerics and mortar coupling we consider discretizations of a model elliptic problem by means of different numerical methods applied separately in different subdomains termed multinumerics coupled using the mortar technique the grids need not match along the interfaces we are also interested in the multiscale setting where the subdomains are partitioned by a mesh of size h whereas the interfaces are partitioned by a mesh of much coarser size h and where lower order polynomials are used in the subdomains and higher order polynomials are used on the mortar interface mesh we derive several fully computable a posteriori error estimates which deliver a guaranteed upper bound on the error measured in the energy norm our estimates are also locally efficient and one of them is robust with respect to the ratio h h under an assumption of sufficient regularity of the weak solution the present approach allows bounding separately and comparing mutually the subdomain and interface errors a subdomain interface adaptive refinement s

comparison of recent estimators of interclass correlation from familial data the asymptotic and finite sample properties of several recent estimators of interclass correlation are compared to more traditional estimators in the case of a variable number of siblings per family it is shown that karlin s family weighted pairwise estimator karlin cameron and williams 1981 proceedings of the national academy of science 78 2664 2668 is virtually equivalent to the ensemble estimator rosner donner and hennekens 1977 applied statistics 26 179 187 thus suggesting an estimator of the former s asymptotic variance further an estimator proposed by srivastava 1984 biometrika 71 177 185 is shown to be identical to the modified sib mean estimator konishi 1982 annals of the institute of statistical mathematics 34 505 515 when the sib sib correlation is estimated by the method of unweighted group means although the estimator due to srivastava has smaller asymptotic variance than the other two the gain in efficiency is slight for familial data both asymptotically and in finite samples

weakly hyperbolic equations with non analytic coefficients and lower order terms in this paper we consider weakly hyperbolic equations of higher orders in arbitrary dimensions with time dependent coefficients and lower order terms we prove the gevrey well posedness of the cauchy problem under c k regularity of coefficients of the principal part and natural levi conditions on lower order terms which may be only continuous in the case of analytic coefficients in the principal part we establish the c infty well posedness the proofs are based on using the quasi symmetriser for the corresponding companion system and inductions on the order of equation and on the frequency regions the main novelty compared to the existing literature is the possibility to include lower order terms to the equation which have been untreatable until now in these problems as well as considering any space dimensions we also give results on the ultradistributional and distributional well posedness of the problem and we look at new effects for equations with discontinuous lower order terms

well posedness of hyperbolic systems with multiplicities and smooth coefficients we study hyperbolic systems with multiplicities and smooth coefficients in the case of non analytic smooth coefficients we prove well posedness in any gevrey class and when the coefficients are analytic we prove c infty well posedness the proof is based on a transformation to block sylvester form introduced by d ancona and spagnolo boll umi 8 1b 169 185 1998 which increases the system size but does not change the eigenvalues this reduction introduces lower order terms for which appropriate levi type conditions are found these translate then into conditions on the original coefficient matrix this paper can be considered as a generalisation of garetto and ruzhansky math ann 357 2 401 440 2013 where weakly hyperbolic higher order equations with lower order terms were considered

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

polynomial degree robust a posteriori estimates in a unified setting for conforming nonconforming discontinuous galerkin and mixed discretizations we present equilibrated flux a posteriori error estimates in a unified setting for conforming nonconforming discontinuous galerkin and mixed finite element discretizations of the two dimensional poisson problem relying on the equilibration by the mixed finite element solution of patchwise neumann problems the estimates are guaranteed locally computable locally efficient and robust with respect to polynomial degree maximal local overestimation is guaranteed as well numerical experiments suggest asymptotic exactness for the incomplete interior penalty discontinuous galerkin scheme

estimation of parent offspring correlation summary when families have different numbers of offspring srivastava 1984 provided an easily computable estimator as an alternative to the maximum likelihood estimator of parentoffspring correlation some properties of this estimator are discussed vis a vis with those of ensemble and pairwise estimators further we derive the small sample distribution of srivastava s estimator under the assumption of null parent offspring correlation in the process we demonstrate that a certain function of the classical sib mean estimator has student s t distribution despite differing sib ship sizes

quantile estimation from repeated measurements abstract quantile estimators for a nonparametric components of variance situation are proposed consistency and asymptotic normality are proved situations with different numbers of measurements for different subjects are considered measurements on separate subjects are assumed to be independent whereas measurements on the same subject have a fixed dependence the estimators are obtained by inverting weighted empirical distribution functions an optimal estimator and a simple estimator based on within subject averages are studied small sample properties are studied by simulation as an illustration the estimators are applied to give normal limits for differential light sensitivity of the human eye

estimation of interclass correlation under circular covariance summary the maximum likelihood estimates of the parent sib interclass correlation and other parameters are obtained when the between sibs correlation matrix has a circular structure the problem of testing hypotheses about interclass correlation is also considered

cluster robust bootstrap inference in quantile regression models abstractin this article i develop a wild bootstrap procedure for cluster robust inference in linear quantile regression models i show that the bootstrap leads to asymptotically valid inference on the entire quantile regression process in a setting with a large number of small heterogeneous clusters and provides consistent estimates of the asymptotic covariance function of that process the proposed bootstrap procedure is easy to implement and performs well even when the number of clusters is much smaller than the sample size an application to project star data is provided supplementary materials for this article are available online

semiparametric bayesian modeling of random genetic effects in family based association studies we consider the inference problem of estimating covariate and genetic effects in a family based case control study where families are ascertained on the basis of the number of cases within the family however our interest lies not only in estimating the fixed covariate effects but also in estimating the random effects parameters that account for varying correlations among family members these random effects parameters though weakly identifiable in a strict theoretical sense are often hard to estimate due to the small number of observations per family a hierarchical bayesian paradigm is a very natural route in this context with multiple advantages compared with a classical mixed effects estimation strategy based on the integrated likelihood we propose a fully flexible bayesian approach allowing nonparametric modeling of the random effects distribution using a dirichlet process prior and provide estimation of both fixed effect and random effects parameters using a markov chain monte carlo numerical integration scheme the nonparametric bayesian approach not only provides inference that is less sensitive to parametric specification of the random effects distribution but also allows possible uncertainty around a specific genetic correlation structure the bayesian approach has certain computational advantages over its mixed model counterparts data from the prostate cancer genetics project a family based study at the university of michigan comprehensive cancer center including families having one or more members with prostate cancer are used to illustrate the proposed methods a small scale simulation study is carried out to compare the proposed nonparametric bayes methodology with a parametric bayesian alternative

a posteriori error estimates for the mortar mixed finite element method several a posteriori error estimators for mortar mixed finite element discretizations of elliptic equations are derived a residual based estimator provides optimal upper and lower bounds for the pressure error an efficient and reliable estimator for the velocity and mortar pressure error is also derived which is based on solving local element problems in a higher order space the interface flux jump term that appears in the estimators can be used as an indicator for driving an adaptive process for the mortar grids only

a galerkin characteristic unified finite element method for moving thermal fronts in porous media abstract we investigate the performance of a unified finite element method for the numerical solution of moving fronts in porous media under non isothermal flow conditions the governing equations consist of coupling the darcy equation for the pressure to two convection diffusion reaction equations for the temperature and depth of conversion the aim is to develop a non oscillatory unified galerkin characteristic method for efficient simulation of moving fronts in porous media the method is based on combining the modified method of characteristics with a galerkin finite element discretization of the governing equations the main feature of the proposed unified finite element method is that the same finite element space is used for all solutions to the problem including the pressure velocity temperature and concentration analysis of convergence and stability is also presented in this study and error estimates in the l 2 norm are established for the numerical solutions in addition due to the lagrangian treatment of convection terms the standard courant friedrichs lewy condition is relaxed and the time truncation errors are reduced in the diffusion reaction part we verify the method for the benchmark problem of moving fronts around an array of cylinders the numerical results obtained demonstrate the ability of the proposed method to capture the main flow features

a comparison of confidence interval methods for the intraclass correlation coefficient summary different methods of obtaining confidence intervals for the intraclass correlation coefficient p in the unbalanced one way random effects model are investigated focusing on applications to family studies methods based on simple modifications of formulas for the case of equal group sizes are found to provide adequate coverage at small to moderate values of p a method based on the large sample standard error of the sample intraclass correlation as derived by smith 1956 annals of human genetics 21 363 373 is shown to provide consistently good coverage at all values of p a method proposed by thomas and hultquist 1978 annals of statistics 6 582 587 also provides consistently good coverage but generates mean interval widths substantially greater than those generated by smith s method at values of p likely to arise in practice

a unifying theory of a posteriori error control for nonconforming finite element methods residual based a posteriori error estimates were derived within one unifying framework for lowest order conforming nonconforming and mixed finite element schemes in carstensen numer math 100 617 637 2005 therein the key assumption is that the conforming first order finite element space v h c annulates the linear and bounded residual l written v h c subseteq rm ker ell that excludes particular nonconforming finite element methods ncfems on parallelograms in that v h c not subset rm ker ell the present paper generalises the aforementioned theory to more general situations to deduce new a posteriori error estimates also for mortar and discontinuous galerkin methods the key assumption is the existence of some bounded linear operator pi v h c rightarrow v h nc with some elementary properties it is conjectured that the more general hypothesis h1 h3 can be established for all known ncfems applications on various nonstandard finite element schemes for the laplace stokes and navier lame equations illustrate the presented unifying theory of a posteriori error control for ncfem

the asymptotic variance of the interclass correlation coefficient summary in genetics the term interclass correlation has been used to refer to the parent offspring and son daughter correlations within families under the assumption of variable family sizes and normality we derive the asymptotic variance of the maximum likelihood estimator of the sondaughter interclass correlation

properties of alternative estimators of familial correlations under variable sibship size selected distributional properties of a variety of estimators of familial correlations spouse parent child and sibling were investigated numerically focusing particularly on sibling correlations under variable sibship size maximum likelihood estimators were evaluated for each of the three familial relationships an additional parent offspring estimator was studied using a parent midoffspring estimate pooled over variable sibship size for sibling intraclass correlations three estimators based on analysis of variance and three pairwise estimators using different weighting functions for variable sibship sizes were investigated correlations were estimated from data simulated under eight sampling conditions each replicated 1 000 times using two sets of true parameter values moderate and large sample sizes and normal versus highly non normal sample distributions of data the estimators are nearly unbiased and efficient but none of the sibling correlation estimators are normally distributed in small samples estimates from highly non normal data are nearly unbiased but are less efficient than those from normal data

robust asymptotic sampling theory for correlations in pedigrees methods to unravel the genetic determinants of non mendelian diseases lie at the next frontier of statistical approaches for human genetics it is generally agreed that before proceeding with segregation or linkage analysis the trait under study ought to be shown to exhibit familial correlation by coding dichotomous traits as binary variables a single robust approach in the estimation of pedigree correlations rather than two distinct approaches can be used to assess the potential heritability of a trait and latterly to examine the mode of inheritance the asymptotic theory to conduct hypothesis tests and confidence intervals for correlations among different members of nuclear families is well established but is applicable only if the nuclear families are independent as a further contribution to the literature we derive the asymptotic sampling distribution of correlations between random variables among arbitrary pairs of members in extended families for the pearson product moment estimator with generalized weights this derivation is done without assuming normality of the traits the sampling distribution is shown to be asymptotically normal to first order and hence large sample hypothesis tests and confidence intervals with estimates of the variances and correlation coefficients are proposed discussion concludes with an example and a suggestion for future research

a posteriori error estimate for the mixed finite element method a computable error bound for mixed finite element methods is established in the model case of the poisson problem to control the error in the h div x l 2 norm the reliable and efficient a posteriori error estimate applies e g to raviart thomas brezzi douglas marini and brezzi douglas fortin marini elements

on the properties of maximum likelihood estimators of familial correlations under variable sibship size selected distributional properties of the maximum likelihood estimator and its z transformation of three familial correlations parental parent offspring filial were investigated numerically for the case of nuclear families with variable sibship size this investigation was based on six different sets of the three correlations and four different sample sizes defining 24 sampling conditions which were replicated 1 000 times each it was found that the distributional properties of the correlation estimator are affected by the magnitude of the correlations even in large samples although approximate normality is achieved locally fisher s z transformation here used only in its interclass form achieves reduction of skewness stabilization of variance and approach to normality already in small samples except for the filial correlation where it may be deemed inappropriate in smaller samples for both the correlation estimator and its z transformation the estimated relative efficiency was shown to be high better than 90 in most sampling conditions suggesting that the estimated minimum variance bound is a satisfactory estimator of the sampling variance it is concluded that the maximum likelihood estimation of familial correlations under variable sibship size is feasible and when prudently applied especially in the form of their z transformations provides an appropriate method in analyses of family studies

wave equation for sums of squares on compact lie groups in this paper we investigate the well posedness of the cauchy problem for the wave equation for sums of squares of vector fields on compact lie groups we obtain the loss of regularity for solutions to the cauchy problem in local sobolev spaces depending on the order to which the hormander condition is satisfied but no loss in globally defined spaces we also establish gevrey well posedness for equations with irregular coefficients and or multiple characteristics as in the sobolev spaces if formulated in local coordinates we observe well posedness with the loss of local gevrey order depending on the order to which the hormander condition is satisfied

a comparison of parent offspring correlation estimators in terms of large sample mean squared error and bias in the analysis of familial data there has been some confusion regarding the best estimator of the parent offspring correlation and or regression rather than rely on simulation evidence we examine explicit formulae for the bias and mean squared error of four asymptotically unbiased estimators the pairwise correlation and regression coefficients the sib mean regression coefficient and the ensemble estimator in terms of bias it is shown that the ensemble estimator is a better estimator of the interclass correlation than the pairwise in terms of mean squared error the pairwise correlation is on balance the best estimator certainly when the intraclass correlation is less than about 3 this watershed value has been observed by other workers in simulation studies and varies from about 3 for families with a low mean number of progeny to about 1 for those with a high mean number an explicit expression for the watershed value is obtained in terms of the arithmetic mean the harmonic mean and the variance of the family size distribution

estimating intraclass correlation for binary data summary this paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study some of the estimators are very specific while others result from general methods such as pseudo likelihood and extended quasi likelihood estimation the simulation study identifies several useful estimators one of which does not seem to have been considered previously for binary data estimators based on extended quasi likelihood are found to have a substantial bias in some circumstances

estimation of interclass and intraclass correlations in multivariate familial data asymptotically normal estimators of interclass and intraclass correlations are derived for more than two quantitative characteristics of parent and siblings in a simple random sampling of families that have different numbers of offspring these estimators are proposed as an alternative to the maximum likelihood estimators which can be found only by iterative methods requiring prohibitively large amounts of computation the asymptotic variances of the proposed estimators are also given in an illustrative example these easily computable estimators are seen to be comparable to the corresponding maximum likelihood estimators

a posteriori error estimates for a discontinuous galerkin method applied to elliptic problems log number r74 abstract a posteriori error estimates for locally mass conservative methods for subsurface flow are presented these methods are based on discontinuous approximation spaces and referred to as discontinuous galerkin methods in the case where penalty terms are added to the bilinear form one obtains the nonsymmetric interior penalty galerkin methods in a previous work we proved optimal rates of convergence of the methods applied to elliptic problems here h adaptivity is investigated for flow problems in 2d we derive global explicit estimators of the error in the l 2 norm and we numerically investigate an implicit indicator of the error in the energy norm model problems with discontinuous coefficients are considered

analysis of familial data linear model approach summary a linear model approach is proposed for deriving the maximum likelihood estimates of the mother sib interclass correlation and other parameters from familial data when the families have unequal numbers of offspring it leads to an algorithm which involves the maximization of an explicit function of a variable for estimating one parameter and direct substitutions for other parameters the algorithm is believed to be much simpler and more practical than that proposed by rosner 1979 some other advantages of the linearmodel approach are also discussed

regression analysis in the presence of heterogeneous intraclass correlations summary in the statistical analysis of twinship and familial data one often encounters the need for regression methods that control for the possibly different aggregation of the twins and the members of the families according to their type e g monozygotic dizygotic for twinship data we present the maximum likelihood solution for the regression analysis of data in the presence of heterogeneous intraclass correlations this work extends previous results for the case of a homogeneous intraclass correlation an application of the methods for the analysis of twinship data is included

a note on weakly hyperbolic equations with analytic principal part in this note we show how to include low order terms in the c well posedness results for weakly hyperbolic equations with analytic time dependent coefficients this is achieved by doing a different reduction to a system from the previously used one we find the levi conditions such that the c well posedness continues to hold

error indicators for incompressible darcy flow problems using enhanced velocity mixed finite element method abstract local mesh adaptivity serves as a practical tool in numerical simulations to accurately capture features of interest while reducing computational time and memory requirements in this work we suggest a refinement strategy based on pressure and flux error estimates for numerical simulation of an incompressible single phase flow and transport process in the subsurface porous media we derive a posteriori error estimates for an enhanced velocity mixed finite element method evmfem as a spatial domain decomposition approach we note that the flux errors play an important role in coupled flow and transport systems later demonstrated using numerical experiments a comparison between explicit residual based error estimators and an implicit error estimator based upon the post processing proposed by arbogast and chen 1995 shows that the latter performs better a residual based error estimator for pressure was found to be both computationally efficient while sufficiently indicating the large error subdomains numerical studies are also presented that confirm our theoretical derivations while demonstrating the advantages of post processing in detecting velocity errors

hyperbolic systems with non diagonalisable principal part and variable multiplicities i well posedness in this paper we analyse the well posedness of the cauchy problem for a rather general class of hyperbolic systems with space time dependent coefficients and with multiple characteristics of variable multiplicity first we establish a well posedness result in anisotropic sobolev spaces for systems with upper triangular principal part under interesting natural conditions on the orders of lower order terms below the diagonal namely the terms below the diagonal at a distance k to it must be of order k this setting also allows for the jordan block structure in the system second we give conditions for the schur type triangularisation of general systems with variable coefficients for reducing them to the form with an upper triangular principal part for which the first result can be applied we give explicit details for the appearing conditions and constructions for 2 times 2 and 3 times 3 systems complemented by several examples

a posteriori error estimates for lowest order mixed finite element discretizations of convection diffusion reaction equations we establish residual a posteriori error estimates for lowest order raviart thomas mixed finite element discretizations of convection diffusion reaction equations on simplicial meshes in two or three space dimensions the upwind mixed scheme is considered as well and the emphasis is put on the presence of an inhomogeneous and anisotropic diffusion dispersion tensor and on a possible convection dominance global upper bounds for the approximation error in the energy norm are derived where in particular all constants are evaluated explicitly so that the estimators are fully computable our estimators give local lower bounds for the error as well and they hold from the cases where convection or reaction are not present to convection or reaction dominated problems we prove that their local efficiency depends only on local variations in the coefficients and on the local peclet number moreover the developed general framework allows for asymptotic exactness and full robustness with respect to inhomogeneities and anisotropies the main idea of the proof is a construction of a locally postprocessed approximate solution using the mean value and the flux in each element known in the mixed finite element method and a subsequent use of the abstract framework arising from the primal weak formulation of the continuous problem numerical experiments confirm the guaranteed upper bound and excellent efficiency and robustness of the derived estimators

a test of hypothesis on familial correlations when familial data are analysed the model usually employed assumes independence of family observations and constancy of interclass and intraclass correlations a statistic for testing the validity of the assumptions of family independence and constant interclass and intraclass correlations is developed the test statistic is for constant family size it has an asymptotic chi square distribution an example to illustrate the theory is given using frets s data on head lengths a recommendation is made on how to apply the test to the general case of varying sizes another recommendation is made on models to be tried once the null hypothesis is rejected

a note on the analysis of familial data because families have varying numbers of offspring the maximum likelihood estimators of the interclass or parent offspring and intraclass or offspring offspring correlations are difficult to compute srivastava 1984 for this reason alternative estimators have been proposed which are not necessarily asymptotically efficient however maximum likelihood estimators of the inter and intraclass correlations in families of constant size can be obtained in closed form

goal oriented adaptive mesh refinement for discontinuous petrov galerkin methods this article lays a mathematical foundation for goal oriented adaptive mesh refinement and a posteriori error estimation with discontinuous petrov galerkin dpg finite element methods a goal ori

estimation of the interclass correlation coefficient summary a noniterative method for estimating the interclass correlation coefficient is derived from the technique of weighted sums of squares the asymptotic variance of this estimator is derived under the assumption of normality through extensive monte carlo simulations the sample variance of this estimator is found not to differ greatly from that of the maximum likelihood estimator an important problem in genetics is the estimation of the degree of resemblance between a mother and her children as measured by the interclass correlation coefficient because parents produce differing numbers of offspring during their reproductive period the maximum likelihood estimation of the interclass correlation presents computational difficulties requiring an iterative solution therefore a number of noniterative estimators have been proposed in the literature these estimators will be shown to be associated with special cases of the generalized estimator derived from the weighted sums of squares of measurements on parents and offspring because our purpose is to provide a comprehensive approach to the noniterative point and interval estimation problems for the interclass correlation coefficient the asymptotic variance of the proposed estimator is derived under the assumption of normality moreover the sample variances of two special cases of the proposed estimator are compared to that of the maximum likelihood estimator through monte carlo simulations by a theoretical argument it is shown that the estimator proposed by srivastava 1984 has a uniformly smaller asymptotic variance than the ensemble estimator proposed by rosner donner hennekens 1977 smith 1957 used the weighted sums of squares approach for the estimation problem concerning the intraclass correlation coefficient which measures the degree to which siblings resemble one another our results together with those of smith 1957 provide a unified approach to estimation problems concerning familial correlations among a parent and offspring

testing hypotheses about interclass correlations from familial data testing problems concerning interclass correlations from familial data are considered in the case where the number of siblings varies among families under the assumption of multivariate normality two test procedures are proposed for testing the hypothesis that an interclass correlation is equal to a specified value to compare the properties of the tests including a likelihood ratio test monte carlo experiments are performed several test statistics are derived for testing whether two variables about a parent and child are uncorrelated the proposed tests are compared with previous test procedures using monte carlo simulation a general procedure for finding confidence intervals for interclass correlations is also derived

a posteriori error estimates for a discontinuous galerkin approximation of second order elliptic problems several a posteriori error estimators are introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem in addition to residual type estimators we introduce some estimators that are couched in the ideas and techniques of domain decomposition results of numerical experiments are presented

sibling and parent offspring correlation estimation with variable family size abstract a method for estimating intrafamilial correlations under variable family sizes involving weightings of paired data points is introduced classical methods of intrafamilial correlation estimation and those in current use are outlined and critically analyzed extensions of the proposed estimation method to more general data structures are delineated

hyperbolic equations with non analytic coefficients we prove that the cauchy problem for a hyperbolic homogeneous equation with mathcal c infty coefficients depending on time is well posed in every gevrey class although in general it is not well posed in mathcal c infty provided the characteristic roots satisfy the condition lambda i t 2 lambda j t 2 leq m lambda i t lambda j t 2 quad i neq j

robust a posteriori error estimation for nonconforming finite element approximation the equilibrated residual method for a posteriori error estimation is extended to nonconforming finite element schemes for the approximation of linear second order elliptic equations where the permeability coefficient is allowed to undergo large jumps in value across interfaces between differing media the estimator is shown to provide a computable upper bound on the error and up to a constant depending only on the geometry provides two sided bounds on the error the robustness of the estimator is also studied and the dependence of the constant on the jumps in permeability is given explicitly

homogeneous weakly hyperbolic equations with time dependent analytic coefficients abstract this paper concerns the cauchy problem for homogeneous weakly hyperbolic equations with time depending analytic coefficients we give a sufficient condition for the c well posedness which is also necessary if the space dimension is equal to one the main point of the paper consists in expressing our condition only in terms of the coefficients of the operator without needing to know the behavior of the characteristic roots this is made possible by using the so called standard symmetrizer of a companion hyperbolic matrix

a residual based error estimator for mortar finite element discretizations a residual based error estimator for the approximation of linear elliptic boundary value problems by nonconforming finite element methods is introduced and analyzed in particular we consider mortar finite element techniques restricting ourselves to geometrically conforming domain decomposition methods using p1 approximations in each subdomain additionally a residual based error estimator for crouzeix raviart elements of lowest order is presented and compared with the error estimator obtained in the more general mortar situation it is shown that the computational effort of the error estimator can be considerably reduced if the special structure of the lagrange multiplier is taken into account

continuous interior penalty hp finite element methods for advection and advection diffusion equations a continuous interior penalty hp finite element method that penalizes the jump of the discrete solution across mesh interfaces is introduced error estimates are obtained for first order and advection dominated transport operators the analysis relies on three technical results that are of independent interest an hp inverse trace inequality a local discontinuous to continuous hp interpolation result and hp error estimates for continuous l2 orthogonal projections

a priori error analysis for transient problems using enhanced velocity approach in the discrete time setting abstract time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run in this paper we derive theoretical convergence error estimates in discrete time setting for transient problems with the dirichlet boundary condition enhanced velocity mixed fem as domain decomposition method is used in the space discretization and the backward euler method and the crank nicolson method are considered in the discrete time setting enhanced velocity scheme was used in the adaptive mesh refinement dealing with heterogeneous porous media 1 2 for single phase flow and transport and demonstrated as mass conservative and efficient method numerical tests validating the backward euler theory are presented these error estimates are useful in the determining of time step size and the space discretization size

normalizing transformations of some statistics in multivariate analysis summary a general procedure for finding normalizing transformations is applied to various statistics in multivariate analysis it is shown that fisher s z transformation for a sample correlation coefficient in a normal sample and wilson hilferty s approximation for a chi squared variate can be derived by the same line of approach

unified primal formulation based a priori and a posteriori error analysis of mixed finite element methods we derive in this paper a unified framework for a priori and a posteriori error analysis of mixed finite element discretizations of second order elliptic problems it is based on the classical primal weak formulation the postprocessing of the potential proposed in t arbogast and z chen on the implementation of mixed methods as nonconforming methods for second order elliptic problems math comp 64 1995 943 972 and the discrete friedrichs inequality our analysis in particular avoids any explicit use of the uniform discrete inf sup condition and in a straightforward manner and under minimal necessary assumptions known convergence and superconvergence results are recovered the same framework then turns out to lead to optimal a posteriori energy error bounds in particular estimators for all families and orders of mixed finite element methods on grids consisting of simplices or rectangular parallelepipeds are derived they give a guaranteed and fully computable upper bound on the energy error represent error local lower bounds and are robust under some conditions on the diffusion dispersion tensor they are thus suitable for both overall error control and adaptive mesh refinement moreover the developed abstract framework and a posteriori error estimates are quite general and apply to any locally conservative method we finally prove that in parallel and simultaneously in converse to galerkin finite element methods under some circumstances the weak solution is the orthogonal projection of the postprocessed mixed finite element approximation onto the h 1 0 space and also establish several links between mixed finite element approximations and some generalized weak solutions

hyperbolic second order equations with non regular time dependent coefficients in this paper we study weakly hyperbolic second order equations with time dependent irregular coefficients this means assuming that the coefficients are less regular than holder the characteristic roots are also allowed to have multiplicities for such equations we describe the notion of a very weak solution adapted to the type of solutions that exist for regular coefficients the construction is based on considering friedrichs type mollifiers of coefficients and corresponding classical solutions and their quantitative behaviour in the regularising parameter we show that even for distributional coefficients the cauchy problem does have a very weak solution and that this notion leads to classical or to ultradistributional solutions under conditions when such solutions also exist in concrete applications the dependence on the regularising parameter can be traced explicitly

score tests for interclass correlation in familial data we consider a generalized interclass correlation model which can be considered as a sister brother interclass correlation model and which incorporates the parent child interclass correlation model as a special case our main interest is in testing the significance of the interclass correlation for this we develop a score test an adjusted score test corrected for small samples is also obtained maximum likelihood estimates of the parameters under the null hypothesis required for the score test are obtained using an estimating equation approach of paul 1990 biometrilka 77 549 555 the score test and the adjusted score test for the parent child interclass correlation are then compared through simulation with the likelihood ratio test and a test statistic zp based on the pairwise estimator of the parent child interclass correlation and its asymptotic standard error based on size and power we recommend the score test for large k number of families and the adjusted score test when k is small

on the gevrey well posedness of the cauchy problem for weakly hyperbolic equations of higher order abstract we shall consider the cauchy problem for weakly hyperbolic equations of higher order with coefficients depending only on time the regularities of the distinct characteristic roots and the multiple characteristic roots independently influence gevrey well posedness of the cauchy problem

combined maximum likelihood estimates for the equicorrelation coefficient combined maximum likelihood estimates for equicorrelation covariance matrices are considered the case of a common equicorrelation rho and possibly different standard deviations sigma 1 sigma k among k experimental groups is examined first and the estimation of rho sigma 1 sigma k is discussed second under the assumption of a common standard deviation and possibly different equicorrelations the estimation of rho 1 rho k sigma is considered in each case maximum likelihood solutions and corresponding large sample variances are presented