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

quantum stochastic calculus associated with quadratic quantum noises we first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non solvable lie algebra consisting of all linear combinations of the generalized gross laplacian and its adjoint annihilation operator creation operator conservation and time and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes and the quantum ito formula is revisited the existence and uniqueness of solution of a quantum stochastic differential equation is proved the unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined the quantum stochastic calculus extends the hudson parthasarathy quantum stochastic calculus

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

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

a numerical study on the solution of the cauchy problem in elasticity this work deals with the cauchy problem in two dimensional linear elasticity the equations of the problem are discretized through a standard fem approach and the resulting ill conditioned discrete problem is solved within the frame of the tikhonov approach the choice of the required regularization parameter is accomplished through the generalized cross validation criterion on this basis a numerical experimentation has been performed and the calculated solutions have been used to highlight the sensitivity to the amount of known data the noise always present in the data the regularity of boundary conditions and the choice of the regularization parameter the aim of the numerical study is to implicitly device some guidelines to be used in the solution of this kind of problems

the asymptotic variance matrices of the sample correlation matrix in elliptical and normal situations and their proportionality abstract this note presents the asymptotic variance matrices of the sample correlation matrix in elliptical and normal situations and generalizes the scalar proportionality result to the multivariate case

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

robust estimation of mean squared error of small area estimators abstract a well known model due to fay and herriot for estimating small area domain means i is considered given i s it is assumed that the survey estimators y i are independent with means i and known variances di i 1 t further the i s are assumed to be independent with means x i and unknown variance a where x i is a vector of benchmark variables related to i and is a vector of regression parameters an empirical best linear unbiased prediction eblup estimator or an empirical linear bayes estimator t i y of i is obtained it is shown that an estimator of mean squared error mse of t t y derived by prasad and rao under normality of i and y i given i is robust with respect to nonnormality of the i s specifically it is shown that the prasad rao estimator of mse is correct to terms of order o t 1 for large t assuming only certain moment conditions on the i s and normally distributed survey errors results of a simulation study on the accur

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

direct solution of ill posed boundary value problems by radial basis function collocation method numerical solution of ill posed boundary value problems normally requires iterative procedures in a typical solution the ill posed problem is first converted to a well posed one by assuming the missing boundary values the new problem is solved by a conventional numerical technique and the solution is checked against the unused data the problem is solved iteratively using optimization schemes until convergence is achieved the present paper offers a different procedure using the radial basis function collocation method we demonstrate that the solution of certain ill posed problems can be accomplished without iteration this method not only is efficient and accurate but also circumvents the stability problem that can exist in the iterative method copyright 2005 john wiley sons ltd

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

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

distribution spaces and a new construction of stochastic processes associated with the grassmann algebra we associate with the grassmann algebra a topological algebra of distributions which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments as well as their derivatives

the detection of the source of acoustical noise in two dimensions we consider the problem of detecting the source of acoustical noise inside the cabin of a midsize aircraft from measurements of the acoustical pressure field inside the cabin mathematically this field satisfies the helmholtz equation in this paper we consider the model two dimensional case we show that any regular solution of this equation admits a unique representation by a single layer potential so that the problem is reduced to the solution of a linear integral equation of the first kind we prove uniqueness of reconstruction and obtain a sharp stability estimate finally for two geometries and sources of noise simulating the cabin of the aircraft and two engines we give results of the numerical solution of this integral equation comparing regularization by the truncated singular value decomposition and the conjugate gradient method

dispersion matrix in balanced mixed anova models the inverse of the dispersion matrix plays an important role in mixed model analysis searle and henderson j amer statist assoc 74 1979 465 showed that for a general balanced mixed anova model such an inverse can be expression in the same form as the dispersion matrix i e a linear combination of kronecker products however the coefficients of such a linear combination are given in a way that it is not easy to see what each coefficient is in this paper we give explicit expressions for these coefficients an application of the result is considered

nonparametric estimation of residual variance revisited summary several difference based estimators of residual variance are compared for finite sample size since the introduction of a rather simple estimator by gasser sroka jennensteinmetz 1986 other proposals have been made here the one given by hall kay titterington 1990 is of particular interest it minimizes the asymptotic variance unfortunately it has severe problems with finite sample bias and the estimator of gasser et al 1986 proves still to be a good choice a new estimator is introduced compromising between bias and variance

on inequality constrained generalized least squares selections in the general possibly singular gauss markov model a projector theoretical approach abstract this paper deals with the general possibly singular linear model it is assumed that in addition to the sample information we have some nonstochastic prior information concerning the unknown regression coefficients that can be expressed in form of linear independent inequality constraints since these constraints are part and parcel of the model an inequality constrained generalized least squares icgls problem arises with some hitherto unknown aspects based on a projector theoretical approach we show how the set of icgls selections under the constrained model is related to the set of gls selections under the associated unconstrained model as a by product we obtain an interesting method for determining an icgls selection from a gls selection the insights gained from our considerations might also be useful in a future study of the statistical properties of icgls estimators certain special model cases are also considered some results discussed by werner and by firoozi are reobtained

on a quasi reversibility regularization method for a cauchy problem of the helmholtz equation in this paper we consider the cauchy problem for the helmholtz equation in a rectangle where the cauchy data is given for y 0 and boundary data are for x 0 and x p the solution is sought in the interval 0

wald consistency and the method of sieves in reml estimation we prove that for all unconfounded balanced mixed models of the analysis of variance estimates of variance components parameters that maximize the restricted gaussian likelihood are consistent and asymptotically normal and this is true whether normality is assumed or not for a general nonnormal mixed model we show estimates of the variance components parameters that maximize the restricted gaussian likelihood over a sequence of approximating parameter spaces i e a sieve constitute a consistent sequence of roots of the reml equations and the sequence is also asymptotically normal the results do not require the rank p of the design matrix of fixed effects to be bounded an example shows that in some unbalanced cases estimates that maximize the gaussian likelihood over the full parameter space can be inconsistent given the condition that ensures consistency of the sieve estimates 1 introduction in many cases exploration of asymptotic properties of maximum likelihood ml estimates led to one of two types of consistency cramer 1946 or wald 1949 types the former establishes the consistency of some root of the likelihood equation s but usually gives no indication on how to identify such a root when the roots of the likelihood equation s are

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

several inequalities involving khatri rao products of positive semidefinite matrices abstract the khatri rao and tracy singh products for partitioned matrices are viewed as generalized hadamard and generalized kronecker products respectively based on the connection between the khatri rao and tracy singh products we establish new inequalities involving khatri rao products of positive semidefinite matrices the results lead to inequalities involving hadamard products as a special case

an operator marching method for inverse problems in range dependent waveguides abstract for large scale inverse problems in acoustics and electromagnetics numerical schemes based on direct methods e g fem and meshless methods often result in huge linear systems and thus are not feasible in terms of computing speed and memory storage this work proposes the inverse fundamental operator marching method based on the dirichlet to neumann map for solving large scale inverse boundary value problems in range dependent waveguides truncated singular value decomposition is employed to solve ill conditioned linear systems arising in marching process and the number of propagating modes in the waveguide assumes the role of a regularization parameter numerical results show that the method is computationally efficient highly accurate stable with respect to data noise for retrieving the propagating part of the starting field it particularly suits to long range wave propagation in slowly varying stratified waveguide

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

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

dual formulation of multiple reciprocity method for the acoustic mode of a cavity with a thin partition abstract the dual formulation of the multiple reciprocity method mrm is employed to solve the acoustic mode of a cavity with a thin partition in order to avoid the spurious eigenvalues and non uniqueness of the solution in the case of zero thickness for the partition the hypersingular equation for mrm is considered to determine the invariant quantity of influence coefficients more efficiently an objectivity concept i e a frame of indifference is used by means of co ordinate transformation a generalized eigenvalue problem is derived and transformed into a standard eigenvalue problem through the state space formulation the spurious roots in mrm are examined and filtered out by using the hypersingular formulation three examples including finite thickness of the partition zero thickness and no partition are shown to check the validity of the proposed method also the analytical solution if available the fem results obtained by petyt and by abaqus and experimental measurements are compared with those of the proposed method and it is found that the agreement between them is very good

reml estimation asymptotic behavior and related topics the restricted maximum likelihood reml estimates of dispersion parameters variance components in a general non normal mixed model are defined as solutions of the reml equations in this paper we show the reml estimates are consistent if the model is asymptotically identifiable and infinitely informative under the location invariant class and are asymptotically normal a n if in addition the model is asymptotically nondegenerate the result does not require normality or boundedness of the rank p of design matrix of fixed effects moreover we give a necessary and sufficient condition for asymptotic normality of gaussian maximum likelihood estimates mle in non normal cases as an application we show for all unconfounded balanced mixed models of the analysis of variance the reml anova estimates are consistent and are also a n provided the models are nondegenerate the mle are consistent a n if and only if certain constraints on p are satisfied

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

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

improved nonnegative estimation of variance components in some mixed models with unbalanced data mixed models involving two variance components are considered when the data are unbalanced one variance component corresponding to a random effect and a second variance component corresponding to experimental error for estimating the random effect variance component several nonnegative estimators are derived the estimators have explicit expressions and are easily computable the performances of the various estimators are studied by simulating their mean squared errors and biases using some one way models with unbalanced data and specific recommendations are made on the choice of the nonnegative estimator to be used in practical applications some generalizations are obtained for estimating a randomeffect variance component in a more general model with unbalanced data the analysis of variance anova estimator and the proposed estimators are computed using real data for two examples the anova estimator has a value that is substantially different from the other estimators in the two examples the sim

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

a regularization method for a cauchy problem of the helmholtz equation we investigate a cauchy problem for the helmholtz equation a modified boundary method is used for solving this ill posed problem some holder type error estimates are obtained the numerical experiment shows that the modified boundary method works well

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

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

maximum likelihood estimation for array processing in colored noise direction of arrival estimation of multiple sources using a uniform linear array in noise with unknown covariance is considered the noise is modeled as a spatial autoregressive process with unknown parameters both stochastic and deterministic signal models are considered for the random signal case an approximate maximum likelihood estimator of the signal and noise parameters is derived it requires numerical maximization of a compressed likelihood function over the unknown arrival angles analytical expressions for the mles of the signal covariance and the ar parameters are given similar results for the case of deterministic signals are also presented

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

application of bem boundary element method based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries a method employing holograms that conform with arbitrarily shaped sources has been developed for enhancing conventional near field acoustic holography which has been limited to sources with simple geometries e g planar or cylindrical surfaces four holography transformation algorithms have been developed based on acoustic holography theory and the boundary element method bem singular value decomposition svd has been incorporated into the algorithms in order to alleviate the ill posed nature frequently encountered in backward reconstruction of a field a pulsating sphere a cylinder with spherical endcaps and a vibrating piston set in a rigid sphere have been adopted in a numerical simulation for verifying the algorithms satisfactory agreement has been achieved between the holographically transformed results and the analytical solutions

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

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

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

balance and orthogonality in designs for mixed classification models a classification model is easiest to analyze when it has a balanced design many of the nice features of balanced designs are retained by error orthogonal designs which were introduced in a recent paper by the authors the present paper defines a kind of partially balanced design and shows that this partial balance is sufficient to ensure the error orthogonality of a mixed classification model results are provided that make the partial balance condition easy to check it is shown that for a maximal rank error orthogonal design the type i sum of squares for a random effect coincides with the type ii sum of squares

regularization of the cauchy problem for the helmholtz equation by using meyer wavelet in this paper we investigate a cauchy problem associated with helmholtz type equation in an infinite strip this is a classical severely ill posed problem i e the solution if it exists does not depend continuously on the data or cauchy data a small perturbation in the data can cause a dramatically large error in the solution for 0

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

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

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

on the reconstruction of the vibro acoustic field over the surface enclosing an interior space using the boundary element method the vibrational velocity sound pressure and acoustic power on the vibrating boundary comprising an enclosed space are reconstructed by the boundary element method based on the measured field pressures the singular value decomposition is used to obtain the inverse solution in the least square sense and to express the acoustic modal expansion between the measurement and source fields in general such an inverse operation has been considered an ill posed problem having a divergence phenomenon involved with extremely small measurement errors the ill conditioned nature of the acoustic inverse problem is caused by the singularity of the transfer matrix which produces nonradiating wave components in order to minimize the singularity and to also reduce the number of measurement points optimal measurement positions are determined by the effective independence method regularization methods are used to stabilize the reconstructed field by suppressing nonradiating components resulting in the singular transfer

isotropic spectral additive models of the covariogram summary a class of additive covariance models of an isotropic random process is proposed motivated by the spectral representation of the covariance function model parameters are estimated by using a special case of the minimum norm quadratic estimation estimator whose asymptotic moments have convenient expressions in terms of spectral densities fitting a model in this class is equivalent to fitting an additive model of the spectral density the class of spectral additive models proposed is dense in the set of summable covariance functions having a spectral density allowing approximately unbiased estimation of an arbitrary covariance function and its spectral density theoretical results are supported by numerical comparison with commonly used models a procedure to assist model selection is proposed the techniques are illustrated with an application to contaminant data

multiple population models for multivariate random length data with applications in clinical trials this paper focuses on the development and study of multiple population models for multivariate random length data of the type often encountered in clinical trials if experimental outcomes per subject consist of multiple measurements of a quantitative variable and the number of these measurements then a multivariate random length vector is observed for this type of data the experimental treatment is likely to affect both the quantitative measurements and the number of these measurements one example of such data is from the national heart lung and blood institute type ii coronary intervention study brensike et al 1982 controlled clinical trials 3 91 111 1984 circulation 69 313 324 the outcome data consist of vectors of lesion sizes with lengths determined by the number of underlying lesions assessed from the patients angiograms where both the numbers and the lesion sizes depend on patients overall disease status we propose models which can realistically describe the relationships between the quantitative variables and the number of responses the asymptotic covariance of the maximum likelihood estimators is obtained data from the type ii study are analyzed using this multiple population model

jordan algebras and bayesian quadratic estimation of variance components the authors consider a linear model ey x cov y v where v is a quadratic subspace a jordan algebra using this property it is shown how multiplication computation of g inverses determination of a neutral element can be done more efficiently in v finally this technique is applied to obtain formulae for locally optimal estimators and bayesian estimators

principal component analysis for multivariate familial data summary the use of a principal component analysis is considered for multivariate data on families with different numbers of siblings the coefficients in principal components are given as the eigenvectors of the weighted sums of squares and products matrix from the sibling data asymptotic distributions of the eigenvalues and eigenvectors of the estimated covariance matrix are obtained for an elliptical population asymptotic distributions of statistics associated with reduction of dimensionality are also derived the results can be used to construct approximate confidence intervals for the coefficients and variances of principal components

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

reconstruction of the electric field of the helmholtz equation in three dimensions in this paper we rigorously investigate the truncation method for the cauchy problem of helmholtz equations which is widely used to model propagation phenomena in physical applications the truncation method is a well known approach to the regularization of several types of ill posed problems including the model postulated by reginska and reginski 2006 under certain specific assumptions we examine the ill posedness of the non homogeneous problem by exploring the representation of solutions based on fourier mode then the so called regularized solution is established with respect to a frequency bounded by an appropriate regularization parameter furthermore we provide a short analysis of the nonlinear forcing term the main results show the stability as well as the strong convergence confirmed by the error estimates in l 2 norm of such regularized solutions besides the regularization parameters are formulated properly finally some illustrative examples are provided to corroborate our qualitative analysis

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

solving non linear estimation equations summary in this paper we consider the numerical computation of a vector parameter estimate 0 which is a root of a system of unbiased non linear estimation equations a sequence 0 r is constructed which converges with a probability approaching 1 to 0 from any starting value 0 0 unlike newton type algorithms the 0 r do not involve matrices of partial derivatives furthermore it can be shown that 0 r 0 is of the order op n 2 so that great accuracy is achieved in very few iterations when the 0 r do not have closed forms an approximation is suggested an alternative and usually simpler way is also found for deriving analytically the expected value of the matrix of partial derivatives in the asymptotic covariance matrix of 0 the efficiency of the proposed algorithm is demonstrated numerically and compared with that of the em and the newton raphson algorithms applications to some well known statistical problems including missing data analysis variance component models familial correlations and errors in variables models are also briefly discussed

matrix results on the khatri rao and tracy singh products abstract we establish a connection between the khatri rao and tracy singh products introduced by khatri and rao c g khatri c r rao sankhya 30 1968 167 180 and tracy and singh d s tracy r p singh statistica neerlandica 26 1972 143 157 respectively and present further results including matrix equalities and inequalities involving the two products also we give two statistical applications

transformations for white noise functionals several results concerning the spaces e and e of test and generalized white noise functionals respectively are obtained the irreducibility of the canonical commutation relation for operators on e and on e is proved it is shown that the fourier mehler transform f0 on e is the adjoint of a continuous linear operator g0 on e moreover a characterization theorem for the fourier mehler transform is proved in particular the fourier transform is the unique up to a constant continuous linear operator f on e such that fd q f and fq d f here d and q are differentiation and multiplication operators respectively several one parameter transformation groups acting on e and the lie algebra generated by their infinitesimal generators are also discussed

boundary infinite elements for the helmholtz equation in exterior domains a novel approach to the development of infinite element formulations for exterior problems of time harmonic acoustics is presented this approach is based on a functional which provides a general framework for domain based computation of exterior problems special cases include non reflecting boundary conditions such as the dtn method a prominent feature of this formulation is the lack of integration over the unbounded domain simplifying the task of discretization the original formulation is generalized to account for derivative discontinuities across infinite element boundaries typical of standard infinite element approximations continuity between finite elements and infinite elements is enforced weakly precluding compatibility requirements various infinite element approximations for two dimensional configurations with circular interfaces are presented implementation requirements are relatively simple numerical results demonstrate the good performance of this scheme 1998 john wiley sons ltd

helmholtz equation least squares method for reconstructing the acoustic pressure field a method using spherical wave expansion theory to reconstruct acoustic pressure field from a vibrating object is developed the radiated acoustic pressures are obtained by means of an expansion of independent functions generated by the gram schmidt orthonormalization with respect to the particular solutions to the helmholtz equation on the vibrating surface under consideration the coefficients associated with these independent functions are determined by requiring the assumed form of solution to satisfy the pressure boundary condition at the measurement points the errors incurred in this process are minimized by the least squares method once these coefficients are specified the acoustic pressure at any point including the source surface is completely determined in this paper this method is used to reconstruct the surface acoustic pressures based on the measured acoustic pressure signals in the field it is shown that this method can be applied to both separable and nonseparable geometries and the

comparison of regularization methods for solving the cauchy problem associated with the helmholtz equation in this paper several boundary element regularization methods such as iterative conjugate gradient tikhonov regularization and singular value decomposition methods for solving the cauchy problem associated to the helmholtz equation are developed and compared regularizing stopping criteria are developed and the convergence as well as the stability of the numerical methods proposed are analysed the cauchy problem for the helmholtz equation can be regularized by various methods such as the general regularization methods presented in this paper but more accurate results are obtained by classical methods such as the singular value decomposition and the tikhonov regularization methods copyright 2004 john wiley sons ltd

an alternating iterative algorithm for the cauchy problem associated to the helmholtz equation in this paper the iterative algorithm proposed by kozlov et al comput maths math phys 31 1991 45 for obtaining approximate solutions to the ill posed cauchy problem for the helmholtz equation is analysed the technique is then numerically implemented using the boundary element method bem the numerical results confirm that the iterative bem produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data an efficient stopping regularising criterion is also proposed

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

dual reciprocity boundary element method solution of the cauchy problem for helmholtz type equations with variable coefficients in this paper the application of the dual reciprocity boundary element method drbem to the cauchy problem for helmholtz type equations with variable coefficients is investigated the resulting system of linear algebraic equations is ill conditioned and therefore its solution is regularized by employing the zeroth order tikhonov functional while the choice of the regularization parameter is based on the l curve method numerical results are presented for cauchy problems in smooth and piecewise smooth geometries as well as simply and doubly connected domains the accuracy convergence and stability of the proposed numerical method with respect to various approximating functions various drbem discretizations and various levels of noise added in the boundary data respectively are also analysed

inequalities involving hadamard products of positive semidefinite matrices abstract an inequality established by g p h styan 1973 linear algebra appl 6 217 240 is on the hadamard product and a correlation matrix an inequality obtained by b y wang and f zhang 1997 linear and multilinear algebra 43 315 326 involves the hadamard product and schur complements these two inequalities hold in the positive definite matrix case based on albert s theorem we present their extensions to cover the positive semidefinite matrix case we also give relevant inequalities

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

multi parameter transformation groups on white noise functionals several multi parameter transformation groups acting on the space of test white noise functionals are constructed by means of the operator theory based on white noise distribution theory several lie algebras containing infinite dimensional laplacians and their associated lie groups are also discussed