tail behavior of regression estimators and their breakdown points following jureckova 1981 we introduce a finite sample measure of performance of regression estimators based on tail behavior the least squares estimator is studied in detail and we find that it achieves good tail performance under strictly gaussian conditions however the tail performance of the least squares estimator is found to be extremely poor in the case of heavy tailed error distributions further analysis of the least squares estimator with light tailed errors indicates the strong influence of the design matrix in determining tail performance turning to the tail behavior of various robust estimators of the parameters of the linear model we focus on tail performance under heavy algebraic tailed errors the 11 estimator is seen to be a leading case we find a simple characterization of its tail behavior in terms of the design configuration and show that a broad class of m estimators have the same performance perhaps most significantly it is shown that our finite sample measure of tail performance is for heavy tailed error distributions essentially the same as the finite sample concept of breakdown point introduced by donoho and huber 1983 this finding provides an important probabilistic interpretation of the breakdown point and clarifies the role of tail behavior as a quantitative measure of robustness this link is further explored for high breakdown regression estimators including rousseeuw s 1984 leastmedian of squares estimator

a rank one reduction formula and its applications to matrix factorizations let a in r m times n denote an arbitrary matrix if x in r n and y in r m are vectors such that omega y t ax ne 0 then the matrix b a omega 1 axy t a a has rank exactly one less than the rank of a this wedderburn rank one reduction formula is easy to prove yet the idea is so powerful that perhaps all matrix factorizations can be derived from it the formula also appears in places such as the positive definite secant updates bfgs and dfp as well as the abs methods by repeatedly applying the formula to reduce ranks a biconjugation process analogous to the gram schmidt process with oblique projections can be developed this process provides a mechanism for constructing factorizations such as text ldm t qr and svd under a common framework of a general biconjugate decomposition v t au omega that is diagonal and nonsingular two characterizations of biconjugation provide new insight into the lanczos method and its breakdown one characterization shows that

a class of abs algorithms for diophantine linear systems systems of integer linear diophantine equations arise from various applications in this paper we present an approach based upon the abs methods to solve a general system of linear diophantine equations this approach determines if the system has a solution generalizing the classical fundamental theorem of the single linear diophantine equation if so a solution is found along with an integer abaffian rank deficient matrix such that the integer combinations of its rows span the integer null space of the cofficient matrix implying that every integer solution is obtained by the sum of a single solution and an integer combination of the rows of the abaffian we show by a counterexample that in general it is not true that any set of linearly independent rows of the abaffian forms an integer basis for the null space contrary to a statement by egervary finally we show how to compute the hermite normal form for an integer matrix in the abs framework

extended rank reduction formulas containing wedderburn and abaffy broyden spedicato rank reducing processes abstract the wedderburn rank reduction formula and the abaffy broyden spedicato abs algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes such as gram schmidt conjugate direction and lanczos methods we present a rank reduction formula for transforming the rows and columns of a extending the wedderburn rank reduction formula and the abs approach by repeatedly applying the formula to reduce the rank an extended rank reducing process is derived the biconjugation process associated with the wedderburn rank reduction process and the scaled extended abs class of algorithms are shown to be in our proposed rank reducing process while the process is more general to produce several other effective reduction algorithms to compute various structured factorizations the process provides a general finite iterative approach for constructing factorizations of a and a t under a common framework of a general decomposition v t a p we also show that the biconjugation process associated with the wedderburn rank reduction process can be derived from the scaled abs class of algorithms applied to a or a t finally we provide a list of some well known reduction procedures as special cases of our extended rank reducing process the approach is general enough to produce various structured decompositions as well

m estimates of location for the robust central tendency of fuzzy data the aumann type mean has been shown to possess valuable properties as a measure of the location or central tendency of fuzzy data associated with a random experiment however concerning robustness its behavior is not appropriate the aumann type mean is highly affected by slight changes in the fuzzy data or when outliers arise in the sample robust estimators of location on the other hand avoid such adverse effects for this purpose this paper considers the m estimation approach and discusses conditions under which this alternative yields valid fuzzy valued m estimators the resulting m estimators are applied to a real life example finally some simulation studies show empirically the suitability of the introduced estimators

imposing boundary conditions in sinc method using highest derivative approximation sinc approximate methods are often used to solve complex boundary value problems such as problems on unbounded domains or problems with endpoint singularities a recent implementation of the sinc method li c and wu x numerical solution of differential equations using sinc method based on the interpolation of the highest derivatives applied mathematical modeling 31 1 2007 1 9 in which sinc basis functions are used to approximate the highest derivative in the governing equation of the boundary value problem is evaluated for structural mechanics applications in which interlaminar stresses are desired we suggest an alternative approach for specifying the boundary conditions and we compare the numerical results for analysis of a laminated composite timoshenko beam implementing both li and wu s approach and our alternative approach for applying the boundary conditions for the timoshenko beam problem we obtain accurate results using both approaches including transverse shear stress by integration of the 3d equilibrium equations of elasticity the beam results indicate our approach is less dependent on the selection of the sinc mesh size than li and wu s sihd we also apply sihd to analyze a classical laminated composite plate for the plate example we experience difficulty in obtaining a complete system of equations using li and wu s approach for our approach we suggest that additional necessary information may be obtained by applying the derivatives of the boundary conditions on each edge using this technique we obtain accurate results for deflection and stresses including interlaminar stresses by integration of the 3d equilibrium equations of elasticity our results for both the beam and the plate problems indicate that this approach is easily implemented has a high level of accuracy and good convergence properties

on inconsistent bayes estimates of location on montre que dans certaines situations relativement naturelles les estimateurs de position bayesiens sont inconsistants

evaluation of layerwise mixed theories for laminated plates analysis the evaluation of mixed layerwise theories to calculate the in plane and out of plane responses of thick plates in two dimensional modeling of multilayered structures is made the employed models which were proposed by the author in earlier works a priori fulfill the continuity of transverse shear and normal stress components at the interface between two adjacent layers a reissner s mixed variational equation is used to derive the governing equations in terms of introduced stress and displacement variables the interface continuity conditions are imposed by writing the governing equations at a multilayered level the related standard displacement formulations are also discussed for comparison purpose closed form solutions are presented for plates made of orthotropic lamina and bent by harmonic distribution of transverse pressure symmetrically and unsymmetrically laminated as well as sandwich plates have been investigated a comparison with a three dimensional elasticity analysis shows that present mixed layerwise models furnish a better description of the in plane and out of plane response of thick plates with respect to existing layerwise and equivalent single layer theories in particular the proposed models describe with excellent accuracy the transverse shear and normal stress fields unlike available current models these fields are herein determined a priori without requiring implementation of any postprocessing procedures the distribution of the transverse displacement and transverse normal stress in the plate thickness direction are also shown for most of the problems

breakdown points of affine equivariant estimators of multivariate location and covariance matrices finite sample replacement breakdown points are derived for different types of estimators of multivariate location and covariance matrices the role of various equivariance properties is illustrated the breakdown point is related to a measure of performance based on large deviations probabilities finally we show that one step reweighting preserves the breakdown point

breakdown points of t type regression estimators summary to bound the influence of a leverage point generalised m estimators have been suggested however the usual generalised m estimator of regression has a breakdown point that is less than the inverse of its dimension this paper shows that dimension independent positive breakdown points can be attained by a class of well defined generalised mestimators with redescending scores the solution can be determined through optimisation of t type likelihood applied to properly weighted residuals the highest breakdown point of is attained by cauchy score these bounded influence and high breakdown estimators can be viewed as a fully iterated version of the one step generalised m estimates of simpson ruppert carroll 1992 with the two advantages of easier interpretability and avoidance of undesirable roots to estimating equations given the design dependent weights they can be computed via em algorithms empirical investigations show that they are highly competitive with other robust estimators of regression

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

how many variables should be entered in a regression equation abstract the optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points as the number of regressors grows large the sp criterion provides an asymptotically optimal rule for the number of variables to enter

a high order laminated plate theory with improved in plane responses in order to improve the accuracy of the in plane responses of the shear deformable laminated composite plate theories a new high order laminated plate theory was developed based upon reissner s new mixed variational principle int j num meth eng 20 1366 1984 to this end a zig zag shaped c0 function and legendre polynomials were introduced into the approximate in plane displacement distributions across the plate thickness the accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by pagano j comp mat 3 398 1969 a comparison with the exact solutions obtained for several symmetric and asymmetric cross ply laminates indicates that the present theory accurately estimates in plane responses even for small span to thickness ratios

geometrically nonlinear stress recovery in composite laminates a procedure is presented to compute the interlaminar stresses in laminated plates using the intralaminar stresses and cross section rotations from a plate analysis for cases in which geometric nonlinearities are important the procedure is based on integrating the geometrically nonlinear equilibrium equations from the theory of elasticity simplified for the case of moderate rotations integration is accomplished numerically by using the intralaminar stresses and cross section rotations from a finite element plate analysis finite difference representations of the derivatives of these intralaminar stresses and rotations and an iteration procedure iteration being required because of the nonlinear nature of the problem for purposes of illustration the procedure is applied to two semi infinite isotropic cross ply and angle ply plate example problems one problem considers a transverse load acting on a portion of the plate and the other considers a follower type shear load the problems are selected because they exhibit a variety of interlaminar stress responses thereby providing a test for the developed procedure the interlaminar stresses computed with the developed procedure are compared with the stresses computed using a three dimensional finite element analysis that serves as a benchmark comparisons are also made by using closedform expressions for the intralaminar stresses in the developed procedure the interlaminar stresses computed using the developed procedure agree well with the stresses as computed by both comparison approaches extensions of the procedure are discussed

prediction of interlaminar stresses in laminated plates using globalorthogonal interpolation polynomials a postprocessor for displacement based finite element solutions of laminated plates under transverse loads is developed to obtain the resulting interlaminar stresses the postprocessor can be used for the finite element solution that has been obtained using either the classical lamination plate theory or the first order shear deformation theory the equilibrium equations of elasticity are integrated directly to obtain interlaminar stresses these equations include the influence of the products of in plane stresses and out of plane rotations and thus can be used to obtain interlaminar stresses for geometrically nonlinear problems to obtain accurately the derivatives of in plane stresses the finite element nodal displacement data are first interpolated using polynomials with global support i e the interpolating polynomials are defined over the whole domain two types of polynomials chebyshev and a class of orthogonal polynomials that can be generated for a given location of known data points are used a least squares technique is used to find the undetermined coefficients in the global approximation for evaluation purposes the results for interlaminar stresses for a set of examples obtained from the present code are compared with those obtained from exact three dimensional theory of elasticity a good agreement is shown furthermore to the best of our knowledge the present paper is the first to present the results for interlaminar normal stress in a two layered antisymmetric angle ply square plate without using the three dimensional elasticity solution it is observed that the shape of through the t hickness distribution of interlaminar normal stress depends on the side to thickness ratio and that the maximum interlaminar normal stress increases rapidly as the side to thickness ratio increases

asymptotically min max bias robust m estimates of scale for positive random variables abstract asymptotically min max bias robust m estimates of scale are obtained for positive random variables with e contaminated distributions using any one of a broad class of loss functions of positive and negative bias any such estimate is a scaled order statistic with the order statistic and scaling constant determined by e the nominal distribution and the loss function some calculations for specific cases show that for a large range of e the min max order statistic solution has a breakdown point near 5 and is well approximated by a scaled median some calculations and monte carlo results indicate that the asymptotic result has considerable finite sample size relevance by virtue of the squared bias being at least as large as the variance for rather modest sample sizes depending on e and by virtue of attractive mean squared error performance in the presence of even rather small fractions of contamination

multilayered shell theories accounting for layerwise mixed description part 1 governing equations a reissner mixed variational equation is employed in this paper to derive the differential governing equations of multilayered double curved shells made of orthotropic laminae in linear static cases a layerwise description is referred to by assuming two independent fields in the thickness direction for the transverse stress both shear and normal components and displacement variables in each layer interlaminar values are used as the unknown variables of the introduced expansions the continuity conditions of displacements and transverse shear and normals stresses at the interfaces between two consecutive layers referred to as c 0 z requirements have been a priori fulfilled these have been used to drive the governing equations from a layer to a multilayered level classical displacement formulations and related equivalent single layer equations have been derived for comparison purposes no assumptions have been made concerning the terms of type thickness to radii shell ratio h r donnell s shallow shell type equations are given as particular cases for all of the considered theories indicial notations and arrays have been used extensively to handle the presented developments in a concise manner numerical evaluations and comparisons to exact and other available two dimensional solutions are given in a companion paper e carrera multilayered shell theories accounting for layerwise mixed description part 2 numerical evaluations aiaa journal vol 37 no 9 1999 pp 1117 1124

calculation of interlaminar stresses in laminated plates using walsh transforms the walsh differential operator approach has much to recommend it from the point of view of computational efficiency over the standard methods for determining the interlaminar tractions from finite element displacement data as may be seen from the simplicity of the fortran routine and the ease with which the nonlinear traction tems may be modeled

linear detection of a weak signal in additive cauchy noise the detection of a weak signal in additive cauchy noise is of great importance in many applications a locally optimum detector lod exists for such a scenario however it is non linear in nature in general implementation of non linear detectors is difficult in practice and linear detectors with good properties such as high asymptotic relative efficiency are with respect to the lod are often desirable in this paper we propose a linear detector for a weak signal in additive cauchy noise the proposed test statistic is a linear combination of order statistics for the special case of a constant signal in additive cauchy noise we prove the asymptotic normality of the trimmed linear detector and show that the are of the trimmed linear detector with respect to the lod is unity extensive simulation results are provided to demonstrate that the loss in the performance of the linear detector is very small compared with the non linear lod we also discuss the hardware complexities of the lod and the linear detector and demonstrate the advantages of the linear detector over the lod in terms of hardware implementation

on a certain mixed variational theorem and a proposed application formulation d une equation variationnelle pour les deplacements et certaines contraintes en vue d une application aux plaques elastiques stratifiees isotropes et anisotropes

residuals in nonlinear regression abstract the authors employ a quadratic expansion to investigate the behavior of the ordinary residuals in nonlinear regression in particular they derive quadratic approximations for the mean and variance of the ordinary residuals and the covariances between the ordinary residuals and the fitted values this investigation leads to the conclusion that the ordinary residuals can produce misleading results when used in diagnostic methods analogous to those for linear regression consequently a new type of residual that overcomes many of the potential shortcomings of the ordinary residuals is suggested author

a direct projection method for sparse linear systems an oblique projection method is adapted to solve large sparse unstructured systems of linear equations this row projection technique is a direct method which can be interpreted as an oblique kaczmarz type algorithm and is also related to other standard solution methods when a sparsity preserving pivoting strategy is incorporated it is demonstrated that the technique can be superior in terms of both fill in and arithmetic complexity to more standard sparse algorithms based on gaussian elimination this is especially true for systems arising from stiff ordinary differential equations problems in chemical kinetics studies

error analysis and correction of discrete solutions from finite element codes many structures are an assembly of individual shell components therefore results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory this paper examines the problem of applying shell theory to the error analysis and the correction of finite element results the general approach to error analysis and correction is discussed first relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures next the problem of error analysis of plate structures is examined in more detail the method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates preliminary numerical results are included

all subsets regression in a proportional hazards model summary this paper shows that within the framework of the proportional hazards model all subsets regression can be performed with very little computational effort a selection criterion based on a wald statistic is motivated by an argument similar to crossvalidation in which the status of one observation is changed from uncensored to censored this criterion is formally equivalent to mallows s cp and thus the problem is reduced to one readily handled by standard statistical packages the procedure is applied to some multiple myeloma data to give results remarkably different from those obtained by previous workers using stepwise procedures new insights are gained and the superiority of all subsets regression over stepwise regression is clearly demonstrated

median regression for ordered discrete response abstract we introduce a semiparametric median regression approach to ordered discrete responses generalizing the maximum score estimation of manski 1985 for binary response the identification and a s consistency are proved we assume that there exists a latent continuous variable and several variations of the median regression approach depending on the restriction on the thresholds for the latent variable are examined for some cases bounds for the scale are derived we also derive bounds for the finite sample breakdown point of the median regression method to show its robustness

outlier resistance in small samples summary this paper presents a new measure of outlier resistance based on huber s maximum bias after standardizing by the maximum bias of the median for the same situation outlier resistance seems to be essentially independent of n and depends on the fraction of contamination the advantages over alternative measures of resistance involve this relative stability with the sample size and the ability to measure resistance to a large fraction of outliers as an example this method of measuring outlier resistance is applied to a comparison of a 20 trimmed mean with a huber m estimator

biased bootstrap methods for reducing the effects of contamination contamination of a sampled distribution for example by a heavy tailed distribution can degrade the performance of a statistical estimator we suggest a general approach to alleviating this problem using a version of the weighted bootstrap the idea is to tilt away from the contaminated distribution by a given but arbitrary amount in a direction that minimizes a measure of the new distribution s dispersion this theoretical proposal has a simple empirical version which results in each data value being assigned a weight according to an assessment of its influence on dispersion importantly distance can be measured directly in terms of the likely level of contamination without reference to an empirical measure of scale this makes the procedure particularly attractive for use in multivariate problems it has several forms depending on the definitions taken for dispersion and for distance between distributions examples of dispersion measures include variance and generalizations based on high order moments practicable measures of the distance between distributions may be based on power divergence which includes hellinger and kullback leibler distances the resulting location estimator has a smooth redescending influence curve and appears to avoid computational difficulties that are typically associated with redescending estimators its breakdown point can be located at any desired value 0 1 2 simply by trimming to a known distance depending only on and the choice of distance measure from the empirical distribution the estimator has an affine equivariant multivariate form further the general method is applicable to a range of statistical problems including regression

admissible variable selection procedures when fitting regression models by least squares for prediction given data with a single dependent variable arising from a normal linear regression model a variable selection procedure completely specifies a least squares fit by choosing the subset of the independent variables to include in the model for loss equal to squared error of prediction we prove that all variable selection procedures are admissible for choosing among least squares fits of the regression model

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

on asymptotically correct linear laminated plate theory abstract the focus of this paper is the development of asymptotically correct theories for laminated plates the material properties of which vary through the thickness and for which each lamina is orthotropic this work is based on the variational asymptotical method a mathematical technique by which the three dimensional analysis of plate deformation can be split into two separate analyses a one dimensional through the thickness analysis and a two dimensional plate analysis the through the thickness analysis includes elastic constants for use in the plate theory and approximate closed form recovering relations for all three dimensional field variables expressed in terms of plate variables in general the specific type of plate theory that results from this procedure is determined by the procedure itself however in this paper only reissner like plate theories are considered often called first order shear deformation theories this paper makes three main contributions first it is shown that construction of an asymptotically correct reissner like theory for laminated plates of the type considered is not possible in general second a new point of view on the variational asymptotical method is presented leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible third numerical results from such an optimum reissner like theory are presented these results include comparisons of plate displacement as well as of three dimensional field variables and are the best of all extant reissner like theories indeed they even surpass results from theories that carry many more generalized displacement variables

a new method to discriminate between enzyme kinetic models abstract a novel statistical procedure s zwanzig math opsforsch statist ser statist 11 23 47 1980 is applied to discriminate between kinetic models of enzyme reactions two examples are elucidated on the basis of numerically simulated data 1 a discrimination between a michaelis menten model and a hill equation 2 b discrimination between competitive and noncompetitive inhibition of a two substrate reaction next the proposed method is applied to assess a kinetic model of the allosteric enzyme phosphofructokinase from the malarial parasite plasmodium berghei it is demonstrated that the novel procedure allows a more sensitive discrimination as it is obtained with alternative statistical tests

cumulative chi squared statistic as a tool for testing goodness of fit on caracterise le khi deux cumule dans l analyse de variance a un critere comme la somme ponderee de variables khi deux independantes a un degre de liberte

a sparse approximate inverse preconditioner for nonsymmetric linear systems this paper is concerned with a new approach to preconditioning for large sparse linear systems a procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient type methods some theoretical properties of the preconditioner are discussed and numerical experiments on test matrices from the harwell boeing collection and from tim davis s collection are presented our results indicate that the new preconditioner is cheaper to construct than other approximate inverse preconditioners furthermore the new technique insures convergence rates of the preconditioned iteration which are comparable with those obtained with standard implicit preconditioners

admissible selection of an accurate and parsimonious normal linear regression model let mo be a normal linear regression model and let m1 mk be distinct proper linear submodels of mo let k e 0 k be a model selection rule based on observed data from the true model given k let the unknown parameters of the selected model ms be fitted by the maximum likelihood method a loss function is introduced which depends additively on two parts i a measure of the difference between the fitted model ms and the true model and ii a measure cs of the complexity of the selected model a natural model selection rule k which minimizes an empirical version of this loss is shown to be admissible and very nearly bayes

interlaminar stresses by sinc method based on interpolation of the highest derivative computation of interlaminar stresses from one dimensional equivalent single layer beam theories using the sinc method based on interpolation of the highest derivative is performed the method is proposed to be an efficient tool for determining through the thickness variations of interlaminar stresses by the equilibrium equations of three dimensional elasticity because the required higher order derivatives of displacements are accurately obtained without postprocessing an improvement over presently used finite element methods in functionally graded material the sinc method offers additional benefits because the method employs numerical indefinite integration by double exponential transformation through the thickness integration can be performed numerically without computing additional integration weights we obtain interlaminar stresses in symmetric cross ply laminates and functionally graded sandwich composites using the sinc method based on interpolation of the highest derivative to approximately solve the static governing equations of the timoshenko beam theory and the bickford beam theory displacements and stresses from the present approach are compared with three dimensional finite element method results obtained with abaqus standard our results indicate that the interlaminar stresses throughout the majority of the length of the beam are accurately approximated with the sinc method the present results are significantly erroneous near the boundary because of three dimensional edge effects not captured by the one dimensional analysis

a study of transverse normal stress effect on vibration of multilayered plates and shells this paper evaluates transverse normal stress zzeffect on vibration of multilayered structures to this purpose a mixed plate model initially introduced by toledano and murakami has been extended to dynamics analysis of double curved shells these models allow both continuous interlaminar transverse shear and normal stresses as well as the zigzag form of the displacement distribution in the shell thickness directions to be modelled governing equations have been derived by employing a reissner s mixed theorem classical models on the basis of standard displacement formulations have been considered for comparison purposes the evaluations of transverse stress effects have been conducted by comparing constant linear and higher order distributions of transverse displacement components in the plate thickness directions free vibrational response of layered simply supported plates cylindrical and spherical shells made of isotropic as well as orthotropic layers has been analyzed the numerical investigation carried out and comparison with earlier results has concluded that 1 the possibility of describing interlaminar continuous transverse normal stress makes the mixed theories more attractive with respect to other available modelling 2 any refinements of classical models are meaningless unless the effects of interlaminar continuous transverse shear and normal stresses are both taken into account in a multilayered shell theory

the equivalence of two models for ordinal data summary the equivalence of the grouped continuous and continuation ratio models for ordinal data when the complementary log log link is used is demonstrated recent experience using two regression models for ordinal data gave essentially identical results when the complementary log log transform was used for the probabilities pregibon 1980 implies that these models are the same the present note makes the equivalence explicit suppose that y is an ordinal response variable whose values are labelled 1 k let 7rj x pr y j i x for an observation with covariate vector x and yj x 1 x rj x pr y k j i x and set bj x pr y ij y j x 7tj x i yj l x j 1 k 1 grouped continuous models fit a linear predictor to some monotonic function f of the cumulative probabilities yj x namely f 7j x oj oc x continuation ratio models use the probabilities bj x instead of the yj s that is

application of the variational asymptotical method to laminated composite plates this method is a technique by which the geometrically nonlinear three dimensional analysis of plate deformation can be split into a linear one dimensional through the thickness analysis and a nonlinear two dimensional plate analysis the elastic constants used in the plate analysis are obtained in closed form from the through the thickness analysis along with approximate closed form three dimensional distributions of displacement strain and stress the development of such a theory is presented herein for laminated plates in which each lamina exhibits monoclinic symmetry about its own midplane

the effect of an outlier on l estimators of location in symmetric distributions the effect is studied of an outlier which has the same symmetric distribution as the other observations except for a change in location and a possible increase in scale we show that the median is the most bias resistant estimator in the class of l statistics with symmetric nonnegative coefficients that add up to one for a class of distributions which includes the normal double exponential and logistic distributions

a class of direct methods for linear systems a class of methods of direct type for solving determined or underdetermined full rank or deficient rank linear systems is presented and theoretically analyzed the class can be considered as a generalization of the methods of brent and brown as restricted to linear systems and implicitly contains orthogonal lu andll t factorization methods

an alternative to the standard bayesian procedure for discrimination between normal linear models summary we consider the standard bayesian procedure for discrimination focusing on its tendency to give low posterior probabilities to some correct models even in conditions of moderate to large sampling sizes furthermore in some situations that could well occur in practice the standard procedure is even asymptotically inconsistent we claim that the explanation is that the standard procedure inflates the posterior probability of the model that has the smallest expected increase in information about its parameters we then propose to modify it by an amount related to the expected gain in information and show that the lindley paradox does not occur finally we obtain the limiting alternative criterion that results by letting the prior densities become noninformative which enables us to measure how sensitive the discrimation is to the informative prior densities used