sensitivity analysis for certain permutation inferences in matched observational studies summary in observational studies treatments are not randomly assigned to experimental units so that randomization tests and their associated interval estimates are not generally applicable in an effort to compensate for the lack of randomization treated and control units are often matched on the basis of observed covariates however the possibility remains of bias due to residual imbalances in unobserved covariates a general though simple method is proposed for displaying the sensitivity of permutation inferences to a range of assumptions about unobserved covariates in matched observational studies the sensitivity analysis is applicable to wilcoxon s signed rank test to the mcnemar cox test for paired binary responses and to some matching problems with a variable number of controls

randomization inference for treatment effect variation summary applied researchers are increasingly interested in whether and how treatment effects vary in randomized evaluations especially variation that is not explained by observed covariates we propose a model free approach for testing for the presence of such unexplained variation to use this randomization based approach we must address the fact that the average treatment effect which is generally the object of interest in randomized experiments actually acts as a nuisance parameter in this setting we explore potential solutions and advocate for a method that guarantees valid tests in finite samples despite this nuisance we also show how this method readily extends to testing for heterogeneity beyond a given model which can be useful for assessing the sufficiency of a given scientific theory we finally apply our method to the national head start impact study which is a large scale randomized evaluation of a federal preschool programme finding that there is indeed significant unexplained treatment effect variation

quantile comparison functions in two sample problems with application to comparisons of diagnostic markers abstract in this article a control percentile test a chi squared test and a kolmogorov type test are proposed for comparing two distributions from incomplete survival data these tests are obtained by examining a vertical shift comparison function at a single point a finite number of points and an entire set of points on an interval the proposed methods also have applications in receiver operating characteristic roc analysis which has been widely used in such diverse fields as signal detection theory psychology epidemiology and medicine the results are derived under very general conditions that hold for the well known random censorship and random truncation models the performances of the proposed procedures are studied using monte carlo simulation the methods are applied to analyze mayo clinic ovarian carcinoma data

mellin polar coordinate moment and its affine invariance abstract the moment based method is a fundamental approach to the extraction of affine invariants however only integer order traditional moments can be used to construct affine invariants no invariants can be constructed by moments with an order lower than 2 consequently the obtained invariants are sensitive to noise in this paper the moment order is generalized from integer to non integer however the moment order cannot simply be generalized from integer to non integer to achieve affine invariance the difficulty of this generalization lies in the fact that the angular factor owing to shearing in the affine transform can hardly be eliminated for non integer order moments in order to address this problem the mellin polar coordinate moment mpcm is proposed which is directly defined by a repeated integral the angular factor can easily be eliminated by appropriately selecting a repeated integral a method is provided for constructing affine invariants by means of mpcms the traditional affine moment invariants amis can be derived in terms of the proposed mpcm furthermore affine invariants constructed with real order lower than 2 mpcms can be derived using the proposed method these invariants may be more robust to noise than amis several experiments were conducted to evaluate the proposed method performance

numerical experiments using hierarchical finite element method for nonlinear heat conduction in plates in this paper we consider a nonlinear hierarchical finite element method for heat conduction problems over two or three dimensional plates problems considered are nonlinear because the heat conductivity parameter depends upon the temperature itself this paper explores a new technique recently proposed by the first author which transforms a nonlinear parabolic problem to a linear problem at the discrete level we present several numerical examples which demonstrate the efficiency of the current technique

superconvergence of the iterated galerkin methods for hammerstein equations in this paper the well known iterated galerkin method and iterated galerkin kantorovich regularization method for approximating the solution of fredholm integral equations of the second kind are generalized to hammerstein equations with smooth and weakly singular kernels the order of convergence of the galerkin method and those of superconvergence of the iterated methods are analyzed numerical examples are presented to illustrate the superconvergence of the iterated galerkin approximation for hammerstein equations with weakly singular kernels

assessing the sensitivity of regression results to unmeasured confounders in observational studies this paper presents a general approach for assessing the sensitivity of the point and interval estimates of the primary exposure effect in an observational study to the residual confounding effects of unmeasured variable after adjusting for measured covariates the proposed method assumes that the true exposure effect can be represented in a regression model that includes the exposure indicator as well as the measured and unmeasured confounders one can use the corresponding reduced model that omits the unmeasured confounder to make statistical inferences about the true exposure effect by specifying the distributions of the unmeasured confounder in the exposed and unexposed groups along with the effects of the unmeasured confounder on the outcome variable under certain conditions there exists a simple algebraic relationship between the true exposure effect in the full model and the apparent exposure effect in the reduced model one can then estimate the true exposure effect by making a simple adjustment to the point and interval estimates of the apparent exposure effect obtained from standard software or published reports the proposed method handles both binary response and censored survival time data accommodates any study design and allows the unmeasured confounder to be discrete or normally distributed we describe applications on two major medical studies

confidence intervals for uncommon but dramatic responses to treatment a small literature discusses locally most powerful rank tests when only a fraction of treated subjects respond to treatment the ranks used in these tests are very different from conventional ranks being relatively flat for low responses and then rising steeply and the associated tests are much more powerful than conventional rank tests when indeed only a small fraction of treated subjects exhibit dramatic responses because the tests are derived from considerations of local power they do not yield a plausible family of models for effect and therefore they do not yield confidence intervals for the magnitude of effect formed by inverting the tests there is a similarity between these tests and another family of tests originally motivated by different considerations involving peak performance in small subsets exploiting this similarity a method for obtaining confidence statements is proposed in the case of observational studies sensitivity to unobserved bias from nonrandom assignment of treatments is also examined two examples are used as illustrations i a study of smoking during pregnancy and its effects on birth weight in which smokers are matched to six controls and ii a matched pair study of damage to dna among workers at aluminum production plants

constructing a confidence interval for the fraction who benefit from treatment using randomized trial data the fraction who benefit from treatment is the proportion of patients whose potential outcome under treatment is better than that under control inference on this parameter is challenging since it is only partially identifiable even in our context of a randomized trial we propose a new method for constructing a confidence interval for the fraction when the outcome is ordinal or binary our confidence interval procedure is pointwise consistent it does not require any assumptions about the joint distribution of the potential outcomes although it has the flexibility to incorporate various user defined assumptions our method is based on a stochastic optimization technique involving a second order asymptotic approximation that to the best of our knowledge has not been applied to biomedical studies this approximation leads to statistics that are solutions to quadratic programs which can be computed efficiently using optimization tools in simulation our method attains the nominal coverage probability or higher and can have narrower average width than competitor methods we apply it to a trial of a new intervention for stroke

normalization and shape recognition of three dimensional objects by 3d moments abstract in this paper we are primarily concerned with the recognition of three dimensional 3d objects on the basis of the geometry of their physical surface the 3d moments are defined on the object s surface with two main aims 1 to derive a normalized version irrespective of position size and orientation for each imaged object and 2 to establish global descriptors extracted from normalized shapes in order to make up a representative feature vector to be used in recognition tasks the source data are multiple orthographic views of 3d objects with known viewpoint specifications a volume intersection procedure is used in the recovery of 3d object surface from two dimensional 2d data the problem of normalization to achieve recognition of 3d objects is dealt with and a heuristic solution is proposed to lessen the inherent ambiguity of the principal axes method for object orientation experimental results are described with ten object categories showing excellent percentage classification success rates by using only a small number of normalized moments as elements of the feature vector

error estimates and automatic time step control for nonlinear parabolic problems i in this note we extend results by one of the authors on time discretization error estimates and related automatic time step control for stiff ordinary differential equations to the case of a nonlinear parabolic problem the method for time discretization is the so called discontinuous galerkin method based on using piecewise polynomials of degree q geqq 0 we consider in this note the case q 0 corresponding to a variant of the backward euler method we prove a new almost optimal error estimate and present a related new algorithm for automatic time step control this algorithm is very simple but yet is efficient and gives control of the global error

n dimensional moment invariants and conceptual mathematical theory of recognition n dimensional solids the proof of the generalized fundamental theorem of moment invariants gftmi is presented for n dimensional pattern recognition on the basis of gftmi the moment invariants of affine transformation and subgroups of affine transformation are constructed using these invariants the conceptual mathematical theory of recognition of geometric figures solids and their n dimensional generalizations is worked out by means of this theory it is possible for the first time to analyze scenes consisting not only of polygons and polyhedra but also scenes consisting of geometric figures and solids with curved contours and surfaces respectively in general it is the author s opinion that this theory is a useful step toward the essential development of robot vision and toward creating machine intelligence to make machines able to think by means of geometric concepts of different generalities and dimensions and by associations of these concepts

the h p and h p versions of the finite element methods in 1 dimension part iii the adaptive h p version abstract the paper is the third and final part in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimension the first part analyzed the p version and the second part concentrated on the h and h p version this paper analyzes a theoretical frame of the adaptive h p version and based on it the authors provide concrete algorithm for the one dimensional problem it is proven that in the case that the solution has x sub alpha type singularity the adaptive algorithm give an exponential rate of convergence very close to the optimal one analyzed in the second part of the paper additional keyword error analysis

balanced risk set matching a new form of matching optimal balanced risk set matching is applied in an observational study of a treatment cystoscopy and hydrodistention given in response to the symptoms of the chronic nonlethal disease interstitial cystitis when a patient receives the treatment at time t that patient is matched to another patient with a similar history of symptoms up to time t who has not received the treatment up to time t this is risk set matching by using a penalty function in integer programming in a new way we force the marginal distributions of symptoms to be balanced in the matched treated and control groups among all balanced matchings we pick the one that is optimal in the sense of minimizing the multivariate pretreatment covariate distance within matched pairs under a simple model for the treatment assignment mechanism we study the sensitivity of the findings to hidden biases in particular we show that a simple conventional sensitivity analysis is appropriate with risk set matching when the

a discontinuous galerkin method for parabolic problems with modified hp finite element approximation technique abstract a recent paper hideaki kaneko kim s bey gene j w hou discontinuous galerkin finite element method for parabolic problems preprint november 2000 nasa is generalized to a case where the spatial region is taken in r 3 the region is assumed to be a thin body such as a panel on the wing or fuselage of an aerospace vehicle the traditional h as well as hp finite element methods are applied to the surface defined in the x y variables while through the thickness the technique of the p element is employed time and spatial discretization scheme developed in kaneko et al 2000 based upon an assumption of certain weak singularity of u t 2 is used to derive an optimal a priori error estimate for the current method

recognitive aspects of moment invariants moment invariants are evaluated as a feature space for pattern recognition in terms of discrimination power and noise tolerance the notion of complex moments is introduced as a simple and straightforward way to derive moment invariants through this relation properties of complex moments are used to characterize moment invariants aspects of information loss suppression and redundancy encountered in moment invariants are investigated and significant results are derived the behavior of moment invariants in the presence of additive noise is also described

rotation moment invariants for recognition of symmetric objects in this paper a new set of moment invariants with respect to rotation translation and scaling suitable for recognition of objects having n fold rotation symmetry are presented moment invariants described earlier cannot be used for this purpose because most moments of symmetric objects vanish the invariants proposed here are based on complex moments their independence and completeness are proven theoretically and their performance is demonstrated by experiments

3d rotation invariants by complex moments a generalization of the complex moments from 2d to 3d is described group representation theory is used to construct 3d rotation invariants from them the algorithm for automatic generating of the invariants of higher orders is proposed an algorithm for automatic generation of higher order invariants is proposed the linearly dependent invariants are eliminated the invariants are experimentally tested on 3d graphical models and also on real volumetric data

sensitivity of two sample permutation inferences in observational studies abstract in observational studies subjects are not randomly assigned to treatment or control so they may differ in their chances of receiving the treatment a simple method is developed and demonstrated for displaying the sensitivity of conventional two group permutation inferences to departures from random assignment of treatments the unmatched case discussed here differs in certain technical and computational details from the matched case discussed previously however the underlying model and the method for quantifying departures from randomization are the same the method may be applied to wilcoxon s rank sum test the gehan and log rank tests for censored outcomes mantel s test for scored categories and fisher s exact test for binary responses the method embeds the usual randomization reference distribution in a one parameter family of departures involving an unobserved covariate that would have been controlled by adjustments had it been observed as this parameter is varied the sensitivity

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

effects attributable to treatment inference in experiments and observational studies with a discrete pivot summary in randomisation and permutation inference pivotal arguments remove the hypothesised treatment effect thereby basing inferences on the null distribution in which the treatment has no effect this is common for instance with additive treatment effects the current paper uses attributable effects to expand substantially the scope of pivotal arguments attributable effects are defined for three cases namely the 2 x 2 contingency table displacement effects and the mann whitney wilcoxon statistic and in each case removing an appropriate attributable effect restores the familiar null randomisation distribution of the associated statistic yielding exact inferences the procedure extends immediately for use in sensitivity analysis in nonrandomised observational studies

randomization based inference within principal strata in randomized studies treatment comparisons conditional on intermediate postrandomization outcomes using standard analytic methods do not have a causal interpretation an alternative approach entails treatment comparisons within principal strata defined by the potential outcomes for the intermediate outcome that would be observed under each treatment assignment in this article we develop methods for randomization based inference within principal strata we compare our proposed methods with existing large sample methods as well as traditional intent to treat approaches this research is motivated by hiv prevention studies where few infections are expected and inference is desired within the always infected principal stratum that is all individuals who would become infected regardless of randomization assignment

adaptive finite element methods for parabolic problems v long time integration we continue our previous work on adaptive finite element methods for parabolic problems now with particular emphasis on long time integration for semidefinite problems

time discretization of parabolic problems by the hp version of the discontinuous galerkin finite element method the discontinuous galerkin finite element method dgfem for the time discretization of parabolic problems is analyzed in the context of the hp version of the galerkin method error bounds which are explicit in the time steps as well as in the approximation orders are derived and it is shown that the hp dgfem gives spectral convergence in problems with smooth time dependence in conjunction with geometric time partitions it is proved that the hp dgfem results in exponential rates of convergence for piecewise analytic solutions exhibiting singularities induced by incompatible initial data or piecewise analytic forcing terms for the h version dgfem algebraically graded time partitions are determined that give the optimal algebraic convergence rates a fully discrete hp scheme is discussed exemplarily for the heat equation the use of certain mesh design principles for the spatial discretizations yields exponential rates of convergence in time and space numerical examples confirm the theoretical results

3 d moment forms their construction and application to object identification and positioning the 3 d moment method is applied to object identification and positioning a general theory of deriving 3 d moments invariants is proposed the notion of complex moments is introduced complex moments are defined as linear combinations of moments with complex coefficients and are collected into multiplets such that each multiplet transforms irreducibly under 3 d rotations the application of the 3 d moment method to motion estimation is also discussed using group theoretic techniques various invariant scalars are extracted from compounds of complex moments via clebsch gordon expansion twelve moment invariants consisting of the second order and third order moments are explicitly derived based on a perturbation formula it is shown that the second order moment invariants can be used to predict whether the estimation using noisy data is reliable or not the new derivation of vector forms also facilities the calculation of motion estimation in a tensor approach vectors consisting of the third order moments can be derived in a similar manner

discontinuous galerkin finite element method for parabolic problems in this paper we develop a time and its corresponding spatial discretization scheme based upon the assumption of a certain weak singularity of u t t l 2 w email protected u email protected 2 for the discontinuous galerkin finite element method for one dimensional parabolic problems optimal convergence rates in both time and spatial variables are obtained a discussion of automatic time step control method is also included

inference for non random samples observational data are often analysed as if they had resulted from a controlled study and yet the tacit assumption of randomness can be crucial for the validity of inference we take some simple statistical models and supplement them by adding a parameter which reflects the degree of non randomness in the sample for a randomized study is known to be 0 we examine the profile log likelihood for and the sensitivity of inference to small non zero values of particular models cover the analysis of survey data with item non response the paired comparison t test and two group comparisons using observational data with covariates some practical examples are discussed allowing for sampling bias increases the uncertainty of estimation and weakens the significance of treatment effects sometimes substantially so

geometric moment invariants this paper derives moment invariants in an intuitive way by multiple integrals of invariant geometric primitives like distance area and volume many existing 2 d and 3 d moment invariants are re expressed to prove the correctness of this method furthermore this construction method can be easily extended to higher dimensional space and get higher order moment invariants explicit expressions of 3 d moment invariants are generated automatically with the help of symbolic computation software and can be regarded as a kind of shape descriptor for the representation of solid objects

an approximate and efficient method for optimal rotation alignment of 3d models in many shape analysis applications the ability to find the best rotation that aligns two models is an essential first step in the analysis process in the past methods for model alignment have either used normalization techniques such as pca alignment or have performed an exhaustive search over the space of rotation to find the best optimal alignment while normalization techniques have the advantage of efficiency providing a quick method for registering two shapes they are often imprecise and can give rise to poor alignments conversely exhaustive search is guaranteed to provide the correct answer but even using efficient signal processing techniques this type of approach can be prohibitively slow in this paper we present a new method for aligning two 3d shapes we show that the method is markedly faster than existing approaches based on efficient signal processing and we provide registration results demonstrating that the alignments obtained using our method have a high degree of precision and are markedly better than those obtained using normalization

adaptive finite element methods for parabolic problems iv nonlinear problems we extend our program on adaptive finite element methods for parabolic problems to a class of nonlinear scalar problems we prove a posteriori error estimates design corresponding adaptive algorithms and present some numerical results

dual and simultaneous sensitivity analysis for matched pairs summary when a study shows an association between a treatment and a response before concluding that there is a causal relationship it is useful to assess whether or not an unobserved variable u might explain the observed association sensitivity analysis clarifies the properties u must have in terms of its relationship to the response and its imbalance in the groups being compared a substantial literature has investigated the imbalance or association between u and group assignment this paper develops a dual sensitivity analysis for matched pairs focusing on the strength of the relationship between u and the response required to reduce an observed association to non significance a third simultaneous form of sensitivity analysis models both relationships between u and treatment assignment and u and response the simultaneous form allows one to compare results from the sensitivity analysis to subject matter knowledge about both relationships the methods are illustrated by several examples

the h p and h p versions of the finite element method in 1 dimension this paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting the main emphasis is placed on the analysis when the exact solution has singularity of x type the first part analyzes thep version the second theh version and generalh p version and the final third part addresses the problems of the adaptiveh p version

interference between units in randomized experiments in a randomized experiment comparing two treatments there is interference between units if applying the treatment to one unit may affect other units interference implies that treatment effects are not comparisons of two potential responses that a unit may exhibit one under treatment and the other under control but instead are inherently more complex interference is common in social settings where people communicate compete or spread disease in studies that treat one part of an organism using a symmetrical part as control in studies that apply different treatments to the same organism at different times and in many other situations available statistical tools are limited for instance fisher s sharp null hypothesis of no treatment effect implicitly entails no interference and so his randomization test may be used to test no effect but conventional ways of inverting the test to obtain confidence intervals say for an additive effect are not applicable with interference another commonly used

on the independence of rotation moment invariants abstract the problem of the independence and completeness of rotation moment invariants is addressed in this paper first a general method for constructing invariants of arbitrary orders by means of complex moments is described as a major contribution of the paper it is shown that for any set of invariants there exists a relatively small basis by means of which all other invariants can be generated the method how to construct such a basis and how to prove its independence and completeness is presented some practical impacts of the new results are mentioned at the end of the paper

discrete optimization for interpretable study populations and randomization inference in an observational study of severe sepsis mortality abstractmotivated by an observational study of the effect of hospital ward versus intensive care unit admission on severe sepsis mortality we develop methods to address two common problems in observational studies 1 when there is a lack of covariate overlap between the treated and control groups how to define an interpretable study population wherein inference can be conducted without extrapolating with respect to important variables and 2 how to use randomization inference to form confidence intervals for the average treatment effect with binary outcomes our solution to problem 1 incorporates existing suggestions in the literature while yielding a study population that is easily understood in terms of the covariates themselves and can be solved using an efficient branch and bound algorithm we address problem 2 by solving a linear integer program to use the worst case variance of the average treatment effect among values for unobserved potential outcomes that are compatible with the null hy

the h p and h p versions of the finite element method in 1 dimension part ii the error analysis of the h and h p versions the paper is the second in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimensional setting the first part 1 analyzed thep version the present one concentrates on theh andh p versions

adaptive finite element methods for parabolic problems ii optimal error estimates in l l 2 and l l optimal error estimates are derived for a complete discretization of linear parabolic problems using space time finite elements the discretization is done first in time using the discontinuous galerkin method and then in space using the standard galerkin method the underlying partitions in time and space need not be quasi uniform and the partition in space may be changed from time step to time step the error bounds show in particular that the error may be controlled globally in time on a given tolerance level by controlling the discretization error on each individual time step on the same given level i e without error accumulation effects the derivation of the estimates is based on the orthogonality of the galerkin procedure and the use of strong stability estimates the particular and precise form of these error estimates makes it possible to design efficient adaptive methods with reliable automatic error control for parabolic problems in the norms under consideration

assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome this paper proposes a simple technique for assessing the range of plausible causal con clusions from observational studies with a binary outcome and an observed categorical covariate the technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response a medical study of coronary artery disease is used to illustrate the technique inevitably the results of clinical studies are subject to dispute in observational studies one basis for dispute is obvious since patients were not assigned to treatments at random patients at greater risk may be over represented in some treatment groups this paper proposes a method for assess ing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response despite their limitations observational studies will continue to be a valuable source of information and therefore it is prudent to develop appropriate methods of analysis for them our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u under several sets of assumptions about u both cornfield et al 1959 and bross 1966 have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment that is whether the treatment effect after adjustment for u could be zero our method has two advantages first cornfield et al 1959 and bross 1966 adjust only for the unmeasured binary covariate u whereas we adjust for measured covariates in addition to the unmeasured covariate u second cornfield et al 1959 and bross 1966 1967 only judge whether the effect of the treatment could be zero having adjusted for u where cornfield et al 1959 employ an implicit yet extreme assumption about u in contrast we provide actual estimates of the treatment effect adjusted for both u and the observed categorical covariates under any assumption about u in principle the ith of the n patients under study has both a binary response r1i that would have resulted if he had received the new treatment and a binary response ro0 that would have resulted if he had received the control treatment in this formulation treatment effects are comparisons of r1i and roi such as r1i roi since each patient receives only one treatment either rli or ro0 is observed but not both and therefore comparisons of rli and roi imply some degree of speculation treatment effects defined as comparisons of the two potential responses r1i and roi of individual patients are implicit in fisher s 1953 randomization test of the sharp null

quantiles in nonrandom samples and observational studies abstract in a nonrandom sample or a nonrandomized comparison of treated and control groups methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection quantiles of a single distribution and for a shift in two distributions are both discussed these confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison the inequality has additional applications in particular it greatly accelerates the computations in a sensitivity analysis for the mantel haenszel statistic in a 2 2 s contingency table examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas an observational study of chromosome damage from mercury and a study of the drug allopurinol as a cause of skin rash the proof of the inequality makes use of savage s lattice for ranks and holley s inequality wh

causal estimands and confidence intervals associated with wilcoxon mann whitney tests in randomized experiments although the p value from a wilcoxon mann whitney test is used often with randomized experiments it is rarely accompanied with a causal effect estimate and its confidence interval the natural parameter for the wilcoxon mann whitney test is the mann whitney parameter which measures the probability that a randomly selected individual in the treatment arm will have a larger response than a randomly selected individual in the control arm plus an adjustment for ties we show that the mann whitney parameter may be framed as a causal parameter and show that it is not equal to a closely related and nonidentifiable causal effect the probability that a randomly selected individual will have a larger response under treatment than under control plus an adjustment for ties we review the paradox first expressed by hand that the parameter may imply that the treatment is worse or better than control while the mann whitney parameter shows the opposite unlike the mann whitney parameter is nonidentifiable from a randomized experiment we review some nonparametric assumptions that rule out hand s paradox through bounds on and use bootstrap methods to make inferences on those bounds we explore the relationship of the proportional odds parameter to hand s paradox showing that the paradox may occur for proportional odds parameters between 1 9 and 9 thus large effects are needed to ensure that if treatment appears better by the mann whitney parameter then treatment improves responses in most individuals we demonstrate these issues using a vaccine trial

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

the p and h p versions of the finite element method basic principles and properties in the classical form of the finite element method called the hversion piecewise polynomials of fixed degree p are used and the mesh size h is decreased for accuracy in this paper we discuss the fundamental theoretical ideas behind the relatively recent p version and h p version in the p version a fixed mesh is used and p is allowed to increase the h p version combines both approaches the authors describe and explain the basic properties and characteristics of these newer versions especially in areas where their behavior is significantly different from that of the h version simplified proofs of key concepts are included and computational illustrations of several results are provided a benchmark comparison between the various versions in included

a class of distribution free two sample tests based on placements abstract we consider a class of two sample distribution free tests that are appropriate for situations where one of the sample sizes is large relative to the other these procedures are based on the placements of the observations in the smaller sample among the ordered observations in the larger sample and this class of tests generalizes the mann whitney 1947 procedure in much the same way that the class of linear rank tests generalizes the equivalent wilcoxon 1945 rank sum form optimality criteria for choosing a test from this class are discussed and limiting distributions for the associated class of test statistics are determined for the case where only one of the sample sizes goes to infinity

moment forms invariant to rotation and blur in arbitrary number of dimensions we present the construction of combined blur and rotation moment invariants in arbitrary number of dimensions moment invariants to convolution with an arbitrary centrosymmetric filter are derived first and then their rotationally invariant forms are found by means of group representation theory to achieve the desired combined invariance several examples of the invariants are calculated explicitly to illustrate the proposed procedure their invariance robustness and capability of using in template matching and in image registration are demonstrated on 3d mri data and 2d indoor images