analysis of covariance using the rank transformation the rank transformation refers to the replacement of data by their ranks with a subsequent analysis using the usual normal theory procedure but calculated on the ranks rather than on the data rank transformation procedures have previously been shown by the authors to have properties of robustness and power in both regression and analysis of variance it seems natural to consider the use of the rank transformation in analysis of covariance which is a combination of regression and analysis of variance in this paper the rank transformation approach to analysis of covariance is presented and examined comparisons are made with the rank transformation procedure given by quade 1967 journal of the american statistical association 62 1187 1200 and some standard data sets are used to compare the results of these two procedures a monte carlo simulation study examines the behavior of these methods under the null hypothesis and under alternative hypotheses with both normal and nonnormal distributions all results are compared with the usual analysis of covariance procedure on the basis of robustness and power

assessing normality in random effects models when one uses the unbalanced mixed linear model mathbf y i mathbf x i mathbf alpha mathbf z i mathbf beta i varepsilon i i 1 cdots n to analyze data from longitudinal experiments with continuous outcomes it is customary to assume varepsilon i sim operatorname ind mathscr n mathbf 0 sigma 2 mathbf i i independent of mathbf beta i sim operatorname iid mathscr n mathbf 0 delta where sigma 2 and the elements of an arbitrary mathbf delta are unknown variance and covariance components in this paper we describe a method for checking model adequacy and in particular the distributional assumption on the random effects mathbf beta i we generalize the weighted normal plot to accommodate dependent nonidentically distributed observations subject to multiple random effects for each individual unit under study one can detect various departures from the normality assumption by comparing the expected and empirical cumulative distribution functions of standardized linear combinations of estimated residuals for each of the individual units through application of distributional results for a certain class of estimators to our context we adjust the estimated covariance of the empirical cumulative distribution function to account for estimation of unknown parameters several examples of our method demonstrate its usefulness in the analysis of longitudinal data

fundamentals of traffic flow from single vehicle data a number of new empirical results concerning the density dependence of the velocity distribution and its moments as well as the characteristics of their temporal fluctuations have been determined these are utilized for the specification of some fundamental relations of traffic flow and compared with existing traffic theories

efficient calculation of the green s function for multilayered planar periodic structures an efficient calculation scheme is presented for the periodic green s function in planar multilayered structures the proposed method is based on the static complex image conversion and the ewald sum technique and it converts the slowly convergent green s function into the sum of two rapidly convergent series

an efficient numerical evaluation of the green s function for the helmholtz operator on periodic structures abstract numerical methods which are based on boundary integral formulations require the numerical evaluation of the green s function associated with the problem in the case of periodic structures the green s function is often an infinite series this infinite series may converge slowly making numerical evaluation expensive here we present a practical computer implementation of a technique which dramatically speeds up the convergence of the infinite series green s function associated with the helmholtz operator to show the consequences of using this technique we include some numerical examples

modeling self consistent multi class dynamic traffic flow abstract in this study we present a systematic self consistent multiclass multilane traffic model derived from the vehicular boltzmann equation and the traffic dispersion model the multilane domain is considered as a two dimensional space and the interaction among vehicles in the domain is described by a dispersion model the reason we consider a multilane domain as a two dimensional space is that the driving behavior of road users may not be restricted by lanes especially motorcyclists the dispersion model which is a nonlinear poisson equation is derived from the car following theory and the equilibrium assumption under the concept that all kinds of users share the finite section the density is distributed on a road by the dispersion model in addition the dynamic evolution of the traffic flow is determined by the systematic gas kinetic model derived from the boltzmann equation multiplying boltzmann equation by the zeroth first and second order moment functions integrating both side of the equation and using chain rules we can derive continuity motion and variance equation respectively however the second order moment function which is the square of the individual velocity is employed by previous researches does not have physical meaning in traffic flow although the second order expansion results in the velocity variance equation additional terms may be generated the velocity variance equation we propose is derived from multiplying boltzmann equation by the individual velocity variance it modifies the previous model and presents a new gas kinetic traffic flow model by coupling the gas kinetic model and the dispersion model a self consistent system is presented

proper metrics for clinical trials transformations and other procedures to remove non normality effects a simulation study was performed to study the effects of non normality and to examine procedures to ameliorate possible loss of power when data are incorrectly assumed to be normally distributed it was found that only distributions with high asymmetry or heavy tails seriously affect the t test the box cox likelihood ratio test appears to have some advantages over the others but this must be offset by the greater complexity in making the results understandable to non statisticians the variability in outcomes with the different procedures demonstrates the importance of specifying such procedures a priori

application of aim and mbpe techniques to accelerate modeling of 3 d doubly periodic structures with nonorthogonal lattices composed of bianisotropic media an efficient methodology is introduced for rapid analysis and design of three dimensional 3 d doubly periodic structures over a wide frequency range based on hybrid finite element boundary integral febi methods the 3 d doubly periodic structures can be represented as nonorthogonal lattices composed of general inhomogeneous bianisotropic media with arbitrarily shaped metallic patches based on floquet theory and periodic boundary conditions the original stated problem that involves infinite periodic structures can be converted into a single unit cell using the equivalence principle the derived bi equation formulation is applied to the top and bottom surfaces of the unit cell which results in a perfectly reflectionless boundary condition for the fe based approach then the unit cell was meshed using triangular prismatic volume elements which provide a great deal of flexibility in modeling complex planar geometries with arbitrary shapes in the transverse direction the adaptive integral method aim was employed to accelerate the calculation of the matrix vector product for the bi portion within the iterative solver furthermore a model based parameter estimation mbpe technique was proposed for the wide band interpolation of the required impedance matrix elements in the bi part for near field components that were used in the aim procedure the accuracy and efficiency of the proposed hybrid algorithms are demonstrated by the presented numerical results e g in comparison with analytical solutions several simulation results are presented to illustrate the flexibility of the proposed methods for analysis of frequency selective surfaces with arbitrarily shaped metallic patches bianisotropic materials and nonorthogonal lattice configurations

continental scale relationship between bankfull width and drainage area for single thread alluvial channels we explore the bankfull width wbf versus drainage area ada relationship across a range of climatic and geologic environments and ask 1 is the relationship between ln wbf and ln ada best described by a linear function and 2 can a reliable relationship be developed for predicting wbf with ada as the only independent variable the principal data set for this study was compiled from regional curve studies and other reports that represent 1018 sites 1 m wbf 110 m and 0 50 km2 ada 22 000 km2 in the continental united states two additional data sets were used for validation after dividing the data into small medium and large size basins which respectfully correspond to ada 4 95 km2 4 95 km2 ada 337 km2 and ada 337 km2 regression lines from each data set were compared using one way analysis of covariance ancova a second ancova was performed to determine if mean annual precipitation p is an extraneous factor in the wbf versus ada relationship the ancova results reveal that using ada alone does not yield a reliable wbf versus ada relationship that is applicable across a wide range of environments and that p is a significant extraneous factor in the relationship considering data for very small basins ada 0 49 km2 and very large basins ada 1 0 105 km2 we conclude that a two segment linear model is the most probable form of the ln wbf versus ln ada relationship this study provides useful information for building complex multivariate models for predicting wbf

hybrid fe bi modeling of 3 d doubly periodic structures utilizing triangular prismatic elements and an mpie formulation accelerated by the ewald transformation we present the formulation of a finite element boundary integral method for the analysis of three dimensional doubly periodic structures based on arbitrary nonorthogonal lattice configurations the method starts from a functional description of the field problem where only a single unit cell of the array is considered this unit cell is meshed with triangular prismatic volume elements and the electric field intensity is discretized with edge based expansion functions on the sidewalls of the unit cell phase boundary conditions are employed to relate the fields on opposing walls of the unit cell on the top and or bottom unit cell planar surfaces the mesh is terminated using a mixed potential integral equation the required space domain periodic green s function is calculated after applying the ewald 1921 transformation to convert the slowly converging series representation into two rapidly converging series the method is validated for simple slot and strip frequency selective surfaces as well as microstrip dipole arrays more complex geometries investigated are slot coupled microstrip patches photonic bandgap materials and the so called artificial puck plate frequency selective surface bandpass structure

a test for asymmetry associated with the hodges lehmann estimator abstract one version of the hodges lehmann estimator median xi xj 2 1 i j n is also the minimum distance estimator derived from a particular cramer von mises distance this distance evaluated at that is the minimized distance provides a natural statistic for testing asymmetry of the underlying distribution

integral equation analysis of scattering from doubly periodic array of 3 d conducting objects the integral equation ie method formulated in the spatial domain is employed to calculate the scattering from the doubly periodic array of three dimensional 3 d perfect electric conductor pec objects the special testing and basis functions are proposed to handle the problem with non zero normal components of currents at the boundary of one period moreover a relationship between the scattering from the pec screen and its complementary structure is established in order to efficiently compute the matrix elements from the ie approach an acceleration technique with the exponential convergence rate is applied to evaluate the doubly periodic green s function the formulations in this technique are appropriately modified so that the new form facilitates numerical calculation for the general cases

fdr control with pseudo gatekeeping based on a possibly data driven order of the hypotheses we propose a multiple testing procedure controlling the false discovery rate the procedure is based on a possibly data driven ordering of the hypotheses which are tested at the uncorrected level q until a suitable number is not rejected when the order is data driven larger effect sizes are considered first therefore selecting more interesting hypotheses with larger probability the proposed procedure is valid under independence for the test statistics we also propose a modification which makes our procedure valid under arbitrary dependence it is shown in simulation that we compare particularly well when the sample size is small we conclude with an application to identification of molecular signatures of intracranial ependymoma the methods are implemented in an r package somemtp freely available on cran

a lack of fit test for the mean function in a generalized linear model abstract a supremum type statistic based on partial sums of residuals is proposed to test the validity of the mean function of the response variable in a generalized linear model the proposed test does not need a partition of the space of covariates to handle the case of nonreplication the new test is consistent against the alternative under which the deterministic part of the model is not the one specified in the null hypothesis the asymptotic null distribution of the test statistic can be approximated through simulations this approximation is valid even if the variance of the response variable is misspecified in the model for practical sample sizes the adequacy of this large sample approximation to the null distribution of the test statistic is carefully examined power comparisons with other lack of fit tests are also performed to show the advantage of the test in particular we find that the new procedure is rather sensitive to detect a misspecified mean function if the assumed mean functio

a review of some statistical methods for covariance analysis of categorical data three general methods for covariance analysis of categorical data are reviewed and applied to an example from a clinical trial in rheumatoid arthritis the three methods considered are randomization model nonparametric procedures maximum likelihood logistic regression and weighted least squares analysis of correlated marginal functions a fourth heuristic approach the unweighted linear model analysis is an approximate procedure but it is easy to implement the assumptions and statistical issues for each method are discussed so as to emphasize philosophical differences between their rationales attention is given to computational differences but it is shown that the methods lead to similar results for analogous problems it is argued that the essential differences between the methods lie in their underlying assumptions and the generality of the conclusions which may be drawn

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

on tests applied to residuals abstract the null distribution of a test statistic computed on residuals can be affected by the dependence among the residuals it might be expected however that the dependence decreases as the sample size increases so that the limiting null distribution is the same as if the test were based on independent observations the author investigates whether this large sample equivalence holds for tests of correlation scale difference regression and location difference particular emphasis is placed on showing when rank tests based on residuals have a strongly asymptotically distribution free property u statistic theorems are used to investigate these issues

a new acceleration technique with exponential convergence rate to evaluate periodic green functions we propose a new approach to compute the dynamic potential green function from two and three dimensional periodic arrays of point sources in a three dimensional space the method has at least exponential convergence rate in some cases it has gaussian convergence rate the convergence rate is independent of the position of the observation point in the unit cell the proposed approach can also be used to calculate the derivatives of the green function very efficiently

judgement post stratification for designed experiments in many scientific studies information that is not easily translated into covariates is ignored in the analysis however this type of information may significantly improve inference in this research we apply the idea of judgment post stratification to utilize such information specifically we consider experiments that are conducted under a completely randomized design sets of experimental units are formed and the units in a set are ranked estimation is performed conditional on the sets and ranks we propose a new estimator for a treatment contrast we improve the new estimator by rao blackwellization asymptotic distribution theory and corresponding inferential procedures for both estimators are developed simulation studies quantify the superiority of the new estimators and show their desirable properties for small and moderate sample sizes the impact of the new techniques is illustrated with data from a clinical trial

nonparametric analysis of covariance for comparing change in randomized studies with baseline values subject to error summary change from baseline to a follow up examination can be compared among two or more randomly assigned treatment groups by using analysis of variance on the change scores however a generally more sensitive powerful test can be performed using analysis of covariance anova on the follow up data with the baseline data as a covariate this approach is not without potential problems though the assumption of ordinary ancova of normally distributed errors is speculative for many variables employed in biomedical research furthermore the baseline values are inevitably random variables and often are measured with error this report investigates in this situation the validity and relative power of the ordinary ancova test and two asymptotically distribution free alternative tests one based on the rank transformation and the other based on the normal scores transformation the procedures are illustrated with data from a clinical trial normal and several nonnormal distributions as well as varying degree of variable error are studied by monte carlo methods the normal scores test is generally recommended for statistical practice consider the situation frequently occurring in clinical trials and other biomedical studies where two or more groups are selected at random from the same population and assessed for some variable of interest at the time of randomization assume that the statistical question is whether there is a significant difference among the groups in terms of the distribution of the variable at some time subsequent to randomization a statistical test of the hypothesis of no difference among groups at follow up could be based on the follow up data only since the groups differ only at random at baseline however it may not be efficient to ignore the baseline data feldt 1958 compared three approaches to data analysis stratifying the baseline data and using two way analysis of variance anova using analysis of covariance ancova on the follow up data with the baseline data a covariate and using anova on the change scores he found that ancova is generally the most efficient powerful of these approaches some problems occur in applying ancova in this situation however first the variable of interest at baseline will inevitably be random not fixed by the experimenter this is termed subject variability second the ascertainment of the variable may be subject to error this error can be measurement error or intrasubject error or both measurement error can be due to instrument imprecision or human inability to accurately read an instrument such as a sphygmomanometer or both intrasubject error can arise from diurnal or other short term variability of a physiologic variable such as blood pressure subsequently any of these types of variability will

misspecification tests in econometrics based on ranks abstract this paper introduces a class of rank statistics for use in testing econometric models for misspecification these statistics are ideally suited to survey data since endogenous and exogenous variables in econometric models may therefore be considered exchangeable thus residuals from a wide class of models e g linear regression non linear regression simultaneous equations etc are also exchangeable since rank statistics are distribution free when based on exchangeable data it follows the rank statistics based on these residuals are also distribution free simulation studies in the linear regression case suggest that they have good power characteristics and are distributionally robust in comparison to the usual classical procedures

analysis of honk effect on the traffic flow in a cellular automaton model abstract the paper mainly studies the following vehicle s honk effect on the driver of its predecessors in the single lane cellular automaton model ca model besides the determined condition of honk s state is investigated in detail which has seldom been studied before then the influence of honk sensitivity threshold and slow to start sensitivity threshold on the traffic flow is examined the numerical simulations indicate that the smaller the honk sensitivity threshold or the larger the slow to start sensitivity threshold a heavier synchronized flow can be maintained three main factors of s j transition are then analyzed and the process of s j transition is observed finally a contrastive study is made on the performances of three different ca models from four aspects it is evidenced that the performance of the new ca model proposed in the paper is the best and more consistent with the real traffic therefore the following vehicle s honk effect should not be neglected in study of the traffic flow

fuzzy linear regression using rank transform method in regression analysis the rank transform rt method is known to be neither dependent on the shape of the error distribution nor sensitive to outliers in this paper we construct a so called level fuzzy regression model based on the resolution identity theorem and apply rt method to this model fuzzy regression models with crisp input fuzzy output and fuzzy input fuzzy output are investigated to show the effectiveness of the proposed method to compare its effectiveness with existing methods we introduce a new performance measure in addition we propose a method to obtain a predicted output with respect to a specific target value and show that our model is more robust compared with other methods when the data contain some outliers

integral equation analysis of scattering from multilayered periodic array using equivalence principle and connection scheme an integral equation approach is presented to analyze the two dimensional 2 d scattering from multilayered periodic array the proposed approach is capable of handling scattering from the array filled with different media in different layers combining the equivalence principle algorithm epa and connection scheme epacs it can be avoided to find and evaluate the multilayered periodic green s functions for 2n identical layers the elimination of the unknowns between top and bottom surfaces can be accelerated using the logarithm algorithm more importantly based on epacs an approach is proposed to effectively handle the semi infinitely layered case in which a unit consisting of several layers is repeated infinitely in one direction

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

tests of significance using regression models for ordered categorical data regression models of the type proposed by mccullagh 1980 journal of the royal statistical society series b 42 109 142 are a general and powerful method of analyzing ordered categorical responses assuming categorization of an unknown continuous response of a specified distribution type tests of significance with these models are generally based on likelihood ratio statistics that have asymptotic chi 2 distributions therefore investigators with small data sets may be concerned with the small sample behavior of these tests in a monte carlo sampling study significance tests based on the ordinal model are found to be powerful but a modified test procedure using an f distribution with a finite number of degrees of freedom for the denominator is suggested such that the empirical significance level agrees more closely with the nominal significance level in small sample situations we also discuss the parallels between an ordinal regression model assuming underlying normality and conventional multiple regression we illustrate the model with two data sets one from a study investigating the relationship between phosphorus in soil and plant available phosphorus in corn grown in that soil and the other from a clinical trial comparing analgesic drugs

union intersection rank tests for ordered alternatives in anocova abstract for an analysis of covariance model pertaining to completely randomized as well as complete block designs based on the union intersection principle a general class of permutationally distribution free rank tests for the ordered alternative problem is considered the theory is supplemented by numerical studies

a geometric interpretation of inferences based on ranks in the linear model abstract four different approaches based on ranks to testing hypotheses are unified through the geometry of the linear model the various tests are identified with different but algebraically equivalent forms of the classical f test small sample differences are investigated via a monte carlo study using both rank and signed rank tests

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

detecting skewed errors from regression residuals symmetry of the error distribution is a common assumption in robust estimation of location and regression parameters tests for detecting asymmetry in the location problem are available but their performance in regression situations is unknown here two such tests are investigated and the evidence suggests two conclusions first the tests are valid when applied directly to either robust or least squares residuals as long as the number of parameters estimated is no more than a fourth of the sample size second the effect of the design matrix on power for detecting a skewed error distribution is roughly characterized by a third moment quantity based on least squares analysis