the petrov galerkin and iterated petrov galerkin methods for second kind integral equations we develop in this paper a theoretical framework for the analysis of convergence for the petrov galerkin method and superconvergence for the iterated petrov galerkin method for fredholm integral equations of the second kind as important approaches to the analysis we introduce notions of the generalized best approximation and the regular pair of trial space sequence and test space sequence in hilbert spaces we characterize the regular pair in terms of the angle of two space sequences or the generalized best approximation projections several specific constructions of the petrov galerkin elements for equations of both one dimension and two dimensions are presented and the convergence of the petrov galerkin method and the iterated petrov galerkin method using these elements is proved

barycentric interpolation collocation methods for solving linear and nonlinear high dimensional fredholm integral equations abstract in this article two barycentric interpolation collocation methods are proposed for solving linear and nonlinear high dimensional f r e d h o l m integral equations of the second kind the approaches respectively utilize the modified weighted l a g r a n g e functions and the novel rational functions as the interpolation basis functions they are effective schemes for evaluating the multidimensional undetermined function through the numerical strategies and some composite quadrature formulas the linear and nonlinear f r e d h o l m integral equations are transformed into the corresponding linear and nonlinear algebraic equations further we prove that the discrete collocation methods are equivalent to the n y s t r o m quadrature methods then the convergence analysis is established by the collectively compact theory moreover the error estimation of the approximate solution and the exact solution are also provided numerical examples are presented to illustrate the capability and efficiency of the techniques by compared with the classic l a g r a n g e interpolation collocation method and other methodologies

a comparison of homogeneity tests for regional frequency analysis 1 the assessment of regional homogeneity is a critical point in regional frequency analysis to this end many homogeneity tests have been proposed even though a general comparison among them is still lacking commonly used homogeneity tests based on l moments ratios are considered here in a comparison with two rank tests that do not rely on particular assumptions regarding the parent distribution the performance of these tests is assessed in a series of monte carlo simulation experiments in particular the power and type i error of each test are determined for different scale and shape parameters of the regional parent distributions the tests are also evaluated by varying the number of sites belonging to the region the series length the type of the parent distributions and the degree of heterogeneity we find that l moments based tests are more powerful when the samples are slightly skewed while the rank tests have better performances in case of high skewness on the basis of these findings we propose a simple method to guide the choice of the homogeneity test to be used for the different possible cases

the discrete galerkin method for integral equations a general theory is given for discretized versions of the galerkin method for solving fredholm integral equations of the second kind the discretized galerkin method is obtained from using numerical integration to evaluate the integrals occurring in the galerkin method the theoretical framework that is given parallels that of the regular galerkin method including the error analysis of the superconvergence of the iterated galerkin and discrete galerkin solutions in some cases the iterated discrete galerkin solution is shown to coincide with the nystrom solution with the same numerical integration method the paper concludes with applications to finite element galerkin methods

a new method based on haar wavelet for the numerical solution of two dimensional nonlinear integral equations a new numerical method based on haar wavelet is proposed for two dimensional nonlinear fredholm volterra and volterra fredholm integral equations of first and second kind the proposed method is an extension of the haar wavelet method aziz and siraj ul islam 2013 siraj ul islam et al 2013 and siraj ul islam et al 2014 from one dimensional nonlinear integral equations fredholm and volterra to two dimensional nonlinear integral equations fredholm volterra and volterra fredholm the main characteristic of the method is that unlike several other methods it does not involve numerical integration which results in an improved accuracy of the method in order to show the effectiveness of the method it is applied to several benchmark problems the numerical results are compared with other methods existing in the recent literature

testing for effects on variance in experiments with factorial treatment structure and nested errors there is increased interest in industrial experiments aimed at improving quality by reducing the variability of a product characteristic while maintaining the desired mean level of the characteristic analysis of treatment effects on variability however is more difficult than analyzing the effects on mean performance in this article we extend the results of zelen to test for treatment effects on variance when there are two sources of variability that which exists between production runs or setups and variability within runs bootstrap critical values are developed to handle possibly nonnormal errors at either level of variability

efficient bootstrap simulation on donne deux idees pour renforcer une simulation la premiere est d equilibrer les echantillons simules la seconde est de faire un usage explicite des approximations qui ne demandent pas de simulation

a comparative study of tests for homogeneity of variances with applications to the outer continental shelf bidding data many of the existing parametric and nonparametric tests for homogeneity of variances and some variations of these tests are examined in this paper comparisons are made under the null hypothesis for robustness and under the alternative for power monte carlo simulations of various symmetric and asymmetric distributions for various sample sizes reveal a few tests that are robust and have good power these tests are further compared using data from outer continental shelf bidding on oil and gas leases

adaptive inference for the two sample scale problem some adaptive tests are proposed a for the general two sample scale problem and b for the restricted two sample scale problem in which the random variables are known to be right skewed and also positive valued these are based on either the ratio of the adaptively trimmed sample variances or adaptive rank tests of scale whose quantiles are estimated by means of the bootstrap simulations show that for practical sample sizes these tests tend to perform better than their competitors the methodology is illustrated by an application to a problem considered by nair regarding the breakdown times of an insulating fluid under elevated voltage stress

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

power and robustness of jackknife and likelihood ratio tests for grouped heteroscedasticity abstract the jackknife technique is used to develop robust tests for heteroscedasticity in regression analysis consistent with time series cross sectional studies the variance is assumed constant within subgroups of observations but may vary from group to group we also consider the likelihood ratio lr test and develop a number of modified lr statistics similar to those of bartlett each test is developed in the context of regression where the vector of coefficients may be constant for all groups or may vary between groups a number of sampling experiments reveal that if the disturbance terms are normally distributed bartlett s test is slightly more powerful than either of the jackknife tests however in nonnormal situations jack2 the test based on jackknifing the regression is very robust under h 0 and has substantial power against a number of alternative hypotheses

analysis and output tracking design for the direct contact membrane distillation parabolic system abstract this paper considers the performance output tracking for a boundary controlled direct contact membrane distillation dcmd system first the mathematical properties of a recently developed mathematical model of the dcmd system are discussed this model consists of parabolic equations coupled at the boundary then the existence and uniqueness of the solutions are analyzed using the theory of operators some regularity results of the solution are also established a particular case showing the diagonal property of the principal operator is studied then based on one side feedback law the control problem which consists of tracking both the feed and permeate outlet temperatures of the membrane distillation system is formulated a servomechanism and an output feedback controller are proposed to solve the control problem in addition an extended state observer aimed at estimating both the system state and disturbance based on the temperature measurements of the inlet is proposed thus by some regularity for the reference signal and when the disturbance vanishes we prove the exponential decay of the output tracking error moreover we show the performance of the control strategy in presence of the flux noise

determining the appropriate sample size for nonparametric tests for location shift for the case in which two independent samples arc to be compared using a nonparametric test for location shift we propose a bootstrap technique for estimating the sample sizes required to achieve a specified power the estimator called boot uses information from a small pilot experiment for the special case of the wilcoxon test a simulation study is conducted to compare boot to two other sample size estimators one method called anpv is based on the assumption that the underlying distribution is normal with a variance estimated from the pilot data the other method called noether adapts the sample size formula of noether for use with a location shift alternative the boot and noether sample size estimators are particularly appropriate for this nonparametric setting because they do not require assumptions about the shape of the underlying continuous probability distribution the simulation study shows that a sample size estimates can have large uncertainty b boot is at least as accurate as an

solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method in this paper we will give some results for developing the two dimensional differential transform tddt for double integrals then the tddt method will be developed for solving a class of two dimensional linear and nonlinear volterra integral equations we also give some examples to demonstrate the accuracy of the method

optimal rank based tests for homogeneity of scatter we propose a class of locally and asymptotically optimal tests based on multivariate ranks and signs for the homogeneity of scatter matrices in m elliptical populations contrary to the existing parametric procedures these tests remain valid without any moment assumptions and thus are perfectly robust against heavy tailed distributions validity robustness nevertheless they reach semiparametric efficiency bounds at correctly specified elliptical densities and maintain high powers under all efficiency robustness in particular their normal score version outperforms traditional gaussian likelihood ratio tests and their pseudo gaussian robustifications under a very broad range of non gaussian densities including for instance all multivariate student and power exponential distributions

p values maximized over a confidence set for the nuisance parameter abstract for testing problems of the form h 0 v v 0 with unknown nuisance parameter various methods are used to deal with the simplest approach is exemplified by the t test where the unknown variance is replaced by the sample variance and the t distribution accounts for estimation of the variance in other problems such as the 2 2 contingency table one conditions on a sufficient statistic for 0 and proceeds as in fisher s exact test because neither of these standard methods is appropriate for all situations this article suggests a new method for handling the unknown this new method is a simple modification of the formal definition of a p value that involves taking a maximum over the nuisance parameter space of a p value obtained for the case when is known the suggested modification is to restrict the maximization to a confidence set for the nuisance parameter after giving a brief justification we give various examples to show how this new method gives improved results for 2 2 tabl

linear models for the analysis of variability in factorial designs an application to anthropometric indicators this paper has two aims one is to evaluate in a set of 9740 reference neonates born in five italian centres trieste milan parma rome bari during 1973 1976 the effects of gestational age and birthplace on the variability of crown heel length and head circumference at birth this is a preliminary step in the construction of italian intrauterine growth standards for such anthropometric measures the other aim is to put the various techniques for the analysis of variability into a common framework of linear models either generalized or classical to compare their main features and provide some indications about their application

receiver operator characteristic roc curves and non normal data an empirical study this paper evaluates the performance of several diagnostic kits for assessing levels of serum prostatic acid phosphatase on patients at different stages of cancer of the prostate each patient was studied with several kits we compare results obtained for receiver operator characteristic roc curve methodology with data assumed to follow a normal distribution with log transformed data assumed to follow a normal distribution and when neither of these assumptions holds there were important differences between the results of the different approaches for these data the normal distribution assumption should be used with extreme caution the log transformed based results compared favourably with the non parametric but unconsidered application of the method should be avoided

numerical solution of linear fredholm integral equations via two dimensional modification of hat functions abstract in this work we approximate the solution of the linear fredholm integral equations by means of a new two dimensional modification of hat functions 2d mhfs and a new operational matrix of integration by this idea the basic equations will be changed into the associated systems of algebraic equations also an error analysis is provided under several mild conditions the method is computationally attractive and some numerical examples are provided to illustrate its high accuracy

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

power and sample size calculations for discrete bounded outcome scores we consider power and sample size calculations for randomized trials with a bounded outcome score bos as primary response adjusted for a priori chosen covariates we define bos to be a random variable restricted to a finite interval typically a bos has a j or u shaped distribution hindering traditional parametric methods of analysis when no adjustment for covariates is needed a non parametric test could be chosen however there is still a problem with calculating the power since the common location shift alternative does not hold in general for a bos in this paper we consider a parametric approach and assume that the observed bos is a coarsened version of a true bos which has a logit normal distribution in each treatment group allowing correction for covariates a two step procedure is used to calculate the power firstly the power function is defined conditionally on the covariate values secondly the marginal power is obtained by averaging the conditional power with respect to an assumed distribution for the covariates using monte carlo integration a simulation study evaluates the performance of our method which is also applied to the ecass 1 stroke study

richardson extrapolation of iterated discrete projection methods for eigenvalue approximation in this paper the eigenvalue approximation of a compact integral operator with a smooth kernel is discussed we propose asymptotic error expansions of the iterated discrete galerkin and iterated discrete collocation methods and asymptotic error expansion of approximate eigenvalues we then apply richardson extrapolation to obtain higher order super convergence of eigenvalue approximations numerical examples are presented to illustrate the theoretical estimate

a range test for the equivalency of means under unequal variances in this article we present a range test using a two stage sampling procedure for testing the hypothesis that the normal means are falling into a practical indifference zone both the level and the power associated with the proposed test are controllable and are completely independent of the unknown variances tables needed for implementation are given

a new spectral meshless radial point interpolation smrpi method for the two dimensional fredholm integral equations on general domains with error analysis in this article we present a numerical method to solve two dimensional fredholm integral equations of the second kind on general domains the method utilizes meshless and spectral collocation techniques but it is not traditional meshless collocation method the point interpolation method with the help of strictly positive definite radial basis functions is used to construct shape functions as a basis functions in the frame of spectral collocation methods these basis functions shape functions have kronecker delta function property since the proposed method is meshless it does not need any domain element and so it is independent of the geometry of the domain the method reduces the solution of the two dimensional integral equation to the solution of a linear system of algebraic equations convergence analysis with error estimates are given with full discussion furthermore some numerical examples are presented to show the validity and efficiency of smrpi

estimating the power of the two sample wilcoxon test for location shift summary traditional methods for calculating the power of a statistical test for location shift require knowledge of the shape of the underlying probability distribution the distribution shape however may be unknown this paper describes a bootstrap method for using observed data or pilot data to approximate the power no assumptions need be made about the shape of the underlying continuous probability distribution simulation evidence shows that when applied to the wilcoxon two sample test for location shift the suggested method is reliable the evidence also shows that it is more accurate than a benchmark traditional approach the bootstrap method is applied to a real data example the analysis demonstrates how the method can be used to determine sample sizes and how to choose the more powerful of two alternative tests for location shift

on the behavior of some estimators from probability plots abstract probability plots are popular graphical methods used to assess distributional assumptions under a location scale model the plot tends to lie on a straight line a common practice in this situation is to fit a line through the plot and use the intercept and slope of the fitted line as estimates of the location and scale parameters what are the properties of these estimators estimators from weighted least squares lines are considered and their asymptotic finite sample robustness and optimality properties are discussed included among these are the ordinary least squares estimators and estimators from least squares lines fitted after trimming or winsorizing some of the extreme order statistics

compound random number generators abstract recently marsaglia 1984 proceedings of the sixteenth symposium on the interface noted a trend toward increasingly more demanding use of random number generators after observing that for current uses generators must pass increasingly more sophisticated tests for randomness in order to provide acceptable results marsaglia described a class of combination generators and recommended two specific combination generators that passed an extensive battery of stringent tests for randomness the present article describes an alternative class of generators which produce random values by compounding or intermixing several different sequences of random values these compound generators are easier to implement especially on smaller computers than are marsaglia s recommended generators five specific compound generators two standard generators and marsaglia s two combination generators were subjected to several tests for randomness including marsaglia s stringent tests the standard generator

differential transform method for the system of two dimensional nonlinear volterra integro differential equations in this paper we develop the differential transform method dtm for solving a class of the system of two dimensional linear and nonlinear volterra integro differential equations of the second kind to this end we give some preliminary results of the differential transform and describe the method of this paper we also give some examples to demonstrate the accuracy of the presented method

extrapolation of the iterated collocation method for integral equations of the second kind for integral equations of the second kind with appropriate smoothness of both kernel and exact solution it is known that the iterated collocation method based on discontinuous piecewise polynomials of order r and on collocation at the gauss points can exhibit a uniform superconvergent error of order 2r this paper shows that the order of the iterated collocation approximation on an arbitrary mesh can be further improved by one step of richardson extrapolation assuming the calculation to be repeated with each subinterval halved

distance based tests for homogeneity of multivariate dispersions the traditional likelihood based test for differences in multivariate dispersions is known to be sensitive to nonnormality it is also impossible to use when the number of variables exceeds the number of observations many biological and ecological data sets have many variables are highly skewed and are zero inflated the traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non euclidean dissimilarity would be more appropriate distance based tests of homogeneity of multivariate dispersions which can be based on any dissimilarity measure of choice are proposed here they rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes the tests are straightforward multivariate extensions of levene s test with p values obtained either using the traditional f distribution or using permutation of either least squares or lad residuals examples illustrate the utility of the approach including the analysis of stabilizing selection in sparrows biodiversity of new zealand fish assemblages and the response of indonesian reef corals to an el nino monte carlo simulations from the real data sets show that the distance based tests are robust and powerful for relevant alternative hypotheses of real differences in spread

performance output tracking for a wave equation subject to unmatched general boundary harmonic disturbance in this paper we consider performance output reference tracking for a wave equation with general harmonic disturbance at one end and the control at the other end we first design a state reference system determined completely by the measured output and the reference signal where the parameter update law is presented an adaptive servomechanism output feedback control is then designed it is shown that the closed loop system is well posed three control objectives are achieved a the performance output is tracking the reference signal b all the internal loops are bounded c when the disturbance and reference are disconnected the closed loop is exponentially stable finally the state of system is shown to be tracking the reference state and the updated parameters are convergent to their true values

numerical methods for fredholm integral equations on the square abstract in this paper we shall investigate the numerical solution of two dimensional fredholm integral equations by nystrom and collocation methods based on the zeros of jacobi orthogonal polynomials the convergence stability and well conditioning of the method are proved in suitable weighted spaces of functions some numerical examples illustrate the efficiency of the methods

a fast numerical solution method for two dimensional fredholm integral equations of the second kind based on piecewise polynomial interpolation abstract in this paper we consider fast numerical solution methods for two dimensional fredholm integral equation of the second kind f x y a x y u v f u v du dv g x y x y where a x y u v is smooth and g x y is in l 2 2 discretizing the integral equation by certain quadrature rule we get a linear system to deduce fast approximate solution methods for the resulted linear system we study the approximation of the four variable kernel function a x y u v by piecewise polynomial partition the domain 4 into subdomains of the same size and interpolate the kernel function a x y u v in each subdomain fast matrix vector multiplication algorithms and efficient iterative methods are derived numerical results are given to illustrate the efficiency of our methods

bartlett s cochran s and hartley s tests on variances are liberal when the underlying distribution is long tailed abstract for samples of equal size the p values of bartlett s cochran s and hartley s tests for the equality of several variances obtained under the normality assumption are shown to underestimate the true p values when the parent distribution is a normal or a x 2 1 scale mixture or when there is within sample dependence the proof uses elements of majorization theory when the sample sizes are not equal a partial extension is obtained for the two sample case

the use of bootstrap methods for estimating sample size and analysing health related quality of life outcomes health related quality of life hrqol measures are increasingly used in trials as primary outcome measures investigators are now asking statisticians for advice on how to plan and analyse studies using such outcomes hrqol outcomes like the sf 36 are usual measured on an ordinal scale although most investigators assume that there exists an underlying continuous latent variable and that the actual measured outcomes the ordered categories reflect contiguous intervals along this continuum the ordinal scaling of hrqol measures means they tend to generate data that have discrete bounded and skewed distributions thus standard methods of analysis that assume normality and constant variance may not be appropriate for this reason conventional statistical advice would suggest non parametric methods be used to analyse hrqol data the bootstrap is one such computer intensive non parametric method for estimating sample sizes and analysing data we describe three methods of estimating sample sizes for two group cross sectional comparisons of hrqol outcomes we then compared the power of the three methods for a two group cross sectional study design using bootstrap simulation the results showed that under the location shift alternative hypothesis conventional methods of sample size estimation performed well particularly whitehead s method whitehead s method is recommended if the hrqol outcome has a limited number of discrete values 7 and or the expected proportion of cases at either of the bounds is high if a pilot data set is readily available then bootstrap simulation will provide a more accurate and reliable estimate than conventional methods finally we used the bootstrap for hypothesis testing and the estimation of standard errors and confidence intervals for parameters in an example data set we then compared and contrasted the bootstrap with standard methods of analysing hrqol outcomes in the data set studied with the sf 36 outcome the use of the bootstrap for estimating sample sizes and analysing hrqol data produces results similar to conventional statistical methods these results suggest that bootstrap methods are not more appropriate for analysing hrqol outcome data than standard methods

bootstrap methods for testing homogeneity of variances this article describes the use of bootstrap methods for the problem of testing homogeneity of variances when means are not assumed equal or known the methods are new in this context and allow the use of normal theory test statistics such as f s 2 1 s 2 2 without the normality assumption that is crucial for validity of critical values obtained from the f distribution both asymptotic analysis and monte carlo sampling show that the new resampling procedures compare favorably with older methods in terms of test validity and power

on the bootstrap and confidence intervals we derive an explicit formula for the first term in an unconditional edgeworth type expansion of coverage probability for the nonparametric bootstrap technique applied to a very broad class of studentized statistics the class includes sample mean k sample mean sample correlation coefficient maximum likelihood estimators expressible as functions of vector means etc we suggest that the bootstrap is really an empiric one term edgeworth inversion with the bootstrap simulations implicitly estimating the first term in an edgeworth expansion this view of the bootstrap is reinforced by our discussion of the iterated bootstrap which inverts an edgeworth expansion to arbitrary order by simulating simulations

richardson extrapolation of iterated discrete galerkin solution for two dimensional fredholm integral equations in this paper we study the numerical solution of two dimensional fredholm integral equation by discrete galerkin and iterated discrete galerkin method we are able to derive an asymptotic error expansion of the iterated discrete galerkin solution this expansion covers arbitrarily high powers of the discretization parameters if the solution of the integral equation is smooth the expansion gives rise to richardson type extrapolation schemes which rapidly improve the original rate of the convergence numerical experiments confirm our theoretical results

an analysis of means type test for variances from normal populations after a brief review of the literature a test for homogeneity of variances is presented the test which is the variances analog of the analysis of means anom can be presented in a graphical form this graphical presentation makes it easy for practitioners to assess both practical and statistical significance tables of critical values are presented for balanced designs a large sample version of the test which uses anom critical values is also presented as well as a version of the test for unbalanced designs for which approximate critical values can be calculated monte carlo results indicate that this test has power comparable to well known normal based tests for homogeneity of variances

robustness of size of tests of autocorrelation and heteroscedasticity to nonnormality abstract a comprehensive empirical examination is made of the sensitivity of tests of disturbance covariance in the linear regression model to nonnormal disturbance behaviour tests of autocorrelation appear to be quite robust except for extreme nonnormality but tests for heteroscedasticity are highly susceptible to kurtosis

tracking and disturbance rejection of mimo nonlinear systems with pi controller we study tracking and disturbance rejection of a class of mimo nonlinear systems with linear proportional plus integral pi compensator roughly speaking we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady state i o map then a simple pi compensator can be used to yield a stable unity feedback closed loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors

comparing the variances of dependent groups recently several new attempts have been made to find a robust method for comparing the variances ofj dependent random variables however empirical studies have shown that all of these procedures can give unsatisfactory results this paper examines several new procedures that are derived heuristically one of these procedures was found to perform better than all of the robust procedures studied here and so it is recommended for general use

a statistical model of cluster stability in the current paper we present a method for assessing cluster stability this method combined with a clustering algorithm yields an estimate of the data partition namely the number of clusters we adopt the cluster stability standpoint where clusters are imagined as islands of high density in a sea of low density explicitly a cluster is associated with its high density core our approach offers to evaluate the goodness of a cluster by the similarity amongst the entire cluster and its core we propose to measure this resemblance by two sample tests or by probability distances between appropriate probability distributions the distances are calculated on clustered samples drawn from the source population according to two different distributions the first law is the underlying set distribution the second law is constructed so that it represents the clusters cores here a variant of the k nearest neighbor density estimation is applied so that items belonging to cores have a much higher chance to be selected as the sample distribution is unknown a distribution free two sample test is required to examine the mentioned correspondence for constructing such a test we use distance functions built on negative definite kernels in practice outliers in the samples and limitations of the clustering algorithm heavily contribute to the noise level as a result of this shortcoming the distance values have to be determined for many pairs of samples and therefore an empirical distance s distribution is obtained the distribution is dependent on the examined number of clusters to prevent this property for biasing the results we normalize the distances it is conjectured that the true number of clusters yields the most concentrated normalized distribution to measure the concentration we use the sample mean and the sample 25th percentile the paper exhibits the good performance of the proposed method on synthetic and real world data

on the number of bootstrap simulations required to construct a confidence interval abstract the purpose of this document is to make two points about the effect of the number of bootstrap simulations b on percentile t bootstrap confidence intervals the first point concerns coverage probability the second distance of the simulated critical point form the true critical point derived with b infinity in both cases the author has in mind applications to smooth statistics such as the studentized mean of a sample drawn from a continuous distribution he indicates the change that have to be made if the distribution of the statistic is not smooth additional keywords exponentive functions

sample size determination for some common nonparametric tests abstract the article discusses the problem of determining the number of observations required by some common nonparametric tests so that the tests have power at least 1 against alternatives that differ sufficiently from the hypothesis being tested it is shown that the number of observations depends on certain simple probabilities a method is suggested for fixing the value of the appropriate probability when determining sample size

simulated power functions on etudie par simulation la puissance de huit tests contre des alternatives comportant le meme parametre de puissance inconnu

a finite element splitting extrapolation for second order hyperbolic equations splitting extrapolation is an efficient technique for solving large scale scientific and engineering problems in parallel this article discusses a finite element splitting extrapolation for second order hyperbolic equations with time dependent coefficients this method possesses a higher degree of parallelism less computational complexity and more flexibility than richardson extrapolation while achieving the same accuracy by means of domain decomposition and isoparametric mapping some grid parameters are chosen according to the problem the multiparameter asymptotic expansion of the d quadratic finite element error is also established the splitting extrapolation formulas are developed from this expansion an approximation with higher accuracy on a globally fine grid can be computed by solving a set of smaller discrete subproblems on different coarser grids in parallel some a posteriori error estimates are also provided numerical examples show that this method is efficient for solving discontinuous problems and nonlinear hyperbolic equations

a study of several new and existing tests for heteroscedasticity in the general linear model abstract several optimum non parametric tests for heteroscedasticity are proposed and studied along with the tests introduced in the literature in terms of power and robustness properties it is found that all tests are reasonably robust to the ordinary least squares ols residual estimates number and character of the regressors only a few are robust to both the distributional and independence assumptions about the errors the power of tests can be improved with the ols residual estimates the increased sample size and the variability of the regressors it can be substantially reduced if the observations are not normally distributed and may increase or decrease if the errors are dependent each test is optimum to detect a specific form of heteroscedasticity and a serious power loss may occur if the underlying heteroscedasticity assumption in the data generation deviates from it

nystrom method for fredholm integral equations of the second kind in two variables on a triangle the paper deals with the approximation of the solution of the following bivariate fredholm integral equationf y email protected dk x y f x w x dx g y email protected d where the domain d is a triangle the proposed procedure by a suitable transformation is essentially the nystrom method based on the zeros of univariate jacobi orthogonal polynomials convergence stability and well conditioning of the method are proved in order to illustrate the efficiency of the proposed method some numerical tests are given

robust procedures for testing equality of covariance matrices normal theory tests for common variance are very sensitive to departures from normality in both univariate and multivariate applications for mild departures from normality and moderate sample size nominal a 01 produced type i error rates in excess of 20 in simulation studies since a modification of levene s test has been shown to perform well for the univariate problem two multivariate generalizations of this test are proposed both procedures are robust to departures from normality and are simple computationally comparisons of the power of these two procedures and a procedure proposed previously by tiku and balakrishnan 1985 communications in statisticstheory and methods 14 3033 3051 indicate that the three methods should be viewed as complementary

numerical solution of the two dimensional fredholm integral equations using gaussian radial basis function in this paper we introduce a numerical method for the solution of two dimensional fredholm integral equations the method is based on interpolation by gaussian radial basis function based on legendre gauss lobatto nodes and weights numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the method

new approach to solve two dimensional fredholm integral equations abstract in this paper we present an efficient iterative method based on quadrature formula to solve two dimensional nonlinear fredholm integral equations we investigate the convergence analysis of the proposed method the error estimation is given in terms of uniform and partial modulus of continuity in addition we show the numerical stability analysis of the method with respect to the choice of the first iteration finally some numerical experiments confirm the theoretical results and illustrate the accuracy of the method

a generalized levene s scale test for variance heterogeneity in the presence of sample correlation and group uncertainty we generalize levene s test for variance scale heterogeneity between k groups for more complex data when there are sample correlation and group membership uncertainty following a two stage regression framework we show that least absolute deviation regression must be used in the stage 1 analysis to ensure a correct asymptotic k 12 k 1 distribution of the generalized scale gs test statistic we then show that the proposed gs test is independent of the generalized location test under the joint null hypothesis of no mean and no variance heterogeneity consequently we generalize the recently proposed joint location scale gjls test valuable in settings where there is an interaction effect but one interacting variable is not available we evaluate the proposed method via an extensive simulation study and two genetic association application studies

robust l estimation of scale with an application in astronomy abstract in this article we investigate the robustness properties of a class of l estimators of scale and then develop robust procedures for making inferences about scale we pay particular attention to trimmed estimators that should perform well when the underlying model is gaussian we find that trimmed versions of the efficient linear l estimator for the gaussian distribution perform better than trimmed standard deviation estimators we then apply a trimmed version of the efficient linear l estimator for the gaussian distribution to astronomical data

powerful two sample tests based on the likelihood ratio a new approach to constructing nonparametric tests for the general two sample problem is proposed this approach not only generates traditional tests including the two sample kolmogorov smirnov cramer von mises and anderson darling tests but also produces new powerful tests based on the likelihood ratio although conventional two sample tests are sensitive to the difference in location most of them lack power to detect changes in scale and shape the new tests are location scale and shape sensitive so they are robust against variation in distribution

trajectory planning for boundary controlled parabolic pdes with varying parameters on higher dimensional spatial domains the flatness based design of a feedforward tracking control is considered for the solution of the trajectory planning problem for a boundary controlled diffusion convection reaction system with spatially and temporally varying parameters defined on a 1 les m dimensional parallelepipedon with the nonlinear input being restricted to a m 1 dimensional hyperplane for this an implicit state and input parametrization in terms of a basic output is determined via a volterra type integral equation with operator kernel by recursively computing successive series coefficients a series solution of the integral equation is obtained whose absolute and uniform convergence is verified by restricting the system parameters and the basic output to a certain but broad gevrey class hence prescribing an admissible desired trajectory for the basic output directly yields the feedforward control by evaluating the input parametrization this results in a systematic procedure for trajectory planning and feedforward control design for boundary controlled parabolic distributed parameter systems defined on higher dimensional domains

a proposal for interpreting and reporting negative studies an issue of continuing interest is the interpretation and reporting of negative studies namely studies that do not find statistically significant differences the most common approach is the design power method which determines irrespective of the observed difference what differences the study could have been expected to detect we propose an alternative approach the application of equivalence testing methods where we define equivalence to mean that the actual difference lies within some specified limits this approach in contrast to the design power approach provides a way of quantifying with p values what was actually determined from the study instead of saying what the study may or may not have accomplished with some degree of certainty power for example a possible outcome of the equivalence testing approach is the conclusion at the 5 per cent level that two means or proportions do not differ by more than some specified amount the equivalence testing approach applies to any study design we illustrate the method with a cancer clinical trial and an epidemiologic case control study in addition for those studies in which one cannot specify limits a priori we propose the use of equivalence curves to summarize and present the study results

morphometric analysis for early detection of changes in cellular structure in a toxicological experiment this paper presents a method for semi automatic analysis of morphometry in image cytometry studies we examine morphological changes in neuroblastoma cells caused by a toxin nuclei are automatically recognized from images using a constrained seeded region growing algorithm the shape of the nuclei is quantified by fitting ellipses to the identified regions features such as centroids elongation orientation and size are extracted from this fitting process under certain assumptions it is demonstrated that the log elongation measurement has an asymptotically normal distribution whose variance is dependent only on object size this allows weighted linear models to be fitted to elongation measurements hypothesis tests show that over time there is a significant elongation due to application of the toxin the other variables are not significant but there is a significant image effect the scientific implications of these findings are considered

on sample size of the kruskal wallis test with application to a mouse peritoneal cavity study summary as the nonparametric generalization of the one way analysis of variance model the kruskal wallis test applies when the goal is to test the difference between multiple samples and the underlying population distributions are nonnormal or unknown although the kruskal wallis test has been widely used for data analysis power and sample size methods for this test have been investigated to a much lesser extent this article proposes new power and sample size calculation methods for the kruskal wallis test based on the pilot study in either a completely nonparametric model or a semiparametric location model no assumption is made on the shape of the underlying population distributions simulation results show that in terms of sample size calculation for the kruskal wallis test the proposed methods are more reliable and preferable to some more traditional methods a mouse peritoneal cavity study is used to demonstrate the application of the methods

a meshless method for solving nonlinear two dimensional integral equations of the second kind on non rectangular domains using radial basis functions with error analysis in this paper we present a numerical method for solving two dimensional nonlinear fredholm integral equations of the second kind on a non rectangular domain the method utilizes radial basis functions rbfs constructed on scattered points as a basis in the discrete collocation method the proposed scheme is meshless since it does not need any domain element and so it is independent of the geometry of the domain the method reduces the solution of the two dimensional nonlinear integral equation to the solution of a nonlinear system of algebraic equations error analysis is presented for this method finally numerical examples are included to show the validity and efficiency of the new technique

optimal sample size planning for the wilcoxon mann whitney test there are many different proposed procedures for sample size planning for the wilcoxon mann whitney test at given type i and type ii error rates and respectively most methods assume very specific models or types of data to simplify calculations eg ordered categorical or metric data location shift alternatives etc we present a unified approach that covers metric data with and without ties count data ordered categorical data and even dichotomous data for that we calculate the unknown theoretical quantities such as the variances under the null and relevant alternative hypothesis by considering the following synthetic data approach we evaluate data whose empirical distribution functions match the theoretical distribution functions involved in the computations of the unknown theoretical quantities then well known relations for the ranks of the data are used for the calculations in addition to computing the necessary sample size n for a fixed allocation proportion t n1 n where n1 is the sample size in the first group and n n1 n2 is the total sample size we provide an interval for the optimal allocation rate t which minimizes the total sample size n it turns out that for certain distributions a balanced design is optimal we give a characterization of such distributions furthermore we show that the optimal choice of t depends on the ratio of the two variances which determine the variance of the wilcoxon mann whitney statistic under the alternative this is different from an optimal sample size allocation in case of the normal distribution model

alternative estimation procedures for pr x y in categorized data summary consider two independent random variables x and y the functional r pr x y or x pr x y pr y x is of practical importance in many situations including clinical trials genetics and reliability in this paper several approaches to estimation of x when x and y are presented in discretized categorical form are analyzed and compared asymptotic formulas for the variances of the estimators are derived use of the bootstrap to estimate variances is also discussed computer simulations indicate that the choice of the best estimator depends on the value of x the underlying distribution and the sparseness of the data it is shown that the bootstrap provides a robust estimate of variance several examples are treated

pade type approximation method for two dimensional fredholm integral equations of the second kind two dimensional fredholm integral equation of the second kind 2df ii on a bounded domain d is regarded as the problem with characteristic values a two dimensional function valued pade type approximation 2dfpta is defined its error formulas and convergence theorems are presented to obtain higher order 2dfpta a determinantal expression and its recursive algorithm are given in the end three numerical examples are tested where one on the unit triangle of vertices 0 0 0 1 1 0 and the other two on the square the testing results show that 2dfpta method is more accurate