confidence intervals for an effect size measure based on the mann whitney statistic part 1 general issues and tail area based methods for two random variables x and y pr y x pr y x is advocated as a general measure of effect size to characterize the degree of separation of their distributions it is estimated by u mn a generalization of the mann whitney u statistic derived by dividing u by the product of the two sample sizes it is equivalent to the area under the receiver operating characteristic curve it is readily visualized in terms of two gaussian distributions with appropriately separated peaks the effect of discretization of a continuous variable is explored tail area based confidence interval methods are developed which can be applied to very small samples or extreme outcomes copyright 2005 john wiley sons ltd

estimating treatment effects in a two arm parallel trial of a continuous outcome for a continuous outcome in a two arm trial that satisfies normal distribution assumptions we can transform the standardized mean difference with the use of the cumulative distribution function to be the effect size measure p x

analytic smoothing effect for nonlinear schrodinger equation with quintic nonlinearity abstract we prove the global existence of analytic solutions to nonlinear schrodinger equation with quintic nonlinearity in n space dimensions for sufficiently small cauchy data with exponential decay the smallness assumption on the data is imposed in terms of the critical sobolev space h n 2 1 2 moreover a characterization of some class of analytic functions is given

asymptotic behavior of solutions to time dependent hartree equations on considere le comportement asymptotique pour t grand des solutions du probleme de cauchy pour l equation iu t u f u 2 u t x r r u o x x x r 3 ou f u 2 r 1 u 2 r 3 u t y 2 x y dy

a numerical study of the self similar solutions of the schrodinger map we present a numerical study of the self similar solutions of the localized induction approximation of a vortex filament these self similar solutions which are explicitly known constitute a one parameter family and develop a singularity in finite time we study a number of boundary conditions that allow us to reproduce the mechanism of singularity formation some related questions are also considered

on solutions of the initial value problem for the nonlinear schrodinger equations on considere le probleme aux valeurs initiales pour l equation de schrodinger non lineaire de la forme iu t u f u 2 u t x r r n u 0 x x x r n on etudie la regularite des solutions quand les fonctions initiales ne sont pas regulieres

confidence intervals for probabilities and tolerance regions based on a generalization of the mann whitney statistic abstract inference procedures are proposed for any specified function of two random variables f x y assuming that independent random samples from the x and y populations are available a generalization of the mann whitney statistic is used to obtain point and interval estimates for the probability that f x y falls in a given interval one proposed confidence interval is a modification and improvement to the approach of halperin gilbert and lachin 1987 for estimating pr x y a thorough review is made of the literature on nonparametric confidence bounds for pr x y with emphasis on methods based on the central limit theorem in addition to the improvement of halperin et al s method bounds analogous to the clopper pearson confidence interval for a binomial parameter are proposed simulation results show the performance of the alternative procedures approximate nonparametric tolerance limits for f x y are also proposed the article closes by constructing a two sided tolerance interval for

a modified chebyshev pseudospectral dd algorithm for the gbh equation in this paper a chebyshev spectral collocation domain decomposition dd semi discretization by using a grid mapping derived by kosloff and tal ezer in space is applied to the numerical solution of the generalized burger s huxley gbh equation to reduce roundoff error in computing derivatives we use the above mentioned grid mapping in this work we compose the chebyshev spectral collocation domain decomposition and kosloff and tal ezer grid mapping elaborately firstly the theory of application of the chebyshev spectral collocation method with grid mapping and dd on the gbh equation is presented this method yields a system of ordinary differential algebraic equations daes secondly we use a fourth order runge kutta formula for the numerical integration of the system of daes application of this modified method to the gbh equation show that this method m dd is faster and more accurate than the standard chebyshev spectral collocation dd s dd method

dilation method and smoothing effects of solutions to the benjamin ono equation in this paper we study smoothing effects of solutions to the benjamin ono equation where h is the hilbcrt transform defined by we prove that if h 2 and x x 4 then the solution u of bo belongs to where

domain and range of the modified wave operator for schrodinger equations with a critical nonlinearity we study the final problem for the nonlinear schrodinger equation i partial t u frac 1 2 delta u lambda u frac 2 n u quad t x in mathbf r times mathbf r n where lambda in bf r n 1 2 3 if the final data u in bf h 0 alpha left phi in bf l 2 left 1 left vert x right vert right alpha phi in bf l 2 right with frac n 2 alpha min left n 2 1 frac 2 n right and the norm vert widehat u vert bf l infty is sufficiently small then we prove the existence of the wave operator in l2 we also construct the modified scattering operator from h0 to h0 with frac n 2 delta alpha

on the derivative nonlinear schro dinger equation abstract in this paper we discuss the cauchy problem for the derivative nonlinear schrodinger equation i t 2i x 2 0 0 x x where 0 under an explicit smallness condition of the initial data we prove the unique global existence of solutions to this problem in the usual sobolev spaces in the weighted sobolev spaces and in the schwartz class we describe the smoothing effect in detail furthermore for the data decaying exponentially at infinity we prove that the above equation has unique local solutions which are analytic in the space direction

the asymptotic behavior of nonlinear schrodinger equations on considere l equation de schrodinger non lineaire ns i u t u 2 u p 1 u dans r n n 2 avec 0 soit h o 2 et u l 2 r n u 2 u 2 xu 2 ou u q est la norme l 9 de u soit 1 2 n p 1 4 n 2 alors pour tout u 0 il existe un unique u l 2 r n tel que la solution u t de ns avec u 0 u 0 ait l asymptote libre u quand t lim t u t exp ith 0 u 2 0

a deficiency of the odds ratio as a measure of effect size the odds ratio is probably the most widely used measure of association for binary variables it has many well recognized advantages and disadvantages vis a vis the risk ratio we demonstrate that for chained or conditional probabilities odds ratios can behave paradoxically by failing to show a reinforcement effect that is expressed very clearly when risk ratios are used

local smoothing properties of dispersive equations is it possible for time evolution partial differential equations which are reversible and conservative to smooth locally the initial data for the linear wave equation for instance the answer is no however in 10 t kato found a local smoothing property of the korteweg de vries equation the solution of the initial value problem is locally one derivative smoother than the initial datum kato s proof uses in a curcial way the algebraic properties of the symbol for the korteweg de vries equation and the fact that the underlying spatial dimension is one actually judging from the way several integrations by parts and cancellations conspire to reveal a smoothing effect one would be inclined to believe this was a special property of the k dv equation this is not however the case in this paper we attempt to describe a general local smoothing effect for dispersive equations and systems the smoothing effect is due to the dispersive nature of the linear part of the equation all the physically significant dispersive equations and systems known to us have linear parts displaying this local smoothing property to mention only a few the k dv benjamin ono intermediate long wave various boussinesq and schrodinger equations are included we study thus equations and systems of the form

regularity of solutions to nonlinear dispersive equations on considere le probleme de cauchy pour les equations dispersives non lineaires de la forme t u ip d u f u x r n t u x 0 u 0 x

nonexistence of asymptotically free solutions for a nonlinear schrodinger equation let u be a nontrivial smooth solution to iut u u p 1u if n 1 and 2 p 3 then there does not exist any finite energy free solution v such that u t v t 2 0 as t this extends a theorem of strauss in which the same result was proved for 1 p 2

self similar solutions for the 1 d schrodinger map on the hyperbolic plane in this paper we will study self similar solutions for x t x x ss the equivalent in the minkowski 3 space mathbb r 2 1 to the localized induction approximation flow trying to adapt some results given by gutierrez rivas and vega we will show the existence of a one parameter family of smooth solutions developing a corner in finite time the main difference with respect to the euclidean case studied by those authors will be the proof of the boundedness of t e 1 and e 2 the equivalents of t b and n in mathbb r 2 1

a confidence interval for pr x y estimated from simple cluster samples distribution free confidence intervals based on somers d a simple function of the mann whitney u statistic are developed for pr x y where x and y are the ranks of any two observations from two independent populations the approach accommodates a complex sampling design and explicit formulas are given for simple cluster sampling the method also accommodates simple progressive left and right censoring the accuracy of the interval is shown to improve when the tanh 1 transform is used a bootstrap solution was tried and did not perform as well as the proposed solution

solvability of the localized induction equation for vortex motion the initial and the initial boundary value problems for the localized induction equation which describes the motion of a vortex filament are considered we prove the existence of solutions of both problems globally in time in the sense of distribution by the method of regularization

statistical inference for p x y let x and y be two independent continuous random variables we make statistical inference about p x y the so called stress strength model through the edgeworth expansions and the bootstrap approximations of the studentized wilcoxon mann whitney statistics finite sample accuracy of the confidence intervals is assessed through a simulation study two real data sets are analysed to illustrate our methods copyright 2007 john wiley sons ltd

extending the c statistic to nominal polytomous outcomes the polytomous discrimination index diagnostic problems in medicine are sometimes polytomous meaning that the outcome has more than two distinct categories for example ovarian tumors can be benign borderline primary invasive or metastatic extending the main measure of binary discrimination the c statistic or area under the roc curve to nominal polytomous settings is not straightforward this paper reviews existing measures and presents the polytomous discrimination index pdi as an alternative the pdi assesses all sets of k cases consisting of one case from each outcome category for each category i i 1 k it is assessed whether the risk of category i is highest for the case from category i a score of 1 k is given per category for which this holds yielding a set score between 0 and 1 to indicate the level of discrimination the pdi is the average set score and is interpreted as the probability to correctly identify a case from a randomly selected category within a set of k cases this probability can be split up by outcome category yielding k category specific values that result in the pdi when averaged we demonstrate the measures on two diagnostic problems residual mass histology after chemotherapy for testicular cancer diagnosis of ovarian tumors we compare the behavior of the measures on theoretical data showing that pdi is more strongly influenced by simultaneous discrimination between all categories than by partial discrimination between pairs of categories in conclusion the pdi is attractive because it better matches the requirements of a measure to summarize polytomous discrimination copyright 2012 john wiley sons ltd

binomial confidence intervals abstract for x with binomial n p distribution section 1 gives a one page table of 95 and 99 confidence intervals for p for n 1 2 30 this interval is equivariant under x n x and p 1 p has approximately equal probability tails is approximately unbiased has crow s property of minimizing the sum of the n 1 possible lengths and each of its ends is increasing in x and decreasing in n with about as regular steps as possible sections 2 and 3 consider the usual approximate confidence intervals calculations and asymptotic results show the need for the continuity correction in these even when n is large because of the nonuniformity of the binomial normal convergence as p 0 these intervals fail to have their stated asymptotic confidence coefficients simple corrections are given for this in the approximate interval x n c n x n 1 x n 1 2n it is shown that the factor c n should be replaced by c n c 2 2c n 1 n

remark on the scattering operator for the cubic nonlinear dirac equation in three space dimensions abstract this paper is concerned with the scattering operator s for the three dimensional dirac equation with a cubic nonlinearity it follows from known results that s is well defined on a neighborhood of 0 in the sobolev space h r 3 c 4 for any 1 in the present paper we prove that for any m n and s max m there exists some neighborhood u of 0 in the weighted sobolev space h s m r 3 c 4 such that s u h s m r 3 c 4

on the bias of commonly used measures of association for 2 x 2 tables summary the odds ratio and the relative risk are commonly used as measures of association in a fourfold table the bias of the standard point estimators of these parameters is investigated for small samples simple alternative estimators that possess superior performance in terms of bias and mean squared error are suggested

l c ℝn decay of classical solutions for nonlinear schrodinger equations on etudie le probleme aux valeurs initiales pour l equation de schrodinger non lineaire iu t u f u 2 u u o x x x r n t r 1 n 11 sous de bonnes hypotheses de regularite sur f et et des conditions de croissance et de signe sur f on montre que les normes maximum des solutions decroissent quand t au meme taux que celles des solutions de l equation de schrodinger libre

geometric optics and long range scattering for one dimensional nonlinear schrodinger equations with the methods of geometric optics used in 2 we provide a new proof of some results of 10 to construct modified wave operators for the one dimensional cubic schrodinger equation we improve the rate of convergence of the nonlinear solution towards the simplified evolution and get better control of the loss of regularity in sobolev spaces in particular using the results of 9 we deduce the existence of a modified scattering operator with small data in some sobolev spaces we show that in terms of geometric optics this gives rise to a random phase shift at a caustic

smoothing effects and dispersion of singularities for the schrodinger evolution group we describe smoothing effects and dispersion of singularities for the schrodinger evolution group in the weighted sobolev spaces under a fairly general assumption on the potential it is shown that all singularities in the wavefunction vanish instantly whenever the initial state has sufficient decay we measure the regularity gained by the wavefunction by the decay property of the initial state no assumptions on the regularity of the initial state are imposed throughout the paper

increasing the power of the mann whitney test in randomized experiments through flexible covariate adjustment the mann whitney u test is frequently used to evaluate treatment effects in randomized experiments with skewed outcome distributions or small sample sizes it may lack power however because it ignores the auxiliary baseline covariate information that is routinely collected wald and score tests in so called probabilistic index models generalize the mann whitney u test to enable adjustment for covariates but these may lack robustness by demanding correct model specification and do not lend themselves to small sample inference using semiparametric efficiency theory we here propose an alternative extension of the mann whitney u test which increases its power by exploiting covariate information in an objective way and which lends itself to permutation inference simulation studies and an application to an hiv clinical trial show that the proposed permutation test attains the nominal type i error rate and can be drastically more powerful than the classical mann whitney u test copyright 2014 john wiley sons ltd

distribution free confidence intervals for pr x1 x2 summary we review the problem of obtaining a distribution free confidence interval for the probability p that one random variable is less than another independent random variable based on the two sample uncensored wilcoxon mann whitney statistic the pivotal quantities used by sen 1967 sankhya series a 29 95 102 and govindarajulu 1968 annals of the institute of statistical mathematics 20 229 238 are modified to take into account that the variance of estimated p depends on p a number of simulations were conducted to compare the various methods the results suggest that the proposed modification is superior in the sense that over the entire range of p the modification generally yields values of coverage probability much closer to nominal coverage than the methods of sen s and govindarajulu g the coverage values for the s and g methods are very close to each other both share the characteristics for one sided lower confidence limits of being conservative for small values of p and nonconservative sometimes extremely so for large values of p one sided upper limits have coverages that are essentially the mirror image of lower limit coverages the contrasts between the modified method and the s and g methods diminish in magnitude as sample size increases but are still nontrivial for a sample size of 80 our tentative conclusion is that the modified procedure is preferable to that of sen and govindarajulu and can be used when the sample size in both groups is equal to or greater than 20 limitations of our simulations are briefly discussed an example illustrating the use of our modified pivotal quantity and comparing it with the s and g results is presented

space time behavior of propagators for schrodinger evolution equations with stark effect abstract we give a detailed description of the space time behavior of the unitary propagator u t s t s r determined by the schrodinger evolution equation i t u 1 2 u e xu v t x u t r x r n where e is a homogeneous electric field and v is a time dependent potential

stability of the self similar dynamics of a vortex filament in this paper we continue our investigation of self similar solutions of the vortex filament equation also known as the binormal flow or the localized induction equation our main result is the stability of the self similar dynamics of small perturbations of a given self similar solution the proof relies on finding precise asymptotics in space and time for the tangent and the normal vectors of the perturbations a main ingredient in the proof is the control of the evolution of weighted norms for a cubic one dimensional schrodinger equation connected to the binormal flow by hasimoto s transform

point and interval estimation of exposure effects and interaction between exposures based on logistic model for observational studies point and interval estimation of exposure effects and interaction between exposures based on logistic model for observational studies

resolution of fourth order problems by the mortar element method we present a resolution of fourth order problems by the mortar element method in the case of spectral discretizations we prove that this approach leads to a well posed discrete problem and the numerical analysis gives an optimal error estimate

a general binomial regression model to estimate standardized risk differences from binary response data estimates of absolute risks and risk differences are necessary for evaluating the clinical and population impact of biomedical research findings we have developed a linear expit regression model lexpit to incorporate linear and nonlinear risk effects to estimate absolute risk from studies of a binary outcome the lexpit is a generalization of both the binomial linear and logistic regression models the coefficients of the lexpit linear terms estimate adjusted risk differences while the exponentiated nonlinear terms estimate residual odds ratios the lexpit could be particularly useful for epidemiological studies of risk association where adjustment for multiple confounding variables is common we present a constrained maximum likelihood estimation algorithm that ensures the feasibility of risk estimates of the lexpit model and describe procedures for defining the feasible region of the parameter space judging convergence and evaluating boundary cases simulations demonstrate that the methodology is computationally robust and yields feasible consistent estimators we applied the lexpit model to estimate the absolute five year risk of cervical precancer or cancer associated with different pap and human papillomavirus test results in 167 171 women undergoing screening at kaiser permanente northern california the lexpit model found an increased risk due to abnormal pap test in hpv negative that was not detected with logistic regression our r package blm provides free and easy to use software for fitting the lexpit model

estimating risk and rate levels ratios and differences in case control studies summary classic or cumulative case control sampling designs do not admit inferences about quantities of interest other than risk ratios and then only by making the rare events assumption probabilities risk dierences and other quantities cannot be computed without knowledge of the population incidence fraction similarly density or risk set case control sampling designs do not allow inferences about quantities other than the rate ratio rates rate dierences cumulative rates risks and other quantities cannot be estimated unless auxiliary information about the underlying cohort such as the number of controls in each full risk set is available most scholars who have considered the issue recommend reporting more than just risk and rate ratios but auxiliary population information needed to do this is not usually available we address this problem by developing methods that allow valid inferences about all relevant quantities of interest from either type of case control study when completely ignorant of or only partially knowledgeable about relevant auxiliary population information copyright 2002 john wiley sons ltd

a practical divergence measure for survival distributions that can be estimated from kaplan meier curves this paper introduces a new simple divergence measure between two survival distributions for two groups of patients the divergence measure between their associated survival distributions is based on the integral of the absolute difference in probabilities that a patient from one group dies at time t and a patient from the other group survives beyond time t and vice versa in the case of non crossing hazard functions the divergence measure is closely linked to the harrell concordance index c the mann whitney test statistic and the area under a receiver operating characteristic curve the measure can be used in a dynamic way where the divergence between two survival distributions from time zero up to time t is calculated enabling real time monitoring of treatment differences the divergence can be found for theoretical survival distributions or can be estimated non parametrically from survival data using kaplan meier estimates of the survivor functions the estimator of the divergence is shown to be generally unbiased and approximately normally distributed for the case of proportional hazards the constituent parts of the divergence measure can be used to assess the proportional hazards assumption the use of the divergence measure is illustrated on the survival of pancreatic cancer patients copyright 2016 john wiley sons ltd

non parametric two sample tests for repeated ordinal responses consider data on two groups of clusters where each cluster consists of many units that respond on an ordinal scale we develop a mann whitney type test to determine whether a typical response from the first group is larger or smaller than a typical response from the second group

long range scattering for nonlinear schrodinger equations in one space dimension we consider the scattering problem for the nonlinear schrodinger equation in 1 1 dimensions open image in new window where x r 0 r p 3 we show that modified wave operators for exist on a dense set of a neighborhood of zero in the lebesgue spacel2 r or in the sobolev spaceh1 r the modified wave operators are introduced in order to control the long range nonlinearity u 2u

conforming spectral approximations for non conforming domain decompositions abstract a spectral domain decomposition scheme is introduced for the numerical solution of second and fourth order elliptic problems the technique is applicable to certain domain decompositions of rectangular or rectangularly decomposable domains it is shown that it yields approximations which are pointwise c 0 continuous across the subdomain interfaces for second order problems and pointwise c 1 continuous across the subdomain interfaces for fourth order problems

weighted sobolev spaces and rapidly decreasing solutions of some nonlinear dispersive wave equations where d is a positive integer a is a d dimensional laplacian and the subscripts x t denote partial differentiations the initial value problems for 1 i 1 3 require the asymptotic conditions as x tends to infinity and one must specify spaces of functions satisfying the desired asymptotic conditions the usual choices of spaces are the sobolev spaces z p well posedness in hs of the initial value problems for 1 1 1 3 was established by many authors 3 5 8 12 181 it is of interest to know that eqs l l 1 3 have solutions decreasing faster than hs convergence as x tends to infinity in particular solutions in the schwartz spaces s for each t provided that their initial data are in s this is motivated by tanaka s result for the korteweg de vries equation 131 which establishes the existence of s solutions by the inverse scattering techniques and by the fact that eqs l l 1 3 have travelling solutions in s solitary waves which may play an important role of asymptotic behavior of solutions as t tends to infinity

events per person time incidence rate a misleading statistic results in risk studies based on events per person time ept technically incidence rate often prove non confirmable the circumstances in which the ept ratio is unquestionably both valid and optimal to compare a high and low risk group a constant hazards situation are discussed however the constant hazards situation seldom applies in medical research when the constant hazards situation does not apply even under optimal circumstances with fixed entry time and follow up time for all those not experiencing the event and absence of censoring ept ratio yields at best ambiguous at worst misleading results more careful design and survival analyses are recommended in place of use of epts

smoothing properties for the higher order nonlinear schrodinger equation with constant coefficients abstract we study local and global existence and smoothing properties for the initial value problem associated to a higher order nonlinear schrodinger equation with constant coefficients which appears as a model for propagation of pulse in an optical fiber

a fully conforming spectral collocation scheme for second and fourth order problems abstract a spectral element scheme is presented for the solution of second and fourth order problems in two and three space dimensions this scheme is based on a collocation formulation and for a certain class of problems results in spectral approximations which are c1 pointwise continuous across the element interfaces for second order problems and c3 pointwise continuous across the element interfaces for fourth order problems

balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity score matched samples the propensity score is a subject s probability of treatment conditional on observed baseline covariates conditional on the true propensity score treated and untreated subjects have similar distributions of observed baseline covariates propensity score matching is a popular method of using the propensity score in the medical literature using this approach matched sets of treated and untreated subjects with similar values of the propensity score are formed inferences about treatment effect made using propensity score matching are valid only if in the matched sample treated and untreated subjects have similar distributions of measured baseline covariates in this paper we discuss the following methods for assessing whether the propensity score model has been correctly specified comparing means and prevalences of baseline characteristics using standardized differences ratios comparing the variance of continuous covariates between treated and untreated subjects comparison of higher order moments and interactions five number summaries and graphical methods such as quantile quantile plots side by side boxplots and non parametric density plots for comparing the distribution of baseline covariates between treatment groups we describe methods to determine the sampling distribution of the standardized difference when the true standardized difference is equal to zero thereby allowing one to determine the range of standardized differences that are plausible with the propensity score model having been correctly specified we highlight the limitations of some previously used methods for assessing the adequacy of the specification of the propensity score model in particular methods based on comparing the distribution of the estimated propensity score between treated and untreated subjects are uninformative

uniqueness properties of solutions to schrodinger equations nx j 1 2 u x 2 x 0 harmonic functions in the unit ball x r n x 2 since harmonic functions are still real analytic in x r n x 1 in fact it is well known that if p x d is a linear elliptic differential operator with real analytic coefficients andp x d u 0 in a open set r n then u is real analytic in hence the s u c p also holds for such solutions through the work of hadamard 28 on the uniqueness of the cauchy problem which is closely related to the strong unique continuation property discussed earlier it became clear for applications in nonlinear problems that it would be desirable to establish the strong unique continuation property for operators whose coefficients are not necessarily real analytic oreven c the first results in this direction were found in the pioneering work of carleman 9 when

on solutions of the initial value problem for the nonlinear schrodinger equations in one space dimension t 0 xe has a regularizing property that the solutions become smooth instantly for t 0 even if their initial data are not smooth for example in l n our aim of this paper is to show that the nls equation 1 1 1 2 has a similar regularizing effect more precisely all solutions of finite energy to 1 1 1 2 are smooth for tq 0 provided the initial functions in hi n or in

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

confidence intervals of the mann whitney parameter that are compatible with the wilcoxon mann whitney test for the two sample problem the wilcoxon mann whitney wmw test is used frequently it is simple to explain a permutation test on the difference in mean ranks it handles continuous or ordinal responses it can be implemented for large or small samples it is robust to outliers it requires few assumptions and it is efficient in many cases unfortunately the wmw test is rarely presented with an effect estimate and confidence interval a natural effect parameter associated with this test is the mann whitney parameter pr x y 0 5 pr x y ideally we desire confidence intervals on that are compatible with the wmw test meaning the test rejects at level if and only if the 100 1 confidence interval on the mann whitney parameter excludes 1 2 existing confidence interval procedures on are not compatible with the usual asymptotic implementation of the wmw test that uses a continuity correction nor are they compatible with exact wmw tests we develop compatible confidence interval procedures for the asymptotic wmw tests and confidence interval procedures for some exact wmw tests that appear to be compatible we discuss assumptions and interpretation of the resulting tests and confidence intervals we provide the wmwtest function of the asht r package to calculate all of the developed confidence intervals

sharp bounds on the relative treatment effect for ordinal outcomes for ordinal outcomes the average treatment effect is often ill defined and hard to interpret echoing agresti and kateri we argue that the relative treatment effect can be a useful measure especially for ordinal outcomes which is defined as pr yi 1 yi 0 pr yi 1 yi 0 with yi 1 and yi 0 being the potential outcomes of unit i under treatment and control respectively given the marginal distributions of the potential outcomes we derive the sharp bounds on which are identifiable parameters based on the observed data agresti and kateri focused on modeling strategies under the assumption of independent potential outcomes but we allow for arbitrary dependence

smoothing effect for nonlinear schrodinger equations in exterior domains abstract we consider the following nonlinear schrodinger equations in exterior domains i t u 1 2 u u 2 u t x r x d u 0 x x x d u t x 0 or u t6v 0 t x r x d where d x rn x r d r 0 and v denotes the outward normal unit vector at x d in this paper we prove the radially symmetric solutions of have a smoothing property

microlocal dispersive smoothing for the schrodinger equation this paper establishes a connection between the microlocal smoothness of solutions of the initial value problem for schrodinger s equation and the global behavior of bicharacteristics of the principal symbol in particular localized initial data gives rise to solutions which are microlocally smooth at all points which are not trapped backwards by the bicharacteristic flow the origin of the phenomenon is in the dispersive nature of the equation the results imply microlocal regularity properties of the fundamental solution 1995 john wiley sons inc

local smoothing effects for a nonlinear timoshenko type equation where x e ir t r 0 here a denotes the usual laplace operator vu is the spatial gradient of u and m s is a nonlinear smooth function the term m jr vu12 du au is usually known as timoshenko s type nonlinearity and appears in a variety of models mostly associated with nonlinear vibrations of beams l results on the existence of global solutions of 1 1 are available in the literature 2 we are concerned here with further properties of the solutions more specifically we show that there is a class of solutions of 1 1 which are locally more regular than their initial data we prove the result assuming a suitable decay of the data at infinity our main results theorems 3 1 and 3 2 in this paper will only be given in the one dimensional case however as will become clear during our proofs several ingredients are valid in any dimension there is a close relationship between solutions of 1 l and solutions of a nonlinear schrodinger equation at the end of this section we will give more details on this fact thanks to this observation our strategy was to combine classical energy estimates with the fact that the operator l a2 at2 avax4 6 almost commutes with the operators pm xu 2td u and

why add anything to nothing the arcsine difference as a measure of treatment effect in meta analysis with zero cells for clinical trials with binary endpoints there are a variety of effect measures for example risk difference risk ratio and odds ratio or the choice of metric is not always straightforward and should reflect the clinical question additional issues arise if the event of interest is rare in systematic reviews trials with zero events in both arms are encountered and often excluded from the meta analysis the arcsine difference as is a measure which is rarely considered in the medical literature it appears to have considerable promise because it handles zeros naturally and its asymptotic variance does not depend on the event probability this paper investigates the pros and cons of using the as as a measure of intervention effect we give a pictorial representation of its meaning and explore its properties in relation to other measures based on analytical calculation of the variance of the arcsine transformation a more conservative variance estimate for the rare event setting is proposed motivated by a published meta analysis in cardiac surgery we examine the statistical properties of the various metrics in the rare event setting we find the variance estimate of the as to be more stable than that of the log or even if events are rare however parameter estimation is biased if the groups are markedly unbalanced though from a theoretical viewpoint the as is a natural choice its practical use is likely to continue to be limited by its less direct interpretation

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

gain of regularity for the kp i equation abstract in this paper we study the smoothness properties of solutions to the kp i equation we show that the equation s dispersive nature leads to a gain in regularity for the solution in particular if the initial data possesses certain regularity and sufficient decay as x then the solution u t will be smoother than for 0 t t where t is the existence time of the solution