linear acoustic formulas for calculation of rotating blade noise a unified approach is used to derive many of the current formulas for calculation of discrete frequency noise of helicopter rotors and propellers both compact and noncompact results are derived the noncompact results are based on the solution of ffowcs williams hawkings fw h equation the compact formulations are obtained as the limit of noncompact source results in particular the linearized acoustic theories of hawkings and lowson farassat hanson woan and gregorek succi and jou are discussed in this paper an interesting thickness noise formula by isom and its extension by ffowcs williams are also presented

numerical simulations of helicopter aerodynamics and acoustics this paper demonstrates several new methods for computing acoustic signals from helicopter rotors in hover and forward flight aerodynamic and acoustic solutions in the near field are computed with two different finite volume flow solvers for the euler equations a solution adaptive unstructured grid euler solver models a rotor in hover while a more conventional structured grid solver is used for forward flight calculations a nonrotating cylindrical surface is then placed around the entire rotor system this surface moves subsonically with the rotor hub in forward flight the finite volume solution is interpolated onto this cylindrical surface at every time step and a kirchhoff integration propagates the acoustic signal to the far field computed values for high speed impulsive noise in hover and forward flight show excellent agreement with experimental data results from the combined finite volume kirchhoff method offer high accuracy with reasonable computer resource requirements

hypothesis testing in a mixture case control model summary we consider a problem of testing mixture proportions using two sample data one from group one and the other from a mixture of groups one and two with unknown proportion for being in group two various statistical applications including microarray study infectious epidemiological studies case control studies with contaminated controls clinical trials allowing nonresponders genetic studies for gene mutation and fishery applications can be formulated in this setup under the assumption that the log ratio of probability density functions from the two groups is linear in the observations we propose a generalized score test statistic to test the mixture proportion under some regularity conditions it is shown that this statistic converges to a weighted chi squared random variable under the null hypothesis of 0 where the weight depends only on the sampling fraction of both groups the permutation method is used to provide more reliable finite sample approximation simulation results and two real data applications are presented

a multivariate multisample quantile test for ordered alternatives abstract we propose and study a multivariate c sample rank test for order restricted alternatives when the underlying distributions have a contaminated component an example concerning lens opacity in adults is presented the asymptotic distributions are obtained under local mixture alternatives and pitman efficiencies are calculated an empirical power study is also included

a note on the identifiability of fixed effect 3pl models in this note we prove that the 3 parameter logistic model with fixed effect abilities is identified only up to a linear transformation of the ability scale under mild regularity conditions contrary to the claims in theorem 2 of san martin et al psychometrika 80 2 450 467 2015a

derivation and implementation of the boundary integral formula for the convective acoustic wave equation in time domain kirchhoff s formula for the convective wave equation is derived using the generalized function theory the generalized convective wave equation for a stationary surface is obtained and the integral formulation the convective kirchhoff s formula is derived the formula has a similar form to the classical kirchhoff s formula but an additional term appears due to a moving medium effect for convenience the additional term is manipulated to a final form as the classical kirchhoff s formula the frequency domain boundary integral can be obtained from the current time domain boundary integral form the derived formula is verified by comparison with the analytic solution of source in the uniform flow the formula is also utilized as a boundary integral equation time domain boundary element method bem analysis using the boundary integral equation is conducted and the results show good agreement with the analytical solution the formula derived here can be useful for sound radiation and scattering by arbitrary bodies in a moving medium in the time domain

testing for a treatment effect in the presence of nonresponders good 1979 biometrics 35 483 489 introduced a new randomization test for the two sample problem where a proportion 1 p of the treatment group does not respond to the treatment and suggested that the wilcoxon test is not effective for this situation we show to the contrary that the wilcoxon test is quite useful when p greater than or equal to 6 and point out an error in his definition of a one tailed randomization test

comment on forest and floods a new paradigm sheds light on age old controversies by younes alila et al 1 the paper by alila et al 2009 hereafter referred to as aksh presents a technique for analyzing altered peak flow frequencies after logging the paper suggests that the established method of chronologically pairing peak flows by corresponding hydrologic input at control and treated watersheds is inappropriate leading to irrelevant research hypotheses and impeding scientific progress in general we agree that analyses of changes in flood frequency are useful for evaluating the effects of watershed disturbance and that simple regression models often provide inadequate descriptions of posttreatment peak flow responses however the proposed method and accompanying discussion have several problems that undercut the strength of the paper s conclusions 2 1 the recovery adjustment used by the method augments the effect the analysis is attempting to detect 3 2 even in the absence of impacts the frequency distribution of observed peaks is expected to have greater variance than that of predicted peaks thereby introducing an artificial shift when comparing upper quantiles of observed and expected frequency distributions 4 3 a more appropriate analysis of uncertainty is needed if the utility of the method is to be validly assessed 5 4 frequency pairing does not overcome the problem of low power in testing for changes in very large events prior to forest regrowth 6 5 the relative merits of alternative statistical approaches are mischaracterized

generalized treatment effects for clinical trials practice in the analysis of clinical trials with continuously measured endpoints is to focus on the difference or percentage change in mean or median response however treatments may have effects on the distribution of responses other than on the average response we sought an approach to such generalized treatment effects that i targets a parameter that is easily understood by our clinical colleagues and ii employs confidence intervals as the basis for inference we consider one such approach based on work in reliability theory namely setting pr y x as the target parameter and compare this approach to an earlier one due to o brien the two approaches have similar properties when they both seek to reject the null hypothesis of no effect due to different variances but differ when the larger variance corresponds to the larger mean in that case our approach views that the larger variance attenuates the effect of the larger mean out suggested approach applies easily to positive control clinical equivalence trials copyright 2000 john wiley sons ltd

asymptotic properties of censored linear rank tests a conjecture of prentice is established which states that for censored linear rank test exact scores based on conditional expectations can be replaced by approximate scores obtained by evaluating the score function at an estimate of the survival function we show that under minimal conditions asymptotically equivalent tests are obtained when either the kaplan meier altshuler or moment estimator of the survival function is used asymptotic normality is also established for a general random censorship model under the null hypothesis and for contiguous alternatives this is used to calculate efficacies and when the censoring times are i i d an expression for the asymptotic relative efficiency is given which is a natural generalization of the one for classical uncensored linear rank tests 1 introduction prentice 1978 has constructed a general class of linear rank tests for a regression model with censored data his approach was to specify a score function for a classical linear rank test in the absence of censoring chernoff and savage 1958 hajek and sidak 1967 to construct all possible rankings of the unobserved uncensored values which were consistent with observed censored sample and then to assign to each observation the average of all possible scores it could have received in the absence of censoring giving equal weighting to each possible uncensored ranking except for a few special scoring functions notably logarithmic or power law scores these averages are unwieldy when there is appreciable censoring and prentice suggested that asymptotically equivalent tests might arise if the score function was evaluated at some suitable estimate of the survivor function this is well known to be true for uncensored data but requires further justification when censoring is present because the estimate of the survivor function is more complicated in this work we show that prentice s conjecture is true under minimal conditions and also we show that it remains true if prentice s moment estimator of the survivor function is replaced by either the kaplan meier estimator or altshuler s estimator asymptotic normality of these tests is established under a random censorship model for the null hypothesis and contiguous alternatives by martingale methods this is used to compute efficacies for a general random censorship model and asymptotic relative efficiencies for i i d potential censoring times where fully efficient linear rank tests exist asymptotic normality for general alternatives has been established in cuzick 1982 by more complicated methods

some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor abstract the study of the inefficiency of the ordinary least squares estimator olse with one regressor by watson 1951 required a lower bound for the efficiency defined as the ratio of the variance of the best linear unbiased estimator blue to the variance of the olse such a lower bound was provided by the cassels inequality 1951 which we note is closely related to five other inequalities including the well known inequality usually attributed to kantorovich 1948 but which was established already by frucht 1943 the main purpose in this paper is to show how these six inequalities are related with a historical perspective we present some proofs and conclude that all six inequalities are essentially equivalent in the sense that any one inequality implies the other five we identify conditions for equality in each inequality and present the six continuous integral analogues we end the paper with english translations of the seminal papers by frucht 1943 and schweitzer 1914 respectively from the spanish and hungarian and a fairly extensive bibliography

commutators and accretive operators abstract in this paper singular values of commutators of hilbert space operators are estimated to this aim the accretivity of a transform of the operators is applied some recent results of kittaneh f kittaneh singular value inequalities for commutators of hilbert space operators linear algebra appl 430 2009 2362 2367 are extended

a posteriori error estimates for linear equations this paper describes upper and lowerp norm error bounds for approximate solutions of the linear system of equationsax b these bounds imply that the error is proportional to the quantity left r right 2 2 left a t r right q 1 wherer is the residual andq is the conjugate index top the constant of proportionality is larger than 1 and lies in a specified range similar results are obtained for approximations toa 1 and solutions of nonsingular linear equations on general spaces

a study of auchmuty s error estimate abstract we analyze the absolute error estimate of auchmuty 1 developed for linear systems in the euclidean norm this estimate and its geometrical interpretation are derived from the kantorovich inequality the estimate is then compared with other estimates known in the literature a probabilistic analysis and extension of the estimate to nonlinear systems are also given we also report on computational test results which indicate that auchmuty s estimate is an appropriate tool for practice

asymptotic theory of propeller noise ii supersonic single rotation propeller this paper gives analytical formulas for the far field harmonic components of the acoustic radiation from a b bladed supersonic single rotation propeller in the asymptotic limit b o the dominant source for radiation in a given direction is identified as located at the mach radius along the blade span the radius that approaches the observer at precisely sonic speed once in each rotation favorable agreement is found between the asymptotic prediction and the results of full numerical evaluation of the radiation integrals singular surfaces in the field are identified from the asymptotic formulas which are extended to include chordwise noncompactness effects these show among other things that supersonic propeller noise is an algebraically decreasing function of tip mach number once chordwise noncompactness effects are taken into account in contrast to the exponential increase with tip mach number of subsonic propeller noise

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

hypothesis testing under mixture models application to genetic linkage analysis summary in this paper we propose a new class of statistics to test a simple hypothesis against a family of alternatives characterized by a mixture model unlike the likelihood ratio statistic whose large sample distribution is still unknown in this situation these new statistics have a simple asymptotic distribution to which to refer under the null hypothesis simulation results suggest that it has adequate power in detecting the alternatives its application to genetic linkage analysis in the presence of the genetic heterogeneity that motivated this work is emphasized

a relationship between two forms of linear rank procedures for censored data summary this paper gives a useful relationship between two popular classes of linear rank statistics for arbitrarily right censored data the relationship allows a linear rank procedure with certain optimal properties to be transformed into the form of a procedure having established asymptotic properties under proportional hazards alternatives

a panel method for arbitrary moving boundaries problems an integral representation of the velocity potential is derived for aerodynamic purposes which aims at handling complex geometry in complicated motion a ground fixed frame is used to describe the governing equation such that the green s function is in its simplest form in this frame the generalized derivatives are then introduced to allow the differentiations of discontinuous function across the moving boundary techniques to derive the integral formulas are originated from farassat s approach in aeroacoustics for treating arbitrary moving boundaries problems

prediction of advanced propeller noise in the time domain this paper presents a brief derivation of a formula for prediction of the noise of high speed propellers in the time domain this formula is based on the solution of a linear wave equation ffowcs williams hawkings equation assuming that the sources are located on the actual blade surface an approximation of this formula using the assumption that the sources are on the mean surface of the blade is also presented which is considerably simpler than the full surface expression both the mean and full surface formulas are suitable for prediction of noise of supersonic sources on the blade they were derived to overcome some of the practical numerical difficulties associated with other acoustic formulations a discussion of coding these formulas for numerical work follows some comparison of predicted results with experimental data is also included which demonstrates the usefulness of the derived analytic expressions

on the use of the generalized t and generalized rank sum statistics in medical research we have used monte carlo methods to compare the type i error properties of the conditional and unconditional versions of the generalized t and the generalized rank sum tests to those of the independent samples t and wilcoxon rank sum tests results showed inflated type i errors for the conditional generalized tests but not for the unconditional tests we also compared the power of the unconditional generalized tests to that of the t and wilcoxon tests under a variety of conditions results showed the generalized tests to be much more efficient than their traditional counterparts in some circumstances but substantially less powerful in others based on these and other considerations we conclude that the application of these newer statistics in medical research needs further consideration

the kantorovich inequality for error analysis of the kalman filter with unknown noise distributions the state space model with random noises is widely used to model dynamic systems in many practical problems the noise terms will have unknown probability distributions which is contrary to the usual assumption of gaussian noises made in state vector estimation this assumption is usually made for reasons of mathematical tractability a problem arises however in that inference based on the incorrect gaussian assumption can lead to misleading or erroneous conclusions this note shows how the kantorovich inequality from probability theory has potential for characterizing the estimation error of a kalman filter in such a non gaussian distribution free setting

an iterative method with error estimators abstract iterative methods for the solution of linear systems of equations produce a sequence of approximate solutions in many applications it is desirable to be able to compute estimates of the norm of the error in the approximate solutions generated and terminate the iterations when the estimates are sufficiently small this paper presents a new iterative method based on the lanczos process for the solution of linear systems of equations with a symmetric matrix the method is designed to allow the computation of estimates of the euclidean norm of the error in the computed approximate solutions these estimates are determined by evaluating certain gauss anti gauss or gauss radau quadrature rules

a generalization of gruss s inequality in inner product spaces and applications a generalization of the classical gruss s integral inequality in inner product spaces is given some applications for positive linear functionals and integrals are also pointed out

accretive operators and cassels inequality abstract let a b 0 and let z m n r such that z lies into the operator ball of diameter ai bi then for all positive definite a m n r tr az a b 2 ab tr az several related reverse inequalities are considered extending some known results

efficient nonparametric estimation of mixture proportions summary by constructing a sequence of multinomial approximations and related maximum likelihood estimators we derive a cramer rao lower bound for nonparametric estimators of the mixture proportions and thereby characterize asymptotically optimal estimators for the case of the sampling model m2 of hosmer 1973 it is shown that the sequence of maximum likelihood estimators which can be obtained explicitly is asymptotically optimal in this sense the results hold true even when the multinomial approximations involve cells chosen adaptively from the data in a wellspecified way

on non parametric and generalized tests for the two sample problem with location and scale change alternatives various tests have been proposed for the two sample problem when the alternative is more general than a simple shift in location non parametric tests o brien s generalized t and rank sum tests and other tests related to the t we show that the generalized tests are directly related to non parametric tests proposed by lepage as a result we obtain a wider more flexible class of o brien type procedures which inherit the level robustness property of non parametric tests we have also computed the tests empirical sizes and powers under several models the non parametric procedures and the related o brien type tests are valid and yield good power in the settings investigated they are preferable to the t test and related procedures whose type i errors differ noticeably from nominal size for skewed and long tailed distributions

some further matrix extensions of the cauchy schwarz and kantorovich inequalities with some statistical applications abstract the well known cauchy schwarz and kantorovich inequalities may be expressed in terms of vectors and a positive definite matrix we consider what happens to these inequalities when the vectors are replaced by matrices the positive definite matrix is allowed to be positive semidefinite singular and the usual inequalities are replaced by lowner partial orderings some examples in the context of linear statistical models are presented

an aerodynamic theory based on time domain aeroacoustics the aerodynamics of propellers and rotors is especially complicated because of the highly three dimensional and compressible nature of the flowfield however when linearized theory is applicable the problem is governed by the wave equation and a numerically efficient integral formulation can be derived this reduces the problem from one in space to one over a surface many such formulations exist in the aeroacoustics literature but these become singular integral equations if one naively tries to use them to predict surface pressures i e for aerodynamics the present paper illustrates how one must interpret these equations in order to obtain nonambiguous results after the regularized form of the integral equation is derived a method for solving it numerically is described numerical results are compared to experimental results for ellipsoids wings and rotors including effects due to lift

inferences for case control and semiparametric two sample density ratio models summary we consider inference in general binary response regression models under retrospective sampling plans prentice pyke 1979 discovered that inference for the odds ratio parameter in a logistic model can be based on a prospective likelihood even though the sampling scheme is retrospective we show that the estimating function obtained from the prospective likelihood is optimal in a class of unbiased estimating functions also we link casecontrol sampling with a two sample biased sampling problem where the ratio of two densities is assumed to take a known parametric form connections between this model and the cox proportional hazards model are pointed out large and small sample size behaviour of the proposed estimators is studied

boundary integral approach to the scattering of nonplanar acoustic waves by rigid bodies the acoustic scattering of an incident wave by a rigid body can be described by a singular fredholm integral equation of the second kind this equation is derived by solving the wave equation using generalized function theory green s function for the wave equation in unbounded space and the acoustic boundary condition for a perfectly rigid body this paper will discuss the derivation of the wave equation its reformulation as a boundary integral equation and the solution of the integral equation by the galerkin method the accuracy of the galerkin method can be assessed by applying the technique outlined in the paper to reproduce the known pressure fields that are due to various point sources from the analysis of these simpler cases the accuracy of the galerkin solution can be inferred for the scattered pressure field caused by the incidence of a dipole field on a rigid sphere the solution by the galerkin technique can then be applied to such problems as a dipole model of a propeller whose pressure field is incident on a rigid cylinder this is the groundwork for modeling the scattering of rotating blade noise by airplane fuselages

using specially designed exponential families for density estimation i this paper have y being portions of the real line or of the plane but the methodology applies just as well to higher dimensionalities and to more complicated spaces estimates of g y are traditionally constructed in two quite different ways by maximum likelihood fitting within some parametric family such as the normal or by nonparametric methods such as kernel density estimation these two methods can be combined by putting an exponential family through a nonparametric estimator the resulting hybrid estimators are the specially designed exponential families of the title figure 1 shows a simple example of this methodology the y are pain i scores for n s 67 women each obtained by averaging the results from a questionnaire administered after an operation the scale runs from y s 0 s w x

case control studies with contaminated controls abstract this paper considers inference about a parametric binary choice model when the data consist of two distinct samples the first is a random sample from the people who made choice 1 say with all relevant covariates completely observed the second is a random sample from the whole population with only the covariates observed this is called a contaminated sampling scheme an example might be where we have a random sample of female labor force participants and their covariate values and a second random sample of working age women with covariates whose participant status is unknown we consider the cases in which the fraction of the population making choice 1 is known and that in which it is not for both cases we give semiparametrically efficient procedures for estimating the choice model parameters

the inefficiency of least squares extensions of the kantorovich inequality abstract four different measures of inefficiency of the simple least squares estimator in the general gauss markoff model are considered previous work on the bounds to some of these measures is briefly reviewed and new bounds are obtained for a particular measure

modifying the t and anova f tests when treatment is expected to increase variability relative to controls summary when similar experimental units are assigned randomly to two groups one to receive a treatment the other to serve as a control the homogeneity of variance assumption underlying the pooled t test is valid under the null hypothesis of no treatment effect thus power and not validity of the pooled t should be the concern in such experiments especially if treatment may affect variability as well as mean response we focus on studies where there is a biological basis e g toxicological studies for expecting a treatment effect on mean response to be accompanied by an increase in variance to detect a change in mean response in such experimental situations we propose a simple modification of the pooled t that is also valid under ho no treatment effect but which can have substantially better power than the pooled t this modification can also be applied to other procedures for testing equality of means when there are two or more treatment groups in addition to the control

error estimates for the solution of linear systems let ax b be a system of linear equations where a is a square and nonsingular matrix when solving it by a direct or an iterative method an approximate solution x is obtained x denotes the current iterate in the case of an iterative method in this paper we propose estimates for the norm of the error e x x these estimates are valid for any nonsingular matrix and for approximations x of x obtained by any method and thus they also implicitly take into account the effect of rounding errors

time domain asymptotics ii application to propeller acoustics the method of time domain asymptotics of double integrals described in paper i this issue is applied to the thickness noise of a simple sector shaped propeller blade with supersonic tip speed and no axial motion the structure of the pressure field is determined by topological changes in the retarded blade shape corresponding to the presence of stationary points of a certain phase function the overall pressure waveform takes the form of a series of short bursts of high pressure fluctuation each burst corresponding to the crossing of a stationary point by the retarded blade shape asymptotic formulae are derived using the asymptotic regime of small chord length the complete near field structure is considered with detailed calculations of the acoustic field near the various transition surfaces in observer space the results are illustrated throughout with waveform graphs and contour plots for a blade with quadratic chord section

welch s approximate solution for the behrens fisher problem the wald likelihood ratio and score statistics have been calculated for the behrens fisher problem these statistics provide asymptotically equivalent and weakly optimal tests the test based on the wald statistic was found to be very similar to the v test discussed by welch 1937 hence the v test was compared with the likelihood ratio and score tests in a power study since the powers were very similar and the v test was more convenient to use from several points of view we recommend this test sizes of the v test as well as a power comparison with the usual pooled t test were also obtained

permutation tests for detecting and estimating mixtures in task performance within groups we propose a two sample permutation test incorporating mixture models as a general tool for detecting and quantifying effects on task performance we illustrate the proposed method with examples where the dependent measures under investigation are recorded for normal controls and relatives of patients with schizophrenia on a delayed response spatial and object working memory task our mixture modelling in relatives allows the component distributions to arise from different continuous parametric families we also investigate the effects of the within family correlation and the prior distribution of the mixing proportion on the test results the power of the test depends on sample sizes the mixing proportion the difference in component means and the ratio of component variances copyright 2002 john wiley sons ltd

choice of test for comparing two groups with particular application to skewed outcomes we consider a clinical trial where a skewed outcome variable is to be compared between two groups while comparison of sample means may lack power we show that power also depends on the nature of the anticipated treatment effect for any given distribution in the control arm there is a family of true distributions in the intervention arm for which the most powerful test is a comparison of arithmetic means similar results hold for a comparison of geometric means and approximately for the wilcoxon rank sum test and a comparison of medians we discuss how these methods could be used in planning the analysis of a clinical trial in which the intervention effect alters the shape of the distribution these ideas are illustrated by a trial in community psychiatry where the primary outcome days in hospital was highly skewed but the intervention was mainly expected to reduce the frequency of values in the tail we show that a comparison of sample means is a reasonable choice in this case despite the skewness

on empirical likelihood for a semiparametric mixture model summary plant and animal studies of quantitative trait loci provide data which arise from mixtures of distributions with known mixing proportions previous approaches to estimation involve modelling the distributions parametrically we propose a semiparametric alternative which assumes that the log ratio of the component densities satisfies a linear model with the baseline density unspecified it is demonstrated that a constrained empirical likelihood has an irregularity under the null hypothesis that the two densities are equal a factorisation of the likelihood suggests a partial empirical likelihood which permits unconstrained estimation of the parameters and which is shown to give consistent and asymptotically normal estimators regardless of the null the asymptotic null distribution of the log partial likelihood ratio is chi squared theoretical calculations show that the procedure may be as efficient as the full empirical likelihood in the regular set up the usefulness of the robust methodology is illustrated with a rat study of breast cancer resistance genes

convergence error and higher order sensitivity estimations differential equation with respect to the design variables the accuracies of the convergence error and higher order sensitivity estimation methods are verified using laplace euler and navier stokes equations the developed methods are used to improve the accuracy of the finite difference sensitivity calculations in iteratively solved problems aboundonthenormvalueofthe finite differencesensitivityerrorinthestatevariablesisminimizedwith respect to the finite difference step size the optimum finite difference step size is formulated as a function of the norm values of both convergenceerror andhigher order sensitivities thesensitivities calculated with the analytical and the finite difference methods are compared the performance of the proposed methods on the convergence of inverse design optimization is evaluated

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

a goodness of fit test for logistic regression models based on case control data summary we test the logistic regression assumption under a case control sampling plan after reparameterisation the assumed logistic regression model is equivalent to a two sample semiparametric model in which the log ratio of two density functions is linear in data by identifying this model with a biased sampling model we propose a kolmogorov smirnovtype statistic to test the validity of the logistic link function moreover we point out that this test statistic can also be used in mixture sampling we present a bootstrap procedure along with some results on simulation and on analysis of two real datasets

convexity conditions of kantorovich function and related semi infinite linear matrix inequalities the kantorovich function x tax x ta 1x where a is a positive definite matrix is not convex in general from a matrix or convex analysis point of view it is interesting to address the question when is this function convex in this paper we prove that the 2 dimensional kantorovich function is convex if and only if the condition number of its matrix is less than or equal to 3 22 thus the convexity of the function with two variables can be completely characterized by the condition number the upper bound 3 22 is turned out to be a necessary condition for the convexity of the kantorovich function in any finite dimensional spaces we also point out that when the condition number of the matrix which can be any dimensional is less than or equal to 5 26 the kantorovich function is convex furthermore we prove that this general sufficient convexity condition can be improved to 2 3 in 3 dimensional space our analysis shows that the convexity of the function is closely related to some modern optimization topics such as the semi infinite linear matrix inequality or robust positive semi definiteness of symmetric matrices in fact our main result for 3 dimensional cases has been proved by finding an explicit solution range to some semi infinite linear matrix inequalities

a note on the operating characteristics of the modified f test brownie boos and hughes oliver 1990 biometrics 46 259 266 suggested a modification to the fixed effects analysis of variance anova f test for use in situations where treatments are likely to affect mean response while simultaneously increasing between subject variability these authors suggest that the modified test 1 is robust against departures from population normality 2 is more powerful than its classical counterpart when the expected alternative form is encountered and 3 will suffer only minor power losses relative to the usual test when alternatives are in the form of simple shifts in location this study shows that the modified test is not generally robust when sampling is from nonnormal distributions and is likely to produce unacceptably high type i error inflations when sampling is from heavy tailed or skewed distributions some power results are also provided for the multisample situation to supplement those of brownie et al who generated results only for the two sample case

empirical likelihood ratio based confidence intervals for mixture proportions we consider the problem of estimating a mixture proportion using data from two different distributions as well as from a mixture of them under the model assumption that the log likelihood ratio of the two densities is linear in the observations we develop an empirical likelihood ratio based statistic for constructing confidence intervals for the mixture proportion under some regularity conditions it is shown that this statistic converges to a chi squared random variable simulation results indicate that the performance of this statistic is satisfactory as a by product we give estimators for the two distribution functions connections with case control studies and discrimination analysis are pointed out

linear rank tests for the nonresponders problem with censored data summary in a two sample setting a two parameter mixture model is postulated for the treated patients where a proportion of the patients improve and the remaining proportion of nonresponders behave like the control patients the response is subject to random censoring censored data versions of linear rank statistics are developed in order to detect improvement due to treatment the tests are compared to standard tests such as the logrank test in terms of asymptotic relative efficiency empirical power and performance on real data

perturbation analysis for the operator equationtx bin banach spaces letx1 x2be two banach spaces over the complex fieldcand lett x1 x2be a bounded linear operator with the generalized inverset lett t tbe a bounded linear operator with t t 1 suppose thatdimkert dimkert orr t kert 0 thenthas the generalized inverset i t t 1t with t t 1 t t this result generalizes theorem 3 9 ofna using this result we give some results of the perturbation analysis for the operator equationtx b

two sample rank tests for detecting changes that occur in a small proportion of the treated population in the course of studying a biological phenomenon thought to be a precursor to chromosome breakage researchers have found that treatments sometimes produce a higher proportion of outliers than do controls our examples pertain to smokers and patients undergoing chemotherapy although the statistical methods developed here would apply to subjects exposed to any other health hazard we formulate the problem in a nonparametric setting locally most powerful rank tests are obtained for mixture alternatives in one instance the approximate scores test has the simple form of counting the number of treatment responses above a combined sample percentile our test statistics are compared to the wilcoxon and normal scores tests using empirical power studies and asymptotic efficiencies

a revisit of the tonal noise of small rotors in this study asymptotic analysis of the frequency domain formulation to compute the tonal noise of the small rotors in the now ubiquitously multi rotor powered drones is conducted simple scaling laws are proposed to evaluate the impacts of the influential parameters such as blade number flow speed rotation speed unsteady motion thrust and observer angle on the tonal noise the rate of noise increment with thrust or rotational speed is determined by orders of blade passing frequency harmonics and the unsteady motion the axial mean flow influence can be approximated by quadratic functions at given thrust the sound decreases rapidly with the radius and blade number as the surface pressure becomes less intensive the higher tonal harmonics are significantly increased if unsteady motions although of small amplitude are existed as indicated by the defined sensitivity function emphasizing that the unsteady motions should be avoided for quiet rotor designs the scaling laws are examined by comparing with the full computations of the rotor noise using the frequency domain method the implementation of which has been validated by comparing with experiments good data collapse is obtained when the proposed scaling laws which highlights the dominant influence of the design parameters are incorporated

fast estimates for the diagonal of the inverse of large scale matrices appearing in applications abstract for large scale problems the explicit computation of the inverse of a given matrix has high computational complexity and therefore a crucial problem is its efficient approximation in this work we present a readily implementable procedure for approximating individual diagonal elements and the entire diagonal of the inverse of large scale diagonalizable matrices in particular based on extrapolation procedures backward stable families of low cost estimates approximating efficiently the theoretical values are proposed several applications involving the precision matrix in statistics the matrix resolvent in network analysis matrices coming from economic problems and from the discretization of physical problems require the diagonal elements of the inverse of the associated matrix for these classes of problems the effectiveness of the derived estimates is validated through several numerical examples implemented in serial and parallel forms openmp on the high performance computing system aris

a method for discovering kantorovich type inequalities and a probabilistic interpretation abstract the kantorovich inequality z az z a 1z 1 n 2 4 1 n can be proved using convexity and elementary geometry this method of proof is generalized so that it can often yield the upper and lower bounds for f z az z bz z cz where a b c are commuting n x n hermitian matrices and z is a unit vector in c n among the examples is the mulholland smith inequality it is also shown that our method finds probability distributions giving f e e e its upper and lower bounds

comparing two samples extensions of the t rank sum and log rank tests abstract i consider the problem of testing that two populations are identical with respect to the distribution of a continuous variable against the alternative that values tend to be larger in one population i observe that the t rank sum and log rank tests are insensitive for a large class of alternatives that may be expected to occur commonly in practice propose a criterion for identifying this problem in a particular data set and propose corresponding extensions of the conventional methods the proposed methods should be useful for both identifying and interpreting group differences

a rational arnoldi approach for ill conditioned linear systems for the solution of full rank ill posed linear systems a new approach based on the arnoldi algorithm is presented working with regularized systems the method theoretically reconstructs the true solution by means of the computation of a suitable function of matrix in this sense the method can be referred to as an iterative refinement process numerical experiments arising from integral equations and interpolation theory are presented finally the method is extended to work in connection with the standard tikhonov regularization with the right hand side contaminated by noise

new inequalities of the kantorovich type for bounded linear operators in hilbert spaces some new inequalities of the kantorovich type are established they hold for larger classes of operators and subsets of complex numbers than considered before in the literature and provide refinements of the classical results in the case when the involved operator satisfies the usual conditions several new reverse inequalities for the numerical radius of a bounded linear operator are obtained as well

a test for partial differential expression even in a single tissue type cancer is often a collection of different diseases each with its own genetic mechanism consequently a gene may be expressed in some but not all of the tissues in a s

a new aerodynamic integral equation based on an acoustic formula in the time domain an aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented based on a time dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed the ffowcs williams hawking formulation the loading terms and a conventional thickness source terms are retained two surface and three line integrals are employed to solve an equation for the loading noise the near field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface a singular integral equation is thereby derived for the unknown surface pressure and is amenable to numerical solutions using galerkin or collocation methods the technique is useful for studying the nonuniform inflow to the propeller

acoustic waveform singularities from supersonic rotating surface sources this paper discusses the analytical characteristics of waveforms produced by rotating surface sources with tip mach number 1 the analysis covers both monopole and quadrupole sources that have the greatest importance for prediction of high speed rotor noise by using idealized source distributions over the rectangular surfaces it is shown that the lighthiu curle analogy with time derivatives taken outside the integrals poses no additional difficulty attributable to numerical error the integrals themselves require careful analysis of critical points in the integrand so that an adaptive integration grid can be developed for each time step a mathematical analysis of the integrands arising from the idealized sources predicts a logarithmic singularity at critical points in the monopole waveform and a single pole singularity at such points in the quadrupole waveform the computation bears out these predictions

some remarks on matrix norms condition numbers and error estimates for linear equations abstract inequalities between some norms of rectangular matrices and the corresponding relationships between condition numbers are established and clearly arranged in two simple diagrams furthermore some well known error estimates for linear equations in the nonsingular case are shown to be valid for all submultiplicative matrix norms the new proofs work without using infinite series

compressible helicoidal surface theory for propeller aerodynamics and noise acceleration potential techniques from three dimensional thin wing theory have been generalized for propeller and prop fan analysis helicoidal reference surfaces take the place of the planar surface in wing theories otherwise the theories are equivalent the acoustic branch of the theory including nonlinear source terms extends and unifies frequency domain noise theories dating back to gutin for aerodynamic applications it is shown that prop fans satisfy well known criteria for use of linearized theory at transonic speeds by virtue of small aspect ratio and small thickness ratio the results are in the form of integral equations for downwash as functions of thickness and steady or unsteady loading distributions for the case of no rotation the kernel functions reduce to well known kernels of wing theory the analysis within the restrictions of linearization treats rigorously any planform and any flight condition including the combination of subsonic roots and supersonic tips typical of prop fans the effects of thickness camber angle of attack sweep offset blade interference and tip relief are all treated without approximation

comparison of two tests useful in situations where treatment is expected to increase variability relative to controls the type i error and power characteristics of the modified t test were compared with those of the generalized t test results suggested that in contrast to the generalized t test the modified t test can be seriously non robust to departures from population normality with such departures often producing anti conservative results neither test held an absolute power advantage over the other when responses were from normal distributions but the modified t test was generally more powerful for these conditions in comparison with the pooled samples t test both tests were usually much more efficient when treatment caused increases both in mean response and between subject variance and suffered only small disadvantages when between subject variance was unchanged by treatment given these results and other considerations recommendations for use of these recently devised tests are given

extension of kirchhoff s formula to radiation from moving surfaces kirchhoff s formula for radiation from a closed surface has been used recently for prediction of the noise of high speed rotors and propellers because the closed surface on which the boundary data are prescribed in these cases is in motion an extension of kirchhoff s formula to this condition is required in this paper such a formula obtained originally by morgans for the interior problem is derived for regions exterior to surfaces moving at speeds below the wave propagation speed by making use of some results of generalized function theory it is shown that the usual kirchhoff formula is a special case of the main result of the paper the general result applieds to a deformable surface however the special form it assumes for a rigid surface in motion is also noted some possible areas of application of the formula to problems of current interest in aeroacoustics are discussed

the e mom approach for approximating matrix functionals abstract the approximation of matrix functionals appears in many applications arising from the fields of mathematics statistics mechanics networks machine learning and physics in this paper we estimate matrix functionals of the form x t f a y where a r p p is a given diagonalizable matrix x y r p k are skinny block vectors with k p columns and f is a smooth function defined on the spectrum of the matrix a we apply a direct approach based on the extrapolation of the moments of the given matrix for estimating this kind of matrix functionals this approach avoids the application of the polarization identity is fairly inexpensive and leads to a stable procedure moreover we develop a detailed backward error analysis for the derived estimates several numerical results illustrating the effectiveness of the direct method are presented and concrete classes of matrices suitable for the extrapolation estimates are proposed

a global newton method ii analytic centers this paper modifies the convergence conditions of a back tracking global newton method announced in goldstein 1991 making them sharper and easier to apply a new version of the kantorovich inequalities is presented that is simple to state and prove an application is made to the centering problem for polytopes based on an idea of ye 1989 an algorithm is given for the feasibility problem of linear inequalities

modifying the t test for assessing the correlation between two spatial processes clifford richardson and hm they require the estimation of an effective sample size that takes into account the spatial structure of both processes clifford et al developed their method on the basis of an approximation of the variance of the sample correlation coefficient and assessed it by monte carlo simulations for lattice and non lattice networks of moderate to large size in the present paper the variance of the sample covariance is computed for a finite number of locations under the multinormality assumption and the mathematical derivation of the definition of effective sample size is given the theoretically expected number of degrees of freedom for the modified t test with renewed modifications is compared with that computed on the basis of equation 2 9 of clifford et al 1989 the largest differences are observed for small numbers of locations and high autocorrelation in particular when the latter is present with opposite sign in the two processes basic references that were missing in clifford et al 1989 are given and inherent ambiguities are discussed

a complementary result of kantorovich type order preserving inequalities by micic pecaric seo abstract we shall discuss operator inequalities which are obtained by elementary lemma lemma 3 1 associated with holder mccarthy and kantorovich inequalities firstly we shall give the following complementary result to micic et al linear algebra appl 360 2003 15 let a and b be two strictly positive operators on a hilbert space h such that m1i a m1i 0 and m2i b m2i 0 where m1 m1 0 m2 m2 0 and a b a if p 1 and q 1 then the following inequality holds q 1 q 1 q q m 2 p m 2 p q m 2 m 2 m 2 m 2 p m 2 m 2 p q 1 a q b p for m 2 p 1 q m 2 p m 2 p m 2 m 2 m 2 p 1 q b if p m 1 m 1 p m 1 m 1 p q 1 m 1 m 1 q 1 m 1 p m 1 p q m 1 m 1 p m 1 m 1 p q b q a p for m 1 p 1 q m 1 p m 1 p m 1 m 1 m 1 p 1 q we remark that a is shown in linear algebra appl 360 2003 15 as an extension of two variable version of our previous one variable one j inequal appl 2 1998 137 secondly we shall show the following extension of two parameters type of an extension of fujii et al sci math 1 1998 307 on the determinant of an operator let t be strictly positive operators on a hilbert space h such that mi t mi 0 then the following inequality holds s h p q x t q t p x x x t p for p 0 and q 0 wheresh p q is defined by s h p q m p q h q h p 1 e log h q h p 1 if q h p 1 log h qh p andthe determinant x t for strictly positive operator t at a unit vector x in hilbert space h is defined by x t exp log t x x as an application of this result we shall give an alternative proof of two variable version of characterization of the chaotic order in linear algebra appl ibid theorem 4 4

tests for genetic linkage and homogeneity this report concerns likelihood ratio tests in a heterogeneous model for linkage where the recombination fraction has a binomial mixture distribution with an unknown proportion of unlinked families we consider families of unequal sizes with known or unknown phase data in both cases the limit distributions of the linkage test statistics are a mixture of a mass at and of a x2 1 distribution in equal proportions and homogeneity test statistics tend to the supremum of gaussian processes the critical values of the homogeneity tests are simulated and the power functions of the linkage and homogeneity tests are compared in a simulation study

estimation of the bilinear form y f a x for hermitian matrices abstract for a hermitian matrix a c p p given vectors x y c p and for suitable functions f the bilinear form y f a x is estimated by extending the extrapolation method proposed by c brezinski in 1999 families of one term and two term estimates e f c and e f n k n k z respectively are derived by extrapolation of the moments of the matrix a for the positive definite case bounds for the optimal value of which leads to an efficient one term estimate in only one matrix vector product are derived for f a a 1 a formula approximating this optimal value of is specified numerical results for several matrix functions and comparisons are provided to demonstrate the effectiveness of the extrapolation method