on a misconception involving point collocation and the rayleigh hypothesis it is shown that the rayleigh hypothesis does not govern convergence of the simple point collocation approach to the numerical solution of scattering by a sinusoidal grating a previously developed numerical technique interval arithmetic is employed to perform some decisive numerical experiments which not only support but guarantee the validity of this conclusion

the helmholtz equation least squares method and rayleigh hypothesis in near field acoustical holography in this paper we present a numerical investigation of reconstructing time harmonic acoustic pressure field in two dimensional space by using a series expansion the so called helmholtz equation least squares hels method series expansion methods or the rayleigh methods have been widely used in predicting the scattered acoustic pressure with regularization they can also be applied to reconstruction of acoustic pressure on the source surface from the measurements taken in the field and hels is the first such attempt for these problems in this paper we establish hels in the framework of the rayleigh methods and reveal its interrelationship with the rayleigh hypothesis in particular to regularize a reconstruction problem we use the method of quasisolutions i e a tikhonov regularization with an a posteriori choice of the regularization parameter it is shown that without regularization hels can still yield a satisfactory reconstruction of acoustic radiation from an arbitrary object when enough me

confidence interval construction for proportion difference in small sample paired studies paired dichotomous data may arise in clinical trials such as pre post test comparison studies and equivalence trials reporting parameter estimates e g odds ratio rate difference and rate ratio along with their associated confidence interval estimates becomes a necessity in many medical journals various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions nevertheless the performance of these asymptotic methods may have poor coverage properties in small samples in this article we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small sample paired data specifically we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test the exact unconditional confidence interval guarantees the coverage probability and it is recommended if strict control of coverage probability is required however the exact method tends to be overly conservative and computationally demanding our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small sample designs and yet they are relatively easy to implement computationally we illustrate the methods using real examples from a pain management study and a cancer study

homogeneous linear predictor models for contingency tables maximum likelihood ml inference for the class of homogeneous linear predictor hlp models for contingency tables is described hlp models constrain the expected table counts m through l m x where the link l is allowed to be a many to one nonlinear function generalized log linear association trend marginal cumulative probit and conditional marginal homogeneity models are given as specific examples ml fit results which include point estimates goodness of fit statistics and asymptotic based approximate distributions are described and compared for equivalent hlp models the results are valid for a wide variety of sampling plans including combinations of product multinomial and poisson sampling an important practical implication of this article is that the implementation of ml fitting and theory is straightforward and an attractive alternative to weighted least squares estimation for hlp models

equivalence test and confidence interval for the difference in proportions for the paired sample design summary this paper considers a model for the di erence of two proportions in a paired or matched design of clinical trials case control studies and also sensitivity comparison studies of two laboratory tests this model includes a parameter indicating both interpatient variability of response probabilities and their correlation under the proposed model we derive a one sided test for equivalence based upon the e cient score equivalence is defined here as not more than 100 per cent inferior mcnemar s test for significance is shown to be a special case of the proposed test further a score based confidence interval for the di erence of two proportions is derived one of the features of these methods is applicability to the 2 2 table with o diagonal zero cells all the mcnemar type tests and confidence intervals published so far cannot apply to such data a monte carlo simulation study shows that the proposed test has empirical significance levels closer to the nominal a level than the other tests recently proposed and further that the proposed confidence interval has better empirical coverage probability than those of the four published methods 1998 john wiley sons ltd

confidence intervals for differnces in correlated binary proportions by w l may and w d johnson statistics in medicine 16 2127 2136 1997

a comparison of methods for the construction of confidence interval for relative risk in stratified matched pair designs a stratified matched pair study is often designed for adjusting a confounding effect or effect of different trails centers groups in modern medical studies the relative risk is one of the most frequently used indices in comparing efficiency of two treatments in clinical trials in this paper we propose seven confidence interval estimators for the common relative risk and three simultaneous confidence interval estimators for the relative risks in stratified matched pair designs the performance of the proposed methods is evaluated with respect to their type i error rates powers coverage probabilities and expected widths our empirical results show that the percentile bootstrap confidence interval and bootstrap resampling based bonferroni simultaneous confidence interval behave satisfactorily for small to large sample sizes in the sense that i their empirical coverage probabilities can be well controlled around the pre specified nominal confidence level with reasonably shorter confidence widths and ii the empirical type i error rates of their associated test statistics are generally closer to the pre specified nominal level with larger powers they are hence recommended two real examples from clinical laboratory studies are used to illustrate the proposed methodologies

profile likelihood inference for highly accurate diagnostic tests nous envisageons une inference sur la vraisemblance de profil basee sur la distribution multinomiale pour evaluer la precision d un test diagnostic la methode s applique a des donnees ordinales quand la precision est evaluee au moyen de l aire sous la courbe caracteristique du receveur courbe roc des resultats de simulation suggerent que les intervalles de confiance derives ont vies probabilites de couverture acceptables meme lorsque les tailles d echantillons sont petites et que le test diagnostic a une haute precision les methodes s etendent a des contextes stratifies et a des situations ou les evaluations sont correlees nous illustrons les methodes sur des donnees provenant d un essai clinique sur la detection du cancer de l ovaire

on tests of equivalence via non unity relative risk for matched pair design matched pair design is often used in clinical trials to increase the efficiency of treatment comparison we consider the problem of equivalence test with a relative risk endpoint in matched pair studies with binary outcomes and develop several score and wald type statistics for testing a hypothesis of non unity relative risk examples from an assessment of hiv screening test and a cross over clinical trial of soft contact lenses are used to illustrate the proposed methods through simulations we compare the empirical performance of these tests with the test proposed by lachenbruch and lynch we show that a score test based on a reparameterized multinomial model by tango performs best in the sense that the test satisfactorily controls the type i error rate and its empirical type i error rates are generally much closer to the prespecified nominal significance level than those of the other tests

a stability analysis of a eulerian solution method for moving boundary problems in electrochemical machining we investigate the front tracking method using marker points for the numerical solution of a class of moving boundary problems which arise in connection with certain two dimensional electrochemical machining problems the numerical method is expressed as a system of n nonlinear autonomous ordinary differential equations odes for describing the movement of n marker points on the moving boundary the system has been analysed in some cases with respect to the local stability of equilibrium solutions and to the global stability of nonequilibrium solutions the linearised local stability of the equilibrium solution is investigated in terms of the jacobi matrix for the system of odes closed form expressions for the eigenvalues and the eigenvectors of the jacobi matrix have been derived part of the method comprises the solution of a dirichlet boundary value problem this is carried out using various boundary collocation methods which are investigated the mathematical numerical model has features which are in accordance with those of the physical problem this has also been demonstrated by actual computation of some examples

multiple imputation for the comparison of two screening tests in two phase alzheimer studies two phase designs are common in epidemiological studies of dementia and especially in alzheimer research in the first phase all subjects are screened using a common screening test s while in the second phase only a subset of these subjects is tested using a more definitive verification assessment i e golden standard test when comparing the accuracy of two screening tests in a two phase study of dementia inferences are commonly made using only the verified sample it is well documented that in that case there is a risk for bias called verification bias when the two screening tests have only two values e g positive and negative and we are trying to estimate the differences in sensitivities and specificities of the tests one is actually estimating a confidence interval for differences of binomial proportions estimating this difference is not trivial even with complete data it is well documented that it is a tricky task in this paper we suggest ways to apply imputation procedures in order to correct the verification bias this procedure allows us to use well established complete data methods to deal with the difficulty of the estimation of the difference of two binomial proportions in addition to dealing with incomplete data we compare different methods of estimation and evaluate the use of multiple imputation in this case our simulation results show that the use of multiple imputation is superior to other commonly used methods we demonstrate our finding using alzheimer data

improved confidence intervals for the difference between binomial proportions based on paired data existing methods for setting confidence intervals for the difference theta between binomial proportions based on paired data perform inadequately the asymptotic method can produce limits outside the range of validity the exact conditional method can yield an interval which is effectively only one sided both these methods also have poor coverage properties better methods are described based on the profile likelihood obtained by conditionally maximizing the proportion of discordant pairs a refinement methods 5 and 6 which aligns 1 alpha with an aggregate of tail areas produces appropriate coverage properties a computationally simpler method based on the score interval for the single proportion also performs well method 10

how many variables should be entered in a regression equation abstract the optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points as the number of regressors grows large the sp criterion provides an asymptotically optimal rule for the number of variables to enter

comments on on a misconception involving point collocation and the rayleigh hypothesis with reply for original paper by christiansen and kleinman see ieee trans antennas propag vol 44 p 1309 16 1996 oct in the study of diffraction and scattering manenkov suggests that christiansen and kleinman have incorrectly interpreted some of the results which they refer to in their references he discusses various instances a reply is then given by christiansen and kleinman

regularized gaussian discriminant analysis through eigenvalue decomposition abstract friedman proposed a regularization technique rda of discriminant analysis in the gaussian framework rda uses two regularization parameters to design an intermediate classifier between the linear the quadratic the nearest means classifiers in this article we propose an alternative approach called edda that is based on the reparameterization of the covariance matrix k of a group gk in terms of its eigenvalue decomposition k k d k a k d k where k specifies the volume of density contours of gk the diagonal matrix of eigenvalues specifies its shape the eigenvectors specify its orientation variations on constraints concerning volumes shapes orientations k a k and d k lead to 14 discrimination models of interest for each model we derived the normal theory maximum likelihood parameter estimates our approach consists of selecting a model by minimizing the sample based estimate of future misclassification risk by cross validation numerical experiments on simulated and rea

correlation and high dimensional consistency in pattern recognition abstract classical discriminant analysis breaks down when the feature vectors are of extremely high dimension for example when the basic observation is a random function observed over a fine grid alternative methods have been developed assuming a simplified form for the covariance structure we analyze the high dimensional asymptotics of some of these methods emphasizing the effects of correlations such as occur when the baseline is random for instance the euclidean distance classifier which has been proposed for generic use in high dimensional classification problems is dimensionally inconsistent under a simple repeated measurement model we provide exponential bounds for the error rates of several classifiers we develop new dimensionally consistent methods to deal with the effects of correlation in high dimensional problems

multinomial poisson homogeneous models for contingency tables a unified approach to maximum likelihood inference for a broad new class of contingency table models is presented the model class comprises multinomial poisson homogeneous mph models which can be characterized by an independent sampling plan and a system of homogeneous constraints h m 0 where m is the vector of expected table counts maximum likelihood ml fitting and large sample inference for mph models are described the mph models are partitioned into well defined equivalence classes and explicit comparisons of the large sample behaviors of ml estimators of equivalent models are given the equivalence theory not only unifies a large collection of previously known results it also leads to useful generalizations and many new results the practical computational implication is that ml fit results for any particular mph model can be obtained directly from the ml fit results for any conveniently chosen equivalent model issues of hypothesis testability and parameter estimability are also addressed to illustrate an example based on statistics journal citation patterns is given for which the data can be used to test the hypothesis that a certain model holds but they cannot be used to estimate any of that model s parameters

confidence intervals for differences in correlated binary proportions an experiment to assess the efficacy of a particular treatment or process often produces dichotomous responses either favourable or unfavourable when we administer the treatment on two occasions to the same subjects we often use mcnemar s test to investigate the hypothesis of no difference in the proportions on the two occasions that is the hypothesis of marginal homogeneity a disadvantage in using mcnemar s statistic is that we estimate the variance of the sample difference under the restriction that the marginal proportions are equal a competitor to mcnemar s statistic is a wald statistic that uses an unrestricted estimator of the variance because the wald statistic tends to reject too often in small samples we investigate an adjusted form that is useful for constructing confidence intervals quesenberry and hurst and goodman discussed methods of construction that we adapt for constructing confidence intervals for the differences in correlated proportions we empirically compare the coverage probabilities and average interval lengths for the competing methods through simulation and give recommendations based on the simulation results

confidence intervals for the mean of a variable taking the values 0 1 and 2 the problem of setting a confidence interval for the mean of a variable on 0 1 2 arises in three contexts paired organ procedure rates estimation of gene frequency and three point likert scales an effective approach to its estimation may be based on a good interval for a paired difference of proportions four good methods due to newcombe and tango are shown to have much better performance than more naive methods over regions of the parameter space corresponding to the above applications

the effective condition number applied to error analysis of certain boundary collocation methods abstract the boundary collocation method bcm is widely used in the engineering community for the numerical solution of linear boundary value problems it is commonly stated that the results computed by this method are affected by large rounding errors this conclusion is based on a simple worst case analysis using the conventional condition number for linear systems in this paper we present a refined error analysis for a class of boundary value problems using the concept of effectively well conditioned systems this analysis leads to much smaller a priori bounds for the rounding error in the computed bcm solution these smaller bounds imply that the numerically computed solution expresses much more accurately than previously supposed properties of the ideal bcm solution computed with infinite precision therefore the intrinsic properties of the bcm can be investigated through numerical computations to a far larger extent than previously supposed thus allowing for a numerical diagnostic investigation of the bcm for example when the bcm is applied to problems with certain geometries it is observed that the approximation does not converge using our new smaller error bounds we conclude that the lack of convergence of the bcm solution for these geometries is due to the bcm itself and not to rounding errors

a family of confidence intervals for the ratio of two binomial proportions the power divergence family of statistics introduced by cressie and read 1984 journal of the royal statistical society series b 46 440 464 is used to obtain approximate confidence intervals for the ratio of two proportions intervals based on inverting the pearson likelihood ratio and freeman tukey statistics are included in this family small sample comparisons of the intervals are presented

weighted distance weighted discrimination and its asymptotic properties while distance weighted discrimination dwd is an appealing approach to classification in high dimensions it was designed for balanced datasets in the case of unequal costs biased sampling or unbalanced data there are major improvements available using appropriately weighted versions of dwd wdwd a major contribution of this paper is the development of optimal weighting schemes for various nonstandard classification problems in addition we discuss several alternative criteria and propose an adaptive weighting scheme awdwd and demonstrate its advantages over nonadaptive weighting schemes under some situations the second major contribution is a theoretical study of weighted dwd both high dimensional low sample size asymptotics and fisher consistency of dwd are studied the performance of weighted dwd is evaluated using simulated examples and two real data examples the theoretical results are also confirmed by simulations

the validity and power of tests for equality of two correlated proportions with measurements taken on subjects over time on matched pairs of subjects or on clusters of subjects the data often contain pairs of correlated dichotomous responses mcnemar s test is perhaps the best known test to compare two correlated binomial proportions the salient feature of mcnemar s test is that we compute the variance of the contrast estimator under the restriction that the null hypothesis is true wald s test on the other hand does not require that restriction as a consequence wald s statistic is always greater in magnitude than mcnemar s statistic when the marginal proportions are unequal but there is a problem with the validity of both mcnemar s test and wald s test with small to moderate samples there have been various modifications suggested for mcnemar s test to improve its performance we propose a modified wald s test that is valid in small to moderate samples and maintains good power we also evaluate the performance of mcnemar s test and wald s test with and without modifications to enhance validity as well as the performance of the large sample likelihood ratio test and an exact test of the equality of correlated binomial proportions in a smaller study we compare the behaviour of a test based on the james stein estimator of the common odds ratio proposed by liang and zeger to mcnemar s test and wald s test

interval estimation of the difference in proportions under m to one matching when the number of potential controls is large relative to the number of available cases or when little effort needs to be expended in collecting the relevant information on the controls we often apply multiple matching to attain the validity or increase the efficiency of our inference in epidemiological studies in this paper we focus interval estimation on the difference in proportions for m to one matching we consider four asymptotic interval estimators including the estimator directly using the mantel haenszel mh point estimator the estimator using the tanh 1 x transformation the estimator derived from the cochran mantel haenszel cmh test statistic and the estimator derived from the quadratic inequality developed in this paper to evaluate and compare the performance of these estimators we employ monte carlo simulation we find that the estimator directly using the mh estimator can have the coverage probability less than the desired confidence level when the number of matched sets is small we note that the estimator derived from the quadratic inequality can perform well when the underlying difference is close to 0 even for a small number of matched sets however this estimator tends to have the coverage probability less than the desired confidence level as well when the underlying difference in proportions is large by contrast the estimator using the cmh statistic tends to have the coverage probability larger than the desired confidence level when the underlying difference is small we also find that the estimator using the tanh 1 x transformation consistently outperforms the interval estimator directly using the mh estimator we use the data regarding the association between induced abortions and ectopic pregnancy to illustrate the use of these estimators copyright 2005 john wiley sons ltd

on small sample confidence intervals for parameters in discrete distributions summary the traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level in constructing such intervals for parameters in discrete distributions less conservative behavior results from inverting a single two sided test than inverting two separate one sided tests of half the nominal level each we illustrate for a variety of discrete problems including interval estimation of a binomial parameter the difference and the ratio of two binomial parameters for independent samples and the odds ratio

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

on the convergence of a perturbation series solution for reflection from periodic rough surfaces in 1977 rosich and wait see radio science vol 12 no 5 p 719 29 sept oct 1977 presented a general expression for a perturbation series solution to electromagnetic em reflection from an imperfectly conducting periodic rough surface this is the first known publication of such a general result although this expression was shown to be consistent with earlier published results all questions concerning the convergence of the series were deferred this paper takes a first step in addressing this oversight

comparative analysis of two rates in this paper we examine comparative analysis of rates with a view to each of the usual comparative parameters rate difference rd rate ratio rr and odds ratio or and with particular reference to first principles for rd and rr we show the prevailing statistical practices to be rather poor we stress the need for restricted estimation of variance in the chi square function underlying interval estimation and also point estimation and hypothesis testing for rr analysis we propose a chi square formulation analogous to that for rd and thus one which obviates the present practice of log transformation and its associated use of taylor series approximation of the variance as for or analysis we emphasize that the chi square function introduced by cornfield for unstratified data and extended by gart to the case of stratified analysis is based on the efficient score and thus embodies its optimality properties we provide simulation results to evince the better performance of the proposed parameter constrained procedures over the traditional ones

standard errors and confidence intervals of norm statistics for educational and psychological tests norm statistics allow for the interpretation of scores on psychological and educational tests by relating the test score of an individual test taker to the test scores of individuals belonging to the same gender age or education groups et cetera given the uncertainty due to sampling error one would expect researchers to report standard errors for norm statistics in practice standard errors are seldom reported they are either unavailable or derived under strong distributional assumptions that may not be realistic for test scores we derived standard errors for four norm statistics standard deviation percentile ranks stanine boundaries and z scores under the mild assumption that the test scores are multinomially distributed a simulation study showed that the standard errors were unbiased and that corresponding wald based confidence intervals had good coverage finally we discuss the possibilities for applying the standard errors in practical test use in education and psychology the procedure is provided via the r function check norms which is available in the mokken package

interval estimation for the difference between independent proportions comparison of eleven methods several existing unconditional methods for setting confidence intervals for the difference between binomial proportions are evaluated computationally simpler methods are prone to a variety of aberrations and poor coverage properties the closely interrelated methods of mee and miettinen and nurminen perform well but require a computer program two new approaches which also avoid aberrations are developed and evaluated a tail area profile likelihood based method produces the best coverage properties but is difficult to calculate for large denominators a method combining wilson score intervals for the two proportions to be compared also performs well and is readily implemented irrespective of sample size

simultaneously modeling joint and marginal distributions of multivariate categorical responses abstract we discuss model fitting methods for analyzing simultaneously the joint and marginal distributions of multivariate categorical responses the models are members of a broad class of generalized logit and loglinear models we fit them by improving a maximum likelihood algorithm that uses lagrange s method of undetermined multipliers and a newton raphson iterative scheme we also discuss goodness of fit tests and adjusted residuals and give asymptotic distributions of model parameter estimators for this class of models inferences are equivalent for poisson and multinomial sampling assumptions simultaneous models for joint and marginal distributions may be useful in a variety of applications including studies dealing with longitudinal data multiple indicators in opinion research cross over designs social mobility and inter rater agreement the models are illustrated for one such application using data from a recent general social survey regarding opinions about various types of government s

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

score and profile likelihood confidence intervals for contingency table parameters a straightforward approach to computing score and profile likelihood confidence intervals for contingency table parameters is described the computational approach herein avoids two main limitations of existing methods 1 compared with existing methods this paper s approach is applicable to a much broader class of parameters 2 unlike existing methods this paper s approach is not case specific and hence lends itself to a general yet very simple computational algorithm this paper describes the sliding quadratic computational algorithm and illustrates its use on examples that have not been previously considered in the literature a small scale simulation study highlights the advantage of using score and profile likelihood intervals rather than wald intervals

approximate interval estimation of the ratio of binomial parameters a review and corrections for skewness various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically it is found that the method based on likelihood scores koopman 1984 biometrics 40 513 517 miettinen and nurminen 1985 statistics in medicine 4 213 226 performs best in achieving the nominal confidence coefficient but it may distribute the tail probabilities quite disparately using general theory of bartlett 1953 biometrika 40 306 317 1955 biometrika 42 201 203 we correct this method for asymptotic skewness following gart 1985 biometrika 72 673 677 we extend this correction to the case of estimating the common ratio in a series of two by two tables computing algorithms are given and applied to numerical examples parallel methods for the odds ratio and the ratio of poisson parameters are noted

the convergence of point matching techniques the influence of node distribution on the convergence of the point matching technique is examined through example solutions of several diffraction problems the adaptive collocation of nodes is proposed for two dimensional diffraction and scattering problems for the regions with smooth boundaries this technique provides rapid convergence of the computational process the relation between the adaptive nodes distribution and the zeros of the szego polynomials is derived

planar diffraction analysis of homogeneous and longitudinally inhomogeneous gratings based on legendre expansion of electromagnetic fields planar grating diffraction analysis based on legendre expansion of electromagnetic fields is reported in contrast to conventional rcwa in which the solution is obtained using state variables representation of the coupled wave amplitudes here the solution is expanded in terms of legendre polynomials this approach without facing the problem of numerical instability and inevitable round off errors yields well behaved algebraic equations for deriving diffraction efficiencies and can be employed for analysis of different types of gratings thanks to the recursive properties of legendre polynomials for longitudinally inhomogeneous gratings wherein differential equations with non constant coefficients are encountered it can also be used to analyze the whole structure at one stroke although this is the only case for which the presented approach is efficient from both aspects of stability and computation load the presented approach is applied to different test cases and justified by comparison of the results to those obtained using previously reported methods the method is general and can handle many different cases like thick gratings non bragg incidence and cases in which higher diffracted orders or evanescent orders corresponding to real eigenvalues have to be included in the solution of the maxwell s equations in deriving the formulation a rigorous approach is followed

confidence intervals from the difference between two correlated proportions abstract when data arise as matched binary pairs it is often of interest to test whether or not the probabilities of an odd pair of each type are equal construction of a small sample confidence interval for the difference in these probabilities is more difficult and either approximate or conservative methods need be resorted to two methods are suggested in this article one a natural asymptotic method and the other a more generally applicable conservative method the coverage probability and average width are studied for small and moderate sample sizes

simple improved confidence intervals for comparing matched proportions for binary matched pairs data this article discusses interval estimation of the difference of probabilities and an odds ratio for comparing success probabilities we present simple improvements of the commonly used wald confidence intervals for these parameters the improvement of the interval for the difference of probabilities is to add two observations to each sample before applying it the improvement for estimating an odds ratio transforms a confidence interval for a single proportion

pseudo score confidence intervals for parameters in discrete statistical models we propose pseudo score confidence intervals for parameters in models for discrete data the confidence interval is obtained by inverting a test that uses a pearson chi squared statistic to compare fitted values for the working model with fitted values of the model when a parameter of interest takes various fixed values for multinomial models the pseudo score method simplifies to the score method when the model is saturated and otherwise it is asymptotically equivalent to score and likelihood ratio test based inferences for cases in which ordinary score methods are impractical such as when the likelihood function is not an explicit function of model parameters the pseudo score method is feasible we illustrate the method for four such examples generalizations of the method are also presented for future research including inference for complex sampling designs using a quasilikelihood pearson statistic that compares fitted values for two models relative to the variance of the observations under the simpler model

confidence intervals of the difference between areas under two roc curves in matched pair experiments in a matched pair study when outcomes of two diagnostic tests are ordinal continuous the difference between two correlated areas under roc curves aucs is usually used to compare the overall discriminatory ability of two diagnostic tests this article considers confidence interval ci construction problems of difference between two correlated aucs in a matched pair experiment and proposes 13 hybrid cis based on variance estimates recovery with the maximum likelihood estimation delong s statistic wilson score statistic ws and ws with continuity correction the modified wald statistic mw and mw with continuity correction and agresti coull statistic and three bootstrap resampling based cis for comparison we present traditional parametric and nonparametric cis simulation studies are conducted to assess the performance of the proposed cis in terms of empirical coverage probabilities empirical interval widths and ratios of the mesial noncoverage probabilities to the noncoverage probabilities two examples from clinical studies are illustrated by the proposed methodologies empirical results evidence that the hybrid agresti coull ci with the empirical estimation eac behaved most satisfactorily because its coverage probability was quite close to the prespecified confidence level with short interval width hence we recommend the usage of the eac ci in applications

two sided confidence intervals for the single proportion comparison of seven methods simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals criteria appropriate to the evaluation of various proposed methods include closeness of the achieved coverage probability to its nominal value whether intervals are located too close to or too distant from the middle of the scale expected interval width avoidance of aberrations such as limits outside 0 1 or zero width intervals and ease of use whether by tables software or formulae seven methods for the single proportion are evaluated on 96 000 parameter space points intervals based on tail areas and the simpler score methods are recommended for use in each case methods are available that aim to align either the minimum or the mean coverage with the nominal 1 alpha