moment based criteria for determining bioequivalence summary in comparative bioavailability trials the focus in the determination of bioequivalence has been to show that the average bioavailability on a test formulation is similar to the average bioavailability on a reference formulation it has been argued that this is not adequate to insure interchangeability of formulations we introduce a moment based criterion which ensures interchangeability for at least a certain proportion of the population an algorithm is given for determining the constant in the criterion an example is used to illustrate how the criterion may be applied

inferences on the common coefficient of variation the coefficient of variation is often used as a measure of precision and reproducibility of data in medical and biological science this paper considers the problem of making inference about the common population coefficient of variation when it is a priori suspected that several independent samples are from populations with a common coefficient of variation the procedures for confidence interval estimation and hypothesis testing are developed based on the concepts of generalized variables the coverage properties of the proposed confidence intervals and type i errors of the proposed tests are evaluated by simulation the proposed methods are illustrated by a real life example

jordan all derivable points in the algebra of all upper triangular matrices abstract let tm n be the algebra of all n n upper triangular matrices we say that l tm n is a jordan derivable mapping at g if st ts s t s t t s t s for any s t tm n with st g an element g tm n is called a jordan all derivable point of tm n if every jordan derivable linear mapping at g is a derivation in this paper we show that every element in tm n is a jordan all derivable point

a robust double exponential formula for fourier type integrals abstract a double exponential transformation is presented to obtain a quadrature formula for fourier type integrals 0 f x sin x d x or 0 f x cos x d x where f x is a slowly decaying analytic function on 0 it is an improved version of what we previously proposed in 1991 the transformation x t is such that it maps the interval 0 onto and that while the integrand after the transformation decreases double exponentially at large negative t the points of the formula approaches to zeros of sin x or cos x double exponentially at large positive t then the trapezoidal formula with an equal mesh size is applied to the integral over after the transformation which gives an efficient quadrature formula for the fourier type integrals the present transformation is improved in the sense that it can integrate a function f z with singularities in the finite z plane more efficiently than the one previously proposed

error control of a numerical formula for the fourier transform by ooura s continuous euler transform and fractional fft in this paper we consider a method for fast numerical computation of the fourier transform of a slowly decaying function with given accuracy in a given range of the frequency recently some useful formulas for the fourier transform have been proposed to resolve the difficulty of the computation caused by the slow decay and the oscillation of the integrand in particular ooura proposed formulas with continuous euler transformation and showed their effectiveness it has however also been reported that their errors become large outside some ranges of the frequency then for an illustrative representative of the formulas in order to compute the fourier transform with given accuracy in a given frequency range we choose the parameters in the formula based on its error analysis furthermore by combining the formula and fractional fft a generalization of the fast fourier transform fft we execute the computation in the same order of computation time as that of the fft

anova under unequal error variances by taking a generalized approach to findingp values the classical f test of the one way anova is extended to the case of unequal error variances the relationship of this result to other solutions in the literature is discussed an exact test for comparing variances of a number of populations is also developed scheff6 s procedure of multiple comparison is extended to the case of unequal variances the possibility and the approach that one can take to extend the results to simple designs involving more than one factor are briefly discussed

inferences on the within subject coefficient of variation the within subject coefficient of variation wcv is widely used as a measure of precision and reproducibility of data in medical and biological science in this paper generalized confidence intervals and tests for a single wcv is developed using the concept of generalized pivots under the assumption of one way random effect model this approach is further extended to two sample cases the resulting procedures are easy to compute and have good properties in term of coverage probabilities and type i error control at small sample sizes the proposed methods are illustrated by a real life example

receiver operating characteristic analysis under tree orderings of disease classes receiver operating characteristic roc curve and its summary statistics e g the area under curve auc are commonly used to evaluate the diagnostic accuracy for disease processes with binary classification the roc curve has been extended to roc surface for scenarios with three ordinal classes or to hyper surface for scenarios with more than three classes for classifier under tree or umbrella ordering in which the marker measurement for one class is lower or higher than those for the other classes the commonly adopted diagnostic measures are the naive auc nauc based on a pooled class of all the unordered classes and the umbrella volume uv based on the concept of volume under surface however both nauc and uv have some limitations for example nauc depends on the sampling weights for all the classes in population and uv has only been introduced for three class settings in this article we initiate the idea of a new roc framework for tree or umbrella ordering denoted as troc and propose the area under troc curve denoted as tauc as an appropriate diagnostic measure the proposed troc and tauc share many nice features with the traditional roc and auc both parametric and nonparametric approaches are explored to construct the confidence interval estimation of tauc the performances of these methods are compared in simulation studies under a variety settings at the end the proposed methods are applied to a published microarray data set

a generalization of the continuous euler transformation and its application to numerical quadrature the continuous euler transformation which was proposed by the present author to accelerate the convergence of integrals of fourier type is an analogue of the well known euler transformation for series in this paper we propose new continuous transformations including a generalization of the continuous euler transformation we show that the generalized continuous euler transformation is applicable to not only a fourier type integral but also an oscillatory integral with an algebraically decaying integrand we also show some numerical examples using the generalized continuous euler transformation

the double exponential formula for oscillatory functions over the half infinite interval abstract the double exponential formula is known to be very powerful for evaluation of various kinds of integrals in particular integrals with end point singularities or integrals over the half infinite interval it is also known that a weak point of this formula is the inefficiency when applied to a slowly decaying oscillatory integral over the half infinite interval such as i 0 f1 x sin x dx f1 x is an algebraic function in this paper we propose a new type of the double exponential formula which is quite efficient for evaluation of the integral mentioned above it is based on such a transformation that makes the points of the formula after the transformation approach to the zeros of sin x double exponentially for large x

an exact test for testing the equality of parameter matrices in two multivariate linear models abstract a method of testing the hypothesis of the kind h 0 c 1 m c 2 m in two independent multivariate linear models is presented using the concept of generalized p values introduced by tsui and weerahandi k w tsui s weerahandi generalized p values in significance testing of hypothesis in the presence of nuisance parameters j amer statist assoc 84 1989 602 607 under the assumption of error matrix variate normality and heteroscedasticity this method calculates the exact p value in the generalized sense nel d g nel tests for equality of parameter matrices in two multivariate linear models j multivariate anal 61 1997 29 37 provided an approximate degrees of freedom test to test this hypothesis

tests for individual and population bioequivalence based on generalized p values the u s food and drug administration fda has proposed new regulations that address the prescribability and switchability of new formulations of already approved drugs these new criteria are known respectively as population and individual bioequivalence two methods have been proposed in the bioequivalence literature for assessing population and individual bioequivalence that calculate an upper 95 per cent confidence bound for the bioequivalence criterion in question and then test bio equivalence by comparing this bound to the limit established by the fda in this paper we propose applying the generalized test function gtf methodology of tsui and weerahandi journal of the american statistical association 1989 602 607 to this problem to produce tests based on a generalized p value gpv this methodology allows us to construct hypothesis tests in the presence of nuisance parameters using simulation we show that these tests perform well in comparison to the confidence interval methods and have superior power for assessing population bioequivalence copyright 2003 john wiley sons ltd

characterization of generalized jordan left derivations on real nest algebras abstract let a be a real nest algebra of b h where h is a real and separable hilbert space we show that the following conditions are equivalent for a weak topology continuous linear map a b h 1 is a left preserving kernel into range mapping i e t ker t ran t for any t a 2 is a generalized left inner derivations i e t t a bt for some a b b h 3 is a generalized jordan left derivations i e t 2 t t t t t i t for any t a 4 is a left 1 preserving kernel into range mapping i e t ker t ran t for any rank one operator t a

spherical bessel transform via exponential sum approximation of spherical bessel function abstract a new algorithm for numerical evaluation of spherical bessel transform is proposed in this paper in this method the spherical bessel function is approximately represented as an exponential sum with complex parameters this is obtained by expressing an integral representation of spherical bessel function in complex plane and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double exponential transformation the number of terms in the expression is reduced using the modified balanced truncation method the residual part of integrand is also expanded by exponential functions using prony like method the spherical bessel transform can be evaluated analytically on arbitrary points in half open interval

generalized p values and confidence intervals for variance components applications to army test and evaluation various mixed models that are relevant for analyzing army test data are described along with several hypothesis testing and interval estimation problems the problems come up in the context of inv

fiducial generalized confidence intervals generalized pivotal quantities gpqs and generalized confidence intervals gcis have proven to be useful tools for making inferences in many practical problems although gcis are not guaranteed to have exact frequentist coverage a number of published and unpublished simulation studies suggest that the coverage probabilities of such intervals are sufficiently close to their nominal value so as to be useful in practice in this article we single out a subclass of generalized pivotal quantities which we call fiducial generalized pivotal quantities fgpqs and show that under some mild conditions gcis constructed using fgpqs have correct frequentist coverage at least asymptotically we describe three general approaches for constructing fgpqs a recipe based on invertible pivotal relationships and two extensions of it and demonstrate their usefulness by deriving some previously unknown gpqs and gcis it is fair to say that nearly every published gci can be obtained using one of these recipes as an inte

local derivations on operator algebras abstract when attempting to find sufficient conditions for a linear mapping to be a derivation an obvious candidate is the concept of a local derivation local derivations on operator algebras have been investigated in recent papers of kadison j algebra130 1990 494 509 and larson and sourour proc symp pure math 51 1990 187 194 a local derivation is a norm continuous linear map from an operator algebra a into an a bimodule m which agrees with some derivation at each point in the algebra we show that if a is the direct limit of finite dimensional csl algebras via extendable embeddings e g a triangular af algebra then a local derivation on a must be a derivation further we show that for many finite dimensional operator algebras any inner local derivation must be an inner derivation

posterior predictive p values extending work of rubin this paper explores a bayesian counterpart of the classical p value namely a tail area probability of a test statistic under a null hypothesis the bayesian formulation using posterior predictive replications of the data allows a test statistic to depend on both data and unknown nuisance parameters and thus permits a direct measure of the discrepancy between sample and population quantities the tail area probability for a test statistic is then found under the joint posterior distribution of replicate data and the nuisance parameters both conditional on the null hypothesis this posterior predictive p value can also be viewed as the posterior mean of a classical p value averaging over the posterior distribution of nuisance parameters under the null hypothesis and thus it provides one general method for dealing with nuisance parameters two classical examples including the behrens fisher problem are used to illustrate the posterior predictive p value and some of its interesting properties which also reveal a new bayesian interpretation for some classical p values an application to multiple imputation inference is also presented a frequency evaluation shows that in general if the replication is defined by new nuisance parameters and new data then the type i frequentist error of an level posterior predictive test is often close to but less than and will never exceed 2

confidence intervals for steady state availability of a system with exponential operating time and lognormal repair time long run availability of a system assuming lognormal repair times and exponential failure times is considered with many repairable systems the time to repair is well characterized by a lognormal distribution however due to the difficulties associated with the lognormal distribution repair times are often modeled using the lognormal distribution assuming that the variance of the lognormal distribution is known or by using some other distribution such as the exponential distribution instead of the lognormal distribution in this paper using the generalized p value approach we propose confidence intervals and exact tests for steady state availability of systems using the two parameter lognormal distribution for repair time and exponential distribution for operating time here both parameters of the lognormal distribution are assumed to be unknown a couple of examples are given to illustrate the proposed procedures a simulation study is given to demonstrate the performance of the proposed procedure results are extended for the long run availability of a system consisting of several independent parallel sub systems

assessment of individual and population bioequivalence using the probability that bioavailabilities are similar in this paper a new method for the assessment of both individual and population bioequivalence is proposed that is derived from the approach of schall and luus 1993 statistics in medicine 12 1109 1124 the method considers the probability that the bioavailability of the test product is close to the bioavailability of the reference product against the probability that the bioavailability of the reference product is close to itself when administered on different occasions the method can accommodate unequal variances of the bioavailabilities of the test and reference formulations as well as formulation by subject interaction it is thus as general and comprehensive as the methods proposed by sheiner 1992 statistics in medicine 11 1777 1778 and schall and luus 1993 but the resulting bioequivalence criteria are simple and easy to interpret

a continuous euler transformation and its application to the fourier transform of a slowly decaying fuction the euler transformation is a linear sequence transformation to accelerate the convergence of an alternating series the sequence of weights of the transformation is extended to a continuous weight function which can accelerate fourier type integrals including hankel transforms with a slowly convergent integrand we show that the continuous weight function can also be used to compute the fourier transform of a slowly decaying function using fft

comments on chiang 2001 we read with great interest the article by andy k l chiang 2001 the author has written a very clear article explaining the idea of surrogate variables for computing confidence intervals for any function of the variance components in a mixedor random effects model with balanced data however we would like to point out that the idea is not new and has already been introduced under the name generalized confidence interval by weerahandi 1993 in fact hamada and weerahandi 2000 have actually applied the generalized confidence interval idea to gauge rr the idea was also given in the book by weerahandi 1995 p 255 for the one way random model using the notations for the two way random model given in professor chiang s article suppose that we want a confidence interval for 72 a0 a2b oa note that

testing reliability in a stress strength model when x and y are normally distributed we consider the stress strength problem in which a unit of strength x is subjected to environmental stress y an important problem in stress strength reliability concerns testing hypotheses about the reliability parameter r p x yl in this article we consider situations in which x and y are independent and have normal distributions or can be transformed to normality we do not require the two population variances to be equal our approach leads to test statistics which are exact p values that are represented as one dimensional integrals on the basis of the p value one can also construct approximate confidence intervals for the parameter of interest we also present an extension of the testing procedure to the case in which both strength and stress depend on covariates for comparative purposes the bayesian solution to the problem is also presented we use data from a rocket motor experiment to illustrate the procedure

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

bayesian and non bayesian solutions to analysis of covariance models under heteroscedasticity a single factor fixed effect analysis of covariance model with one or more covariates is considered without the assumption of equal error variance using the generalized definition of p values exact tests are derived for testing the equality of treatment effect and testing whether the effect of the covariate is significant in a bayesian setup it is shown that these generalized p values can be produced by the posterior predictive p value approach by using an appropriate noninformative prior examples and simulation studies are given to illustrate the proposed procedures and their advantages over the classical f tests

exact inference for growth curves with intraclass correlation structure summary we consider repeated observations taken over time for each of several subjects for example one might consider the growth curve of a cohort of babies over time we assume a simple linear growth curve model exact results based on sufficient statistics exact tests of the null hypothesis that a coefficient is zero or exact confidence intervals for coefficients are not available to make inference on regression coefficients when an intraclass correlation structure is assumed this paper will demonstrate that such exact inference is possible using generalized inference

generalized p values and the multivariate behrens fisher problem abstract tsui and weerahandi 1989 defined generalized p values for testing statistical hypothesis in the presence of nuisance parameters and applied to obtain an exact solution to the univariate behrens fisher problem johnson and weerahandi 1988 provided a bayesian solution to the multivariate behrens fisher problem with the help of the cauchy schwarz inequality we provide an upper bound for the generalized p value for the multivariate case also we extend the result of tsui and weerahandi to present a second upper bound

generalized fiducial inference for ultrahigh dimensional regression in recent years the ultrahigh dimensional linear regression problem has attracted enormous attention from the research community under the sparsity assumption most of the published work is devoted to the selection and estimation of the predictor variables with nonzero coefficients this article studies a different but fundamentally important aspect of this problem uncertainty quantification for parameter estimates and model choices to be more specific this article proposes methods for deriving a probability density function on the set of all possible models and also for constructing confidence intervals for the corresponding parameters these proposed methods are developed using the generalized fiducial methodology which is a variant of fisher s controversial fiducial idea theoretical properties of the proposed methods are studied and in particular it is shown that statistical inference based on the proposed methods will have correct asymptotic frequentist property in terms of empirical perform

on confidence intervals of a common intraclass correlation coefficient this study presents a novel approach for the confidence interval estimation of a common intraclass correlation coefficient derived from several samples under unequal family sizes this approach is developed using the concept of generalized pivots comparisons are made with a large sample procedure on the coverage probabilities

models and confidence intervals for true values in interlaboratory trials we consider the one way random effects model with unequal sample sizes and heterogeneous variances using the method of generalized confidence intervals we develop a new confidence interval procedure for the mean additionally we investigate two alternative models based on different sets of assumptions regarding between group variability and derive generalized confidence interval procedures for the mean these procedures are applicable to small samples statistical simulation is used to demonstrate that the coverage probabilities of these procedures are close enough to the nominal value so that they are useful in practice although the methods are quite general the procedures are explained with the backdrop of interlaboratory studies

the subject by formulation interaction as a criterion of interchangeability of drugs summary the primary purpose of a bioequivalence study is often to meet the regulatory requirement of similar average bioavailabilities this is usually done by estimating the mean difference between formulations in a crossover design however a small difference as well as a rather narrow confidence interval might be obtained also if the subjects respond differently to the formulations i e if there is a nonnegligible subject by formulation interaction hence it can be argued that this interaction should be part of the criterion of interchangeability to be able to study this interaction the ordinary simple crossover design is not appropriate instead a design where each formulation is administered at least twice to each subject is desirable such a design is obtained by repeating a simple crossover layout to evaluate the impact of the subject by formulation interaction the ratio of the variance components of the interaction and the error is estimated this approach is illustrated by an example two different formulations of a drug are considered bioequivalent if their average bioavailabilities are similar the assessment of this similarity is usually based on an interval estimate of the mean difference between the formulations however this focus on means is an insufficient criterion since a small difference as well as a rather narrow confidence interval might be obtained also if the formulation differences show a considerable variation among subjects the impact on drug interchangeability of this so called subject byformulation interaction is discussed for example by hwang et al 1978 in order to estimate this interaction they suggest a design where each formulation is administered at least twice to each subject in this paper we briefly discuss how to design and analyze a bioequivalence study in order to evaluate the impact of the subject by formulation interaction as a measure of the magnitude of the interaction we propose the ratio of the variance components of the interaction and the error the ideas of the paper are illustrated with data from a comparative study of two generic formulations of furosemide

p values for composite null models abstract the problem of investigating compatibility of an assumed model with the data is investigated in the situation when the assumed model has unknown parameters the most frequently used measures of compatibility are p values based on statistics t for which large values are deemed to indicate incompatibility of the data and the model when the null model has unknown parameters p values are not uniquely defined the proposals for computing a p value in such a situation include the plug in and similar p values on the frequentist side and the predictive and posterior predictive p values on the bayesian side we propose two alternatives the conditional predictive p value and the partial posterior predictive p value and indicate their advantages from both bayesian and frequentist perspectives

on steady state availability of a system with lognormal repair time assuming two parameter lognormal distribution for repair times statistical inference for the steady state availability of a system is considered for the failure time distribution weibull gamma and lognormal distributions were considered using the generalized p value approach we propose confidence intervals and exact tests for the steady state availability of a system a couple of examples are given to illustrate the proposed procedures

a non inferiority test for diagnostic accuracy based on the paired partial areas under roc curves non inferiority is a reasonable approach to assessing the diagnostic accuracy of a new diagnostic test if it provides an easier administration or reduces the cost the area under the receiver operating characteristic roc curve is one of the common measures for the overall diagnostic accuracy however it may not differentiate the various shapes of the roc curves with different diagnostic significances the partial area under the roc curve pauroc may present an alternative that can provide additional and complimentary information for some diagnostic tests which require false positive rate that does not exceed a certain level non parametric and maximum likelihood methods can be used for the non inferiority tests based on the difference in paired paurocs however their performance has not been investigated in finite samples we propose to use the concept of generalized p value to construct a non inferiority test for diagnostic accuracy based on the difference in paired paurocs simulation results show that the proposed non inferiority test not only adequately controls the size at the nominal level but also is uniformly more powerful than the non parametric methods the proposed method is illustrated with a numerical example using published data

inferences on the mean response in a log regression model the generalized variable approach this paper proposes a novel approach for the confidence interval estimation and hypothesis testing of the mean response in a log regression model using the concept of generalized variable simulation studies demonstrate that the proposed confidence intervals have satisfying coverage probabilities the proposed approach can be simply carried out by a few simulation steps therefore it is an ideal candidate for making inferences about the mean response in a log regression model

bayesian inference for the common location parameter of several shifted exponential populations abstract consider k random samples which are independently drawn from k shifted exponential distributions with respective scale parameters 1 2 k and common location parameter on the basis of the given samples and in a bayesian framework we address the problem of point and interval estimation of the location parameter under the conjugate priors which are usually proper priors moreover we also address the problem of testing the equality of the location parameters we propose bayesian hypothesis testing procedures for the equality of the location parameters under the noninformative prior the noninformative prior is usually improper which yields a calibration problem that makes the bayes factor to be defined up to a multiplicative constant so we propose the default bayesian hypothesis testing procedures based on the fractional bayes factor and the intrinsic bayes factors under the reference priors our proposed bayesian procedures are compared and contrasted via a comparison study a simulation study and a real world data analysis to the existing classical exact procedures proposed by tippett tippett s method tippett 1931 fisher fisher s method fisher 1932 stouffer inverse normal method stouffer et al 1949 and george logit method george 1977 and to the generalized variable procedures proposed by tsui and weerahandi generalized p value method tsui and weerahandi 1989

a bayesian solution to the multivariate behrens fisher problem abstract we consider the problem of finding the posterior probabilities of ellipsoids for the difference between two multivariate normal means we do not require the two population covariance matrices to be equal therefore our results pertain to the multivariate behrens fisher problem a hotelling t 2 like quantity is defined and its cdf is expressed as a linear combination of the cdf s of some f distributions this representation enables us to compute desired probabilities exactly using only one dimensional numerical integrations the calculation can easily be done with natural conjugate priors as well as with diffuse priors our main theoretical result concerning convolutions of multivariate t distributions is of some general interest for the univariate case we suggest a much simpler proof than that of ruben 1960 we also give some bounds and approximations for the posterior probabilities of ellipsoids the computation of these approximations requires much less computer time than the computatio

reconciling bayesian and frequentist evidence in the one sided testing problem abstract for the one sided hypothesis testing problem it is shown that it is possible to reconcile bayesian evidence against h 0 expressed in terms of the posterior probability that h 0 is true with frequentist evidence against h 0 expressed in terms of the p value in fact for many classes of prior distributions it is shown that the infimum of the bayesian posterior probability of h 0 is equal to the p value in other cases the infimum is less than the p value the results are in contrast to recent work of berger and sellke 1987 in the two sided point null case where it was found that the p value is much smaller than the bayesian infimum some comments on the point null problem are also given

generalized p values in significance testing of hypotheses in the presence of nuisance parameters abstract this article examines some problems of significance testing for one sided hypotheses of the form h 0 0 versus h 1 0 where is the parameter of interest in the usual setting let x be the observed data and let t x be a test statistic such that the family of distributions of t x is stochastically increasing in define cx as x t x t x 0 the p value is p x sup 0 pr x cx in the presence of a nuisance parameter there may not exist a nontrivial cx with a p value independent of we consider tests based on generalized extreme regions of the form cx x t x x t x x and conditions on t x x are given such that the p value p x sup 0 pr x cx is free of the nuisance parameter where t is stochastically increasing in we provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions a problem for which the fixed level testing approach

generalized fiducial inference a review and new results abstractr a fisher the father of modern statistics proposed the idea of fiducial inference during the first half of the 20th century while his proposal led to interesting methods for quantifying uncertainty other prominent statisticians of the time did not accept fisher s approach as it became apparent that some of fisher s bold claims about the properties of fiducial distribution did not hold up for multi parameter problems beginning around the year 2000 the authors and collaborators started to reinvestigate the idea of fiducial inference and discovered that fisher s approach when properly generalized would open doors to solve many important and difficult inference problems they termed their generalization of fisher s idea as generalized fiducial inference gfi the main idea of gfi is to carefully transfer randomness from the data to the parameter space using an inverse of a data generating equation without the use of bayes theorem the resulting generalized fiducial distribution gfd can

the fractional fourier transform and applications this paper describes the fractional fourier transform which admits computation by an algorithm that has complexity proportional to the fast fourier transform algorithm whereas the discrete fourier transform dft is based on integral roots of unity e 2 pi i n the fractional fourier transform is based on fractional roots of unity e 2 pi i alpha where alpha is arbitrary the fractional fourier transform and the corresponding fast algorithm are useful for such applications as computing dfts of sequences with prime lengths computing dfts of sparse sequences analyzing sequences with noninteger periodicities performing high resolution trigonometric interpolation detecting lines in noisy images and detecting signals with linearly drifting frequencies in many cases the resulting algorithms are faster by arbitrarily large factors than conventional techniques

testing regression equality with unequal variances on obtient un test exact similaire a celui de chow 1960 qui comporte une simple integration unidimensionnelle

design and analysis of intra subject variability in cross over experiments recently interest has grown in the development of inferential techniques to compare treatment variabilities in the setting of a cross over experiment in particular comparison of treatments with respect to intra subject variability has greater interest than has inter subject variability we begin with a presentation of a general approach for statistical inference within a cross over design we discuss three different statistical models where model choice depends on the design and assumptions about carry over effects each model incorporates t variate random subject effects where t is the number of treatments we develop maximum likelihood ml and restricted maximum likelihood reml approaches to derive parameter estimators and we consider a special case in which closed form expressions for the variance component estimators are available finally we illustrate the methodologies with the analysis of data from three examples

confidence intervals for p y1 y2 with normal outcomes in linear models recently there is an emerging interest in the inference of p y1 y2 where y1 and y2 stand for two independent continuous random variables so far most of the research in this field focuses on simply comparing two outcomes without adjusting for covariates this paper mainly presents a large sample approach based on a noncentral t distribution for the confidence interval estimation of p y1 y2 with normal outcomes in linear models furthermore the performance of the proposed large sample approach is compared with that of a generalized variable approach and a bootstrap approach simulation studies demonstrate that for small to medium sample sizes both the large sample approach and the generalized variable approach provide confidence intervals with satisfying coverage probabilities whereas the bootstrap approach can be slightly liberal for certain scenarios the proposed approaches are applied to three real life data sets copyright 2008 john wiley sons ltd

testing variance components in mixed models with generalized p values abstract a procedure for testing one sided hypotheses on variance components in a balanced random effects model is developed the testing is performed on the basis of a generalized p value and involves a one dimensional numerical integration in the special case for which the conventional methods provide an exact test this test is equivalent to the usual f test the test is also generalized bayes in the sense that under a certain diffuse prior the p value is numerically the same as the posterior probability of the null hypothesis

function classes for double exponential integration formulas the double exponential de formulas for numerical integration are known to be highly efficient more efficient than the single exponential se formulas in many cases function classes suited to the se formulas have already been investigated in the literature through rigorous mathematical analysis whereas this is not the case with the de formulas this paper identifies function classes suited to the de formulas in a way compatible with the existing theoretical results for the se formulas the de formulas are good for more restricted classes of functions but more efficient for such functions two concrete examples demonstrate the subtlety in the behavior of the de formulas that is revealed by our theoretical analysis

all derivable points in continuous nest algebras let a be an operator algebra on a hilbert space we say that an element g a is an all derivable point of a for the strong operator topology if every strong operator topology continuous derivable linear mapping at g i e st s t s t for any s t algn with st g is a derivation let n be a continuous nest on a complex and separable hilbert space h we show in this paper that every orthogonal projection operator p m 0 m n is an all derivable point of algn for the strong operator topology

inference for the reliability function based on progressively type ii censored data from the pareto model the generalized variable approach abstract the problem of hypothesis testing and interval estimation based on the generalized variable method for the reliability function of pareto distribution using progressively type ii censored data with fixed removals are considered the confidence limits and testing procedures have to be numerically obtained however the required computations are simple and straightforward there are no exact or approximate testing procedures and confidence intervals for reliability parameter of a pareto distribution based on the progressively type ii right censored data with random or fixed removals available in the literature in addition generalized coverage probabilities generalized size of the test and adjusted and unadjusted generalized powers of the test are also discussed comparison of the reliability function under the classical paradigm and the generalized paradigm is done citing an illustrative example and an example based on the simulated data to demonstrate the advantages and merits of the proposed generalized variable method over the classical method

interval estimation and hypothesis testing of intraclass correlation coefficients the generalized variable approach in this paper we propose a novel approach using the concept of generalized variable gv for the confidence interval estimation of the difference of two intraclass correlation coefficients under unequal family sizes this approach can also easily provide p values for hypothesis testing simulation results show that the gv approach can provide confidence intervals with good coverage properties and perform hypothesis testing with satisfactory type i error control furthermore the confidence intervals and p values by gv approach can be easily obtained by simulation therefore the gv approach is a suitable candidate for making inference concerning two intraclass correlation coefficients

joint confidence region estimation for area under roc curve and youden index in the field of diagnostic studies the area under the roc curve auc serves as an overall measure of a biomarker diagnostic test s accuracy youden index defined as the overall correct classification rate minus one at the optimal cut off point is another popular index for continuous biomarkers of binary disease status although researchers mainly evaluate the diagnostic accuracy using auc for the purpose of making diagnosis youden index provides an important and direct measure of the diagnostic accuracy at the optimal threshold and hence should be taken into consideration in addition to auc furthermore auc and youden index are generally correlated in this paper we initiate the idea of evaluating diagnostic accuracy based on auc and youden index simultaneously as the first step toward this direction this paper only focuses on the confidence region estimation of auc and youden index for a single marker we present both parametric and non parametric approaches for estimating joint confidence region of auc and youden index we carry out extensive simulation study to evaluate the performance of the proposed methods in the end we apply the proposed methods to a real data set copyright 2013 john wiley sons ltd

inferences on the mean of zero inflated lognormal data the generalized variable approach this paper considers the problems of confidence interval estimation and hypothesis testing for the mean of zero inflated lognormal data we present an unified novel approach based on the concepts of generalized test variables and generalized pivotal quantities simulation results demonstrate that the coverage accuracy of proposed confidence intervals and the type i error control of the proposed exact tests are satisfactory

generalized confidence intervals abstract the definition of a confidence interval is generalized so that problems such as constructing exact confidence regions for the difference in two normal means can be tackled without the assumption of equal variances under certain conditions the extended definition is shown to preserve a repeated sampling property that a practitioner expects from exact confidence intervals the proposed procedure is also applied to the problem of constructing confidence intervals for the difference in two exponential means and for variance components in mixed models a repeated sampling property of generalized p values is also given with this characterization one can carry out fixed level tests of parameters of continuous distributions on the basis of generalized p values finally pratt s paradox is revisited and a procedure that resolves the paradox is given

exact tests that recover interblock information in balanced incomplete blocks designs abstract consider a balanced incomplete blocks design in which treatment effects are fixed and blocks are random assume that the number of blocks is greater than i the number of treatments the objective is to test the null hypothesis that there are no differences in treatment effects other null hypotheses are that v treatment contrasts are 0 where v may be any number from 1 to i 1 the usual exact test for no treatment effects is the f test based entirely on intrablock estimates a long standing problem has been to find good exact tests that use both intrablock and interblock estimates e g see houtman and speed 1983 p 1078 scheffe 1959 p 175 in this study such exact tests are found furthermore they are easy to implement and perform much better than the usual f test

generalized fiducial inference for wavelet regression we apply fisher s fiducial idea to conduct statistical inference for wavelet regression we first develop a general methodology for handling model selection problems within the fiducial framework with this new methodology we then propose fiduical based methods for performing wavelet curve estimation as well as constructing both pointwise and curvewise confidence intervals it is shown that under some mild regularity conditions both the new fiducial based pointwise and curvewise confidence intervals have asymptotically correct coverage furthermore simulation results show that these new fiducial based methods especially for constructing pointwise confidence intervals also possess promising empirical properties to the best of our knowledge this is the first time that the fiducial idea has been applied to a nonparametric estimation problem

on the exact interval estimation for the difference in paired areas under the roc curves an important measure for comparison of accuracy between two diagnostic procedures is the difference in paired areas under the receiver operating characteristic roc curves non parametric and maximum likelihood methods have been proposed for interval estimation for the difference in paired areas under roc curves however these two methods are asymptotic procedures and their performance in finite sample sizes has not been thoroughly investigated we propose to use the concept of generalized pivotal quantities gpqs to construct an exact confidence interval for the difference in paired areas under roc curves a simulation study is conducted to empirically investigate the probability coverage and expected length of the three methods for various combinations of sample sizes values of the area under the roc curve and correlations simulation results demonstrate that the exact confidence interval based on the concept of gpqs provides not only sufficient probability coverage but also reasonable expected length numerical examples using published data sets illustrate the proposed method

inferences on standardized mean difference the generalized variable approach the standardized mean difference has been widely used as the most common index of effect magnitude in many applied fields in this paper we propose a novel approach using the concept of generalized variable for the confidence interval estimation and hypothesis testing of standardized mean difference furthermore we extend this approach to compare standardized mean differences between two studies or between two strata simulation results demonstrate that the proposed approach can provide confidence intervals with excellent coverage properties and can perform hypothesis testing with satisfactory type i error control

all derivable points of operator algebras abstract let a be an operator subalgebra in b h where h is a hilbert space we say that an element z a is an all derivable point of a for the norm topology strongly operator topology etc if every norm topology strongly operator topology etc continuous derivable linear mapping at z i e st s t s t for any s t a with st z is a derivation in this paper we show that every invertible operator in the nest algebra alg n is an all derivable point of the nest algebra for the strongly operator topology we also prove that every nonzero element of the algebra of all 2 2 upper triangular matrixes is an all derivable point of the algebra

some tests for variance components using generalized p values the concept of a generalized p value introduced by tsui and weerahandi is applied for testing hypotheses in two situations testing the significance of a variance component in a general balanced mixed model when an exact f test does not exist and comparing randomeffects variance components in two independent balanced mixed models extensions to the unbalanced cases are also indicated the proposed test is compared with the test based on the satterthwaite approximation through their simulated type i error probabilities the simulations indicate that the test based on the generalized p value hastype i error probabilities less than the chosen significance level most of the time whereas the type i error probabilities of the satterthwaite approximate test can be much larger than the significance level the results are illustrated using two examples