algorithm of adaptive fourier decomposition the present paper is a continuing work on the recently established adaptive fourier decomposition afd mainly stressing on the algorithm aspect including algorithm analysis and numerical examples afd is a variation and realization of greedy algorithm matching pursuit suitable for the hardy h2 and the l2 spaces applying afd to a given signal one obtains a series expansion in the basic signals called mono components that possess non negative analytic phase derivatives functions or equivalently meaningful analytic instantaneous frequencies afd is shown to be robust with computational complexity comparable with dft consistent to the greedy algorithm principle experiments show that afd produces pre mono component series with efficient energy decay that also leads to efficient pointwise convergence both in terms of computer running time

chebyshev pseudospectral solution of second order elliptic equations with finite element preconditioning abstract a new chebyshev pseudospectral algorithm for second order elliptic equations using finite element preconditioning is proposed and tested on various problems bilinear and biquadratic lagrange elements are considered as well as bicubic hermite elements the numerical results show that bilinear elements produce spectral accuracy with the minimum computational work l shaped regions are treated by a subdomain approach

b splines of blaschke product type in this paper we construct a class of new splines related to a blaschke product they emerge naturally when studying the filter functions of a class of linear time invariant systems which are related to the boundary values of a blaschke product for the purpose of sampling non bandlimited signals using nonlinear fourier atoms the new splines generalize the well known symmetric b splines we establish their properties such as integral representation property a partition of unity property a recurrence relation and difference property we also investigate their random behaviour finally our numerical experiments confirm our theories

two families of unit analytic signals with nonlinear phase abstract this paper focuses on constructing two families of unit analytic signals with nonlinear phase the first is the 2 periodic extension of the nonlinear fourier atoms viz e i a t a 1 t r where a t is the poisson kernel of the unit circle associated with a in the unit disc in the complex plane and satisfies a t 2 a t 2 and the second consists of e i a t a 1 t r that are the images of the nonlinear fourier atoms under cayley transform these unit analytic signals are mono components based on which one can define meaningful instantaneous frequency the pairs 1 a t and 1 a t form canonical pairs the real signals cos a t corresponding to the first family coincide with the notion of normalized intrinsic mode functions we finally point out that starting from nonlinear fourier atoms the gram schmidt procedure leads to laguerre bases

chirp transforms and chirp series abstract motivated by the recent work on the non harmonic fourier atoms initiated by t qian and the non harmonic fourier series which originated from the celebrated work of paley and wiener we introduce an integral version of the non harmonic fourier series called chirp transform as an integral transform with kernel e i t the chirp transform is an unitary isometry from l 2 r d onto l 2 r d and it can be explicitly defined in terms of generalized hermite polynomials the corresponding chirp series take e i n t as a basis which in some sense is dual to the theory of non harmonic fourier series which take e i n t as a basis the chirp version of the shannon sampling theorem and the poisson summation formula are also considered by dealing with sampling points which may non equally distributed since the chirp transform interchanges weighted derivatives into multiplications it plays a role in solving certain differential equations with variable coefficients in addition we extend t qian s theorem on the characterization of a measure to be a linear combination of a number of harmonic measures on the unit disc with positive integer coefficients to that with positive rational coefficients

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

confidence intervals associated with tests for bioequivalence summary previously the connection between bioequivalence tests and their associated confidence intervals was not well understood in fact the oc level two one sided tests approach was thought to be associated with a 1 20c confidence interval in this paper we build up connections which allow us to construct 1 oc confidence intervals from cx level tests and vice versa when applied to the cc level two one sided tests the resultant 1 oc confidence intervals are properly contained in westlake s 1 oc symmetric interval 1976 our approach is readily generalized to different settings including the nonparametric setting the ratio parameter setting and the repeated confidence interval setting

applied nonparametric statistics 2nd ed 1991 applied nonparametric statistics 2nd ed technometrics vol 33 no 3 pp 364 365

balanced risk set matching a new form of matching optimal balanced risk set matching is applied in an observational study of a treatment cystoscopy and hydrodistention given in response to the symptoms of the chronic nonlethal disease interstitial cystitis when a patient receives the treatment at time t that patient is matched to another patient with a similar history of symptoms up to time t who has not received the treatment up to time t this is risk set matching by using a penalty function in integer programming in a new way we force the marginal distributions of symptoms to be balanced in the matched treated and control groups among all balanced matchings we pick the one that is optimal in the sense of minimizing the multivariate pretreatment covariate distance within matched pairs under a simple model for the treatment assignment mechanism we study the sensitivity of the findings to hidden biases in particular we show that a simple conventional sensitivity analysis is appropriate with risk set matching when the

the nonexistence of 100 1 alpha confidence sets of finite expected diameter in errors in variables and related models on montre que pour certains modeles il est impossible de construire des intervalles de confiance pour les parametres cles qui aient a la fois une confiance positive et une longueur esperee finie

a new method for choosing sample size for confidence interval based inferences scientists often need to test hypotheses and construct corresponding confidence intervals in designing a study to test a particular null hypothesis traditional methods lead to a sample size large enough to provide sufficient statistical power in contrast traditional methods based on constructing a confidence interval lead to a sample size likely to control the width of the interval with either approach a sample size so large as to waste resources or introduce ethical concerns is undesirable this work was motivated by the concern that existing sample size methods often make it difficult for scientists to achieve their actual goals we focus on situations which involve a fixed unknown scalar parameter representing the true state of nature the width of the confidence interval is defined as the difference between the random upper and lower bounds an event width is said to occur if the observed confidence interval width is less than a fixed constant chosen a priori an event validity is said to occur if the parameter of interest is contained between the observed upper and lower confidence interval bounds an event rejection is said to occur if the confidence interval excludes the null value of the parameter in our opinion scientists often implicitly seek to have all three occur width validity and rejection new results illustrate that neglecting rejection or width and less so validity often provides a sample size with a low probability of the simultaneous occurrence of all three events we recommend considering all three events simultaneously when choosing a criterion for determining a sample size we provide new theoretical results for any scalar mean parameter in a general linear model with gaussian errors and fixed predictors convenient computational forms are included as well as numerical examples to illustrate our methods

comparison of different methods for decision making in bioequivalence assessment if the regulatory requirements are symmetrical the use of symmetrical confidence intervals as a decision rule for bioequivalence assessment leads as shown by simulations to better level properties and an inferior power compared to a rule based on shortest confidence intervals a choice between these two approaches will have to depend on a loss function for asymmetric regulatory requirements symmetrical confidence intervals should not be used however a decision can still be based on posterior probabilities pr theta epsilon r1 r2 x or shortest confidence intervals for purposes of inference presentation and interpretation of results we think that the use of symmetrical confidence intervals alone can be misleading and we therefore recommend that the posterior probabilities and densities or at least the shortest confidence intervals be given

constrained simultaneous confidence intervals for multiple comparisons with the best for comparing k treatment effects 01 02 ok often the parameters of primary interest are 0i maxeioi0 i 1 k in this article we develop constrained 100p two sided simultaneous confidence intervals for 0i maxj i0j which we refer to as constrained mcb intervals it turns out that the lower bounds of the intervals imply indifference zone selection inference and the upper bounds of these intervals imply subset selection inference each given at the same confidence level 100p as mcb we also extend our

confidence intervals for a difference between proportions based on paired data we construct several explicit asymptotic two sided confidence intervals cis for the difference between two correlated proportions using the method of variance of estimates recovery mover the basic idea is to recover variance estimates required for the proportion difference from the confidence limits for single proportions the ci estimators for a single proportion which are incorporated with the mover include the agresti coull the wilson and the jeffreys cis our simulation results show that the mover type cis based on the continuity corrected coefficient and the tango score ci perform satisfactory in small sample designs and spare data structures we illustrate the proposed cis with several real examples copyright 2009 john wiley sons ltd

a unifying approach for confidence intervals and testing of equivalence and difference summary general families of null hypotheses are defined which refer to problems of testing equivalence and difference between treatments corresponding confidence intervals have been proposed in the literature in a different context the unifying approach demonstrates how waiving of particular one sided tests in the parameter space relates to the construction of the corresponding confidence interval

discrete sequential boundaries for clinical trials summary pocock 1977 o brien fleming 1979 and slud wei 1982 have proposed different methods to construct discrete sequential boundaries for clinical trials these methods require that the total number of decision times be specified in advance in the present paper we propose a more flexible way to construct discrete sequential boundaries the method is based on the choice of a function a t which characterizes the rate at which the error level ac is spent the boundary at a decision time is determined by a t and by past and current decision times but does not depend on the future decision times or the total number of decision times

a sampling theorem for non bandlimited signals using generalized sinc functions a ladder shaped filter of two real parameters a 1 a 2 1 1 is introduced in this note the impulse response of the corresponding linear time invariant lti system is a generalized sinc function of two parameters consequently a generalized shannon type sampling theorem is established for a class of non bandlimited signals with special spectrum properties associated with a ladder shaped filter of two parameters finally a mathematical characterization for the class of non bandlimited signals satisfying the generalized sampling theorem is offered these signals are restrictions to the real line of certain analytic functions in stripped domains symmetric about the real axis in the complex plane for these signals their spectra in higher frequency bands are measured by the spectrum of their base bands

pooling batches in drug stability study by using constant width simultaneous confidence bands one important study objective in drug stability studies is to estimate the shelf life of a drug a key statistical problem involved in this is how to assess the practical equivalence of different batches of the same drug so that different batches can be subgrouped to produce a single shelf life for the drug in this paper constant width simultaneous confidence bands are proposed to quantify the magnitude of difference between different batches with a particular view to establish the practical equivalence of different batches this approach is suitable for the situation that the intercepts and slopes of the regression lines for the batches cannot be assumed to be equal it is shown how constant width simultaneous confidence bands can be easily constructed for the multiple comparison of several general linear regression models in particular it is shown that constant width simultaneous confidence bands have a better chance to establish the equivalence than and so are preferable to the hyperbola shaped simultaneous confidence bands considered j am stat assoc 2004 99 395 403

an isoparametric spectral element method for solution of the navier stokes equations in complex geometry abstract an isoparametric spectral element technique is presented for solution of the two dimensional navier stokes equations in arbitrary curvy geometries the spatial discretization is described and the method is illustrated by solution of poisson s equation in a cylindrical annulus a fractional step navier stokes solver based on a discretely consistent poisson equation for the pressure is then presented and exponential convergence in space is demonstrated for the case of separated flow between eccentric rotating cylinders the technique is made efficient by the use of explicit collocation rather than galerkin operators for the convective terms and use of static condensation to solve the elliptic equations resulting from the stokes problem the algorithm is amenable to a high degree of parallelism in both multiprocessor and vector pipeline environments

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

nontrivial harmonic waves with positive instantaneous frequency abstract the concept of time varying frequency is fundamental in communications and nature one description of a time varying frequency is the instantaneous frequency of a signal our concern is the design of analytic signals with nonlinear phase and positive instantaneous frequency in this paper a kind of nontrivial orthonormal harmonic waves are derived by applying the gram schmidt procedure to the blaschke products furthermore we show the orthonormal harmonic waves satisfy the analytic condition and have positive instantaneous frequencies which are tightly associated with the average frequencies of the two mono component analytic signals at each time as a consequence non stationary signals can be decomposed into the superposition of nontrivial harmonic waves related conclusions are established for the orthonormal analytic signals on the whole time range

analytic signals and harmonic measures abstract we prove that a sufficient and necessary condition for h e i s i e i s where h is hilbert transformation is a continuous and strictly increasing function with r 2 is that d s is a harmonic measure on the line the counterpart result for the periodic case is also established the study is motivated by and has significant impact to time frequency analysis especially to aspects of analytic signals inducing instantaneous amplitude and frequency as a by product we introduce the theory of hardy space preserving weighted trigonometric series and fourier transformations induced by harmonic measures in the respective contexts

characterization of analytic phase signals in many cases a real valued signal g t may be associated with a complex valued signal a t e i q t the analytic signal associated with g t with the characteristic properties g t a t cos q t and h a cos q t a t sin q t using such obtained amplitude frequency modulation the instantaneous frequency of g t at the time t 0 may be defined to be q t 0 provided q t 0 0 the purpose of this note is to characterize in terms of analytic functions the unimodular functions f t c t is t c 2 t s 2 t 1 a e that satisfy hc t s t this corresponds to the case a t 1 in the above formulation we show that a unimodular function satisfies the required condition if and only if it is the boundary value of a so called inner function in the upper half complex plane we also give through an explicit formula a large class of functions of which the parametrization c t cos q t is available and the extra condition q t 0 a e is enjoyed this class of functions contains blaschke products in the upper half complex plane as a proper subclass studied by picinbono in 1

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

a multivariate test for population bioequivalence in this article we propose a multivariate generalization of the criteria for testing univariate population bioequivalence recently a number of approaches for testing multivariate equivalence have appeared in the literature most of them consider a multivariate equivalence region which implies simultaneous comparison of means in each dimension in contrast our proposal combines a comparison of means and a comparison of variances into a single aggregate criterion using the trace of the covariance matrix as a scalar measure of the total variability we use a confidence interval approach to multivariate population bioequivalence testing similar to the univariate case two versions of the modified large sample confidence interval for the linearized multivariate criterion are constructed in a simulation study we evaluate the empirical coverage of these confidence intervals and rejection rates of the corresponding tests in finite samples the proposed methodology is illustrated with an example of testing equivalence of the spray pattern of nasal sprays

modified large sample confidence intervals for linear combinations of variance components we consider the problem of setting a confidence interval or bound for a linear combination of variance components related to a multivariate normal distribution which includes important applications such as comparing variance components and testing the bioequivalence between two drug products the lack of an exact confidence interval for a general linear combination of variance components spurred the development of a modified large sample mls method that was shown to be superior to many other approximation methods but existing mls method requires the use of independent estimators of variance components using a chi squared representation of a quadratic form of a multivariate normal vector we extend the mls method to situations in which estimators of variance components are dependent using edgeworth and cornish fisher expansions we explicitly derive the second order asymptotic coverage error of the mls confidence bound our results show that the mls confidence bound is not second order accurate in ge

the bedrosian identity for hp functions abstract we establish a necessary and sufficient condition for f h p r g h q r with p 1 q 1 1 to satisfy the bedrosian identity h f g f h g where h denotes the hilbert transform as applications we prove the bedrosian theorem for this identity and give a characterization of f satisfying the identity when g is a finite linear combination of complex sinusoids we also show that if f is of low fourier frequency then it is necessary for g to have high fourier frequency in order to satisfy the bedrosian identity

analytic unit quadrature signals with nonlinear phase abstract the notion of intrinsic mode functions imfs in the algorithm of hilbert huang transform hht n e huang z shen s r long m c wu h h shih q zheng n c yen c c tung h h liu the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis proc r soc london a 454 1998 903 995 is essentially an engineering description in relation to mono components of nonlinear and non stationary signals in this note we prove a version of bedrosian s theorem on the unit circle we give a sufficient condition together with an example for nonlinear phases t that make the unit quadrature signals e i t to be analytic we also establish a corresponding relationship between the periodic and non periodic signals on the whole time range

equivalence and interval testing for lehmann s alternative abstract equivalence and interval tests for lehmann s alternative that extend the well known savage test for one sided hypotheses are proposed the proposed tests are shown to be unbiased with a strictly unimodal power function provided the sample sizes in both treatment groups are equal by means of a numerical investigation of the bias in the case of unequal sample sizes that are not too far apart the suggested tests still turn out to provide practicable solutions because the computational effort to perform the suggested tests is considerable tables containing the critical values are displayed to perform these tests easily a numerical analysis of the power function of the interval test establishes this procedure as a powerful tool for detection of a significantly relevant difference in the small sample case in contrast to the case of interval testing the fact arises that the performance of a powerful equivalence study under lehmann s alternative requires an extensive amount of data because the p

characterizing the hilbert transform by the bedrosian theorem abstract it is proved that a bounded linear translation invariant operator on l 2 r d satisfies the bedrosian theorem if and only if it is a linear combination of the compositions of the partial hilbert transforms and the identity operator this observation justifies a definition of multidimensional analytic signals in the papers t bulow g sommer hypercomplex signals a novel extension of the analytic signal to the multidimensional case ieee trans signal process 49 2001 2844 2852 and s l hahn multidimensional complex signals with single orthant spectra proc ieee 80 1992 1287 1300

sequential confidence regions in inverse regression problems for the inverse regression problem and more generally the set estimation of a ratio of regression parameters we construct a 1 confidence sequence applying such a confidence sequence we can construct a 1 sequential confidence interval with the length less than a prespecified quantity