a composite auditory model for processing speech sounds a composite inner ear model containing the middle ear basilar membrane bm hair cells and hair cell nerve fiber synapses is presented the model incorporates either a linear bm stage or a nonlinear one the model with the nonlinear bm generally shows a high degree of success in reproducing the qualitative aspects of experimentally recorded cat auditory nerve fiber responses to speech in modeling fiber population responses to speech and speech in noise it was found that the bm nonlinearity allows bands of fibers in the model to synchronize strongly to a common spectral peak in the stimulus a cross channel correlation algorithm has been devised to further process the model s population outputs with output from the nonlinear bm model the cross channel correlation values are appreciably reduced only at those channels whose cfs coincide with the formant frequencies this observation also holds to a large extent for noisy speech

models for longitudinal data with random effects and ar 1 errors abstract for longitudinal data on several individuals linear models that contain both random effects across individuals and autocorrelation in the within individual errors are studied a score test for autocorrelation in the within individual errors for the conditional independence random effects model is first developed an explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and autoregressive ar 1 errors is then derived empirical bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with ar 1 errors model are also considered a numerical example is presented to illustrate these methods

auditory filter nonlinearity in mild moderate hearing impairment sensorineural hearing loss has frequently been shown to result in a loss of frequency selectivity less is known about its effects on the level dependence of selectivity that is so prominent a feature of normal hearing the aim of the present study is to characterize such changes in nonlinearity as manifested in the auditory filter shapes of listeners with mild moderate hearing impairment notched noise masked thresholds at 2 khz were measured over a range of stimulus levels in hearing impaired listeners with losses of 20 50 db growth of masking functions for different notch widths are more parallel for hearing impaired than for normal hearing listeners indicating a more linear filter level dependent filter shapes estimated from the data show relatively little change in shape across level the loss of nonlinearity is also evident in the input output functions derived from the fitted filter shapes reductions in nonlinearity are clearly evident even in a listener with only 20 db hearing loss

a hybrid estimator in nonlinear and generalised linear mixed effects models summary a hybrid method that combines laplace s approximation and monte carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family an asymptotic theory of this hybrid method for parametric estimation without requiring the true mixing distribution to belong to the assumed parametric family is developed to explain these results this hybrid method and its asymptotic theory are also extended to generalised linear mixed effects models

the relationship between frequency selectivity and pitch discrimination sensorineural hearing loss this study tested the relationship between frequency selectivity and the minimum spacing between harmonics necessary for accurate fo discrimination fundamental frequency difference limens fo dls were measured for ten listeners with moderate sensorineural hearing loss snhl and three normal hearing listeners for sine and random phase harmonic complexes bandpass filtered between 1500 and 3500 hz with fo s ranging from 75 to 500 hz or higher all listeners showed a transition between small good fo dls at high fo s and large poor fo dls at low fo s although the fo at which this transition occurred fo tr varied across listeners three measures thought to reflect frequency selectivity were significantly correlated to both the fo tr and the minimum fo dl achieved at high fo s 1 the maximum fo for which fo dls were phase dependent 2 the maximum modulation frequency for which amplitude modulation and quasi frequency modulation were discriminable and 3 the equivalent rectangular bandwidth of the auditory filter estimated using the notched noise method these results provide evidence of a relationship between fo discrimination performance and frequency selectivity in listeners with snhl supporting spectral and spectro temporal theories of pitch perception that rely on sharp tuning in the auditory periphery to accurately extract fo information

psychometric functions for frequency discrimination from listeners with sensorineural hearing loss psychometric functions for pulsed pure tone frequency discrimination were obtained from hearing impaired listeners at frequencies with normal hearing and at frequencies with mild or moderate hearing losses the general form of psychometric functions at hearing impaired frequencies was found to be the same as at normal hearing frequencies i e d was linear with the frequency difference between tones in hz for all but one psychometric function the addition of an intercept term to the fitting equation did not account for significantly more variance than did the slope term alone therefore it was concluded that psychometric functions for frequency discrimination can be adequately described with only one parameter the slope of the psychometric function deficits in discrimination at hearing loss frequencies were manifested by more gradual slopes of psychometric functions procedures for normalizing psychometric functions are presented which facilitate comparisons of normal and impaired frequency discrimination data across studies and frequencies comparisons of dlf s difference limen for frequency obtained with adaptive and fixed procedures show a bias toward larger dlf s with adaptive procedures but only at higher frequencies a discussion of equal interval and equal ratio adaptive stepping rules indicates that an equal ratio rule may be preferable

frequency resolution and discrimination of constant and dynamic tones in normal and hearing impaired listeners frequency resolution and three tasks of frequency discrimination were measured at 500 and 4000 hz in 12 normal and 12 hearing impaired listeners a three interval two alternative forced choice procedure was used frequency resolution was measured with an abbreviated psychoacoustical tuning curve frequency discrimination was measured for 1 a fixed frequency standard and target 2 a fixed frequency standard and a frequency transition target and 3 frequency transition standard and a frequency transition target the 50 ms frequency transitions had the same final frequency as the standards but the initial frequency was lowered to obtain about 79 discrimination performance there was a strong relationship between poor frequency resolution and elevated pure tone thresholds but only a very weak relationship between poor frequency discrimination and elevated pure tone thresholds several hearing impaired listeners had normal discrimination performance together with pure tone thresholds of 80 90 db hl a slight correlation was found between word recognition and frequency discrimination but a detailed comparison of the phonetic errors and either the frequency discrimination or frequency resolution tasks failed to suggest any consistent interdependencies these results are consistent with previous work that has suggested that frequency resolution and frequency discrimination are independent processes

the iwasawa main conjecture for semistable abelian varieties over function fields we prove the iwasawa main conjecture over the arithmetic mathbb z p extension for semistable abelian varieties over function fields of characteristic p 0

minimizing separable convex functions subject to simple chain constraints minimizing a separable convex objective subject to an ordering restriction on its variables is a generalization of a class of problems in statistical estimation and inventory control it is shown that a pool adjacent violators pav algorithm can be used to compute an optimal solution of this problem as well as the minimal and maximal extended solutions which provide lower and upper bounds on all optimal solutions and solve certain subproblems these results unify and extend several previously known results in addition it is shown that a pav algorithm can be applied to solving the problem with integer constraints on the variables

relations between frequency selectivity temporal fine structure processing and speech reception in impaired hearing frequency selectivity temporal fine structure tfs processing and speech reception were assessed for six normal hearing nh listeners ten sensorineurally hearing impaired hi listeners with similar high frequency losses and two listeners with an obscure dysfunction od tfs processing was investigated at low frequencies in regions of normal hearing through measurements of binaural masked detection tone lateralization and monaural frequency modulation fm detection lateralization and fm detection thresholds were measured in quiet and in background noise speech reception thresholds were obtained for full spectrum and lowpass filtered sentences with different interferers both the hi listeners and the od listeners showed poorer performance than the nh listeners in terms of frequency selectivity tfs processing and speech reception while a correlation was observed between the monaural and binaural tfs processing deficits in the hi listeners no relation was found between tfs processing and frequency selectivity the effect of noise on tfs processing was not larger for the hi listeners than for the nh listeners finally tfs processing performance was correlated with speech reception in a two talker background and lateralized noise but not in amplitude modulated noise the results provide constraints for future models of impaired auditory signal processing

optimal lipschitzian selection operator in quasi convex optimization abstract given a bounded real function f defined on a closed bounded real interval i the problem is to find a quasi convex function f which minimizes the supremum of f s f s for all s in i over the class of all quasi convex functions f on i such a nearest function f is not unique in general for each f is it possible to select a nearest f so that the selection operator f f satisfies a lipschitz condition with some constant c if so does there exist an operator for which c is minimum it is shown that there exists a maximal nearest function f so that the operator f f is such an optimal lipschitzian selection operator with c 2

shape invariant modeling of circadian rhythms with random effects and smoothing spline anova decompositions medical studies often collect physiological and or psychological measurements over time from multiple subjects to study dynamics such as circadian rhythms under the assumption that the expected response functions of all subjects are the same after shift and scale transformations shape invariant models have been applied to analyze this kind of data the shift and scale parameters provide efficient and interpretable data summaries while the common shape function is usually modeled nonparametrically to provide flexibility however due to the deterministic nature of the shift and scale parameters potential correlations within a subject are ignored furthermore the shape of the common function may depend on other factors such as disease in this article we propose shape invariant mixed effects models a second stage model with fixed and random effects is used to model individual shift and scale parameters a second stage smoothing spline anova model is used to study potential covariate effects on the common shape function we apply our methods to a real data set to investigate disease effects on circadian rhythms of cortisol a hormone that is affected by stress we find that patients with cushing s syndrome lost circadian rhythms and their 24 hour means were elevated to very high levels patients with major depression had the same circadian shape and phases as normal subjects however their 24 hour mean levels were elevated and amplitudes were dampened for some patients

o n algorithms for discrete n point approximation by quasi convex functions this article considers the problem of approximating a function defined on a finite set of n 1 points by quasi convex functions defined there and constructs linear time o n algorithms for computation of optimal solutions

a generalized mazur s theorem and its applications we generalize a theorem of mazur concerning the universal norms of an abelian variety over a d p extension of a complete local field then we apply it to the proof of a control theorem for abelian varieties over global function fields

pairings and functional equations over the gl2 extension we construct a pairing on the dual selmer group over the gl2 extension q e p of an elliptic curve without complex multiplication and with good ordinary reduction at a prime p 5 whenever it satisfies certain conjectured torsion properties this gives a functional equation of the characteristic element which is compatible with the conjectural functional equation of the p adic l function as an application we reduce the parity conjecture for the p selmer rank and the analytic root number for the twists of elliptic curves with self dual artin representation to the case when the artin representation factors through the quotient of gal q e p q b y its maximal pro p normal subgroup this gives a new proof of the parity conjecture whenever the elliptic curve e has a p isogeny over the rationals

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

an algorithm for discrete approximation by quasi convex functions on rm abstract let s be a finite subset of rm having n elements a real valued function k on s is said to be quasiconvex if there exists a quasi convex function k defined on the convex hull co s of s such that k k on s given a real function on s the problem is to find a best quasi convex approximation g to in the uniform norm in this article the greatest quasi convex minorant of is characterized and the maximal best approximation to is identified as a shift of the minorant an algorithm for computing this best approximation is developed and its complexity is analyzed as a function of n when m 2 the algorithm involves computation of on line or semidynamic convex hulls the problem has applications in curve fitting and graphics

maximum likelihood computations with repeated measures application of the em algorithm abstract the purpose of this article is to consider the use of the em algorithm dempster laird and rubin 1977 for both maximum likelihood ml and restricted maximum likelihood reml estimation in a general repeated measures setting using a multivariate normal data model with linear mean and covariance structure anderson 1973 several models and methods of analysis have been proposed in recent years for repeated measures data ware 1985 presented an overview because the em algorithm is a general purpose iterative method for computing ml estimates with incomplete data it has often been used in this particular setting dempster et al 1977 andrade and helms 1984 jennrich and schluchter 1985 there are two apparently different approaches to using the em algorithm in this setting in one application each experimental unit is observed under a standard protocol specifying measurements at each of n occasions or under n conditions and incompleteness implies that the number of measurements actua

a general approach for two stage analysis of multilevel clustered non gaussian data in this article we propose a two stage approach to modeling multilevel clustered non gaussian data with sufficiently large numbers of continuous measures per cluster such data are common in biological and medical studies utilizing monitoring or image processing equipment we consider a general class of hierarchical models that generalizes the model in the global two stage gts method for nonlinear mixed effects models by using any square root n consistent and asymptotically normal estimators from stage 1 as pseudodata in the stage 2 model and by extending the stage 2 model to accommodate random effects from multiple levels of clustering the second stage model is a standard linear mixed effects model with normal random effects but the cluster specific distributions conditional on random effects can be non gaussian this methodology provides a flexible framework for modeling not only a location parameter but also other characteristics of conditional distributions that may be of specific interest for estimation of the population parameters we propose a conditional restricted maximum likelihood creml approach and establish the asymptotic properties of the creml estimators the proposed general approach is illustrated using quartiles as cluster specific parameters estimated in the first stage and applied to the data example from a collagen fibril development study we demonstrate using simulations that in samples with small numbers of independent clusters the creml estimators may perform better than conditional maximum likelihood estimators which are a direct extension of the estimators from the gts method

linear time algorithms for convex and monotone approximation abstract this article presents algorithms of linear time complexity o n for computation of optimal solutions to the two problems of convex and monotone approximation where data points are approximated respectively by convex and monotone nondecreasing functions on a grid of n 1 points for the convex approximation case the algorithms are based on a linear programming approach which exploits the structure of matrices involved and uses a special pivoting procedure to obtain a maximal optimal solution analogously in the monotone approximation case the algorithms compute maximal and minimal optimal solutions which also enclose any other optimal solution between them computational results are presented

a case study in exploratory functional data analysis geometrical features of the internal carotid artery this pilot study is a product of the aneurisk project a scientific program that aims at evaluating the role of vascular geometry and hemodynamics in the pathogenesis of cerebral aneurysms by means of functional data analyses we explore the aneurisk dataset to highlight the relations between the geometric features of the internal carotid artery expressed by its radius profile and centerline curvature and the aneurysm location after introducing a new similarity index for functional data we eliminate ancillary variability of vessel radius and curvature profiles through an iterative registration procedure we then reduce data dimension by means of functional principal components analysis last a quadratic discriminant analysis of functional principal components scores allows us to discriminate patients with aneurysms in different districts

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

relation between derived band auditory brainstem response latencies and behavioral frequency selectivity derived band click evoked auditory brainstem responses abrs were obtained for normal hearing nh and sensorineurally hearing impaired hi listeners the latencies extracted from these responses as a function of derived band center frequency and click level served as objective estimates of cochlear response times for the same listeners auditory filter bandwidths at 2 khz were estimated using a behavioral notched noise masking paradigm generally shorter derived band latencies were observed for the hi than for the nh listeners only at low click sensation levels prolonged latencies were obtained for some of the hi listeners the behavioral auditory filter bandwidths accounted for the across listener variability in the abr latencies cochlear response time decreased with increasing filter bandwidth consistent with linear system theory the results link cochlear response time and frequency selectivity in human listeners and offer a window to better understand how hearing impairment affects the spatiotemporal cochlear response pattern

pontryagin duality for iwasawa modules and abelian varieties we prove a functional equation for two projective systems of finite abelian p groups an and bn endowed with an action of z d such that an can be identified with the pontryagin dual of bn for all n let k be a global field let l be a z d extension of k d 1 unramified outside a finite set of places let a be an abelian variety over k we prove an algebraic functional equation for the pontryagin dual of the selmer group of a

an o n algorithm for least squares quasi convex approximation this article is concerned with the approximation problem of fitting n data points by a quasi convex function using the least squares distance function an algorithm of o n worst case time complexity for computing a best fit is developed this problem arises in the context of curve fitting or statistical estimation

the deterioration of hearing with age frequency selectivity the critical ratio the audiogram and speech threshold the frequency selectivity of the auditory system was measured by masking a sinusoidal signal 0 5 2 0 or 4 0 khz or a filtered speech signal with a wideband noise having a notch or stopband centered on the signal as the notch was widened performance improved for both types of signal but the rate of improvement decreased as the age of the 16 listeners increased from 23 to 75 years indicating a loss in frequency selectivity with age auditory filter shapes derived from the tone in noise data show a that the passband of the filter broadens progressively with age and b that the dynamic range of the filter ages like the audiogram that is the range changes little with age before 55 but beyond this point there is an accelerating rate of loss the speech experiment shows comparable but smaller effects the filter width measurements show that the critical ratio is a poor estimator of frequency selectivity because it confounds the tuning of the system with the efficiency of the signal detection and speech processing mechanisms that follow the filter an alternative one point measure of frequency selectivity which is both sensitive and reliable is developed via the filter shape model of masking

accelerated degradation tests modeling and analysis high reliability systems generally require individual system components having extremely high reliability over long periods of time short product development times require reliability tests to be conducted with severe time constraints frequently few or no failures occur during such tests even with acceleration thus it is difficult to assess reliability with traditional life tests that record only failure times for some components degradation measures can be taken over time a relationship between component failure and amount of degradation makes it possible to use degradation models and data to make inferences and predictions about a failure time distribution this article describes degradation reliability models that correspond to physical failure mechanisms we explain the connection between degradation reliability models and failure time reliability models acceleration is modeled by having an acceleration model that describes the effect that temperature or another accelerating variable has on

the role of stimulus complexity spectral overlap and pitch for gap detection thresholds in young and old listeners thresholds for detecting a gap between two complex tones were determined for young listeners with normal hearing and old listeners with mild age related hearing loss the leading tonal marker was always a 20 ms 250 hz complex tone with energy at 250 500 750 and 1000 hz the lagging marker also tonal could differ from the leading marker with respect to fundamental frequency f0 the presence versus absence of energy at f0 and the degree to which it overlapped spectrally with the leading marker all stimuli were presented with steeper 1 ms and less steep 4 ms envelope rise and fall times f0 differences decreases in the degree of spectral overlap between the markers and shallower envelope shape all contributed to increases in gap detection thresholds age differences for gap detection of complex sounds were generally small and constant when gap detection thresholds were measured on a log scale when comparing the results for complex sounds to thresholds obtained for pure tones in a previous study by heinrich and schneider 2006 j acoust soc am 119 2316 2326 thresholds increased in an orderly fashion from markers with identical within channel pure tones to different between channel pure tones to complex sounds this pattern of results was true for listeners of both ages although younger listeners had smaller thresholds overall

best quasi convex uniform approximation une fonction reelle bornee g sur 0 1 est quasiconvexe si on a g x max g s g t pour tous x s t tels que 0 s x s t 1 soit k l ensemble de ces fonctions quasiconvexes le probleme considere est celui de la meilleure approximation uniforme quasi convexe d une fonction continue f sur 0 1 c a d le probleme de trouver g k telle que f g inf f g g k

suppression and comodulation masking release in normal hearing and hearing impaired listeners the detectability of a sinusoidal signal embedded in a masker at the signal frequency can be improved by simultaneously presenting additional maskers in off frequency regions if the additional maskers and the on frequency masker component have the same temporal envelope this effect is commonly referred to as comodulation masking release cmr recently it was hypothesized that peripheral nonlinear processes such as suppression may play a role in cmr over several octaves when the level of the off frequency masker component is higher than the level of the on frequency masker component the aim of the present study was to test this hypothesis by measuring suppression and cmr within the same subjects for various frequency level combinations of the off frequency masker component experimental data for normal hearing listeners show a large overlap between the existence regions for suppression and cmr hearing impaired subjects with a sensorineural hearing loss show on average negligible suppression and cmr the data support the hypothesis that part of the cmr in experiments with large spectral distances and large level differences between the masker components is due to the nonlinear processing at the level of the cochlea

an o n algorithm for weighted least squares regression by integer quasi convex and unimodal or umbrella functions the problem of fitting n data points by an integer quasi convex also quasi concave umbrella or unimodal function using the weighted least squares distance function is considered an algorithm of linear time o n worst case complexity and thus optimal is constructed for computing a best fit this problem arises in the context of curve fitting or statistical estimation

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

some alternatives to asymptotic tests for the analysis of pharmacogenetic data using nonlinear mixed effects models nonlinear mixed effects models allow investigating individual differences in drug concentration profiles pharmacokinetics and responses pharmacogenetics focuses on the genetic component of this variability two tests often used to detect a gene effect on a pharmacokinetic parameter are 1 the wald test assessing whether estimates for the gene effect are significantly different from 0 and 2 the likelihood ratio test comparing models with and without the genetic effect because those asymptotic tests show inflated type i error on small sample size and or with unevenly distributed genotypes we develop two alternatives and evaluate them by means of a simulation study first we assess the performance of the permutation test using the wald and the likelihood ratio statistics second for the wald test we propose the use of the f distribution with four different values for the denominator degrees of freedom we also explore the influence of the estimation algorithm using both the first order conditional estimation with interaction linearization based algorithm and the stochastic approximation expectation maximization algorithm we apply these methods to the analysis of the pharmacogenetics of indinavir in hiv patients recruited in the cophar2 anrs 111 trial results of the simulation study show that the permutation test seems appropriate but at the cost of an additional computational burden one of the four f distribution based approaches provides a correct type i error estimate for the wald test and should be further investigated

design in nonlinear mixed effects models optimization using the fedorov wynn algorithm and power of the wald test for binary covariates we extend the methodology for designs evaluation and optimization in nonlinear mixed effects models with an illustration of the decrease of human immunodeficiency virus viral load after antiretroviral treatment initiation described by a bi exponential model we first show the relevance of the predicted standard errors ses given by the computation of the population fisher information matrix using the r function pfim in comparison to those computed with the stochastic approximation expectation maximization algorithm implemented in the monolix software we then highlight the usefulness of the fedorov wynn fw algorithm for designs optimization compared to the simplex algorithm from the predicted se of pfim we compute the predicted power of the wald test to detect a treatment effect as well as the number of subjects needed to achieve a given power using the fw algorithm we investigate the influence of the design on the power and show that for optimized designs with the same total number of samples the power increases when the number of subjects increases and the number of samples per subject decreases a simulation study is also performed with the nlme function of r to confirm this result and show the relevance of the predicted powers compared to those observed by simulation

evaluation by simulation of tests based on non linear mixed effects models in pharmacokinetic interaction and bioequivalence cross over trials we propose tests based on non linear mixed effects models nlmem in pharmacokinetic interaction and bioequivalence cross over trials comparing two treatments or two formulations to compare the logarithm of the area under the curve auc using these models two approaches are studied in the first one concentration data are analysed globally with and without the estimation of a treatment effect and in the second one they are analysed separately in each treatment group with the estimation of the individual parameters four tests for comparison of the logarithm auc between two treatment arms are studied a likelihood ratio test lrt a wald test and two tests parametric and non parametric comparing the individual empirical bayes eb estimates these tests are adapted to the case of equivalence except the lrt which does not have any simple extension we evaluate by simulation of the type i error and the power for both comparison and equivalence tests they are compared to the standard tests recommended by the fda and the emea based on non compartmental nc auc trials for a usual pk model are simulated under h0 and several h1 using s plus software and analysed with the nlme function different configurations of the number of subjects n 12 24 and 40 and of the number of samples per subject j 10 5 and 3 are studied the type i error of lrt and wald comparison test in the 5000 replications of interaction cross over trials is found to be 20 9 per cent and 21 7 per cent respectively in the original design n 12 j 10 which is far superior to 5 per cent and decreases when n increases when n is fixed is found to increase with j power is satisfactory for both tests after correction of the significance threshold results of eb and nc tests are similar with satisfactory powers and a type i error close to 5 per cent except when j 3 for eb tests similar results are obtained for equivalence tests except for eb and nc student tests which are not of a great interest nc tests keep their place when the number of samples per subject j is large but nlmem seem useful for cross over studies performed in special populations where j limited the evaluation by monte carlo simulations of empirical threshold seems however necessary because of the inflation of the type i error copyright 2005 john wiley sons ltd

quasi convex optimization given a bounded real function f defined on a closed bounded real interval i the problem is to find a quasi convex function f so as to minimize the supremum of f s f s for all s in i over the class of all quasi convex functions f on i this article obtains optimal solutions to the problem and derives their properties this problem arises in the context of curve fitting or estimation

lp approximation by quasi convex and convex functions abstract in this article a problem of approximation from nonconvex sets is considered let lp 1 p be the lebesgue space of extended real functions on a compact real interval given a subset p of quasi convex functions and a function in lp the problem is to find a best lp approximation to from p lp it is shown that if p is closed under pointwise convergence of sequences of functions then a best approximation exists also investigated are properties of norm bounded subsets and convergent sequences of quasi convex functions since convex and monotone functions are quasi convex the results are applicable to the problems of approximation from subsets of convex and monotone functions in particular the convex problem is analyzed in some detail

integer isotone optimization consider the following integer isotone optimization problem given an n vector x find an n vector y with integer components so as to minimize max w j x j y j 1 leq j leq n subject to y 1 leq y 2 leq cdots leq y n where each weight w j 0 in this article the dual of this problem is defined a strong duality theorem is established and the set of all optimal solutions is shown to be all monotonic integer vectors lying in a vector interval in addition algorithms are obtained for computation of optimal solutions having the worst case time complexity o n 2 when w j are arbitrary and o n when w j 1 for all j the problem considered is of isotonic regression type and has practical applications for example to estimation and curve fitting it is also of independent mathematical interest the problem and the results can be easily extended to a partially ordered set

a bayesian approach to nonlinear random effects models nonlinear random effects models are considered from the bayesian point of view the method of analysis follows closely that of lindley and smith 1972 journal of the royal statistical society series b 34 1 42 the numerical method is related to the em algorithm

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

bayesian approach for a nonlinear growth model nonlinear least squares methods are currently used for fitting a well known growth model namely the jenss model to the length measurements of a child followed throughout the first six years of life an empirical bayes approach is developed for fitting the model and the prior distribution of the growth model parameters is estimated from a large sample of least squares parameters an expression which is proportional to the posterior distribution is derived so that the posterior mode can be estimated given the observations on a child this posterior mode provides bayes estimates of the jenss curve parameters for the child

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

selmer groups over mathbb z _p d extensions consider an abelian variety a defined over a global field k and let l k be a mathbb z p d extension unramified outside a finite set of places of k with mathrm gal l k gamma let lambda gamma mathbb z p gamma denote the iwasawa algebra in this paper we study how the characteristic ideal of the lambda gamma module x l the dual p primary selmer group varies when l k is replaced by a strict intermediate mathbb z p e extension

a relative off set orthogonality convergence criterion for nonlinear least squares an orthogonality convergence criterion using relative offset is proposed this criterion is compared to currently used criteria and its advantages are discussed