on testing an unspecified function through a linear mixed effects model with multiple variance components summary we examine a generalized f test of a nonparametric function through penalized splines and a linear mixed effects model representation with a mixed effects model representation of penalized splines we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null the procedure can be used to test a nonparametric function or varying coefficient with clustered data compare two spline functions test the significance of an unspecified function in an additive model with multiple components and test a row or a column effect in a two way analysis of variance model through a spectral decomposition of the residual sum of squares we provide a fast algorithm for computing the null distribution of the test which significantly improves the computational efficiency over bootstrap the spectral representation reveals a connection between the likelihood ratio test lrt in a multiple variance components model and a single component model we examine our methods through simulations where we show that the power of the generalized f test may be higher than the lrt depending on the hypothesis of interest and the true model under the alternative we apply these methods to compute the genome wide critical value and p value of a genetic association test in a genome wide association study gwas where the usual bootstrap is computationally intensive up to 108 simulations and asymptotic approximation may be unreliable and conservative

modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

theory of differential forms on manifolds in this paper we establish a hodge type decomposition for the lp space of differential forms on closed i e compact oriented smooth rieman nian manifolds critical to the proof of this result is establishing an lp es timate which contains as a special case the l2 result referred to by morrey as gaffney s inequality this inequality helps us show the equivalence of the usual definition of sobolev space with a more geometric formulation which we provide in the case of differential forms on manifolds we also prove the lp boundedness of green s operator which we use in developing the lp theory of the hodge decomposition for the calculus of variations we rigorously verify that the spaces of exact and coexact forms are closed in the lp norm for nonlinear analysis we demonstrate the existence and uniqueness of a solution to the a harmonic equation

detecting a major gene in an f2 population the aim of this paper is to study the behavior of the likelihood ratio test for the detection of a major gene in an f2 population the model is a mixture of three normal distributions where the proportions are known the information matrix is not positive definite and therefore classical results cannot be used an example concerning beans is given

likelihood ratio testing for admixture models with application to genetic linkage analysis we consider likelihood ratio tests lrt and their modifications for homogeneity in admixture models the admixture model is a two component mixture model where one component is indexed by an unknown parameter while the parameter value for the other component is known this model is widely used in genetic linkage analysis under heterogeneity in which the kernel distribution is binomial for such models it is long recognized that testing for homogeneity is nonstandard and the lrt statistic does not converge to a conventional 2 distribution in this article we investigate the asymptotic behavior of the lrt for general admixture models and show that its limiting distribution is equivalent to the supremum of a squared gaussian process we also discuss the connection and comparison between lrt and alternative approaches such as modifications of lrt and score tests including the modified lrt fu chen and kalbfleisch 2006 statistica sinica 16 805 823 the lrt is an omnibus test that is powerful to detect general alternative hypotheses in contrast alternative approaches may be slightly more powerful to detect certain type of alternatives but much less powerful for others our results are illustrated by simulation studies and an application to a genetic linkage study of schizophrenia

exponential decay for binary time varying covariates in cox models cox models are commonly used in the analysis of time to event data one advantage of cox models is the ability to include time varying covariates often a binary covariate that codes for the occurrence of an event that affects an individual subject a common assumption in this case is that the effect of the event on the outcome of interest is constant and permanent for each subject in this paper we propose a modification to the cox model to allow the influence of an event to exponentially decay over time methods for generating data using the inverse cumulative density function for the proposed model are developed likelihood ratio tests and aic are investigated as methods for comparing the proposed model to the commonly used permanent exposure model a simulation study is performed and 3 different data sets are presented as examples

dirac harmonic equations for differential forms abstract in this paper we introduce the dirac harmonic equation for differential forms and prove some basic norm inequalities including the caccioppoli type inequality poincare type inequality and the weak reverse holder inequality for the solutions of this kind of differential equations

the statistical performance of an mcf 7 cell culture assay evaluated using generalized linear mixed models and a score test biological assays often utilize experimental designs where observations are replicated at multiple levels and where each level represents a separate component of the assay s overall variance statistical analysis of such data usually ignores these design effects whereas more sophisticated methods would improve the statistical power of assays this report evaluates the statistical performance of an in vitro mcf 7 cell proliferation assay e screen by identifying the optimal generalized linear mixed model glmm that accurately represents the assay s experimental design and variance components our statistical assessment found that 17 oestradiol cell culture assay data were best modelled with a glmm configured with a reciprocal link function a gamma error distribution and three sources of design variation plate to plate well to well and the interaction between plate to plate variation and dose the gamma distributed random error of the assay was estimated to have a coefficient of variation cov 3 2 per cent and a variance component score test described by x lin found that each of the three variance components were statistically significant the optimal glmm also confirmed the estrogenicity of five weakly oestrogenic polychlorinated biphenyls pcbs 17 49 66 74 and 128 based on information criteria the optimal gamma glmm consistently out performed equivalent naive normal and log normal linear models both with and without random effects terms because the gamma glmm was by far the best model on conceptual and empirical grounds and requires only trivially more effort to use we encourage its use and suggest that naive models be avoided when possible copyright 2006 john wiley sons ltd

non regular maximum likelihood problems four non regular estimation problems are reviewed and discussed one the unbounded likelihood problem involves distributions with infinite spikes for which maximum likelihood can fail to give consistent estimators a comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case an application to the box cox shifted power transform is given the other three problems occur when the true parameter lies in some special subregion in one the constrained parameter problem the subregion is a boundary the other two the embedded model and the indeterminate parameters problems occur when the model takes on a special form in the subregion these last two problems have previously been investigated separately we show that they are equivalent in some situations both often arise in non linear models and we give a directed graph approach which allows for their occurrence in nested model building it is argued that many non regular problems can be handled systematically without having to resort to elaborate technical assumptions relatively uncomplicated methods may be used provided that the underlying nature of the non regularity is understood

testing the correlation for clustered categorical and censored discrete time to event data when covariates are measured without with errors summary in the analysis of clustered categorical data it is of common interest to test for the correlation within clusters and the heterogeneity across different clusters we address this problem by proposing a class of score tests for the null hypothesis that the variance components are zero in random effects models for clustered nominal and ordinal categorical responses we extend the results to accommodate clustered censored discrete time to event data we next consider such tests in the situation where covariates are measured with errors we propose using the simex method to construct the score tests for the null hypothesis that the variance components are zero key advantages of the proposed score tests are that they can be easily implemented by fitting standard polytomous regression models and discrete failure time models and that they are robust in the sense that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates the asymptotic properties of the proposed tests are studied we illustrate these tests by analyzing two data sets and evaluate their performance with simulations

on some nonregular tests for a modified weibull model summary certain tests on the parameters of a modified weibull distribution are considered nonregular asymptotic behaviour of likelihood based test statistics is observed competing tests based on extreme order statistics are investigated and comparisons are made of power functions

integral estimates for null lagrangians sobolev spaces of differential forms are studied lp projections onto exact forms are introduced as a tool to obtain integral estimates for null lagrangians new results on compensated compactness are given and mean coercive variational integrals are found existence of minima of certain mean coercive functionals is established

bounds for ratios of modified bessel functions and associated turan type inequalities abstract new sharp inequalities for the ratios of bessel functions of consecutive orders are obtained using as main tool the first order difference differential equations satisfied by these functions many already known inequalities are also obtainable and most of them can be either improved or the range of validity extended it is shown how to generate iteratively upper and lower bounds which are converging sequences in the case of the i functions few iterations provide simple and effective upper and lower bounds for approximating the ratios i x i 1 x and the condition numbers x i x i x for any x 0 for the ratios k x k 1 x the same is possible but with some restrictions on using these bounds turan type inequalities are established extending the range of validity of some known inequalities and obtaining new inequalities as well for instance it is shown that k 1 x k 1 x k x 2 1 x 0 1 1 and that the inequality is the best possible this proves and improves an existing conjecture

a new type of sharp bounds for ratios of modified bessel functions abstract the bounds for the ratios of first and second kind modified bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications we obtain new bounds which are accurate in a large region of parameters and which are sharper than previous bounds the new bounds are obtained by a qualitative analysis of the riccati equation satisfied by these ratios a procedure is considered in which the bounds obtained from the analysis of the riccati equation are used to define a new function satisfying a new riccati equation which yields sharper bounds similar ideas can be applied to other functions

inference and testing on the boundary in extended constant conditional correlation garch models we consider inference and testing in extended constant conditional correlation garch models in the case where the true parameter vector is a boundary point of the parameter space this is of particular importance when testing for volatility spillovers in the model the large sample properties of the qmle are derived together with the limiting distributions of the related lr wald and lm statistics due to the boundary problem these large sample properties become nonstandard the size and power properties of the tests are investigated in a simulation study as an empirical illustration we test for no volatility spillovers between foreign exchange rates

global weighted inequalities for operators and harmonic forms on manifolds abstract in this paper both the local and global weighted sobolev poincare imbedding inequalities and poincare inequalities for the composition t g are established where t is the homotopy operator and g is green s operator applied to a harmonic forms on manifolds

varying coefficient models we explore a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables general algorithms are presented for estimating the models flexibly and some examples are given this class of models ties together generalized additive models and dynamic generalized linear models into one common framework when applied to the proportional hazards model for survival data this approach provides a new way of modelling departures from the proportional hazards assumption

the schwarzian newton method for solving nonlinear equations with applications the author acknowledges financial support from ministerio de economia y competitividad project mtm2012 34787

a new class of models for bivariate joint tails summary a fundamental issue in applied multivariate extreme value analysis is modelling dependence within joint tail regions the primary focus of this work is to extend the classical pseudopolar treatment of multivariate extremes to develop an asymptotically motivated representation of extremal dependence that also encompasses asymptotic independence starting with the usual mild bivariate regular variation assumptions that underpin the coefficient of tail dependence as a measure of extremal dependence our main result is a characterization of the limiting structure of the joint survivor function in terms of an essentially arbitrary non negative measure that must satisfy some mild constraints we then construct parametric models from this new class and study in detail one example that accommodates asymptotic dependence asymptotic independence and asymmetry within a straightforward parsimonious parameterization we provide a fast simulation algorithm for this example and detail likelihood based inference including tests for asymptotic dependence and symmetry which are useful for submodel selection we illustrate this model by application to both simulated and real data in contrast with the classical multivariate extreme value approach which concentrates on the limiting distribution of normalized componentwise maxima our framework focuses directly on the structure of the limiting joint survivor function and provides significant extensions of both the theoretical and the practical tools that are available for joint tail modelling

tests of homogeneity for generalized linear models abstract we propose two tests for testing homogeneity among clustered data adjusting for the effects of covariates the first is a score test for a generalized linear model with random effect in which the distribution of the response variable given the random effect is entirely defined in contrast to the likelihood ratio test however the score test does not require estimation of the parameters of a mixed effects model nor specification of the mixing distribution the second test is proposed in the framework of the generalized estimating equation gee approach in deriving this test we need only the specification of the marginal expectation and variance of the response variable and the fourth moment for the overdispersion term whereas for deriving the score test for mixed effects models the entire conditional distribution must be specified we demonstrate that the two tests are identical when the covariance matrix assumed in the gee approach is that of the random effects model in both approaches

testing for garch effects a one sided approach arch models often lie at the boundary of the parameter space under conditional homoskedasticity which invalidates the usual s2 distribution of lr and wald tests although lm tests are not a ected the one sided nature of the alternative hypothesis should result in more powerful tests we propose a simple one sided version of the lm test which is closely related to the kuhn tucker multiplier test we also present critical values for lr wald and one sided lm tests the results of a monte carlo comparison suggest that one sided tests are indeed more powerful than their two sided counterparts 1998 elsevier science s a all rights reserved jel classification c22

functional mixed effects models in this article a new class of functional models in which smoothing splines are used to model fixed effects as well as random effects is introduced the linear mixed effects models are extended to nonparametric mixed effects models by introducing functional random effects which are modeled as realizations of zero mean stochastic processes the fixed functional effects and the random functional effects are modeled in the same functional space which guarantee the population average and subject specific curves have the same smoothness property these models inherit the flexibility of the linear mixed effects models in handling complex designs and correlation structures can include continuous covariates as well as dummy factors in both the fixed or random design matrices and include the nested curves models as special cases two estimation procedures are proposed the first estimation procedure exploits the connection between linear mixed effects models and smoothing splines and can be fitted using existing software the second procedure is a sequential estimation procedure using kalman filtering this algorithm avoids inversion of large dimensional matrices and therefore can be applied to large data sets a generalized maximum likelihood gml ratio test is proposed for inference and model selection an application to comparison of cortisol profiles is used as an illustration

sharp bounds for cumulative distribution functions abstract ratios of integrals can be bounded in terms of ratios of integrands under certain monotonicity conditions this result related to l hopital s monotone rule can be used to obtain sharp bounds for cumulative distribution functions we consider the case of noncentral cumulative gamma and beta distributions three different types of sharp bounds for the noncentral gamma distributions also called marcum functions are obtained in terms of modified bessel functions and one additional type of function a second modified bessel function two error functions or one incomplete gamma function for the noncentral beta case the bounds are expressed in terms of kummer functions and one additional kummer function or an incomplete beta function these bounds improve previous results with respect to their range of application and or its sharpness

a note on computing the smallest conic singular value abstract the goal of this note is to study the smallest conic singular value of a matrix from a lagrangian duality viewpoint and provide an efficient method for its computation

the analysis of group truncated binary data with random effects injury severity in motor vehicle accidents the analysis of group truncated binary data has been previously considered by o neill and barry 1995b biometrics 51 533 541 where the analysis assumed that responses within each group were independent in this paper we consider the analysis of such data when there is group level heterogeneity a generalized linear mixed model is hypothesized to model the response and maximum likelihood estimates are derived for the truncated case a score test is derived to test for heterogeneity finally the method is applied to a set of traffic accident data

miscellanea random coefficient autoregressive models for longitudinal data summary stable autoregressive models with exogenous covariates can be used to mimic nonstationary stabilising growth profiles in longitudinal data if different individuals have very different trajectories the autoregressive parameters can be interpreted as random variables varying from one individual to the next if all random effects are assumed gaussian the model will be quite easy to estimate although the marginal distributions of the observations will no longer be gaussian however this kind of model can only be used when the observations are equally spaced

a simple estimator for a shared frailty regression model summary we propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution inferences for the frailty parameter can be obtained by using output from cox regression analyses the computational burden is substantially less than that of the other approaches to estimation the large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes the methods are motivated by studies of familial associations in the natural history of diseases their practical utility is illustrated with sib pair data from beaver dam wisconsin

interval estimation for log linear models with one variable subject to non ignorable non response log linear models for multiway contingency tables where one variable is subject to non ignorable non response will often yield boundary solutions with the probability of non respondents being classified in some cells of the table estimated as 0 the paper considers the effect of this non standard behaviour on two methods of interval estimation based on the distribution of the maximum likelihood estimator the first method relies on the estimator being approximately normally distributed with variance equal to the inverse of the information matrix it is shown that the information matrix is singular for boundary solutions but intervals can be calculated after a simple transformation for the second method based on the bootstrap asymptotic results suggest that the coverage properties may be poor for boundary solutions both methods are compared with profile likelihood intervals in a simulation study based on data from the british general election panel study the results of this study indicate that all three methods perform poorly for a parameter of the non response model whereas they all perform well for a parameter of the margin model irrespective of whether or not there is a boundary solution

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

geometrically concave univariate distributions in this paper our aim is to show that if a probability density function is geometrically concave convex then the corresponding cumulative distribution function and the survival function are geometrically concave convex too under some assumptions the proofs are based on the so called monotone form of l hospital s rule and permit us to extend our results to the case of the concavity convexity with respect to holder means to illustrate the applications of the main results we discuss in details the geometrical concavity of the probability density function cumulative distribution function and survival function of some common continuous univariate distributions moreover at the end of the paper we present a simple alternative proof to schweizer s problem related to the mulholland s generalization of minkowski s inequality

censored survival data with misclassified covariates a case study of breast cancer mortality abstract from a cancer registry in the san francisco bay area we obtained survival data for 2 495 women diagnosed with breast cancer at ages 55 64 we relate mortality among these women to the time since diagnosis and to the stage of the disease at diagnosis we divide the study period extending through 10 years into five two year periods and for each stage we assume a constant hazard rate during each of these periods let jk be the j k matrix of hazard rates for the j 5 periods and k 5 stages the most general model allows jk to vary freely a plot of maximum likelihood estimates of the hazard rates shows some tendency for increase with stage but no simple patterns or parallelism across stage we seek more restrictive models to get simpler interpretations the exponential model assumes that although jk may vary with stage it is constant over the five periods for each stage this model which assumes no dependence of hazard rate on time since diagnosis is quite restrictive and i

joint estimation of location dispersion and random effects in robust design this article presents a methodology for simultaneously modeling three components of a general mixed model approach to robust design location fixed effects dispersion effects and random effects control noise and random factors can be accommodated with this approach parameters associated with all three are estimated jointly using residual maximum likelihood and assuming normality simulated and real datasets illustrate the key concepts and advantages over previously proposed approaches

open capture recapture models with heterogeneity ii jolly seber model summary estimation of abundance is important in both open and closed population capture recapture analysis but unmodeled heterogeneity of capture probability leads to negative bias in abundance estimates this article defines and develops a suite of open population capture recapture models using finite mixtures to model heterogeneity of capture and survival probabilities model comparisons and parameter estimation use likelihood based methods a real example is analyzed and simulations are used to check the main features of the heterogeneous models especially the quality of estimation of abundance survival recruitment and turnover the two major advances in this article are the provision of realistic abundance estimates that take account of heterogenetiy of capture and an appraisal of the amount of overestimation of survival arising from conditioning on the first capture when heterogeneity of survival is present

miscellanea an extension of morel nagaraj s finite mixture distribution for modelling multinomial clustered data morel nagaraj 1993 proposed a finite mixture distribution for modelling multinomial extra variation when the extra variation is believed to be caused by clumped multinomial sampling with one clumping we propose an extension of the model to incorporate possible multiple clumping we show that the extended finite mixture distribution is a multinomial mixing distribution with different mixing coefficients we derive maximum likelihood estimating equations and an asymptotic approximation to the fisher information matrix for the parameters of the model a real life dataset is analysed

inference from grouped data in three parameter weibull models with applications to breakdown voltage experiments an important objective of breakdown voltage experiments is to estimate either the threshold below which no breakdown occurs or other voltage levels below which breakdown occurs with a small probability a commonly used statistical technique in these studies is to fit a three parameter weibull distribution to the experimental data difficulties in applying the method of maximum likelihood to three parameter weibull models due to nonregularity have led to a variety of alternative approaches in the literature in practice however voltage breakdown and other failure time data are usually discretized or rounded off for grouped data from the weibull model there are still difficulties in applying likelihood methods when the sample size is moderate because of the so called embedded model problem after a brief review of this problem and related likelihood theory we show how the difficulties can be resolved and how likelihood based confidence intervals for the weibull parameters and quantiles can be constru

sensitivity of score tests for zero inflation in count data in many biomedical applications count data have a large proportion of zeros and the zero inflated poisson regression zip model may be appropriate a popular score test for zero inflation comparing the zip model to a standard poisson regression model was given by van den broek similarly for count data that exhibit extra zeros and are simultaneously overdispersed a score test for testing the zip model against a zero inflated negative binomial alternative was proposed by ridout hinde and demetrio however these test statistics are sensitive to anomalous cases in the data and incorrect inferences concerning the choice of model may be drawn in this paper diagnostic measures are derived to assess the influence of observations on the score statistics two examples that motivated the application of zero inflated regression models are considered to illustrate the importance of sensitivity analysis of the zero inflation tests

multi level block permutation under weak and reasonable assumptions mainly that data are exchangeable under the null hypothesis permutation tests can provide exact control of false positives and allow the use of various non standard statistics there are however various common examples in which global exchangeability can be violated including paired tests tests that involve repeated measurements tests in which subjects are relatives members of pedigrees any dataset with known dependence among observations in these cases some permutations if performed would create data that would not possess the original dependence structure and thus should not be used to construct the reference null distribution to allow permutation inference in such cases we test the null hypothesis using only a subset of all otherwise possible permutations i e using only the rearrangements of the data that respect exchangeability thus retaining the original joint distribution unaltered in a previous study we defined exchangeability for blocks of data as opposed to each datum individually then allowing permutations to happen within block or the blocks as a whole to be permuted here we extend that notion to allow blocks to be nested in a hierarchical multi level definition we do not explicitly model the degree of dependence between observations only the lack of independence the dependence is implicitly accounted for by the hierarchy and by the permutation scheme the strategy is compatible with heteroscedasticity and variance groups and can be used with permutations sign flippings or both combined we evaluate the method for various dependence structures apply it to real data from the human connectome project hcp as an example application show that false positives can be avoided in such cases and provide a software implementation of the proposed approach

bias reduced and separation proof gee with small or sparse longitudinal binary data generalized estimating equation gee is a popular approach for analyzing correlated binary data however the problems of separation in gee are still unknown the separation created by a covariate often occurs in small correlated binary data and even in large data with rare outcome and or high intra cluster correlation and a number of influential covariates this paper investigated the consequences of separation in gee and addressed them by introducing a penalized gee termed as pgee the pgee is obtained by adding firth type penalty term which was originally proposed for generalized linear model score equation to standard gee and shown to achieve convergence and provide finite estimate of the regression coefficient in the presence of separation which are not often possible in gee further a small sample bias correction to the sandwich covariance estimator of the pgee estimator is suggested simulations also showed that the gee failed to achieve convergence and or provided infinitely large estimate of the regression coefficient in the presence of complete or quasi complete separation whereas the pgee showed significant improvement by achieving convergence and providing finite estimate even in the presence of near to separation the pgee also showed superior properties over the gee furthermore the bias corrected sandwich estimator for the pgee estimator showed substantial improvement over the standard sandwich estimator by reducing bias in estimating type i error rate an illustration using real data also supported the findings of simulation the pgee with bias corrected sandwich covariance estimator is recommended to use for small to moderate size sample n 50 and even can be used for large sample if there is any evidence of separation or near to separation

higher order likelihood inference in meta analysis and meta regression this paper investigates the use of likelihood methods for meta analysis within the random effects models framework we show that likelihood inference relying on first order approximations while improving common meta analysis techniques can be prone to misleading results this drawback is very evident in the case of small sample sizes which are typical in meta analysis we alleviate the problem by exploiting the theory of higher order asymptotics in particular we focus on a second order adjustment to the log likelihood ratio statistic simulation studies in meta analysis and meta regression show that higher order likelihood inference provides much more accurate results than its first order counterpart while being of a computationally feasible form we illustrate the application of the proposed approach on a real example

weighted integral inequalities for solutions of the a harmonic equation we prove the parametric versions of ar weighted integral inequalities for differential forms satisfying the a harmonic equation these results can be considered as extensions of the classical inequalities for sobolev functions

permutation tests for random effects in linear mixed models summary inference regarding the inclusion or exclusion of random effects in linear mixed models is challenging because the variance components are located on the boundary of their parameter space under the usual null hypothesis as a result the asymptotic null distribution of the wald score and likelihood ratio tests will not have the typical 2 distribution although it has been proved that the correct asymptotic distribution is a mixture of 2 distributions the appropriate mixture distribution is rather cumbersome and nonintuitive when the null and alternative hypotheses differ by more than one random effect as alternatives we present two permutation tests one that is based on the best linear unbiased predictors and one that is based on the restricted likelihood ratio test statistic both methods involve weighted residuals with the weights determined by the among and within subject variance components the null permutation distributions of our statistics are computed by permuting the residuals both within and among subjects and are valid both asymptotically and in small samples we examine the size and power of our tests via simulation under a variety of settings and apply our test to a published data set of chronic myelogenous leukemia patients

smoothing spline anova for time dependent spectral analysis in this article we propose a smoothing spline anova model ss anova to estimate and to make inference on the time varying log spectrum of a locally stationary process the time varying spectrum is assumed to be smooth in both time and frequency this assumption essentially turns a time frequency spectral estimation problem into a 2 dimensional surface estimation problem a smooth localized complex exponential slex basis is used to calculate the initial periodograms and a ss anova is fitted to the log periodograms this approach allows the time and frequency domains to be modeled in a unified approach and jointly estimated inference procedures such as confidence intervals and hypothesis tests proposed for the ss anova can be adopted for the time varying spectrum because of the smoothness assumption of the underlying spectrum once we have the estimates on a time frequency grid we can calculate the estimate at any given time and frequency this leads to a high computational efficiency because for

on the asymptotics of constrained local m estimators we discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and more generally m estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set s we give a counterexample showing that regularity of s in the sense of clarke is not sufficient for asymptotic equivalence of n consistent locally optimal m estimators we argue further that stronger properties such as so called near convexity or prox regularity of s are required in order to ensure that any two n consistent locally optimal m estimators have the same asymptotics

generating survival times to simulate cox proportional hazards models with time varying covariates simulations and monte carlo methods serve an important role in modern statistical research they allow for an examination of the performance of statistical procedures in settings in which analytic and mathematical derivations may not be feasible a key element in any statistical simulation is the existence of an appropriate data generating process one must be able to simulate data from a specified statistical model we describe data generating processes for the cox proportional hazards model with time varying covariates when event times follow an exponential weibull or gompertz distribution we consider three types of time varying covariates first a dichotomous time varying covariate that can change at most once from untreated to treated e g organ transplant second a continuous time varying covariate such as cumulative exposure at a constant dose to radiation or to a pharmaceutical agent used for a chronic condition third a dichotomous time varying covariate with a subject being able to move repeatedly between treatment states e g current compliance or use of a medication in each setting we derive closed form expressions that allow one to simulate survival times so that survival times are related to a vector of fixed or time invariant covariates and to a single time varying covariate we illustrate the utility of our closed form expressions for simulating event times by using monte carlo simulations to estimate the statistical power to detect as statistically significant the effect of different types of binary time varying covariates this is compared with the statistical power to detect as statistically significant a binary time invariant covariate copyright 2012 john wiley sons ltd

characterizing additively closed discrete models by a property of their maximum likelihood estimators with an application to generalized hermite distributions this article reports on two parameter count distributions satisfying very general conditions that are closed under addition so that their maximum likelihood estimator mle of the population mean is the sample mean the most important of these in practice the generalized hermite distribution is analyzed and a necessary and sufficient condition is given to ensure that the mle is the solution of likelihood equations score test to contrast the poisson assumption is studied and two examples of applications are given

autoregressive generalized linear mixed effect models with crossed random effects an application to intensive binary time series eye tracking data as a method to ascertain person and item effects in psycholinguistics a generalized linear mixed effect model glmm with crossed random effects has met limitations in handing serial dependence across persons and items this paper presents an autoregressive glmm with crossed random effects that accounts for variability in lag effects across persons and items the model is shown to be applicable to intensive binary time series eye tracking data when researchers are interested in detecting experimental condition effects while controlling for previous responses in addition a simulation study shows that ignoring lag effects can lead to biased estimates and underestimated standard errors for the experimental condition effects

likelihood ratio tests with boundary constraints using data dependent degrees of freedom when the null hypothesis constrains parameters to the boundary of the parameter space the asymptotic null distribution of the likelihood ratio statistic is often a mixture of chi squared distributions giving rise to the so called chi bar test where weights can depend on the true unknown parameter and be difficult to calculate we consider the test that conditions on the observed number of null hypothesis parameters in the interior of the parameter space this approach uses simple chi squared thresholds yields conservative asymptotic type i error and is guaranteed to give power improvements over the naive approach of simply ignoring boundary constraints simulations validate the theoretical results illustrate application settings and find power comparable with but usually less than that of the chi bar test copyright 2013 oxford university press

on dependent repeated screening tests a screening test is applied n times to a person with known true status if more than k tests have positive outcomes then the person is assigned to be screen positive otherwise the person is assigned to be screen negative assuming that the tests are exchangeable we can characterize the possible dependence among tests by at most n parameters called canonical moments which can be estimated from the data the performance characteristics of the composite test such as likelihood ratios sensitivity and specificity can be computed based on these estimates thus we can choose n and k so that the desired levels of likelihood ratios sensitivity and specificity can be achieved we study the cases n 2 and n 3 in detail

parameter estimation and inference in the linear mixed model the paper reviews the linear mixed model with a focus on parameter estimation and inference parameter estimation for the different components of the model are reviewed with an emphasis on variance parameter estimation inferential procedures for the fixed effects random effects or a combination of both fixed and random effects are also discussed

estimation of incubation period and generation time based on observed length biased epidemic cohort with censoring for covid 19 outbreak in china the incubation period and generation time are key characteristics in the analysis of infectious diseases the commonly used contact tracing based estimation of incubation distribution is highly influenced by the individuals judgment on the possible date of exposure and might lead to significant errors on the other hand interval censoring based methods are able to utilize a much larger set of traveling data but may encounter biased sampling problems the distribution of generation time is usually approximated by observed serial intervals however it may result in a biased estimation of generation time especially when the disease is infectious during incubation in this paper the theory from renewal process is partially adopted by considering the incubation period as the interarrival time and the duration between departure from wuhan and onset of symptoms as the mixture of forward time and interarrival time with censored intervals in addition a consistent estimator for the distribution of generation time based on incubation period and serial interval is proposed for incubation infectious diseases a real case application to the current outbreak of covid 19 is implemented we find that the incubation period has a median of 8 50 days 95 confidence interval ci 7 22 9 15 the basic reproduction number in the early phase of covid 19 outbreak based on the proposed generation time estimation is estimated to be 2 96 95 ci 2 15 3 86

copula functions for residual dependency most item response theory models are not robust to violations of conditional independence however several modeling approaches e g conditioning on other responses additional random effects exist that try to incorporate local item dependencies but they have some drawbacks such as the nonreproducibility of marginal probabilities and resulting interpretation problems in this paper a new class of models making use of copulas to deal with local item dependencies is introduced these models belong to the bigger class of marginal models in which margins and association structure are modeled separately it is shown how this approach overcomes some of the problems associated with other local item dependency models

global poincare inequalities for green s operator applied to the solutions of the nonhomogeneous a harmonic equation both local and global a r weighted poincare inequalities for green s operator applied to the solutions of the nonhomogeneous a harmonic equation in john domains are established as applications of the poincare inequalities for green s operator the a r weighted sobolev imbedding inequalities for green s operator in john domains are also proved

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

permutation tests for centre effect on survival endpoints with application in an acute myeloid leukaemia multicentre study when analysing multicentre data it may be of interest to test whether the distribution of the endpoint varies among centres in a mixed effect model testing for such a centre effect consists in testing to zero a random centre effect variance component it has been shown that the usual asymptotic 2 distribution of the likelihood ratio and score statistics under the null does not necessarily hold in the case of censored data mixed effects cox models have been used to account for random effects but few works have concentrated on testing to zero the variance component of the random effects we propose a permutation test using random permutation of the cluster indices to test for a centre effect in multilevel censored data results from a simulation study indicate that the permutation tests have correct type i error rates contrary to standard likelihood ratio tests and are more powerful the proposed tests are illustrated using data of a multicentre clinical trial of induction therapy in acute myeloid leukaemia patients copyright 2014 john wiley sons ltd

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints summary the analysis of moment structural models has become an important tool of investigation in behavioural educational and economic studies the chi squared largesample test is routinely employed to assess the goodness of fit of the model considered however in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met here we consider the case where the population value of the parameter vector is a boundary point of the feasible region we show that in this case the asymptotic distribution of test statistic is a mixture of chi squared distributions the problem of finding the corresponding weights is discussed

l φ μ averaging domains and the quasi hyperbolic metric in this paper we first introduce email protected m averaging domains which are generalizations of existing domains such as john domains and l s m averaging domains then we characterize l f m averaging domains using the quasihyperbolic metric finally we give applications to quasiconformal mappings

plmet a novel pseudolikelihood based em test for homogeneity in generalilzed exponential tilt mixture models motivated by analyses of dna methylation data we propose a semiparametric mixture model namely the generalized exponential tilt mixture model to account for heterogeneity between differentially methylated and non differentially methylated subjects in the cancer group and capture the differences in higher order moments e g mean and variance between subjects in cancer and normal groups a pairwise pseudolikelihood is constructed to eliminate the unknown nuisance function to circumvent boundary and non identifiability problems as in parametric mixture models we modify the pseudolikelihood by adding a penalty function in addition the test with simple asymptotic distribution has computational advantages compared with permutation based test for high dimensional genetic or epigenetic data we propose a pseudolikelihood based expectation maximization test and show the proposed test follows a simple chi squared limiting distribution simulation studies show that the proposed test controls type i errors well and has better power compared to several current tests in particular the proposed test outperforms the commonly used tests under all simulation settings considered especially when there are variance differences between two groups the proposed test is applied to a real data set to identify differentially methylated sites between ovarian cancer subjects and normal subjects

tight bounds for the generalized marcum q function abstract in this paper we study the generalized marcum q function of order 0 real defined by q a b 1 a 1 b t e t 2 a 2 2 i 1 a t dt where a 0 b 0 and i stands for the modified bessel function of the first kind our aim is to improve and extend some recent results of wang to the generalized marcum q function in order to deduce some sharp lower and upper bounds in both cases b a and b a we give the best possible upper bound for q a b the key tools in our proofs are some monotonicity properties of certain functions involving the modified bessel function of the first kind these monotonicity properties are deduced from some results on modified bessel functions which have been used in wave mechanics and finite elasticity

group testing regression models with fixed and random effects group testing where subjects are tested in pools rather than individually has a long history of successful application in infectious disease screening in this article we develop group testing regression models to include covariate effects that are best regarded as random we present approaches to fit mixed effects models using maximum likelihood investigate likelihood ratio and score tests for variance components and evaluate small sample performance using simulation we illustrate our methods using chlamydia and gonorrhea data collected by the state of nebraska as part of the infertility prevention project

monotonicity properties and bounds for the chi square and gamma distributions a sharp analysis of the convexity properties of marcum functions is performed monotonicity properties for ratios of consecutive marcum functions are obtained the new bounds for marcum functions improve previous bounds in large regions new and improved monotonicity properties are obtained in the central case the combined bounds obtained for the central case are superior to previous bounds the generalized marcum functions q x y and p x y have as particular cases the non central 2 and gamma cumulative distributions which become central distributions incomplete gamma function ratios when the non centrality parameter x is set to zero we analyze monotonicity and convexity properties for the generalized marcum functions and for ratios of marcum functions of consecutive parameters differing in one unity and we obtain upper and lower bounds for the marcum functions these bounds are proven to be sharper than previous estimations for a wide range of the parameters additionally we show how to build convergent sequences of upper and lower bounds the particularization to incomplete gamma functions together with some additional bounds obtained for this particular case lead to combined bounds which improve previously existing inequalities

flexible modeling of longitudinal highly skewed outcomes the analysis of data from epidemiologic and environmental studies presents challenges such as skewness of distribution rounding and multiple measurements over time to model trends over time based on repeated measurements we propose a general latent model suitable for highly skewed data the model assumes that the observed outcome is determined by an unobservable outcome that follows a weibull distribution to accommodate correlations among repeated responses over time we introduce a general random effect from the power variance function pvf family of distributions including the gamma distribution often employed in the literature the resulting marginal likelihood has a closed form without resorting to numerical or approximation methods we study estimation and hypothesis testing under these models with different choices of random effect distributions simulation studies are conducted to evaluate their performance finally we apply the proposed method to exposure data collected from the michigan polybrominated biphenyl mipbb study

higher integrability of green s operator and homotopy operator abstract we prove the higher integrability and higher order imbedding theorems of the composition of homotopy operator and green s operator we also study analogues of the homotopy operator and green s operator respectively

latent change classes in dichotomous data changes in dichotomous data caused by treatments can be analyzed by means of the so called linear logistic model with relaxed assumptions llra the llra does not require observable criteria representing a single underlying latent trait but it postulates the generalizability of the treatment effects over criteria and subjects to test this latter crucial assumption the mixture llra was proposed that allows directly unobservable types of subjects to have different treatment effects as the earlier methods for estimating the parameters of the mixture llra have specific drawbacks a further method based on the conditional maximum likelihood principle will be presented here in contrast to the earlier conditional methods it uses all of the dichotomous change data while having fewer parameters further its goodness of fit tests become more sensitive to a falsely specified number of change types even though the treatment effects are biased for typically occurring small to moderate sample sizes however parametric bootstrapping of the distributions of the fit statistics is recommended for performing hypotheses tests finally three applications of the new method to empirical data are described first about the effect of the so called trager psychophysical integration second about the effect of autogenic therapy on patients with psychosomatic symptoms and third about the effect of religious education on the attitude towards sects

a two part random effects model for semicontinuous longitudinal data a semicontinuous variable has a portion of responses equal to a single value typically 0 and a continuous often skewed distribution among the remaining values in cross sectional analyses variables of this type may be described by a pair of regression models for example a logistic model for the probability of nonzero response and a conditional linear model for the mean response given that it is nonzero we extend this two part regression approach to longitudinal settings by introducing random coefficients into both the logistic and the linear stages fitting a two part random effects model poses computational challenges similar to those found with generalized linear mixed models we obtain maximum likelihood estimates for the fixed coefficients and variance components by an approximate fisher scoring procedure based on high order laplace approximations to illustrate we apply the technique to data from the adolescent alcohol prevention trial examining reported recent alcohol use for students in g

the analysis of asthma control under a markov assumption with use of covariates in studies of disease states and their relation to evolution data on the state are usually obtained at in frequent time points during follow up moreover in many applications there are measured covariates on each individual under study and interest centres on the relationship between these covariates and the disease evolution we developed a continuous time markov model with use of time dependent covariates and a markov model with piecewise constant intensities to model asthma evolution methods to estimate the effect of covariates on transition intensities to test the assumption of time homogeneity and to assess goodness of fit are proposed we apply these methods to asthma control we consider a three state model and we discuss in detail the analysis of asthma control evolution copyright 2003 john wiley sons ltd

testing the number of components in a normal mixture we demonstrate that under a theorem proposed by vuong the likelihood ratio statistic based on the kullback leibler information criterion of the null hypothesis that a random sample is drawn from a k 0 component normal mixture distribution against the alternative hypothesis that the sample is drawn from a k 1 component normal mixture distribution is asymptotically distributed as a weighted sum of independent chi squared random variables with one degree of freedom under general regularity conditions we report simulation studies of two cases where we are testing a single normal versus a two component normal mixture and a two component normal mixture versus a three component normal mixture an empirical adjustment to the likelihood ratio statistic is proposed that appears to improve the rate of convergence to the limiting distribution

models for the extremes of markov chains the modelling of extremes of a time series has progressed from the assumption of independent observations to more realistic forms of temporal dependence in this paper we focus on markov chains deriving a class of models for their joint tail which allows the degree of clustering of extremes to decrease at high levels overcoming a key limitation in current methodologies theoretical aspects of the model are examined and a simulation algorithm is developed through which the stochastic properties of summaries of the extremal txhaviour of the chain are evaluated the approach is illustrated through a simulation study of extremal events of gaussian autoregressive processes and an application to temperature data