an exact test for multiple inequality and equality constraints in the linear regression model abstract in this article we consider the linear regression model y x e where e is n 0 2i in this context we derive exact tests of the form h r r versus k rk for the case in which 2 is unknown we extend these results to consider hypothesis tests of the form h r1 r1 and r2 r2 versus k rk for each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming for both tests we derive their exact distribution as a weighted sum of snedecor s f distributions normalized by the numerator degrees of freedom of each f distribution of the sum a methodology for computing critical values as well as probability values for the tests is discussed the relationship between this testing framework and the multivariate one sided hypothesis testing literature is also discussed in this context we show that for any size of the hypothesis test h 0 versus k rk the test statistic and critical value obtained a

modeling the amplitude statistics of ultrasonic images in this paper a new statistical model for representing the amplitude statistics of ultrasonic images is presented the model is called the rician inverse gaussian riig distribution due to the fact that it is constructed as a mixture of the rice distribution and the inverse gaussian distribution the probability density function pdf of the riig model is given in closed form as a function of three parameters some theoretical background on this new model is discussed and an iterative algorithm for estimating its parameters from data is given then the appropriateness of the riig distribution as a model for the amplitude statistics of medical ultrasound images is experimentally studied it is shown that the new distribution can fit to the various shapes of local histograms of linearly scaled ultrasound data better than existing models a log likelihood cross validation comparison of the predictive performance of the riig the k and the generalized nakagami models turns out in favor of the new model furthermore a maximum a posteriori map filter is developed based on the riig distribution experimental studies show that the riig map filter has excellent filtering performance in the sense that it smooths homogeneous regions and at the same time preserves details

a two part joint model for the analysis of survival and longitudinal binary data with excess zeros many longitudinal studies generate both the time to some event of interest and repeated measures data this article is motivated by a study on patients with a renal allograft in which interest lies in the association between longitudinal proteinuria a dichotomous variable measurements and the time to renal graft failure an interesting feature of the sample at hand is that nearly half of the patients were never tested positive for proteinuria 1g day during follow up which introduces a degenerate part in the random effects density for the longitudinal process in this article we propose a two part shared parameter model framework that effectively takes this feature into account and we investigate sensitivity to the various dependence structures used to describe the association between the longitudinal measurements of proteinuria and the time to renal graft failure

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

robust wald type tests of one sided hypotheses in the linear model abstract let us consider the linear model y x e in the usual matrix notation where the errors are iid our main objective is to develop robust wald type tests for a large class of hypotheses on by robust we mean robustness in terms of size and power against long tailed error distributions first assume that the error distribution is symmetric about the origin let l and be the least squares and a robust estimator of assume that they are asymptotically normal about with covariance matrices 2 xtx 1 and 2 xtx 1 respectively so could be an m estimator or a high breakdown point estimator robust wald type tests based on denoted by rw are studied here for testing a large class of one sided hypotheses on it is shown that the asymptotic null distribution of rw and that of the usual wald type statistic based on l denoted by w are the same this is a useful result since the critical values and procedures for computing the p values for w are directly applicable to rw as well a more impo

on some properties of digamma and polygamma functions in this note we present some new and structural inequalities for digamma polygamma and inverse polygamma functions we also extend generalize and refine some known inequalities for these important functions

a new parametric method of estimating the joint probability density abstract we present simple parametric methods that overcome major limitations of the literature on joint marginal density estimation in doing so we do not assume any form of marginal or joint distribution furthermore using our method a multivariate density can be easily estimated if we know only one of the marginal densities we apply our methods to financial data

a score test for zero inflation in a poisson distribution when analyzing poisson count data sometimes a lot of zeros are observed when there are too many zeros a zero inflated poisson distribution can be used a score test is presented to test whether the number of zeros is too large for a poisson distribution to fit the data well

bootstrap tests for overdispersion in a zero inflated poisson regression model summaryridout hinde and demetrio 2001 biometrics57 219 223 derived a score test for testing a zero inflated poisson zip regression model against zero inflated negative binomial zinb alternatives they mentioned that the score test using the normal approximation might underestimate the nominal significance level possibly for small sample cases to remedy this problem a parametric bootstrap method is proposed it is shown that the bootstrap method keeps the significance level close to the nominal one and has greater power uniformly than the existing normal approximation for testing the hypothesis

zero inflated poisson regression with an application to defects in manufacturing zero inflated poisson zip regression is a model for count data with excess zeros it assumes that with probability p the only possible observation is 0 and with probability 1 p a poisson random variable is observed for example when manufacturing equipment is properly aligned defects may be nearly impossible but when it is misaligned defects may occur according to a poisson distribution both the probability p of the perfect zero defect state and the mean number of defects in the imperfect state may depend on covariates sometimes p and are unrelated other times p is a simple function of such as p l 1 t for an unknown constant t in either case zip regression models are easy to fit the maximum likelihood estimates mle s are approximately normal in large samples and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the mle s simulations suggest that the confidence intervals based on likelihood ratio test

generalized score test of homogeneity for mixed effects models many important problems in psychology and biomedical studies require testing for overdispersion correlation and heterogeneity in mixed effects and latent variable models and score tests are particularly useful for this purpose but the existing testing procedures depend on restrictive assumptions in this paper we propose a class of test statistics based on a general mixed effects model to test the homogeneity hypothesis that all of the variance components are zero under some mild conditions not only do we derive asymptotic distributions of the test statistics but also propose a resampling procedure for approximating their asymptotic distributions conditional on the observed data to overcome the technical challenge we establish an invariance principle for random quadratic forms indexed by a parameter a simulation study is conducted to investigate the empirical performance of the test statistics a real data set is analyzed to illustrate the application of our theoretical results

specification and testing of some modified count data models abstract this paper explores the specification and testing of some modified count data models these alternatives permit more flexible specification of the data generating process dgp than do familiar count data models e g the poisson and provide a natural means for modeling data that are over or underdispersed by the standards of the basic models in the cases considered the familiar forms of the distributions result as parameter restricted versions of the proposed modified distributions accordingly score tests of the restrictions that use only the easily computed ml estimates of the standard models are proposed the tests proposed by hausman 1978 and white 1982 are also considered the tests are then applied to count data models estimated using survey microdata on beverage consumption

a score test for testing a zero inflated poisson regression model against zero inflated negative binomial alternatives count data often show a higher incidence of zero counts than would be expected if the data were poisson distributed zero inflated poisson regression models are a useful class of models for such data but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the poisson distribution we therefore provide a score test for testing zero inflated poisson regression models against zero inflated negative binomial alternatives

inference when a nuisance parameter is not identified under the null hypothesis many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses this paper studies the asymptotic distribution theory for such tests the asymptotic distributions of standard test statistics are described as functionals of chi square processes in general the distributions depend upon a large number of unknown parameters we show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters and we show that this transformation can be easily approximated via simulation the theory is applied to threshold models with special attention given to the so called self exciting threshold autoregressive model monte carlo methods are used to assess the finite sample distributions the tests are applied to u s gnp growth rates and we find that potter s 1995 threshold effect in this series can be possibly explained by sampling variation

robust bounded influence tests in linear models abstract a robust test that we call an aligned generalized m test for testing subhypotheses in general linear models is developed and its asymptotic properties are studied the test is a robustification of the well known f test and it is an elegant alternative to ronchetti s 1982 class of tests p values associated with it can be approximated readily using existing chi square tables the test is based on an appropriately constructed quadratic form and uses the generalized m estimators of the parameters in the reduced model under the null hypothesis the asymptotic distribution is a central chi square and under contiguous alternatives it is a noncentral chi square with the same degrees of freedom the test can be viewed as a generalization of sen s 1982 m test for linear models the influence function of the test is bounded the bound not only applies to the influence of residuals but to the influence of position in the factor space as well on the other hand sen s test has bounded influence only

modeling heaping in self reported cigarette counts in studies of smoking behavior some subjects report exact cigarette counts whereas others report rounded off counts particularly multiples of 20 10 or 5 this form of data reporting error known as heaping can bias the estimation of parameters of interest such as mean cigarette consumption we present a model to describe heaped count data from a randomized trial of bupropion treatment for smoking cessation the model posits that the reported cigarette count is a deterministic function of an underlying precise cigarette count variable and a heaping behavior variable both of which are at best partially observed to account for an excess of zeros as would likely occur in a smoking cessation study where some subjects successfully quit we model the underlying count variable with zero inflated count distributions we study the sensitivity of the inference on smoking cessation by fitting various models that either do or do not account for heaping and zero inflation comparing the models by means of bayes factors our results suggest that sufficiently rich models for both the underlying distribution and the heaping behavior are indispensable to obtaining a good fit with heaped smoking data the analyses moreover reveal that bupropion has a significant effect on the fraction abstinent but not on mean cigarette consumption among the non abstinent

nonparametric test for monotone variance residual life class of life distributions with hypothesis testing applications the problem of testing exponentiality against decreasing increasing variance remaining life distribution dvrl ivrl is investigated for this aging properties a nonparametric procedure u test is presented the percentiles of this test are tabulated for sample sizes n 5 1 40 it is shown that the proposed test is simple has high relative efficiency for some commonly used alternatives and enjoys a good power data of 40 patients suffering from blood cancer disease leukemia is considered as a practical application of the proposed test in the medical sciences

a score type test for heterogeneity in zero inflated models in a stratified population we propose a score type statistic to evaluate heterogeneity in zero inflated models for count data in a stratified population where heterogeneity is defined as instances in which the zero counts are generated from two sources evaluating heterogeneity in this class of models has attracted considerable attention in the literature but existing testing procedures have primarily relied on the constancy assumption under the alternative hypothesis in this paper we extend the literature by describing a score type test to evaluate homogeneity against general alternatives that do not neglect the stratification information under the alternative hypothesis the limiting null distribution of the proposed test statistic is a mixture of chi squared distributions which can be well approximated by a simple parametric bootstrap procedure our numerical simulation studies show that the proposed test can greatly improve efficiency over tests of heterogeneity that ignore the stratification information an empirical application to dental caries data in early childhood further shows the importance and practical utility of the methodology in using the stratification profile to detect heterogeneity in the population

globally convergent algorithms for estimating generalized gamma distributions in fast signal and image processing many applications in real time signal image and video processing require automatic algorithms for rapid characterizations of signals and images through fast estimation of their underlying statistical distributions we present fast and globally convergent algorithms for estimating the three parameter generalized gamma distribution g gamma d the proposed method is based on novel scale independent shape estimation sise equations we show that the sise equations have a unique global root in their semi infinite domains and the probability that the sample sise equations have a unique global root tends to one the consistency of the global root its scale and index shape estimators is obtained furthermore we establish that with probability tending to one newton raphson nr algorithms for solving the sample sise equations converge globally to the unique root from any initial value in its given domain in contrast to existing methods another remarkable novelty is that the sample sise equations are completely independent of gamma and polygamma functions and involve only elementary mathematical operations making the algorithms well suited for real time both hardware and software implementations the sise estimators also allow the maximum likelihood ml ratio procedure to be carried out for testing the generalized gaussian distribution ggd versus the g gamma d finally the fast global convergence and accuracy of our algorithms for finite samples are demonstrated by both simulation studies and real image analysis

a score test for overdispersion in zero inflated poisson mixed regression model count data with extra zeros are common in many medical applications the zero inflated poisson zip regression model is useful to analyse such data for hierarchical or correlated count data where the observations are either clustered or represent repeated outcomes from individual subjects a class of zip mixed regression models may be appropriate however the zip parameter estimates can be severely biased if the non zero counts are overdispersed in relation to the poisson distribution in this paper a score test is proposed for testing the zip mixed regression model against the zero inflated negative binomial alternative sampling distribution and power of the test statistic are evaluated by simulation studies the results show that the test statistic performs satisfactorily under a wide range of conditions the test procedure is applied to pancreas disorder length of stay that comprised mainly same day separations and simultaneous prolonged hospitalizations

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

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

on the method of logarithmic cumulants for parametric probability density function estimation parameter estimation of probability density functions is one of the major steps in the area of statistical image and signal processing in this paper we explore several properties and limitations of the recently proposed method of logarithmic cumulants molc parameter estimation approach which is an alternative to the classical maximum likelihood ml and method of moments mom approaches we derive the general sufficient condition for a strong consistency of the molc estimates which represents an important asymptotic property of any statistical estimator this result enables the demonstration of the strong consistency of molc estimates for a selection of widely used distribution families originating from but not restricted to synthetic aperture radar image processing we then derive the analytical conditions of applicability of molc to samples for the distribution families in our selection finally we conduct various synthetic and real data experiments to assess the comparative properties applicability and small sample performance of molc notably for the generalized gamma and k families of distributions supervised image classification experiments are considered for medical ultrasound and remote sensing sar imagery the obtained results suggest that molc is a feasible and computationally fast yet not universally applicable alternative to mom molc becomes especially useful when the direct ml approach turns out to be unfeasible

zero inflated poisson and binomial regression with random effects a case study summary in a 1992 technometrics paper lambert 1992 34 1 14 described zero inflated poisson zip regression a class of models for count data with excess zeros in a zip model a count response variable is assumed to be distributed as a mixture of a poisson distribution and a distribution with point mass of one at zero with mixing probability p both p and are allowed to depend on covariates through canonical link generalized linear models in this paper we adapt lambert s methodology to an upper bounded count situation thereby obtaining a zero inflated binomial zip model in addition we add to the flexibility of these fixed effects models by incorporating random effects so that e g the within subject correlation and between subject heterogeneity typical of repeated measures data can be accommodated we motivate develop and illustrate the methods described here with an example from horticulture where both upper bounded count binomial type and unbounded count poisson type data with excess zeros were collected in a repeated measures designed experiment

smooth tests for the zero inflated poisson distribution in this article we construct three smooth goodness of fit tests for testing for the zero inflated poisson zip distribution against general smooth alternatives in the sense of neyman we apply our tests to a data set previously claimed to be zip distributed and show that the zip is not a good model to describe the data at rejection of the null hypothesis of zip the individual components of the test statistic which are directly related to interpretable parameters in a smooth model may be used to gain insight into an alternative distribution

sar amplitude probability density function estimation based on a generalized gaussian model in the context of remotely sensed data analysis an important problem is the development of accurate models for the statistics of the pixel intensities focusing on synthetic aperture radar sar data this modeling process turns out to be a crucial task for instance for classification or for denoising purposes in this paper an innovative parametric estimation methodology for sar amplitude data is proposed that adopts a generalized gaussian gg model for the complex sar backscattered signal a closed form expression for the corresponding amplitude probability density function pdf is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model specifically the recently proposed method of log cumulants molc is applied which stems from the adoption of the mellin transform instead of the usual fourier transform in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant for the developed gg based amplitude model the resulting molc estimates turn out to be numerically feasible and are also analytically proved to be consistent the proposed parametric approach was validated by using several real ers 1 xsar e sar and nasa jpl airborne sar images and the experimental results prove that the method models the amplitude pdf better than several previously proposed parametric models for backscattering phenomena

confidence bands for survival curves under the proportional hazards model summary in this paper we show how to construct simultaneous confidence bands for the subjectspecific survival curve under the cox proportional hazards model the idea is to approximate the distribution of the normalized cumulative hazard estimator by a zero mean gaussian process whose distribution can be easily generated through simulation numerical studies indicate that the proposed bands are appropriate for practical use a liver disease example is presented

maximum likelihood estimation of k distribution parameters via the expectation maximization algorithm maximum likelihood ml estimates of k distribution parameters are derived using the expectation maximization em approach this approach demonstrates the computational advantages compared with 2 d numerical maximization of the likelihood function using a nelder mead approach for large datasets the em approach yields more accurate estimates than those of a non ml estimation technique

empirical fitting of discrete distributions summary short tailed observed frequency distributions are often well fitted by a number of different theoretical discrete distributions with little discriminatory power an example is used to suggest how this may be carried further in some situations

a method for estimating the parameters of the k distribution a method that combines the maximum likelihood and the method of moments for estimating the parameters of the k distribution is proposed the method results in the lowest variance of parameter estimates when compared with existing non ml techniques

modeling daily and weekly moderate and vigorous physical activity using zero inflated mixture poisson distribution recently developed accelerometer devices have been used in large epidemiological studies for continuous and objective monitoring of physical activities typically physical movements are summarized as minutes in light moderate and vigorous physical activities in each wearing day because of preponderance of zeros zero inflated distributions have been used for modeling the daily moderate or higher levels of physical activity yet these models do not fully account for variations in daily physical activity and cannot be extended to model weekly physical activity explicitly while the weekly physical activity is considered as an indicator for a subject s average level of physical activity to overcome these limitations we propose to use a zero inflated poisson mixture distribution that can model daily and weekly physical activity in same family of mixture distributions under this method the likelihood of an inactive day and the amount of exercise in an active day are simultaneously modeled by a joint random effects model to incorporate heterogeneity across participants if needed the method has the flexibility to include an additional random effect to address extra variations in daily physical activity maximum likelihood estimation can be obtained through gaussian quadrature technique which is implemented conveniently in an r package glmmadaptive method performances are examined using simulation studies the method is applied to data from the hispanic community health study study of latinos to examine the relationship between physical activity and bmi groups and within a participant the difference in physical activity between weekends and weekdays

a score test against one sided alternatives abstract a score type statistic t s is introduced for testing h 0 against k 0 and more general one sided hypotheses when nuisance parameters may be present is a vector parameter the main advantages of t s are that it requires estimation of the model only under the null hypothesis and that it is asymptotically equivalent to the likelihood ratio statistic these are precisely the reasons for the popularity of the score tests for testing against two sided alternatives in this sense t s preserves the main attractive features of the classical two sided score test the theoretical results are presented in a general framework where the likelihood based score function is replaced by an estimating function so that the test is applicable even if the exact population distribution is unknown computation of t s is simplified by the fact that it can be computed easily once the corresponding two sided statistic has been computed the relevance and simplicity of t s are illustrated by discussing

analyzing excessive no changes in clinical trials with clustered data this article considers clinical trials in which the efficacy measure is taken from several sites within each patient such as the alveolar bone height of the tooth sites or bone mineral densities of the lumbar spine sites since usually only a small portion of these sites will exhibit changes the conventional method using per patient average gives a diluted result due to excessive no changes in the data different methods have been proposed for this type of data in the case where the observations are mutually independent this includes the popular two part model lachenbruch 2001 statistics in medicine 20 1215 1234 2002 statistical methods in medical research 11 297 302 which is related to the composite approach for discrete and continuous data in shih and quan 1997 statistics in medicine16 1225 1239 2001 statistica sinica 11 53 62 in this article we model the data with excessive zeros no changes in clustered data using a mixture of distributions and taking into account possible measurement errors this mixture model includes the two part model as a special case when one component of the mixture degenerates

on the efficiency of score tests for homogeneity in two component parametric models for discrete data in many applications of two component mixture models for discrete data such as zero inflated models it is often of interest to conduct inferences for the mixing weights score tests derived from the marginal model that allows for negative mixing weights have been particularly useful for this purpose but the existing testing procedures often rely on restrictive assumptions such as the constancy of the mixing weights and typically ignore the structural constraints of the marginal model in this article we develop a score test of homogeneity that overcomes the limitations of existing procedures the technique is based on a decomposition of the mixing weights into terms that have an obvious statistical interpretation we exploit this decomposition to lay the foundation of the test simulation results show that the proposed covariate adjusted test statistic can greatly improve the efficiency over test statistics based on constant mixing weights a real life example in dental caries research is used to illustrate the methodology

robust tests of inequality constraints and one sided hypotheses in the linear model summary for the linear regression model with independent and identically distributed errors robust tests of various hypotheses on the regression parameter are developed by robust we mean robustness of size and power against long tailed error distributions which may not be symmetric the proposed test statistic denoted by fm resembles the usual f statistic the two main results are i under the null hypothesis the asymptotic distribution of fm and that of the least squares based f statistic are the same and ii the pitman asymptotic efficiency of fm relative to f is equal to the asymptotic efficiency of the corresponding m estimator relative to the least squares estimator an example and simulation results illustrate that fm has desirable robustness properties compared to f

a new parametric method of estimating the joint probability density revisited abstract we significantly extend alghalith 2017 in doing so we show that the joint probability density can be estimated without knowing any of the marginal densities or the conditional density moreover we provide a simpler superior alternative to copulas

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

a criterion for burn in that balances mean residual life and residual variance optimum burn in times have been determined for a variety of criteria such as mean residual life and conditional survival in this paper we consider a residual coefficient of variation that balances mean residual life with residual variance to study this quantity we develop a general result concerning the preservation ofbathtub distributions using this result we give a condition so that the residual coefficient of variation is bathtub shaped furthermore we show that it attains its optimum value at a time that occurs after the mean residual life function attains its optimum value but not necessarily before the change point of the failure rate function

inequalities for nbue and nwue life distributions this paper presents a procedure for developing reliability inequalities for several known classes of failure distributions the inequalities are rational functions of the moments and conditional tail moments of the underlying failure distribution the introduction of four new classes of failure distributions based on the variance behavior facilitates the development of certain inequalities for the nbue and nwue distributions

assessing influence for pharmaceutical data in zero inflated generalized poisson mixed models for clustered count data with excess zeros where the observations are either over dispersed or under dispersed the zero inflated generalized poisson mixed zigpm regression model may be appropriate in which the baseline discrete distribution is a generalized poisson distribution which is a natural extension of standard poisson distribution motivated by one data set drawn from a pharmaceutical study influence diagnostics for zigpm models based on case deletion and local influence analysis are developed in this work the one step approximations of the estimates under case deletion model and some case deletion measures are given meanwhile local influence measures are obtained under various perturbations of the observed data or model assumptions results from a pharmaceutical study illustrate the usefulness of the diagnostic statistics

modified lagrange multiplier tests for problems with one sided alternatives abstract a modified lagrange multiplier test statistic is proposed which takes explicit account of the one sided nature of the alternative in problems where the null hypothesis specifies that the true value of the parameter vector lies on the boundary of the parameter space computation of this statistic requires only the constrained maximum likelihood estimator conditions for the consistency of tests based on this statistic are examined and it is shown that the distribution of the statistic is not affected of nuisance parameters are allowed to lie on the boundary of the parameter space

maximum penalized likelihood estimation for independent and markov dependent mixture models summary this paper concerns the use and implementation of maximum penalized likelihood procedures for choosing the number of mixing components and estimating the parameters in independent and markov dependent mixture models computation of the estimates is achieved via algorithms for the automatic generation of starting values for the em algorithm computation of the information matrix is also discussed poisson mixture models are applied to a sequence of counts of movements by a fetal lamb in utero obtained by ultrasound the resulting estimates are seen to provide plausible mechanisms for the physiological process the analysis of count data that are overdispersed relative to the poisson distribution i e variance mean has received considerable recent attention such data might arise in a clinical study in which overdispersion is caused by unexplained or random subject effects alternatively we might observe a time series of counts in which temporal patterns in the data suggest that a poisson model and its implied randomness are inappropriate this paper is motivated by analysis of a time series of overdispersed count data generated in a study of central nervous system development in fetal lambs our data set consists of observed movement counts in 240 consecutive 5 second intervals obtained from a single animal in analysing these data we focus on the use of poisson mixture models assuming independent observations and also markov dependent mixture models or hidden markov models these models assume that the counts follow independent poisson distributions conditional on the rates which are generated from a mixing distribution either independently or with markov dependence we believe finite mixture models are particularly attractive because they provide plausible explanations for variation in the data this paper will emphasize the following issues concerning estimation inference and application of mixture models i choosing the number of model components ii applying the em algorithm to obtain parameter estimates iii generating sufficiently many starting values to identify a global maximum of the likelihood iv avoiding numerical instability

a score test for zero inflation in correlated count data to account for the preponderance of zero counts and simultaneous correlation of observations a class of zero inflated poisson mixed regression models is applicable for accommodating the within cluster dependence in this paper a score test for zero inflation is developed for assessing correlated count data with excess zeros the sampling distribution and the power of the test statistic are evaluated by simulation studies the results show that the test statistic performs satisfactorily under a wide range of conditions the test procedure is further illustrated using a data set on recurrent urinary tract infections

on m tests in linear models summary for subhypothesis testing in some general linear models some tests based on residuals using m estimators are considered and their asymptotic properties are studied