a mixture model for occupational exposure mean testing with a limit of detection sul lhiary information from detectable exposure measurements randomly sampled from a left truncated log normal distribution may be used to evaluate the distribution of nondetectable values that fall below all analytic limit of detection if the proportion of nondetects is larger than expected under log normality alternative models to account for these unobserved data should be considered we discuss one such model that incorporates a mixture of true zero exposures and a log normal distribution with possible left censoring previously considered ill a different context by manitou and halsey 1995 biometrics 51 1570 1578 a particular relationship is demonstrated between maximum likelihood parameter estimates based on this mixture model and those assuming either left tnlllcated or left censored data these results emphasize the heed for caution when choosing a model to fit data involving nondetectable values a one sided likelihood ratio test for colli paring illeall exposure under the mixture model to an occupational exposure limit is then developed and evaluated via simulations all example demonstrates the potential impact of specifying an incorrect model for the ilondetectable value

development of a formal likelihood function for improved bayesian inference of ephemeral catchments 1 the application of formal bayesian inferential approaches in hydrologic modeling is often criticized for requiring explicit assumptions to be made about the distribution of the errors via the likelihood function these assumptions can be adequate in some situations but often little attention is paid to the selection of an appropriate likelihood function this paper investigates the application of bayesian methods in modeling ephemeral catchments we consider two modeling case studies including a synthetically generated data set and a real data set of an arid australian catchment the case studies investigate some typical forms of the likelihood function which have been applied widely by previous researchers as well as introducing new implementations aimed at better addressing likelihood function assumptions in dry catchments the results of the case studies indicate the importance of explicitly accounting for model residuals that are highly positively skewed due to the presence of many zeros zero inflation arising from the dry spells experienced by the catchment specifically the form of the likelihood function was found to significantly impact the calibrated parameter posterior distributions which in turn have the potential to greatly affect the uncertainty estimates in each application the likelihood function that explicitly accounted for the nonconstant variance of the errors and the zero inflation of the errors resulted in 1 equivalent or better fits to the observed discharge in both timing and volume 2 superior estimation of the uncertainty as measured by the reliability and sharpness metrics and 3 more linear quantile quantile plots indicating the errors were more closely matched to the assumptions of this form of the likelihood function

time domain model order reduction using general orthogonal polynomials for k power bilinear systems abstractin this paper we propose a model order reduction mor method based on general orthogonal polynomials for k power bilinear systems in the time domain constructing proper projection matrices by solving a series of linear equations a reduced k power bilinear system is produced which preserves the original coupled structure it can match several expansion coefficients of the original output then the error bound of our algorithm is also investigated moreover the stability of the reduced system is discussed as well finally two numerical examples are provided to illustrate the effectiveness of our algorithm

frequentist validity of posterior quantiles in the presence of a nuisance parameter higher order asymptotics given a random sample from a distribution with density function that depends on an unknown parameter 1 2 we are concerned with frequentist validity up to o n 1 of posterior quantiles of 1 treating 2 as a nuisance parameter we propose to make the best choice of the prior on by matching as far as practicable the posterior and frequentist coverage probabilities up to o n 1

logarithmic transformations in anova a method is presented for choosing an additive constant c when transforming data x to y log x c the method preserves type i error probability and power in anova under the assumption that the x c for some c are log normally distributed the method has advantages similar to those of rank transformations namely it is easy to use and is resistant to extreme observations since the special case c infinity corresponds in anova to y x the method is a useful generalization of least squares

bootstrap confidence intervals for medical costs with censored observations medical costs data with administratively censored observations often arise in cost effectiveness studies of treatments for life threatening diseases mean of medical costs incurred from the start of a treatment until death or a certain time point after the implementation of treatment is frequently of interest in many situations due to the skewed nature of the cost distribution and non uniform rate of cost accumulation over time the currently available normal approximation confidence interval has poor coverage accuracy in this paper we propose a bootstrap confidence interval for the mean of medical costs with censored observations in simulation studies we show that the proposed bootstrap confidence interval had much better coverage accuracy than the normal approximation one when medical costs had a skewed distribution when there is light censoring on medical costs 25 per cent we found that the bootstrap confidence interval based on the simple weighted estimator is preferred due to its simplicity and good coverage accuracy for heavily censored cost data censoring rate 30 per cent with larger sample sizes n 200 the bootstrap confidence intervals based on the partitioned estimator has superior performance in terms of both efficiency and coverage accuracy we also illustrate the use of our methods in a real example

on the stability of projections of balanced realizations abstract this paper generalizes a stability property concerning the state matrix of a balanced realization established by pernebo and silverman it is shown that stability is preserved under a general projection of the state matrix provided that the hankel singular values of the realization are distinct a necessary and sufficient condition for the case with nondistinct hankel singular values is also established

comparing the means and variances of a bivariate log normal distribution for a bivariate log normal distribution a confidence interval is developed for the ratio of the means the generalized confidence interval approach is used for this purpose and the procedure is applicable regardless of the sample size it is also noted that the same approach can be used to obtain a confidence interval for the ratio of the variances a modified signed log likelihood ratio procedure is also described for computing confidence intervals the coverage probabilities of the proposed confidence intervals are estimated by monte carlo and the generalized confidence intervals are found to exhibit satisfactory performance even for small sample sizes numerical results also show that the corresponding test procedures provide larger power compared with the modified signed log likelihood ratio test two examples are given one dealing with the comparison of the means and variances of health care costs and the other dealing with testing mean equivalence in quantitative assays copyright 2007 john wiley sons ltd

asymptotic normality with small relative errors of posterior probabilities of half spaces some examples of half spaces of interest in parameter spaces are in a clinical trial of a treatment versus placebo the half spaces where the treatment is a helpful or b harmful thus one may not only want to test the hypothesis that the treatment c makes no difference but to assign posterior probabilities to a b and c under conditions as unrestrictive as possible on the choice of prior probabilities e g dudley and haughton 2001 more generally we have in mind applications to model selections as in the bic criterion of schwarz 1978 and its extensions poskitt 1987 haughton 1988 specifically to one sided models and multiple data sets dudley and haughton 1997

interval estimates for the ratio and difference of two lognormal means health research often gives rise to data that follow lognormal distributions in two sample situations researchers are likely to be interested in estimating the difference or ratio of the population means several methods have been proposed for providing confidence intervals for these parameters however it is not clear which techniques are most appropriate or how their performance might vary additionally methods for the difference of means have not been adequately explored we discuss in the present article five methods of analysis these include two methods based on the log likelihood ratio statistic and a generalized pivotal approach additionally we provide and discuss the results of a series of computer simulations finally the techniques are applied to a real example

frequentist validity of posterior quantiles for a two parameter exponential family summary berger bernardo s 1989 reference priors and tibshirani 1989 priors are derived for distributions in bar lev reiser s 1982 two parameter exponential family when either the location or the scale parameter is of interest the reference prior is shown to be a tibshirani prior furthermore conditions under which a tibshirani prior is a higherorder matching prior are investigated when both the parameters are of interest it is also shown that the reference prior agrees with the prior matching the posterior and frequentist expansions based on the signed square root of log likelihood ratio the normal inverse gaussian and gamma distributions are used to illustrate the results

on priors providing frequentist validity of bayesian inference for multiple parametric functions summary we characterise priors which match up to o n 1 the posterior joint cumulative distribution function of multiple parametric functions with the corresponding frequentist cumulative distribution function this work extends and unifies the work of ghosh mukerjee 1993 and datta ghosh 1995a on the topic of probability matching priors a set of necessary and sufficient conditions is obtained for the above characterisation some of these conditions depend only on the parametric functions and not on the prior examples are given where the joint probability matching is possible and where it is not possible

lyapunov equations energy functionals and model order reduction of bilinear and stochastic systems we discuss the relation of a certain type of generalized lyapunov equations to gramians of stochastic and bilinear systems together with the corresponding energy functionals while gramians and energy functionals of stochastic linear systems show a strong correspondence to the analogous objects for deterministic linear systems the relation of gramians and energy functionals for bilinear systems is less obvious we discuss results from the literature for the latter problem and provide new characterizations of input and output energies of bilinear systems in terms of algebraic gramians satisfying generalized lyapunov equations in any of the considered cases the definition of algebraic gramians allows us to compute balancing transformations and implies model reduction methods analogous to balanced truncation for linear deterministic systems we illustrate the performance of these model reduction methods by showing numerical experiments for different bilinear systems

assessing the effect of interventions in the context of mixture distributions with detection limits many quantitative assay measurements of metabolites of environmental toxicants in clinical investigations are subject to left censoring due to values falling below assay detection limits moreover when observations occur in both unexposed individuals and exposed individuals who reflect a mixture of two distributions due to differences in exposure metabolism response to intervention and other factors the measurements of these biomarkers can be bimodally distributed with an extra spike below the limit of detection therefore estimating the effect of interventions on these biomarkers becomes an important and challenging problem in this article we present maximum likelihood methods to estimate the effect of intervention in the context of mixture distributions when a large proportion of observations are below the limit of detection the selection of the number of components of mixture distributions was carried out using both bootstrap based and cross validation based information criterion we illustrate our methods using data from a randomized clinical trial conducted in qidong people s republic of china

bayesian prediction with approximate frequentist validity we characterize priors which asymptotically match the posterior coverage probability of a bayesian prediction region with the corresponding frequentist coverage probability this is done considering both posterior quantiles and highest predictive density regions with reference to a future observation the resulting priors are shown to be invariant under reparameterization the role of jeffreys prior in this regard is also investigated it is further shown that for any given prior it may be possible to choose an interval whose bayesian predictive and frequentist coverage probabilities are asymptotically matched

fisherian inference in likelihood and prequential frames of reference summary in celebration of the centenary of the birth of sir ronald fisher this paper explores fisher s conception of statistical inference with special attention to the importance he placed on choosing an appropriate frame of reference to define the inferential model in particular we investigate inferential models which respect the likelihood principle or the prequential principle and argue that these will typically have an asymptotic sampling theory justification

comparisons of two part models with competitors two part models arise when there is a clump of 0 observations in a distribution of continuous non negative responses several methods for comparing two such distributions are available these include the straightforward application of the z test or t test the wilcoxon mann whitney rank sum test the kolmogorov smirnov test and three tests that use a 2 degree of freedom chi 2 test based on the sum of the test for equality of proportions and a conditional chi 2 test for the continuous responses this conditional test may be the z test the rank sum test or the chi 2 corresponding to the kolmogorov smirnov test this study compares the size and power of several of these methods all tests have the appropriate distribution under the null hypothesis if the distribution of the continuous part has finite moments if it does not the z test has no power to detect any alternatives it is found that the 2 d f tests are superior to the others when the larger proportion of 0 values corresponds to the population with the larger mean if the reverse holds the difference in the proportion of zeros reinforces the difference in means and some single part models the rank sum or kolmogorov smirnov do best in those cases the two part models are not far behind although statistically significantly poorer with respect to power published in 2001 by john wiley sons ltd

empirical type likelihoods allowing posterior credible sets with frequentist validity higher order asymptotics summary with reference to a general class of empirical type likelihoods we develop higher order asymptotics for the frequentist coverage of bayesian credible sets based on posterior quantiles and highest posterior density these asymptotics in turn characterise members of the class that allow approximate frequentist validity of such sets it is seen that the usual empirical likelihood does not enjoy this property up to the order of approximation considered here

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

the zeroth law of thermodynamics we discuss a convenient formulation of the most intuitive property of equilibrium the zeroth law of thermodynamics in terms of conditions of dynamical stability for a system which may interact weakly with its surroundings this allows us to provide a completely rigorous though elementary justification of the gibbs canonical ensemble as the description of thermodynamical equilibrium for a spatially confined quantum system with a fixed finite number of particles for quantum systems with variable particle numbers the same kind of assumptions leads to the grand canonical ensemble

two part statistics with paired data in epidemiology we often study data from a mixed distribution i e with a clump of observations at zero and positive continuous data lachenbruch developed statistics for this kind of data for independent samples these tests are the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution this paper concerns the adaptation of these tests to paired samples like lachenbruch we developed two statistics which tend to a two degree of freedom 2 distribution these two part statistics are the sum of mcnemar s test for testing the equality of proportions of zero values and the wilcoxon signed rank test or the paired student s test for testing the equality of the distribution of positive values we studied the behaviour of these tests for various proportions of zeros and mean values of the continuous distribution all tests are efficient when the smaller proportion of zero values corresponds to the population with the larger mean in all other situations the two part statistics are superior to the others these methods are applied to a matched case control study of lower limb venous insufficiency copyright 2004 john wiley sons ltd

unitary equivalence of temperature dynamics for ideal and locally perturbed fermi gas we consider the local perturbation v varepsilon sum limits x y in mathbb z v v x y chi omega x chi omega y a x a y a y a x of the ideal fermi gas on the lattice v where is a finite subset of v and is its indicator the invertibility of moller morphisms for small is proven it follows that in the cyclic gns representation with respect to kms states the dynamics of ideal and locally perturbed fermi gas are unitary equivalent

canonical forms for bilinear systems abstract a method is presented which enables the transformation of the state equations of bilinear systems to canonical forms it is based on the properties of reachability and observability a distinct feature is that the derived canonical forms are unique with respect to their structure and determined by a minimum of non zero parameters

generalised tangential interpolation for model reduction of discrete time mimo bilinear systems in this article we discuss a model order reduction method for multiple input and multiple output discrete time bilinear control systems similar to the continuous time case we will show that a system can be characterised by a series of generalised transfer functions this will be achieved by a multivariate z transform of kernels corresponding to an explicit solution formula for discrete time systems we will further address the problem of generalised tangential interpolation which naturally comes along with this approach we will introduce a reasonable generalisation of the linear 2 norm based on this concept we discuss the choice of interpolation points furthermore an efficient discretisation of continuous time systems is provided the performance of the proposed method is evaluated in some numerical examples and compared with the method of balanced truncation for bilinear systems

bootstrap confidence intervals for a class of parametric problems summary we consider the following class of problems having observed a multivariate normal data vector y with unknown mean vector q covariance matrix the identity find an approximate confidence interval for 0 t q a real valued function of q a simple geometric construction is given which leads to highly accurate solutions this construction shows that the standard approximation based on maximum likelihood theory 04 cz00 can be quite misleading when 0 is nonlinear in q we discuss bootstrap based confidence intervals which remove most of the error in the standard approximation at the expense of considerably more calculation the bootstrap intervals are invariant under transformation of both y and i and so they automatically produce accurate solutions in problems which can be transformed to multivariate normality without requiring knowledge of the normalizing transformation

methods for comparing the means of two independent log normal samples standard methods of using the t test and the wilcoxon test have deficiencies for comparing the means of two skewed log normal samples in this paper we propose two new methods to overcome these deficiencies 1 a likelihood based approach and 2 a bootstrap based approach our simulation study shows that the likelihood based approach is the best in terms of the type i error rate and power when data follow a log normal distribution

on the level error after bartlett adjustment of the likelihood ratio statistic summary it is well known that bartlett adjustment reduces level error of the likelihood ratio statistic from order n l to order n3 2 in the present note we show that level error of the adjusted statistic is actually order n2

smooth quantile ratio estimation in a study of health care expenditures attributable to smoking we seek to compare the distribution of medical costs for persons with lung cancer or chronic obstructive pulmonary disease cases to those without controls using a national survey which includes hundreds of cases and thousands of controls the distribution of costs is highly skewed toward larger values making estimates of the mean from the smaller sample dependent on a small fraction of the biggest values one approach to deal with the smaller sample is to rely on a simple parametric model such as the log normal but this makes the undesirable assumption that the distribution of the log expenditures is symmetric we propose a novel approach to estimate the mean difierence of two highly skewed distributions which we call smooth quantile ratio estimation square square is obtained by smoothing over percentiles the ratio of the cost quantiles of the cases and controls square deflnes a large class of estimators of including 1 the sample mean difference 2 the maximum likelihood estimate under log normal samples and 3 l estimates we detail asymptotic properties of square such as consistency and asymptotic normality and also provide a closed form expression for the asymptotic variance through a simulation study we show that square has lower mean squared error than several competitors including the sample mean difierence and log normal parametric estimates in several realistic situations we apply square to the 1987 national medicare expenditure survey to estimate the difierence in medical expenditures between persons sufiering from the smoking attributable diseases lung cancer and chronic obstructive pulmonary disease and persons without these diseases software in r ihaka and gentleman 1996 for the implementation of square and of all its special cases and the cost data used in this paper are available at http biostat jhsph edu fdominic square html

improved approximate confidence intervals for the mean of a log normal random variable data analysts often compute approximate 100 1 alpha per cent confidence intervals for the mean of a log normal random variable due to the computational effort required for exact intervals we evaluate two simple approximations and demonstrate that the probabilities with which the intervals fail to capture the population mean that is the coverage error can range from well above the desired level alpha to very near zero in small to moderate sample sizes n or 100 the performance of a more sophisticated approximation implemented via numerical integration or bootstrap sampling is noticeably improved but also suffers from coverage errors that are too large when n or 25 a new procedure is developed which outperforms existing approximations computing these improved intervals requires the integration of standard distribution functions the calculations are straightforward however and lead to satisfactory coverage errors for n as small as 5 a related method that avoids the integration step generally outperforms existing simple approximations for n or 100 while maintaining the coverage error at or below alpha programs to implement the new procedures are provided in an appendix

statistical analysis and modeling of coral reef habitats abstract the present study is concerned with the statistical analysis and modeling of the health behavior of coral reef habitats due to changes in environmental conditions the analytical parameter estimates have been developed for the subject probability distribution information collected of stony coral cover from the florida keys over the past several years have been fitted to the three parameter lognormal probability distribution and consequently we can statistically characterize the behavior of the proportion of stony coral cover thus it is shown that true mean estimates from such data had been under reported in the past furthermore a suitable confidence interval of the true mean is presented for the three parameter lognormal probability distribution

frequency interval model reduction of bilinear systems in this technical note a new method for model reduction of bilinear systems is presented the method is developed in particular for many applications in which one is interested to approximate a system in a given frequency interval to this end new generalized frequency interval gramians are introduced for bilinear systems it is shown that these gramians are the solutions to the so called frequency interval generalized lyapunov equations the conditions for these equations to be solvable are derived and an algorithm is proposed to solve such equations iteratively the method is further illustrated with the help of an illustrative example the numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians

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

semiparametric estimation of the distribution of episodically consumed foods measured with error dietary data collected from 24 hour dietary recalls are observed with significant measurement errors in the nonparametric curve estimation literature much of the effort has been devoted to design

comparison of several independent population means when their samples contain log normal and possibly zero observations summary in this paper we consider the problem of testing the mean equality of several independent populations that contain log normal and possibly zero observations we first showed that the currently used methods in statistical practice including the nonparametric kruskal wallis test the standard anova f test and its two modified versions the welch test and the brown forsythe test could have poor type i error control then we propose a likelihood ratio test that is shown to have much better type i error control than the existing methods finally we analyze two real data sets that motivated our study using the proposed test

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

on bartlett adjustments for approximate bayesian inference summary in wide generality the posterior distributions of the likelihood ratio statistic and the posterior ratio statistic are chi squared to error of order o n where n is sample size the error in the chi squared approximation can be reduced to order o n 2 by bartlett correction in this paper explicit formulae are derived for the bartlett adjustment factors of both statistics and the derivations are based on the tierney kass kadane 1989 asymptotic approximation for marginal posterior probability density functions the use of numerical differentiation to facilitate calculation of the bartlett adjustments is also described some applications are considered that concern inference about regression models from both complete and right censored data

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

a decomposition for the likelihood ratio statistic and the bartlett correction a bayesian argument let l n 1 log p x be the log likelihood of an n dimensional x under a p dimensional let j be the mle under h j 1 1 0 j j 0 and 0 be the unrestricted mle define t j as 2n l j 1 1 2 sgn j j 1 j 0 let t t 1 t p then under regularity conditions the following theorem is proved under 0 t is asymptotically n n 1 2 a 0 n 1 a j n 1 o n 3 2 where j is the identity matrix the result is proved by first establishing an analogous result when is random and then making the prior converge to a degenerate distribution the existence of the bartlett correction to order n 3 2 follows from the theorem we show that an edgeworth expansion with error o n 2 for t involves only polynomials of degree less than or equal to 3 and hence verify rigorously lawley s 1956 result giving the order of the error in the bartlett correction as o n 2

time interval model reduction of bilinear systems in this paper a new method for model reduction of bilinear systems is presented the proposed technique is from the family of gramian based model reduction methods the method uses time interval generalised gramians in the reduction procedure rather than the ordinary generalised gramians and in such a way that it improves the accuracy of the approximation within the time interval for which the method is applied the time interval generalised gramians are the solutions to the generalised time interval lyapunov equations the conditions for these equations to be solvable are derived and an algorithm is proposed to solve these equations iteratively the method is further illustrated with the help of two illustrative examples the numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians

spectral properties of sums of certain kronecker products we introduce two kinds of sums of kronecker products and their induced operators we study the algebraic properties of these two kinds of matrices and their associated operators the properties include their eigenvalues their eigenvectors and the relationships between their spectral radii or spectral abscissae furthermore two projected matrices of these kronecker products and their induced operators are also studied

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

h model reduction for discrete time delay systems delay independent and dependent approaches this paper investigates the problem of h model reduction for linear discrete time state delay systems for a given stable system our attention is focused on the construction of reduced order models which guarantee the corresponding error system to be asymptotically stable and have a prescribed h error performance both delay independent and dependent approaches are developed with sufficient conditions obtained for the existence of admissible reduced order solutions since these obtained conditions are not expressed as strict linear matrix inequalities lmis the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to lmi constraints which can be readily solved in standard numerical software in addition the development of reduced order models with special structures such as delay free models and zeroth order models is also addressed the approximation methods presented in this paper can be further extended to cope with systems with unc

likelihood based confidence intervals for a log normal mean to construct a confidence interval for the mean of a log normal distribution in small samples we propose likelihood based approaches the signed log likelihood ratio and modified signed log likelihood ratio methods extensive monte carlo simulation results show the advantages of the modified signed log likelihood ratio method over the signed log likelihood ratio method and other methods in particular the modified signed log likelihood ratio method produces a confidence interval with a nearly exact coverage probability and highly accurate and symmetric error probabilities even for extremely small sample sizes we then apply the methods to two sets of real life data

efficient estimation of log normal means with application to pharmacokinetic data in this paper the problem of interest is efficient estimation of log normal means several existing estimators are reviewed first including the sample mean the maximum likelihood estimator the uniformly minimum variance unbiased estimator and a conditional minimal mean squared error estimator a new estimator is then proposed and we show that it improves over the existing estimators in terms of squared error risk the improvement is more significant with small sample sizes and large coefficient of variations which is common in clinical pharmacokinetic pk studies in addition the new estimator is very easy to implement and provides us with a simple alternative to summarize pk data which are usually modelled by log normal distributions we also propose a parametric bootstrap confidence interval for log normal means around the new estimator and illustrate its nice coverage property with a simulation study our estimator is compared with the existing ones via theoretical calculations and applications to real pk studies

frequentist and bayesian bartlett correction of test statistics based on adjusted profile likelihoods summary for inference about a multidimensional parameter b in the presence of nuisance param

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

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

confidence intervals for the mean of diagnostic test charge data containing zeros in this paper we consider the problem of interval estimation for the mean of diagnostic test charges diagnostic test charge data may contain zero values and the nonzero values can often be modeled by a log normal distribution under such a model we propose three different interval estimation procedures a percentile t bootstrap interval based on sufficient statistics and two likelihood based confidence intervals for theoretical properties we show that the two likelihood based one sided confidence intervals are only first order accurate and that the bootstrap based one sided confidence interval is second order accurate for two sided confidence intervals all three proposed methods are second order accurate a simulation study in finite sample sizes suggests all three proposed intervals outperform a widely used minimum variance unbiased estimator mvue based interval except for the case of one sided lower end point intervals when the skewness is very small among the proposed one sided intervals the bootstrap interval has the best coverage accuracy for the two sided intervals when the sample size is small the bootstrap method still yields the best coverage accuracy unless the skewness is very small in which case the bias corrected ml method has the best accuracy when the sample size is large all three proposed intervals have similar coverage accuracy finally we analyze with the proposed methods one real example assessing diagnostic test charges among older adults with depression

on generalizations of the kms boundary condition we investigate the possibility to generalize the kms boundary condition for a thermodynamical system by following essentially the same procedure that for a finite system would amount to choosing a certain class of more general density functions on phase space or density matrices than the ones corresponding to the canonical or grand canonical ensemble

reduced order aggregated models for bilinear time invariant dynamical systems a necessary and sufficient condition for a bilinear time invariant dynamical system to admit an aggregated reduced order bilinear model is given

a two part model for reference curve estimation subject to a limit of detection reference curves are commonly used to identify individuals with extreme values of clinically relevant variables or stages of progression which depend naturally on age or maturation estimation of reference curves can be complicated by a technical limit of detection lod that censors the measurement from the left as is the case in our study of reproductive hormone levels in boys around the time of the onset of puberty we discuss issues with common approaches to the lod problem in the context of our pubertal hormone study and propose a two part model that addresses those issues one part of the proposed model specifies the probability of a measurement exceeding the lod as a function of age the other part of the model specifies the conditional distribution of a measurement given that it exceeds the lod again as a function of age information from the two parts can be combined to estimate the identifiable portion i e above the lod of a reference curve and to calculate the relative standing of a given measurement above the lod unlike some common approaches to lod problems the two part model is free of untestable assumptions involving unobservable quantities flexible for modeling the observable data and easy to implement with existing software the method is illustrated with hormone data from the third national health and nutrition examination survey

on h2 model reduction of bilinear systems the h 2 model reduction problem for continuous time bilinear systems is studied in this paper by defining the h 2 norm of bilinear systems in terms of the state space matrices the h 2 model reduction error is computed via the reachability or observability gramian necessary conditions for the reduced order bilinear models to be h 2 optimal are given the gradient flow approach is used to obtain the solution of the h 2 model reduction problem the formulation allows certain properties of the original models to be preserved in the reduced order models the model reduction procedure developed can also be applied to finite dimensional linear time invariant systems a numerical example is employed to illustrate the effectiveness of the proposed method

control configuration selection for bilinear systems via generalised hankel interaction index array decentralised and partially decentralised control strategies are very popular in practice to come up with a suitable decentralised or partially decentralised control structure it is important to select the appropriate input and output pairs for control design this procedure is called control configuration selection it is well known that a suitable control configuration selection is an important prerequisite for a successful industrial control in this paper the problem of control configuration selection for multiple input and multiple output mimo bilinear processes is addressed first the concept of the cross gramian is developed for bilinear systems the conditions for the existence of generalised cross gramian are derived it is shown that if the cross gramian exists it is the solution to the generalised sylvester equation to obtain the cross gramian in a more computationally efficient way an iterative method for solving the generalised sylvester equation is proposed the generalised cross gram

sample size and statistical power assessing the effect of interventions in the context of mixture distributions with detection limits often in randomized clinical trials and observational cohort studies a non negative continuously distributed response variable is measured in treatment and control groups in the presence of true zeros for the response variable a two part zero inflated log normal model which assumes that the data has a probability mass at zero and a continuous response for values greater than zero is usually recommended however in some environmental health and human immunodeficiency virus hiv studies quantitative assays for metabolites of toxicants or quantitative hiv rna measurements are subject to left censoring due to values falling below the limit of detection ld here a zero inflated log normal mixture model is often suggested since true zeros are indistinguishable from left censored values due to the ld when the probabilities of true zeros in the two groups are not restricted to be equal the information contributed by values falling below ld is used only to estimate the probability of true zeros in the context of mixture distributions we derived the required sample size to assess the effect of a treatment in the context of mixture models with equal and unequal variances based on the left truncated log normal distribution methods for calculation of statistical power are also presented we calculate the required sample size and power for a recent study estimating the effect of oltipraz on reducing urinary levels of the hydroxylated metabolite aflatoxin m1 afm1 in a randomized placebo controlled double blind phase iia chemoprevention trial in qidong china a monte carlo simulation study is conducted to investigate the performance of the proposed methods copyright 2006 john wiley sons ltd

infereni on full or partial parameters based on the standardized signed log likelihood ratio on etudie des tests et des limites de confiance bases sur la statistique du rapport de log vraisemblance signee en ajustant cette statistique de telle sorte qu a un ordre superieur d approximation la distribution normale standard soit valable

confidence intervals for the log normal mean in this paper we conduct a stimulation study to evaluate coverage error interval width and relative bias of four main methods for the construction of confidence intervals of log normal means the naive method cox s method a conservative method and a parametric bootstrap method the simulation study finds that the naive method is inappropriate that cox s method has the smallest coverage error for moderate and large sample sizes and that the bootstrap method has the smallest coverage error for small sample sizes in addition cox s method produces the smallest interval width among the three appropriate methods we also apply the four methods to a real data set to contrast the differences

on gramians and balanced truncation of discrete time bilinear systems this paper obtains a balanced truncation model reduction method for discrete time bilinear systems after deriving the sufficient conditions for the discrete time bilinear systems to lead to bounded outputs for some bounded inputs we study the properties of the reachability and observability gramians the gramians can be computed by solving two generalized lyapunov equations by balancing the reachability and observability gramians a model reduction method is obtained some propositions of the reduced order models are given a numerical example is given to illustrate the effectiveness of the proposed method

modeling health survey data with excessive zero and k responses zero inflated poisson regression is a popular tool used to analyze data with excessive zeros although much work has already been performed to fit zero inflated data most models heavily depend on special features of the individual data to be specific this means that there is a sizable group of respondents who endorse the same answers making the data have peaks in this paper we propose a new model with the flexibility to model excessive counts other than zero and the model is a mixture of multinomial logistic and poisson regression in which the multinomial logistic component models the occurrence of excessive counts including zeros k where k is a positive integer and all other values the poisson regression component models the counts that are assumed to follow a poisson distribution two examples are provided to illustrate our models when the data have counts containing many ones and sixes as a result the zero inflated and k inflated models exhibit a better fit than the zero inflated poisson and standard poisson regressions