local empirical likelihood inference for varying coefficient density ratio models based on case control data in this article we develop a varying coefficient density ratio model for case control studies the case and control samples come from two different distributions under the model assumption the ratio of the two densities is related to the linear combination of covariates with varying coefficients through a known function a special case is the exponential tilt model where the log ratio of the two densities is a linear function of covariates we propose a local empirical likelihood el approach to estimate the nonparametric coefficient functions under some regularity assumptions the proposed estimators are shown to be consistent and asymptotically normally distributed the sieve empirical likelihood ratio selr test statistic for detecting whether the varying coefficients are really constant and other related hypotheses is constructed and it follows approximately a chi squared distribution we introduce a modified bootstrap procedure to estimate the null distribution of the selr when sample size is s

hypothesis testing in a mixture case control model summary we consider a problem of testing mixture proportions using two sample data one from group one and the other from a mixture of groups one and two with unknown proportion for being in group two various statistical applications including microarray study infectious epidemiological studies case control studies with contaminated controls clinical trials allowing nonresponders genetic studies for gene mutation and fishery applications can be formulated in this setup under the assumption that the log ratio of probability density functions from the two groups is linear in the observations we propose a generalized score test statistic to test the mixture proportion under some regularity conditions it is shown that this statistic converges to a weighted chi squared random variable under the null hypothesis of 0 where the weight depends only on the sampling fraction of both groups the permutation method is used to provide more reliable finite sample approximation simulation results and two real data applications are presented

on the regularity of solutions of an operator riccati equation arising in linear quadratic optimal control problems for hereditary differential systems abstract in this paper operator riccati equations of evolution and algebraic types arising in the linear quadratic optimal control problem for hereditary differential systems are considered regularity results of their solutions are obtained especially for the system with single point delay we show that the optimal feedback kernel function 10 is c this study is motivated by the numerical experiments of k ito and r teglas legendre tau approximation for functional differential equations part ii the linear quadratic optimal control problem siam j control and optimization 25 1987 1379 1408 in computing the optimal feedback gain via an algebraic riccati equation which indicate that such a function is smooth the regularity result is essential in obtaining a rate of convergence of numerical approximations of the optimal feedback gain operator

third order complex time step methods for transient analysis abstract using complex time steps and the method for the first order differential equations third order accurate a stable step by step time integration algorithms with controllable numerical dissipation are constructed for transient analysis the results at two sub step locations are evaluated and combined linearly with the corresponding weighting factors to give higher order accurate results at the end of a time step the sub step locations and the weighting factors are complex numbers the amplification factors at infinity are controlled by another algorithmic parameter a fourth order accurate algorithm is obtained when 1 the algorithmic characteristics and the computational procedure for the present third order algorithms are discussed equivalent algorithms and comparisons with other algorithms are given the present algorithms are found to be competitive with the other third and fourth order accurate algorithms

robustness and power of analysis of covariance applied to data distorted from normality by floor effects homogeneous regression slopes we investigate through computer simulations the robustness and power of two group analysis of covariance test applied to small samples distorted normality by floor effects when the regression slopes are homogeneous we consider four parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regression slopes and two t tests on unadjusted means and on difference scores under the null hypothesis of no difference in means we estimated actual significance levels by comparing observed test statistics to appropriate values from the f and t distributions for nominal significance levels of 0 10 0 05 0 02 and 0 01 we estimated power by similar comparisons under various alternative hypothesis the hierarchical approach that adjusts for non homogeneous slopes if found significant the test that assumes homogeneous regression slopes and the test that estimates separate regression slopes in each treatment were robust in general each test produced power at least equal to that expected from normal theory the textbook approach which does not test for mean differences when there is significant non homogeneity was conservative but also had good power the t tests were robust but had poorer power properties than the above procedures

higher order accurate time step integration algorithms by post integration techniques in this paper a framework to construct higher order accurate time step integration algorithms based on the post integration techniques is presented the prescribed initial conditions are naturally incorporated in the formulations and can be strongly or weakly enforced the algorithmic parameters are chosen such that unconditionally a stable higher order accurate time step integration algorithms with controllable numerical dissipation can be constructed for linear problems besides it is shown that the order of accuracy for non linear problems is maintained through the relationship between the present formulation and the runge kutta method the second order differential equations are also considered numerical examples are given to illustrate the validity of the present formulation copyright 2001 john wiley sons ltd

observer with evolutionary programming based optimal digital tracker for analog neutral multiple time delay systems abstract in this paper the finite time optimal hybrid tracking control problem for analog neutral systems with multiple discrete and distributed time delays is formulated and studied a novel approach that combining the evolutionary programming ep algorithm and the high gain property for analog neutral multiple time delay systems is proposed to achieve the best tracking performance for the first time first the newton center interpolation formula and the linear interpolation formula together with a modified rectangular rule and an augmented state vector are utilized to construct the equivalent digital linear models next according to the separation principle the control gains of the digital tracker and the digital observer are designed separately by the discrete time optimal control theory and prediction based digital redesign method and then combined together to form an observer based optimal time varying digital tracker eventually the process is to combine the high gain property with ep algorithm to search the optimal weighting matrices in the performance index to form an observer with ep based low gain digital tracker to achieve the objective of optimal tracking control an example is given for illustrating the effectiveness of the new tracker design method

approximation schemes for the linear quadratic optimal control problem associated with delay equations the linear regulator problem for delay equations is discussed we propose a theoretical solution involving riccati integral equations and then axiomatically discuss a general approximation scheme the details are given for spline and averaging approximations

exact observability and controllability for linear neutral type systems the problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach the duality with the exact controllabil ity problem is the main tool it is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system a nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator the characterization of the duality between controllability and observability is deduced and then observability conditions are obtained

on stabilization by state feedback for neutral differential difference equations in this paper we consider a class of feedback operators for a linear differential difference equation of the neutral type we show that if a system has unstable neutral root chains any stabilizing feedback operator in this class must contain a derivative of the delayed state component under the assumption of exact controllability we construct a stabilizing feedback operator

optimal control of linear differential difference systems of neutral type abstract the optimal control of linear differential difference systems of neutral type with respect to quadratic performance criteria over an infinite time interval is treated the linear differential difference systems with delays in coordinates derivatives and control actions are analysed dynamic programming is used to determine the optimization equations a set of riccati type equations is obtained the closed loop system synthesis problem is discussed the approximate optimal problem is formulated a connection is established between the original and approximate optimal problems special attention is paid to the suboptimal system synthesis problem

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

on the approximation of eigenvalues associated with functional differential equations abstract in this paper an approximation method based upon spline functions is developed for the eigenvalue problem associated with functional differential equations convergence results are established and the rate of convergence is investigated numerical results for cubic and quintic spline based methods are given the paper concludes with a brief discussion of other possible approximation methods

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

limitations of a class of stabilization methods for delay systems we investigate limitations of certain stabilization methods for time delay systems the class of methods under consideration implements the control law through a volterra integral equation of the second kind using as an example the pole placement approach of manitius and olbrot 1979 we illustrate how instability of the difference part of the control law leads to instability in the closed loop system in the case that implementation is done via numerical quadrature the outcome of our analysis provides computable limitations to stability and a maximum allowable size of the input delay

high order hierarchical a and l stable integration methods numerical integration of stiff first order systems of differential equations is considered it is shown how a c continuous polynomial time discretization in conjunction with a weighted residual method can be used to derive methods corresponding to the diagonal and first subdiagonal pade approximants in this manner a stable schemes of order 2k and l stable schemes of order 2k l are obtained at least for k 4 the methods are hierarchical in the sense that a scheme with a given accuracy embraces the equations of all lower order methods that have the same stability type

lyapunov s functionals and related optimal problems for differential difference systems abstract the optimal control of linear differential difference systems of neutral type with respect to quadratic performance criteria over an infinite time interval is treated the linear differential difference systems with delays in coordinates derivatives and control actions are considered the lyapunov bellman formalism is used to find the optimal solution the global optimality of the solution follows from convexity of the set of admissible controls and of the cost functional and linearity of the constraints the computational procedure is based on considering the approximate optimal problem a connection is established between the original and approximate optimal problems

robustness of the two independent samples t test when applied to ordinal scaled data one may encounter the application of the two independent samples t test to ordinal scaled data for example data that assume only the values 0 1 2 3 from small samples this situation clearly violates the underlying normality assumption for the t test and one cannot appeal to large sample theory for validity in this paper we report the results of an investigation of the t test s robustness when applied to data of this form for samples of sizes 5 to 20 our approach consists of complete enumeration of the sampling distributions and comparison of actual levels of significance with the significance level expected if the data followed a normal distribution we demonstrate under general conditions the robustness of the t test in that the maximum actual level of significance is close to the declared level

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

on strong regular stabilizability for linear neutral type systems the problem of strong stabilizability of linear systems of neutral type is investigated we are interested in the case when the system has an infinite sequence of eigenvalues with vanishing real parts this is the case when the main part of the neutral equation is not assumed to be stable in the classical sense we discuss the notion of regular strong stabilizability and present an approach to stabilize the system by regular linear controls the method covers the case of multivariable control and is essentially based on the idea of infinite dimensional pole assignment proposed in g m sklyar a v rezounenko a theorem on the strong asymptotic stability and determination of stabilizing controls c r acad sci paris ser i math 333 8 2001 807 812 our approach is based on the recent results on the riesz basis of invariant finitedimensional subspaces and strong stability for neutral type systems presented in r rabah g m sklyar a v rezounenko stability analysis of neutral type systems in hilbert space j differential equations 214 2 2005 391 428

periodic output feedback stabilization of neutral systems a new feedback control technique called periodic output feedback is investigated in the context of infinite dimensional linear systems modeled by neutral functional differential equations in this method discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control this work focuses on stabilization of neutral systems with delayed control modeled in the state space w sub 2 sup 1 r 0 r sup n spl times l sup 2 r 0 r sup p where w sub 2 sup 1 r 0 r sup n denotes the sobolev space of r sup n valued absolutely continuous functions with square integrable derivatives on r 0 we show that a class of these systems can be stabilized by periodic output feedback even though their input operators are unbounded we overcome this difficulty by representing the system state using an abstract integral variation of constants formula an algorithm is presented at the end of this paper to construct a periodic output feedback gain function an example is provided to illustrate the construction of the gain function

calculation of power and sample size with bounded outcome scores the two sample wilcoxon rank sum test is the most popular non parametric test for the comparison of two samples when the underlying distributions are not normal although the underlying distributions need not be known in detail to calculate the null distribution of the test statistic parametric assumptions are often made to determine the power of the test or the sample size we encountered difficulties with this approach in the planning of a recent clinical trial in stroke patients it is shown that for power and sample size estimation it can be dangerous to apply the classical formulae routinely especially with outcome scores having a u shaped or a j shaped distribution as an example we have taken the barthel index a quality of life outcome measure in stroke patients further we have investigated alternative methods by means of monte carlo simulation the distributional characteristics of the estimated powers were compared our findings suggest more appropriate computer software is necessary for the calculation of power and sample size when efficacy is measured by a non parametric method

chandrasekhar equations for infinite dimensional systems ii unbounded input and output case abstract a set of equations known as chandrasekhar equations arising in the linear quadratic optimal control problem is considered in this paper we consider the linear time invariant systems defined in hilbert spaces involving unbounded input and output operators for a general class of such systems we derive the chandrasekhar equations and establish the existence uniqueness and regularity results of their solutions

linear quadratic optimal control of hereditary differential systems infinite dimensional riccati equations and numerical approximations recent theory of infinite dimensional riccati equations is applied to the linear quadratic optimal control problem for hereditary differential systems and it is shown that for most such problems the operator solutions of the riccati equations are of trace class i e nuclear with special attention to trace norm convergence an abstract approximation theory is developed and applied to a particular approximation scheme numerical examples are given problems on both finite and infinite time intervals are studied for both the hereditary system and the approximating systems in the infinite time problem characteristic equations are derived for the closed loop eigenvalues and formulas for the corresponding eigenvectors are given

the linear quadratic control problem for infinite dimensional systems with unbounded input and output operators this paper establishes a general semigroup framework for solving quadratic control problems with infinite dimensional state space and unbounded input and output operators

a methodology for the generation of low cost higher order methods for linear dynamics this work presents a methodology which generates efficient higher order methods for linear dynamics by improving the accuracy properties of norsett methods towards those of pade methods the methodology is based on a simple and low cost iterative procedure which is used to implement a set of higher order methods with controllable dissipation a sequence of improved solutions is obtained which correspond to algorithms offering an effective compromise between the efficiency of norsett methods and the accuracy of pade methods moreover a direct control over high frequency dissipation is possible by means of an algorithmic parameter numerical tests are reported which confirm that this set of algorithms is really attractive for linear dynamic analysis copyright 2003 john wiley sons ltd

unconditionally stable higher order newmark methods by sub stepping procedure abstract in this paper a procedure to construct unconditionally stable higher order step by step time integration algorithms based on the newmark method is presented the second order accurate newmark method is extended to third fourth and even higher order by linearly combining the numerical results evaluated at some specific sub step locations the weighting factors and the sub step locations are algorithmic parameters they are chosen to eliminate the leading truncation error terms and to control the stability characteristics the ranges of parameters for unconditionally stable third and fourth order algorithms are given besides by using complex time steps a third order l stable and a fourth order a stable non dissipative algorithms are derived furthermore the accuracy of the excitation responses is shown to be improved by the present procedure as well to maintain high order accuracy the excitation may need to be modified the computational procedure is discussed it is found that there are no changes in the implementation of the underlying newmark method and no extra computations of high order gradients as the numerical results at the sub step locations are obtained independent of one another the evaluations can be computed in parallel comparisons with other higher order algorithms are presented

a time integration algorithm for linear transient analysis based on the reproducing kernel method in this paper a new algorithm based on the reproducing kernel method is presented for linear transient analysis using very large time steps in the conventional time integration methods the required accuracy is always achieved by either decreasing the size of time steps or increasing the order of approximations the proposed method however does not require a restriction on the size of the time step the required approximating functions for integration of governing equations are determined using the concept of reproduction of the solution within each time step a recurrence relationship is obtained through solving the governing equation by the point collocation based reproducing kernel method within the time step in collocation points the values of external excitation can be obtained either through the approximation between the values at the beginning and the end of each time step or assigning the exact values of the external force hence one advantage of this new method is the independency of the sampling rates of external excitation from the size of the time step the proposed method is applied for solving first and second order differential equations and advantages of the method are illustrated through a number of numerical examples

the norsett time integration methodology for finite element transient analysis this paper presents a set of methods for time integration of problems arising from finite element semidiscretizations the purpose is to obtain computationally efficient methods which possess higher order accuracy and controllable dissipation in the spurious high modes the methods are developed and analysed by a general collocation methodology which leads to the class of norsett approximants an algorithmic parameter is used to achieve an effective control over numerical dissipation moreover a simple and efficient implementation scheme is presented at each time step algorithms based on p order collocation polynomials require the solution of p sets of linear algebraic equations with the same coefficient matrix in this way a single factorization is needed and no transformations are required to recover the approximate solution at the end or within the time interval to demonstrate the performance of the proposed algorithms a wide experimental evaluation is carried out on typical test problems in finite element transient analysis

the use of bootstrap methods for estimating sample size and analysing health related quality of life outcomes health related quality of life hrqol measures are increasingly used in trials as primary outcome measures investigators are now asking statisticians for advice on how to plan and analyse studies using such outcomes hrqol outcomes like the sf 36 are usual measured on an ordinal scale although most investigators assume that there exists an underlying continuous latent variable and that the actual measured outcomes the ordered categories reflect contiguous intervals along this continuum the ordinal scaling of hrqol measures means they tend to generate data that have discrete bounded and skewed distributions thus standard methods of analysis that assume normality and constant variance may not be appropriate for this reason conventional statistical advice would suggest non parametric methods be used to analyse hrqol data the bootstrap is one such computer intensive non parametric method for estimating sample sizes and analysing data we describe three methods of estimating sample sizes for two group cross sectional comparisons of hrqol outcomes we then compared the power of the three methods for a two group cross sectional study design using bootstrap simulation the results showed that under the location shift alternative hypothesis conventional methods of sample size estimation performed well particularly whitehead s method whitehead s method is recommended if the hrqol outcome has a limited number of discrete values 7 and or the expected proportion of cases at either of the bounds is high if a pilot data set is readily available then bootstrap simulation will provide a more accurate and reliable estimate than conventional methods finally we used the bootstrap for hypothesis testing and the estimation of standard errors and confidence intervals for parameters in an example data set we then compared and contrasted the bootstrap with standard methods of analysing hrqol outcomes in the data set studied with the sf 36 outcome the use of the bootstrap for estimating sample sizes and analysing hrqol data produces results similar to conventional statistical methods these results suggest that bootstrap methods are not more appropriate for analysing hrqol outcome data than standard methods

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

choice of test for comparing two groups with particular application to skewed outcomes we consider a clinical trial where a skewed outcome variable is to be compared between two groups while comparison of sample means may lack power we show that power also depends on the nature of the anticipated treatment effect for any given distribution in the control arm there is a family of true distributions in the intervention arm for which the most powerful test is a comparison of arithmetic means similar results hold for a comparison of geometric means and approximately for the wilcoxon rank sum test and a comparison of medians we discuss how these methods could be used in planning the analysis of a clinical trial in which the intervention effect alters the shape of the distribution these ideas are illustrated by a trial in community psychiatry where the primary outcome days in hospital was highly skewed but the intervention was mainly expected to reduce the frequency of values in the tail we show that a comparison of sample means is a reasonable choice in this case despite the skewness

a modified wilcoxon test for non negative distributions with a clump of zeros comparing two samples with a continuous non negative score e g a utility score over 0 1 with a substantial proportion say 50 per cent scoring 0 presents distributional problems for most standard tests a wilcoxon rank test can be used but the large number of ties reduces power i propose a new test the wilcoxon rank sum test performed after removing an equal and maximal number of 0 s from each sample this test recovers much of the power compared with a directional modification of a two part test proposed by lachenbruch the truncated wilcoxon has similar power when the non zero scores are independent of the proportion of zeros but unlike the two part test the truncated wilcoxon is relatively unaffected when these processes are dependent

power and sample size requirements for two part models two part models assume the data has a probability mass at zero and a continuous response for values greater than 0 we construct tests based on the proportion of zeros and the difference among the positive values of a response giving rise to a two degree of freedom chi 2 test this note gives the non centrality parameter and finds the power for the test the power is compared to the simulation results in a recent paper we derive sample size calculations we note that some modifications of this procedure may provide better tests if the non zero responses are discrete published in 2001 by john wiley sons ltd

some power considerations when deciding to use transformations conventional wisdom suggests that for small data sets having substantial skew one should attempt to determine the correct distributional form if possible and apply statistical methods appropriate for that distribution transformations such as the log or square root are often used if an appropriate distributional form cannot be determined a distribution free procedure such as a rank transformation or a randomization test procedure can be used to better appreciate the effect of such alternatives on both the type i error and power of detecting differences between treatment groups simulation studies were conducted for responses having specific gamma g r theta and log normal ln m v distributions the gamma and log normal distributions were selected so that they had the same first two moments a simple two group design was assumed the reference group always had an average disease level mu 3 0 mu r theta for gamma mu m for log normal and the treatment group always had means whose reductions ranged from 0 per cent to 50 per cent the effect of distributional type and the degree of skewness was investigated by varying the population parameter values six statistical test procedures were compared for the gamma distributions all test procedures were robust relative to the type i error the ump test based on a ratio of sample means produced the greatest power for all combinations of n r and rt the power losses associated with the randomization test the t test on original scale and the t test on the square root scale were very small 3 per cent to 6 per cent in absolute value for n 10 and 15 and less than 2 per cent for group sizes of 25 or more the power loss associated with the t test on the log scale was much larger ranging from 5 per cent to 10 per cent smaller power than the t test on original scale the wilcoxon rank test produced similar results to that of the log t test for small samples the power for the shifted log x c test increased monotonically to the asymptotic value of the orig t test the same five test procedures based on differences in sample means were then compared for the corresponding log normal distributions the ump test that is log x produced the highest power there was very little power lost for the sqrt t test the loss in power varied between 2 per cent and 5 per cent for the rank test abstract truncated at 400 words

solving initial value problems by differential quadrature method part 1 first order equations in this paper the differential quadrature method is used to solve first order initial value problems the initial condition is given at the beginning of a time interval the time derivative at a sampling grid point within the time interval can be expressed as a weighted linear sum of the given initial condition and the function values at the sampling grid points within the time interval the order of accuracy and the stability property of the quadrature solutions depend on the locations of the sampling grid points it is shown that the order of accuracy of the quadrature solutions at the end of a time interval can be improved to 2n 1 or 2n if the n sampling grid points are chosen carefully in fact the approximate solutions are equivalent to the generalized pade approximations the resultant algorithms are therefore unconditionally stable with controllable numerical dissipation the corresponding sampling grid points are found to be given by the roots of the modified shifted legendre polynomials from the numerical examples the accuracy of the quadrature solutions obtained by using the proposed sampling grid points is found to be better than those obtained by the commonly used uniformly spaced or chebyshev gauss lobatto sampling grid points copyright 2001 john wiley sons ltd

a semiparametric two component compound mixture model and its application to estimating malaria attributable fractions summary malaria remains a major epidemiologic problem in many developing countries malaria is defined as the presence of parasites and symptoms usually fever due to the parasites in endemic areas an individual may have symptoms attributable either to malaria or to other causes from a clinical viewpoint it is important to correctly diagnose an individual who has developed symptoms so that the appropriate treatments can be given from an epidemiologic and economic viewpoint it is important to determine the proportion of malaria affected cases in individuals who have symptoms so that policies on intervention program can be developed once symptoms have developed in an individual the diagnosis of malaria can be based on the analysis of the parasite levels in blood samples however even a blood test is not conclusive as in endemic areas many healthy individuals can have parasites in their blood slides therefore data from this type of study can be viewed as coming from a mixture distribution with the components corresponding to malaria and nonmalaria cases a unique feature in this type of data however is the fact that a proportion of the nonmalaria cases have zero parasite levels therefore one of the component distributions is itself a mixture distribution in this article we propose a semiparametric likelihood approach for estimating the proportion of clinical malaria using parasite level data from a group of individuals with symptoms our approach assumes the density ratio for the parasite levels in clinical malaria and nonclinical malaria cases can be modeled using a logistic model we use empirical likelihood to combine the zero and nonzero data the maximum semiparametric likelihood estimate is more efficient than existing nonparametric estimates using only the frequencies of zero and nonzero data on the other hand it is more robust than a fully parametric maximum likelihood estimate that assumes a parametric model for the nonzero data simulation results show that the performance of the proposed method is satisfactory the proposed method is used to analyze data from a malaria survey carried out in tanzania

the analysis of exact controllability of neutral type systems by the moment problem approach the problem of exact null controllability is considered for a wide class of linear neutral type systems with distributed delay the main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families a complete characterization of this problem is given the minimal time of controllability is specified the results are based on the analysis of the riesz basis property of eigenspaces of the neutral type systems in hilbert space

semiparametric estimation and inference for distributional and general treatment effects summary there is a large literature on methods of analysis for randomized trials with noncompliance which focuses on the effect of treatment on the average outcome the paper considers evaluating the effect of treatment on the entire distribution and general functions of this effect for distributional treatment effects fully non parametric and fully parametric approaches have been proposed the fully non parametric approach could be inefficient but the fully parametric approach is not robust to the violation of distribution assumptions we develop a semiparametric instrumental variable method based on the empirical likelihood approach our method can be applied to general outcomes and general functions of outcome distributions and allows us to predict a subject s latent compliance class on the basis of an observed outcome value in observed assignment and treatment received groups asymptotic results for the estimators and likelihood ratio statistic are derived a simulation study shows that our estimators of various treatment effects are substantially more efficient than the currently used fully non parametric estimators the method is illustrated by an analysis of data from a randomized trial of an encouragement intervention to improve adherence to prescribed depression treatments among depressed elderly patients in primary care practices

hierarchical higher order dissipative methods for transient analysis this work focuses on devising an efficient hierarchy of higher order methods for linear transient analysis equipped with an effective dissipative action on the spurious high modes of the response the proposed strategy stems from the norsett idea and is based on a multi stage algorithm designed to hierarchically improve accuracy while retaining the desired dissipative behaviour computational efficiency is pursued by requiring that each stage should involve just one set of implicit equations of the size of the problem to be solved as standard time integration methods and in addition all the stages should share the same coefficient matrix this target is achieved by rationally formulating the methods based on the discontinuous collocation approach the resultant procedure is shown to be well suited for adaptive solution strategies in particular it embeds two natural tools to effectively control the error propagation one estimates the local error through the next stage solution which is one order more accurate the other through the solution discontinuity at the beginning of the current time step which is permitted by the present formulation the performance of the procedure and the quality of the two error estimators are experimentally verified on different classes of problems some typical numerical tests in transient heat conduction and elasto dynamics are presented copyright 2006 john wiley sons ltd

on the equivalence of the time domain differential quadrature method and the dissipative runge kutta collocation method numerical solutions for initial value problems can be evaluated accurately and efficiently by the differential quadrature method unconditionally stable higher order accurate time step integration algorithms can be constructed systematically from this framework it has been observed that highly accurate numerical results can also be obtained for non linear problems in this paper it is shown that the algorithms are in fact related to the well established implicit runge kutta methods through this relation new implicit runge kutta methods with controllable numerical dissipation are derived among them the non dissipative and asymptotically annihilating algorithms correspond to the gauss methods and the radau iia methods respectively other dissipative algorithms between these two extreme cases are shown to be b stable or algebraically stable as well and the order of accuracy is the same as the corresponding radau iia method through the equivalence it can be inferred that the differential quadrature method also enjoys the same stability and accuracy properties copyright 2001 john wiley sons ltd

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

the log transformation is special the logarithmic log transformation is a simple yet controversial step in the analysis of positive continuous data measured on an interval scale situations where a log transformation is indicated will be reviewed this paper contends that the log transformation should not be classed with other transformations as it has particular advantages problems with using the data themselves to decide whether or not to transform will be discussed it is recommended that log transformed analyses should frequently be preferred to untransformed analyses and that careful consideration should be given to use of a log transformation at the protocol design stage

computer intensive methods for tests about the mean of an asymmetrical distribution abstract for one sided tests about the mean of a skewed distribution the t test is asymptotically robust for validity however it can be quite inaccurate and inefficient with small sample sizes results presented here confirm that a procedure due to johnson should be preferred to the t test when the parent distribution is asymmetrical because it reduces the probability of type i error in cases where the t test has an inflated type i error rate and it is more powerful in other situations but if the skewness is severe and the sample size is small then johnson s test can also be appreciably inaccurate for such situations computer intensive test procedures using bootstrap resampling are proposed and with an extensive monte carlo study it is shown that these procedures are remarkably robust and can result in reduced probabilities of type i and type ii errors compared to johnson s test

unconditionally stable higher order accurate collocation time step integration algorithms for first order equations abstract in this paper unconditionally stable higher order accurate time step integration algorithms for linear first order differential equations based on the collocation method are presented the amplification factor at the end of the spectrum is a controllable algorithmic parameter the collocation parameters for unconditionally stable higher order accurate algorithms are found to be given by the roots of a polynomial in terms of the ultimate amplification factor in general when the numerical solution is approximated by a polynomial of degree n this approximation is at least n th order accurate however by using the above collocation parameters the order of accuracy can be improved to 2 n 1 or 2 n the approximate solutions are found to be equivalent to the generalized pade approximations furthermore it is shown that the accuracy of the particular solution due to excitation given by the present method is compatible with the homogeneous solutions no modification of the collocation parameters is required

unconditionally stable time step integration algorithms based on hamilton s principle unconditionally stable time step integration algorithms derived from hamilton s principle are presented the corresponding constrained variations are assumed to be in the form of k k 1 to ensure vanishing variations at the ends of a time interval the initial conditions are strongly enforced in the formulation the order of accuracy can be 2n 1 or 2n where n is the number of unknown variables the ultimate spectral radii of the algorithms can be controlled directly the approximate solutions are in fact equivalent to the generalized pade approximations for linear second order differential equations hence hamilton s principle can be used to construct unconditionally stable higher order accurate time step integration algorithms directly as well provided the appropriate constrained variations are used

time finite element methods for structural dynamics summary time finite element methods are developed for the equations of structural dynamics the approach employs the time discontinuous galerkin method and incorporates stabilizing terms having least squares form these enable a general convergence theorem to be proved in a norm stronger than the energy norm results are presented from finite difference analyses of the time discontinuous galerkin and least squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics these results show that for particular interpolations the time finite element method exhibits improved accuracy and stability

complex time step newmark methods with controllable numerical dissipation in this paper unconditionally stable higher order accurate time step integration algorithms with controllable numerical dissipation are presented the algorithms are based on the newmark method with complex time steps the ultimate spectral radius the sub step locations j and the weighting factors j are the algorithmic parameters for an algorithm that is 2n 1 th order accurate the sub step locations which may be complex are shown to be the roots of an nth degree polynomial the polynomial is given explicitly in terms of n and the weighting factors are then obtained by solving a system of n simultaneous equations it is further shown that the order of accuracy is increased by one for the non dissipative algorithms with 1 the stability properties of the present algorithms are studied it is shown that if the ultimate spectral radius is set between 1 and 1 the eigenvalues of the numerical amplification matrix are complex with magnitude less than or equal to unity the algorithms are therefore unconditionally c stable when the ultimate spectral radius is set to 0 or 1 the algorithms are found to be equivalent to the first sub diagonal and diagonal pade approximations respectively the present algorithms are more general as the numerical dissipation is controllable and are very suitable for parallel computers the accuracy of the excitation responses is found to be enhanced by the present complex time step procedure to maintain high order accuracy the excitation may need some modifications 1998 john wiley sons ltd

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

a class of nonlinear time delay systems and related optimal problems abstract the method of synthesis for a class of time delay nonlinear systems affine in control is considered the proposed approach is based on the solution of a special optimal control problem the integrand of the optimized functional is chosen in such a way that the bellman equation has a desired solution the nonlinear system design is reduced to the examination of the integrand of the optimized functional to extend the domain of asymptotic stability of the nonlinear system a sequence of the lyapunov krasovskii functionals is used the whole system becomes the system with variable structure the proposed approach gives a systematic framework for an almost sliding mode control

dirichlet boundary control problems for parabolic equations with quadratic cost analyticity and riccati s feedback synthesis riccati type feedback synthesis of optimal controls for dirichlet boundary parabolic equations is considered the functional cost penalizes the l2 energy over 0 t of state and control action u and also final state y t at t t this latter fact makes the functional cost discontinuous on the space of admissible controls l2 0t after overcoming some technical difficulties related to the above mentioned discontinuity we prove that the optimal control uo can be written in the desired feedback form uo t cp t yo t for all 0 t t

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

a unified set of single step asymptotic annihilation algorithms for structural dynamics when solving the equations of structural dynamics using direct time integration meth6ds algorithmic damping is useful in controlling spurious high frequency oscillations ideally an algorithm should possess asymptotic annihilation of the highfrequency response i e spurious oscillations in the high frequencies are eliminated after one time step in this paper a new class of asymptotic annihilation algorithms for structural dynamics is presented that possesses little numerical dissipation in the low frequency regime the algorithms are based upon using finite elements in time the displacement and velocity fields are interpolated independently using time discontinuous functions the equations of motion displacement velocity compatibility and the time continuity of displacement and velocity are satisfied weakly asymptotic annihilation is achieved by choosing the displacement and velocity fields to be of equal order algorithms of any desired order of temporal accuracy can be obtained by appropriate choice of the finite element interpolations in time an analysis of the proposed class of algorithms is given proving the asymptotic annihilation property and the spectral equivalence of the algorithms to the upper diagonal of the pad6 approximation table results from finite difference analyses are presented showing the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low frequency regime

stability analysis and observer design for neutral delay systems this paper deals with the observer design problem for a class of linear delay systems of the neutral type the problem addressed is that of designing a full order observer that guarantees the exponential stability of the error dynamic system an effective algebraic matrix equation approach is developed to solve this problem in particular both the observer analysis and design problems are investigated by using the singular value decomposition technique and the generalized inverse theory sufficient conditions for a neutral type delay system to be exponentially stable are first established then an explicit expression of the desired observers is derived in terms of some free parameters furthermore an illustrative example is used to demonstrate the validity of the proposed design procedure

comparison of two treatments with skewed ordinal responses in clinical studies the proportional odds model is widely used to compare treatment efficacies when the responses are categorically ordered however this model has been shown to be inappropriate when the proportional odds assumption is invalid mainly because it is unable to control the type i error rate in such circumstances to remedy this problem the latent normal model was recently promoted and has been demonstrated to be superior to the proportional odds model however the application of the latent normal model is limited to compare treatments with similar underlying distributions except possibly their means and variances when the underlying distributions are very different in skewness both of the aforementioned procedures suffer from the undesirable inflation of the type i error rate to solve the problem for clinical studies with ordinal responses we provide a viable solution that relies on the use of the latent weibull distribution which is a member of the log location scale family the proposed model is able to control the type i error rate regardless of the degree of skewness of the treatment responses in addition the power of the test also outperforms that of the latent normal model the testing procedure draws on newly developed theoretical results related to latent distributions from the location scale family the testing procedure is illustrated with two clinical examples