on simultaneous assessment of sensitivity and specificity when combining two diagnostic tests diagnostic tests are seldom adopted in isolation few tests have high sensitivity and specificity simultaneously in these cases one can increase either the sensitivity or the specificity by combining two component tests under either the either positive rule or the both positive rule however there is a tradeoff between sensitivity and specificity when these rules are applied we propose three statistical procedures to simultaneously assess the sensitivity and specificity when combining two component tests measurements of interest include rate difference and rate ratio our empirical results demonstrate that i the asymptotic test procedures for both measurements and approximate test procedure for rate difference possess inflated type i error rate ii the exact test procedures for both measurements possess deflated type i error rate and iii the approximate unconditional test procedure for rate ratio becomes an reliable alternative and nicely controls the actual type i error rate in small to moderate sample sizes moreover the approximate unconditional test procedure is computationally less intensive than the exact unconditional test procedure we illustrate our methodologies with a real example from a residual nasopharyngeal carcinoma rnp study

robustness and power of analysis of covariance applied to ordinal scaled data as arising in randomized controlled trials in clinical trials comparing two treatments ordinal scales of three four or five points are often used to assess severity both prior to and after treatment analysis of covariance is an attractive technique however the data clearly violate the normality assumption and in the presence of small samples and large sample theory may not apply the robustness and power of various versions of parametric analysis of covariance applied to small samples of ordinal scaled data are investigated through computer simulation subjects are randomized to one of two competing treatments and the pre treatment or baseline assessment is used as the covariate we compare two parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regressions slopes and the two independent samples t test on difference scores under the null hypothesis of no difference in adjusted treatment means we estimated actual significance levels by comparing observed test statistics to appropriate critical 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 hypotheses the model which assumes homogeneous slopes and the t test on difference scores were robust in the presence of three four and five point ordinal scales the hierarchical approach which first tests for homogeneity of regression slopes and then fits separate slopes if there is significant non homogeneity produced significance levels that exceeded the nominal levels especially when the sample sizes were small the model which assumes homogeneous regression slopes produced the highest power among competing tests for all of the configurations investigated the t test on difference scores also produced good power in the presence of small samples

chaos synchronization of different chaotic systems subjected to input nonlinearity abstract in this paper a unified mathematical expression describing a class of synchronization systems is presented for which the problem of chaos synchronization between different chaotic systems with input nonlinearity has been studied based on lyapunov stability theory a sliding mode controller and some generic sufficient conditions for global asymptotic synchronization are designed such that the error dynamics of two different chaotic motions satisfy stability in the lyapunov sense in spite of the input nonlinearity this technique is applied to achieve chaos synchronization of three pairs of different chaotic systems lorenz chen chen liu and liu lorenz in drive response structure the numerical simulation results demonstrate the validity and feasibility of the proposed controller

control and synchronize a novel hyperchaotic system the control and hybrid projective synchronization hps strategies for a novel hyperchaotic system are investigated firstly the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables secondly based on lyapunov s direct method hps between two novel hyperchaotic systems is studied a new nonlinear feedback vector controller is designed to guarantee hps which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems finally numerical simulations are given to verify the effectiveness of these strategies the proposed methods have certain significances for reducing the cost and complexity for controller implementation

a noniterative sample size procedure for tests based on t distributions a noniterative sample size procedure is proposed for a general hypothesis test based on the t distribution by modifying and extending guenther s approach for the one sample and two sample t tests the generalized procedure is employed to determine the sample size for treatment comparisons using the analysis of covariance ancova and the mixed effects model for repeated measures in randomized clinical trials the sample size is calculated by adding a few simple correction terms to the sample size from the normal approximation to account for the nonnormality of the t statistic and lower order variance terms which are functions of the covariates in the model but it does not require specifying the covariate distribution the noniterative procedure is suitable for superiority tests noninferiority tests and a special case of the tests for equivalence or bioequivalence and generally yields the exact or nearly exact sample size estimate after rounding to an integer the method for calculating the exact power of the two sample t test with unequal variance in superiority trials is extended to equivalence trials we also derive accurate power formulae for ancova and mixed effects model for repeated measures and the formula for ancova is exact for normally distributed covariates numerical examples demonstrate the accuracy of the proposed methods particularly in small samples

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

lmi optimization approach to stabilization of genesio tesi chaotic system via dynamic controller abstract in this paper a design method for a new controller to control the genesio tesi chaotic systems is proposed in this work a dynamic outputs feedback controller for the system is developed for the first time for stability analysis a well known lyapunov stability theorem combining with lmi linear matrix inequality optimization approach is utilized a numerical simulation is presented to show the usefulness of the proposed control scheme

chaotic sliding mode controllers for uncertain time delay chaotic systems with input nonlinearity this paper presents a novel robust chaotic controller for stabilizing uncertain time delay chaotic systems with input nonlinearity based on dynamic output sliding mode control smc lyapunov theory and linear matrix inequality lmi technique the stability of overall uncertain time delay chaotic system with input nonlinearity under the proposed control scheme is guaranteed without the state predictor the selection of sliding surface and the design of control law are two important issues which have been addressed a priori knowledge of upper bounds of uncertainties is not required furthermore the proposed scheme ensures robustness against input nonlinearity time delays nonlinear real valued functions parameter uncertainties and disturbances simultaneously finally simulation results demonstrate the validity of the proposed control methodology

the generalised autocovariance function the generalised autocovariance function is defined for a stationary stochastic process as the inverse fourier transform of the power transformation of the spectral density function depending on the value of the transformation parameter this function nests the inverse and the traditional autocovariance functions a frequency domain non parametric estimator based on the power transformation of the pooled periodogram is considered and its asymptotic distribution is derived the results are employed to construct classes of tests of the white noise hypothesis for clustering and discrimination of stochastic processes and to introduce a novel feature matching estimator of the spectrum

non fragile observer based passive control for uncertain time delay systems subjected to input nonlinearity abstract the problem of non fragile observer based passive control for uncertain time delay systems subjected to input nonlinearity is investigated by using sliding mode control a novel control law is established such that the sliding surface in the state estimation space can be reached in a finite time and chattering reduction is obtained a sufficient condition for passivity and asymptotic stability of the combined system is derived via linear matrix inequality lmi finally a simulation example is presented to show the validity and advantages of the proposed method

a minimum distance estimator for long memory processes this paper considers a minimum distance estimator mde of the differencing para meter of the fractionally integrated white noise model the mde minimizes the differ ence between sample and population autocorrelations the paper presents calculations of asymptotic variances to examine the efficiency of the mde relative to that of the mle for values of the differencing parameter less than l 4 the mde is consistent and asymptotically normal and the asymptotic variance of the mde using the first n auto correlations approaches that of the mle as n increases however there is a substantial efficiency loss if low order autocorrelations are omitted this implies that a non parametric treatment of short run dynamics will involve a substantial loss of efficiency

a new hyperchaotic system from the lu system and its control this paper presents a 4d new hyperchaotic system which is constructed by a linear controller to a 3d lu system some complex dynamical behaviors such as hopf bifurcation chaos and hyperchaos of the simple 4d autonomous system are investigated and analyzed the corresponding hyperchaotic and chaotic attractor is first numerically verified through investigating phase trajectories lyapunove exponents bifurcation path analysis of power spectrum and poincare projections furthermore the design is illustrated with both simulations and experiments finally the control problem of a new hyperchaotic system is investigated using negative feedback control ordinary feedback control dislocated feedback control and speed feedback control are used to suppress hyperchaos to an unstable equilibrium numerical simulations are presented to demonstrate the effectiveness of the proposed controllers

power transformations to induce normality and their applications random variables can have heavily right skewed finite sample distributions even though they might be asymptotically normally distributed we provide a simple method of determining an appropriate power transformation to improve the normal approximation in small samples our method contains the wilson hilferty cube root transformation for x2 random variables as a special case we also provide some important examples including test statistics of goodness of fit and tail index estimators where such power transformations can be applied in particular we study the small sample behaviour of two goodness of fit tests for time series models which have been proposed recently in the literature both tests are generalizations of the popular box ljung pierce portmanteau test one in the time domain and the other in the frequency domain a power transformation with a finite sample mean and variance correction is proposed which ameliorates the small sample effect it is found that the corrected versions of the tests have markedly better size properties the correction is also found to result in an overall increase in power which can be significant under certain alternatives furthermore the corrected tests also have better power than the box ljung pierce portmanteau test unlike the uncorrected versions

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

power and sample size calculations for discrete bounded outcome scores we consider power and sample size calculations for randomized trials with a bounded outcome score bos as primary response adjusted for a priori chosen covariates we define bos to be a random variable restricted to a finite interval typically a bos has a j or u shaped distribution hindering traditional parametric methods of analysis when no adjustment for covariates is needed a non parametric test could be chosen however there is still a problem with calculating the power since the common location shift alternative does not hold in general for a bos in this paper we consider a parametric approach and assume that the observed bos is a coarsened version of a true bos which has a logit normal distribution in each treatment group allowing correction for covariates a two step procedure is used to calculate the power firstly the power function is defined conditionally on the covariate values secondly the marginal power is obtained by averaging the conditional power with respect to an assumed distribution for the covariates using monte carlo integration a simulation study evaluates the performance of our method which is also applied to the ecass 1 stroke study

analysis of sets of two way contingency tables using association models abstract a class of models is introduced for the analysis of group differences in the association between two discrete variables the rc m association model for two way tables is reviewed and alternative weighting systems for identifying interaction parameters are presented this model is generalized for the setting where a two way contingency table is available for two or more groups various restricted models can be used to examine possible sources of intergroup heterogeneity in the association these sources pertain to heterogeneity in the intrinsic association and or in the scores for the row and column variables the importance of weights used to identify the row and column scores is emphasized a classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here

stabilization of parameters perturbation chaotic system via adaptive backstepping technique abstract the work of yassen m t yassen chaos control of chaotic dynamical systems using backstepping design chaos soliton fract 27 2006 537 548 which mainly investigated the stabilization problem for a class of chaotic systems without the parameters perturbation this paper is concerned with stabilization problem for a class of parameters perturbation chaotic systems via both backstepping design method and adaptive technique the proposed controllers can guarantee that the parameters perturbation systems will be stabilized at a fixed bounded point furthermore the paper also proposes controllers to stabilize the uncertain chaotic system at equilibrium point with only backstepping design method finally numerical simulations are given to illustrate the effectiveness of the proposed controllers

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

a test of fit in time series models summary a goodness of fit test statistic for time series models is presented and its asymptotic distribution even when parameters are estimated is derived the statistic is a frequency domain analogue of the box pierce portmanteau statistic the asymptotic power of the test is found and compared to the empirical power of the portmanteau test the small sample properties are investigated by monte carlo methods

the variance profile the variance profile is defined as the power mean of the spectral density function of a stationary stochastic process it is a continuous and nondecreasing function of the power parameter p which returns the minimum of the spectrum p the interpolation error variance harmonic mean p 1 the prediction error variance geometric mean p 0 the unconditional variance arithmetic mean p 1 and the maximum of the spectrum p the variance profile provides a useful characterization of a stochastic process we focus in particular on the class of fractionally integrated processes moreover it enables a direct and immediate derivation of the szego kolmogorov formula and the interpolation error variance formula the article proposes a nonparametric estimator of the variance profile based on the power mean of the smoothed sample spectrum and proves its consistency and its asymptotic normality from the empirical standpoint we propose and illustrate the use of the variance profile for estimating th

performance of analytical methods for overdispersed counts in cluster randomized trials sample size degree of clustering and imbalance many different methods have been proposed for the analysis of cluster randomized trials crts over the last 30 years however the evaluation of methods on overdispersed count data has been based mostly on the comparison of results using empiric data i e when the true model parameters are not known in this study we assess via simulation the performance of five methods for the analysis of counts in situations similar to real community intervention trials we used the negative binomial distribution to simulate overdispersed counts of crts with two study arms allowing the period of time under observation to vary among individuals we assessed different sample sizes degrees of clustering and degrees of cluster size imbalance the compared methods are i the two sample t test of cluster level rates ii generalized estimating equations gee with empirical covariance estimators iii gee with model based covariance estimators iv generalized linear mixed models glmm and v bayesian hierarchical models bayes hm variation in sample size and clustering led to differences between the methods in terms of coverage significance power and random effects estimation glmm and bayes hm performed better in general with bayes hm producing less dispersed results for random effects estimates although upward biased when clustering was low gee showed higher power but anticonservative coverage and elevated type i error rates imbalance affected the overall performance of the cluster level t test and the gee s coverage in small samples important effects arising from accounting for overdispersion are illustrated through the analysis of a community intervention trial on solar water disinfection in rural bolivia

estimation of the interpolation error variance and an index of linear determinism summary the autoregressive and window estimators of the inverse variance ri 0 say are adopted for estimating the interpolation error variance ri o and an index of linear determinism a of a stationary process x the index a is defined as 1 r o ri 0 where r o denotes the variance of x a measures the proportion of total variance explained by the interpolator when interpolating x say from xs s t some uses of a and ri o are discussed the asymptotic distributions of the estimators are derived the order of consistency of the autoregressive and window estimators of a is different when a 0 than when 0 a 1 the finite sample behaviour of the estimators is examined by means of a simulation study

a goodness of fit test for time series with long range dependence we propose a test statistic for goodness of fit in time series with slowly decaying serial correlations the asymptotic distribution of the test statistic originally proposed by milhoj for time series with smooth spectra turns out to be the same under the null hypothesis even if the spectrum has a pole at 0 in particular the test is suitable to detect lack of independence in the observations or estimated residuals if the first few correlations are small but the decay of the correlations is slow

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

adaptive stabilization of uncertain unified chaotic systems with nonlinear input abstract this paper addresses the problem of adaptive stabilization of uncertain unified chaotic systems with nonlinear input in the sector form a novel representation of nonlinear input function that is a linear input with bounded time varying coefficient is firstly established then an adaptive control scheme is proposed based on the new nonlinear input model by using barbalat s lemma the asymptotic stability of the closed loop system is proved in spite of system uncertainties external disturbance and input nonlinearity one of the advantages of the proposed design method is that the prior knowledge on the plant parameter the bound parameters of the uncertainties and the slope parameters inside the sector nonlinearity is not required finally numerical simulations are performed to verify the analytical results

hybrid projective synchronization and control of the baier sahle hyperchaotic flow in arbitrary dimensions with unknown parameters the problem of hybrid projective synchronization hps strategies and control for the baier sahle hyperchaotic flow in arbitrary dimensions with unknown parameters is considered based on the lasalle invariance principle and adaptive control method adaptive controllers and parameters update laws are given for the hps between two identical hyper chaotic systems with fully unknown parameters using this method the baier sahle hyperchaotic flow in arbitrary dimensions is controlled to the unsteady equilibrium points the baier sahle hyperchaotic flow is a useful choice for this analysis since it is a standard model of hyperchaos yet it is simple enough to be analytically tractable in particular the baier sahle hyperchaotic flow has been proposed as an n dimensional nonlinear system model giving the maximal number of positive lyapunov exponents n 2 both a rigorous theoretical analysis and direct numerical simulations are provided to demonstrate the control of hyperchaos in this model the results suggest that the methods used here can be applied to more complicated models from which hyperchaos arises

sample size calculations for ordered categorical data many clinical trials yield data on an ordered categorical scale such as very good good moderate poor under the assumption of proportional odds such data can be analysed using techniques of logistic regression in simple comparisons of two treatments this approach becomes equivalent to the mann whitney test in this paper sample size formulae consistent with an eventual logistic regression analysis are derived the influence on efficiency of the number and breadth of categories will be examined effects of misclassification and of stratification are discussed and examples of the calculations are given

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

controlling hyperchaos in hyperchaotic lorenz system using feedback controllers abstract in this paper the control strategies for hyperchaotic lorenz system is investigated the ordinary dislocated enhancing and speed feedback controls are used to suppress hyperchaos to unstable equilibrium the routh hurwitz criterion is used to derive the conditions of stability of the controlled hyperchaotic systems it is found that the coefficients of enhancing feedback control and dislocated feedback control may be smaller than those of ordinary feedback control so the complexity and cost of the system control are reduced numerical simulations are given to illustrate the effectiveness of the proposed controllers

chaos controlling of extended nonlinear lienard system based on the melnikov theory abstract chaos control may have a dual function to generate chaos or to suppress it by the melnikov theory two criterions of controlling chaos for a class of nonlinear lienard system are established according to the criterions we implement chaos control using non feedback method two illustrative examples a duffing rayleigh oscillator imposed with a weak bounded noise control and a duffing van der pol oscillator subject to a harmonic parametric control are presented here to illustrate the validity of the criterions to better support the results obtained above some indicators are used namely the lyapunov exponent phase portrait poincare cross section and time evolution both two methods lead to fully consistent results

h synchronization of time delayed chaotic systems abstract this paper considers h synchronization of a class of time delayed chaotic systems with external disturbance based on lyapunov theory and linear matrix inequality lmi formulation the dynamic feedback controller is established to not only guarantee synchronization between derive and response systems but also reduce the effect of external disturbance to an h norm constraint then a criterion for existence of the controller is given in terms of lmis finally a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme

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

pragmatical adaptive chaos control from a new double van der pol system to a new double duffing system a new pragmatical adaptive control method for different chaotic systems is proposed traditional chaos control is limited to decrease chaos of one chaotic system this method enlarges the effective scope of chaos control we can control a chaotic system e g a new chaotic double van der pol system to a given chaotic or regular system e g a new chaotic double duffing system or to a damped simple harmonic system by a pragmatical theorem of asymptotical stability based on an assumption of equal probability of initial point an adaptive control law is derived such that it can be proved strictly that the common zero solution of error dynamics and of parameter dynamics is asymptotically stable numerical simulations are given to show the effectiveness of the proposed scheme

a switching scheme for synthesizing attractors of dissipative chaotic systems in this paper a periodic parameter switching scheme is proposed for synthesizing a large class of hyperbolic attractors of continuous time and autonomous dissipative chaotic systems depending linearly on a single real bifurcation parameter it is illustrated by numerical simulations that a wide range of hyperbolic attractors can be obtained by this new scheme the scheme can also be considered as an effective way for control and anticontrol of chaos

issues for covariance analysis of dichotomous and ordered categorical data from randomized clinical trials and non parametric strategies for addressing them analysis of covariance is an effective method for addressing two considerations for randomized clinical trials one is reduction of variance for estimates of treatment effects and thereby the production of narrower confidence intervals and more powerful statistical tests the other is the clarification of the magnitude of treatment effects through adjustment of corresponding estimates for any random imbalances between the treatment groups with respect to the covariables the statistical basis of covariance analysis can be either non parametric with reliance only on the randomization in the study design or parametric through a statistical model for a postulated sampling process for non parametric methods there are no formal assumptions for how a response variable is related to the covariables but strong correlation between response and covariables is necessary for variance reduction computations for these methods are straightforward through the application of weighted least squares to fit linear models to the differences between treatment groups for the means of the response variable and the covariables jointly with a specification that has null values for the differences that correspond to the covariables moreover such analysis is similarly applicable to dichotomous indicators ranks or integers for ordered categories and continuous measurements since non parametric covariance analysis can have many forms the ones which are planned for a clinical trial need careful specification in its protocol a limitation of non parametric analysis is that it does not directly address the magnitude of treatment effects within subgroups based on the covariables or the homogeneity of such effects for this purpose a statistical model is needed when the response criterion is dichotomous or has ordered categories such a model may have a non linear nature which determines how covariance adjustment modifies results for treatment effects insight concerning such modifications can be gained through their evaluation relative to non parametric counterparts such evaluation usually indicates that alternative ways to compare treatments for a response criterion with adjustment for a set of covariables mutually support the same conclusion about the strength of treatment effects this robustness is noteworthy since the alternative methods for covariance analysis have substantially different rationales and assumptions since findings can differ in important ways across alternative choices for covariables as opposed to methods for covariance adjustment the critical consideration for studies with covariance analyses planned as the primary method for comparing treatments is the specification of the covariables in the protocol or in an amendment or formal plan prior to any unmasking of the study

adaptive variable structure control for chaos suppression of unified chaotic systems this paper investigates the chaos suppression problem for a class of unified chaotic systems subject to uncertainties and control input with dead zone nonlinearity using the variable structure control technique a robust adaptive control law is established to suppress chaos in a class of unified chaotic systems even with unknown uncertainties and dead zone nonlinearity in input in particular a switching surface is newly proposed to simplify the task of ensuring the stability of the closed loop system in the sliding mode numerical results validate the effectiveness of the proposed adaptive control scheme

impulsive control of lorenz system abstract in this paper an impulsive control scheme of the lorenz system is presented first we use the theory of impulsive differential equation to find conditions under which impulsively controlled lorenz system is asymptotically stable then we give the estimate of the upper bound of impulse interval for asymptotically stable control numerical experimental results are presented

small sample effects in time series analysis a new asymptotic theory and a new estimate on introduit un modele mathematique qui couvre les effets des petits echantillons dans l approximation de whittle 1953 on montre que l estimation du maximum de vraisemblance exacte est toujours optimale dans ce modele

the optimal control of chen chaotic dynamical system this paper is devoted to study the problem of the optimal control for the equilibrium point of a new chaotic system introduced by chen in a simple three dimensional autonomous system which resembles some familiar features from both the lorenz and rossler systems the stability of the equilibrium points is studied the conditions of the asymptotic stability of the equilibrium point of this system are used to obtain the optimal control functions the general solution of the dynamical system of the perturbed state is obtained as a function of time

consistent testing for serial correlation of unknown form this paper proposes three classes of consistent one sided tests for serial correlation of unknown form for the residual from a linear dynamic regression model that includes both lagged dependent variables and exogenous variables the tests are obtained by comparing a kernel based normalized spectral density estimator and the null normalized spectral density using a quadratic norm the hellinger metric and the kullback leibler information criterion respectively under the null hypothesis of no serial correlation the three classes of new test statistics are asymptotically n 0 1 and equivalent the null distributions are obtained without having to specify any alternative model unlike some conventional tests for serial correlation the null distributions of our tests remain invariant when the regressors include lagged dependent variables under a suitable class of local alternatives the three classes of the new tests are asymptotically equally efficient under global alternatives however their relative efficiencies depend on the relative magnitudes of the three divergence measures our approach provides an interpretation for box and pierce s 1970 test which can be viewed as a quadratic norm based test using a truncated periodogram many kernels deliver tests with better power than box and pierce s test or the truncated kernel based test a simulation study shows that the new tests have good power against an ar 1 process and a fractionally integrated process in particular they have better power than the lagrange multiplier tests of breusch 1978 and godfrey 1978 as well as the portmanteau tests of box and pierce 1970 and ljung and box 1978 the cross validation procedure of beltrao and bloomfield 1987 and robinson 1991a works reasonably well in determining the smoothing parameter of the kernel spectral estimator and is recommended for use in practice

inference for likelihood ratio ordering in the two sample problem abstract we obtain the maximum likelihood estimators of two multinomial probability vectors under the constraint that they are likelihood ratio ordered we extend this estimation approach to the case of two univariate distributions and show strong consistency of the estimators we also derive and study the asymptotic distribution of the likelihood ratio statistic for testing the equality of two discrete probability distributions against the alternative that one distribution is greater than the other in the likelihood ratio ordering sense finally we examine a data set pertaining to average daily insulin dose from the boston collaborative drug surveillance program and compare our testing procedure to testing procedures for other stochastic orderings

quasisymmetric models for the analysis of square contingency tables summary a parametric model is presented for the analysis of square contingency tables where there is a one to one correspondence between the categories of the row variable and the categories of the column variable the model is applicable to cross classifications where the categories are unordered partially ordered or completely ordered but the interpretation of the model and associated parameters is most straightforward when the categories are at least partially ordered connections with the mover stayer model and the usual model of quasisymmetry are described two data sets are used to illustrate the utility of the model

normal based methods for a gamma distribution prediction and tolerance intervals and stress strength reliability in this article we propose inferential procedures for a gamma distribution using the wilson hilferty wh normal approximation specifically using the result that the cube root of a gamma random variable is approximately normally distributed we propose normal based approaches for a gamma distribution for a constructing prediction limits one sided tolerance limits and tolerance intervals b for obtaining upper prediction limits for at least l of m observations from a gamma distribution at each of r locations and c assessing the reliability of a stress strength model involving two independent gamma random variables for each problem a normal based approximate procedure is outlined and its applicability and validity for a gamma distribution are studied using monte carlo simulation our investigation shows that the approximate procedures are very satisfactory for all of these problems for each problem considered the results are illustrated using practical examples our overall conclusion is tha