necessary and sufficient small gain conditions for integral input to state stable systems a lyapunov perspective this paper is concerned with conditions for the stability of interconnected nonlinear systems consisting of integral input to state stable iiss systems with external inputs the treatment of iiss and input to state stable iss systems is unified both necessary conditions and sufficient conditions are investigated using a lyapunov formulation in the presence of model uncertainty this paper proves that for the stability of the interconnected system at least one subsystem is necessarily iss which is a stronger stability property in the set of iiss the necessity of a small gain type property is also demonstrated this paper proposes a common form of smooth lyapunov functions which can establish the iiss and the iss of the interconnection comprising iiss and iss subsystems whenever the small gain type condition is satisfied the result covers situations more general than the earlier study and removes technical conditions assumed in the previous literature global asymptotic stability is discussed as a special case

state dependent scaling design for a unified approach to robust backstepping global robust stabilization of nonlinear systems is characterized as a state dependent scaling problem by choosing scaling functions recursively one can construct robust control laws for an extended class of strict feedback systems

a small gain theorem for switched interconnected nonlinear systems and its applications a small gain theorem for switched interconnected nonlinear systems is set up which provides a tool for analyzing the behavior of switched systems also a method exploiting an average dwell time and the small gain technique is proposed based on the small gain theorem this technical note investigates the problem of global stabilization of switched nonlinear systems in strict feedback form whose all zero dynamics are input to state stable iss or only some are iss and others are not a sufficient condition for the global stabilization problem under a class of switching signals with average dwell time is derived by constructing state feedback controllers for subsystems the result is also applied to a class of switched nonlinear network control systems

two stage tests for studying monotherapy and combination therapy in two by two factorial trials two stage testing involves a preliminary test of a nuisance parameter prior to testing main hypothesis in a two by two factorial trial the treatment interaction is the nuisance to the inference about the efficacy of one of the treatments given alone in comparing a combination therapy to both of its component therapies the nuisance parameter is the difference in the component effects when the preliminary test is an integral part of inference about the main parameter the actual level of significance for the two stage test procedure can be much higher than the desired nominal level if one places no restriction on the value of the nuisance parameter then any two stage test with its significance level properly controlled has undesirable properties this applies to comparative studies of combination agents relative to the component agents when the interaction with an ineffective treatment is null two stage testing may have some power advantage for assessing monotherapy efficacy

a robust analysis of crossover designs using multisample generalized l statistics abstract in a crossover study some or all subjects receive more than one treatment sequentially using a clinical example as motivation we develop multisample generalized l statistics gl statistics to estimate and test for treatment effects in crossovers when the distribution of the response data deviates from normality the basic idea is to adapt simple l statistics such as the trimmed mean and median to data with dependencies gl statistics may be applied to crossovers with more than two periods and or sequences these designs are useful for experiments with two treatments in which carryover and treatment effects might be aliased in the commonly used two period two sequence design as well as for experiments with more than two treatments for data analysis with large samples the asymptotic properties of the gl statistics suggest that the generalized trimmed mean and generalized median often should be strongly consistent and normal a simulation study of a four sequence two period crossover desi

using the maximum test statistic in the two period crossover clinical trial in a two period crossover trial where residual carryover is suspected it is often advised that first period data only be used in an analysis appropriate for a parallel design however it has been shown willan and pater 1986 biometrics 42 593 599 that the crossover analysis is more powerful than the parallel analysis if the residual carryover expressed as a proportion of treatment effect is less than 2 square root of 2 1 rho where rho is the intrasubject correlation coefficient choosing between the analyses based on the empirical evaluation of this condition is equivalent to choosing the analysis with the larger corresponding test statistic approximate nominal significance levels are presented that maintain the desired level when basing the analysis on the maximum test statistic furthermore the power and precision of the analysis based on the maximum test statistic are compared to the crossover and parallel analyses

weak and strong representations for trimmed u statistics weak and strong representations are proved for two classes of trimmed u statistics generalizing the trimmed mean applications of the strong representation theorems include laws of iterated logarithm and invariance principles for trimmed u statistics

further results on output feedback regulation of stochastic nonlinear systems with siiss inverse dynamics this article further discusses the problem of output feedback regulation for more general stochastic nonlinear systems with stochastic integral input to state stable inverse dynamics and focuses on solving the important and unsolved problem proposed in yu and xie yu x and xie x j 2010 output feedback regulation of stochastic nonlinear systems with stochastic iiss inverse dynamics ieee transactions on automatic control 55 304 320 how to weaken the conditions on nonlinearities in drift and diffusion vector fields under the weaker conditions how to make full use of the known information of stochastic nonlinear systems to design an adaptive output feedback controller such that all the closed loop signals are almost surely bounded and the output is driven to zero almost surely

incomplete generalized l statistics given data x 1 x n and a kernel h with m arguments serfling introduced the class of generalized l statistics gl statistics which is defined by taking linear combinations of the ordered h x i1 x im where i 1 i m ranges over all n n m distinct m tuples of 1 n in this paper we derive a class of incomplete generalized l statistics igl statistics by taking linear combinations of the ordered elements from a subset of h x i1 x im with size n n a special case is the class of incomplete u statistics introduced by blom under very general conditions the igl statistic is asymptotically equivalent to the gl statistic as soon as n n n as n which makes the igl much more computationally feasible we also discuss various ways of selecting the subset of h x i x im several examples are discussed in particular some new estimates of the scale parameter in nonparametric regression are introduced it is shown that these estimates are asymptotically equivalent to an igl statistic some extensions for example functionals other than l and multivariate kernels are also addressed

limit theorems for functionals of mixing processes with applications to u statistics and dimension estimation in this paper we develop a general approach for investigating the asymptotic distribution of functional xn f zn k k z of absolutely regular stochastic processes zn n z such functional occur naturally as orbits of chaotic dynamical systems and thus our results can be used to study probabilistic aspects of dynamical systems we first prove some moment inequalities that are analogous to those for mixing sequences with their help several limit theorems can be proved in a rather straightforward manner we illustrate this by re proving a central limit theorem of ibragimov and linnik then we apply our techniques to u statistics matrix equation with symmetric kernel h r r r we prove a law of large numbers extending results of aaronson burton dehling gilat hill and weiss for absolutely regular processes we also prove a central limit theorem under a different set of conditions than the known results of denker and keller as our main application we establish an invariance principle for u processes un h h indexed by some class of functions we finally apply these results to study the asymptotic distribution of estimators of the fractal dimension of the attractor of a dynamical system

robust control for nonlinear systems with structured l 2 gain bounded uncertainty abstract this paper focuses on the problem of robust control design for uncertain nonlinear systems with l 2 gain bounded dynamic uncertainty and periodically time varying memoryless uncertainty the robust performance problem is solved via nonlinear h control with scaling factors it is shown that the scaling factors can be functions of state variables in contrast with linear robust control

a small gain theorem in the absence of strong iiss previous small gain results for interconnected integral input to state iiss systems have been restricted to systems that are strongly iiss this paper removes this restriction by allowing cross terms between external inputs and states in the lyapunov decrease of component systems and subsequently constructing a nonseparable lyapunov function an example demonstrates the use of this new small gain formulation

a remark on the stability of interconnected nonlinear systems we use a notion of generalized l sub 2 gain for nonlinear systems where the gain is considered as a function of the state instead of a global constant for characterizing stability properties of interconnected systems the obtained results generalize the well known small gain theorem

a robust method for shift detection in time series we present a robust test for change points in time series which is based on the two sample hodges lehmann estimator we develop new limit theory for a class of statistics based on the two sample u quantile processes in the case of short range dependent observations using this theory we can derive the asymptotic distribution of our test statistic under the null hypothesis we study the finite sample properties of our test via a simulation study and compare the test with the classical cusum test and a test based on the wilcoxon mann whitney statistic

output feedback control using small gain conditions for stochastic nonlinear systems with siiss inverse dynamics this article further discusses output feedback control for stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics based on the stochastic lasalle theorem and small gain type conditions on siiss an output feedback controller using the backstepping method is constructively designed to guarantee that all the closed loop signals are bounded almost surely and the stochastic closed loop system is globally asymptotically stable in probability

the desirability of adjusting for residual effects in a crossover design summary crossover experiments in which treatments are applied in sequence to the same experimental unit may give misleading results if there are carryover effects from previous treatments in each sequence and these effects are not allowed for in the analysis this paper is concerned with how to decide whether or not to allow for carryover effects the general conclusion is that despite the increased variance resulting from adjustment the safest policy is always to allow for these effects in a crossover design different treatments are applied in turn to the same experimental unit kershner and federer 1981 patterson 1951 the commonest applications are in nutritional trials on animals and in clinical trials of drugs however one difficulty associated with this design is that from the second period onwards a residual or carryover effect may be present due to the treatment applied in the previous period this problem can be mitigated by ensuring that each treatment is preceded equally often by every other treatment williams 1949 has shown how latin squares can be chosen to achieve this balance even with this balance the straightforward comparison of any two treatment means will be biased if their residual effects differ because no treatment is preceded by itself the repetition of one of the periods in order to achieve a complete balance of the residual effects and hence remove the bias is often impossible because of the time that would be required for the extended experiment when crossover designs are used for treatment comparisons the usual procedure is to test for residual effects and only if they are significantly different from zero adjust for them in the estimation of treatment effects the decision whether to adjust or not is therefore based on a significance test applied at an arbitrarily specified significance level if however the precise estimation of treatment effects is of prime interest procedures which lead to estimators that have smallest mean square errors mses are more appropriate the purpose of this paper is to investigate the effectiveness of such a procedure attention is restricted to the case in which it is reasonable to suppose that the duration of residual effects is limited to the period immediately following the direct application of the treatment we shall assume that the major interest is in the effect of the treatments during the period of their application some combination of direct and residual effects would merit consideration if in practice the treatment is to be applied for a longer period

m estimation in cross over trials a robust procedure combined m estimation is proposed for analyzing cross over data with possible within and between subject outliers the mean squared error properties of these combined m estimates for direct treatment effect contrasts and carryover treatment effect contrasts are examined through simulation studies they are found to be superior to those of the generalized least squares estimates when there are possible within and between subject outliers

extended jacobian inverse kinematics algorithm for nonholonomic mobile robots by a generalization of the well known extended jacobian method for stationary manipulators we derive the extended jacobian inverse kinematics algorithm for nonholonomic mobile robots key points of the derivation consist in defining the kinematics of a mobile robot as the end point map of a driftless control system decomposing the space of control functions of this system into a finite and an infinite dimensional subspaces and introducing an augmenting kinematics map subordinated to this decomposition the original kinematics and the augmenting kinematics constitute the extended kinematics the inverse jacobian of the extended kinematics defines the extended jacobian inverse kinematics algorithm by design the algorithm is repeatable as an example we derive a specific extended jacobian inverse kinematics algorithm and illustrate its performance with the computer simulations

a nonparametric approach to the analysis of the two treatment two period four sequence crossover model owing to the estimability problems in the two treatment two period two sequence crossover model the four sequence design ab ba aa bb has gained popularity this paper presents a nonparametric approach to the analysis of the two treatment two period four sequence crossover model using an approach similar to that of koch 1972 biometrics 28 577 584 after forming differences within an experimental unit the benard van elteren test benard and van elteren 1953 proc konink nederlandse akad van wetenshappen series a 56 358 369 uses the transformed data to construct a test of the equality of the direct effects of the treatment a numerical example is presented to illustrate the methodology

a characterization of integral input to state stability the notion of input to state stability iss is now recognized as a central concept in nonlinear systems analysis it provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite l sup 2 gains it plays a central role in recursive design coprime factorizations controllers for nonminimum phase systems and many other areas in this paper a newer notion that of integral input to state stability iiss is studied the notion of iiss generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states in that sense generalizing the linear h sup 2 theory it allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance we obtain several necessary and sufficient characterizations of the iiss property expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations

nonlinear scaling of i iss lyapunov functions while nonlinear scalings of lyapunov functions are also lyapunov functions we provide examples that the same statement does not necessarily hold for input to state stable iss lyapunov functions or for integral iss iiss lyapunov functions we provide sufficient conditions under which a nonlinear scaling of an iss or iiss lyapunov function is also an iss or iiss lyapunov function we also introduce a generalization of the iiss lyapunov function which we term a dissipative iiss lyapunov function that allows for a larger class of nonlinear scalings so that nonlinear scalings of dissipative iiss lyapunov functions are again dissipative iiss lyapunov functions

brief paper capability and limitation of max and sum type construction of lyapunov functions for networks of iiss systems this paper addresses the problem of verifying stability of networks whose subsystems admit dissipation inequalities of integral input to state stability iiss we focus on two ways of constructing a lyapunov function satisfying a dissipation inequality of a given network their difference from one another is elucidated from the viewpoint of formulation relation fundamental limitation and capability one is referred to as the max type construction resulting in a lipschitz continuous lyapunov function the other is the sum type construction resulting in a continuously differentiable lyapunov function this paper presents geometrical conditions under which the lyapunov construction is possible for a network comprising n 2 subsystems although the sum type construction for general n 2 has not yet been reduced to a readily computable condition we obtain a simple condition of iiss small gain in the case of n 2 it is demonstrated that the max type construction fails to offer a lyapunov function if the network contains subsystems which are not input to state stable iss

functional limit theorems for u processes un processus u est une collection de statistiques u indicees par une famille de noyaux symetriques on utilise la theorie limite classique pour demontrer pour le processus u des analogues du theoreme central limite pour les processus empiriques

control of systems without drift via generic loops this paper proposes a simple numerical technique for the steering of arbitrary analytic systems with no drift it is based on the generation of nonsingular loops which allow linearized controllability along suitable trajectories once such loops are available it is possible to employ standard newton or steepest descent methods as classically done in numerical control the theoretical justification of the approach relies on results establishing the genericity of nonsingular controls as well as a simple convergence lemma

choosing appropriate analysis methods for cluster randomised cross over trials with a binary outcome in cluster randomised cross over crxo trials clusters receive multiple treatments in a randomised sequence over time in such trials there is usual correlation between patients in the same cluster in addition within a cluster patients in the same period may be more similar to each other than to patients in other periods we demonstrate that it is necessary to account for these correlations in the analysis to obtain correct type i error rates we then use simulation to compare different methods of analysing a binary outcome from a two period crxo design our simulations demonstrated that hierarchical models without random effects for period within cluster which do not account for any extra within period correlation performed poorly with greatly inflated type i errors in many scenarios in scenarios where extra within period correlation was present a hierarchical model with random effects for cluster and period within cluster only had correct type i errors when there were large numbers of clusters with small numbers of clusters the error rate was inflated we also found that generalised estimating equations did not give correct error rates in any scenarios considered an unweighted cluster level summary regression performed best overall maintaining an error rate close to 5 for all scenarios although it lost power when extra within period correlation was present especially for small numbers of clusters results from our simulation study show that it is important to model both levels of clustering in crxo trials and that any extra within period correlation should be accounted for copyright 2016 john wiley sons ltd

alternatives to the median absolute deviation abstract in robust estimation one frequently needs an initial or auxiliary estimate of scale for this one usually takes the median absolute deviation mad n 1 4826 med xi med j x j because it has a simple explicit formula needs little computation time and is very robust as witnessed by its bounded influence function and its 50 breakdown point but there is still room for improvement in two areas the fact that mad n is aimed at symmetric distributions and its low 37 gaussian efficiency in this article we set out to construct explicit and 50 breakdown scale estimators that are more efficient we consider the estimator sn 1 1926 med med j xi xj and the estimator qn given by the 25 quantile of the distances xi x j i j note that sn and qn do not need any location estimate both sn and qn can be computed using o n log n time and o n storage the gaussian efficiency of sn is 58 whereas qn attains 82 we study sn and qn by means of their influence functions their b

optimal sparse singular value decomposition for high dimensional high order data in this article we consider the sparse tensor singular value decomposition which aims for dimension reduction on high dimensional high order data with certain sparsity structure a method named s

a lyapunov approach to cascade interconnection of integral input to state stable systems this technical note deals with the stability of cascade interconnection of integral input to state iiss time varying systems a new technique to construct smooth lyapunov functions of cascaded systems is proposed from the construction sufficient conditions for internal stability and stability with respect to external signals are derived one of the derived conditions is a trade off between slower convergence of the driving system and steeper input growth of the driven system the trade off is no more necessary if the speed of convergence of the driven system is not radially vanishing the results are related to trajectory based approaches and small gain techniques for feedback interconnection the difference between the feedback case and the cascade case is viewed from the requirement on convergence speed of autonomous parts

state dependent scaling problems and stability of interconnected iiss and iss systems this paper addresses the problem of establishing stability of nonlinear interconnected systems this paper introduces a mathematical formulation of the state dependent scaling problems whose solutions directly provide lyapunov functions proving stability properties of interconnected dissipative systems in a unified manner stability criteria are interpreted as sufficient conditions for the existence of solutions to the state dependent scaling problems computing solutions to the problems is straightforward for systems covered by classical stability criteria it however could be too difficult for systems with strong nonlinearity the main purpose of this paper is to demonstrate the effectiveness beyond formal applicability by focusing on interconnected integral input to state stable iiss systems and input to state stable iss systems this paper derives small gain type theorems for interconnected systems involving iiss systems from the state dependent scaling formulation this paper provides solutions and lyapunov functions explicitly the new framework seamlessly generalizes the iss small gain theorem and classical stability criteria such as the lp small gain theorem the passivity theorems the circle and popov criteria state dependence of the scaling is crucial for effective treatment of essential nonlinearities while constants are sufficient for classical nonlinearities

a comparative study of ordinary cross validation v fold cross validation and the repeated learning testing methods summary concepts of v fold cross validation and repeated learning testing methods have been introduced here in many problems these methods are computationally much less expensive than ordinary cross validation and can be used in its place a comparative study of these three methods has been carried out in detail

construction of lyapunov functions for interconnected parabolic systems an iiss approach this paper is devoted to two issues the first one is to provide lyapunov based tools to establish integral input to state stability iiss and input to state stability iss for some classes of nonlinear parabolic equations the other one is to provide a stability criterion for interconnections of iiss parabolic systems the results addressing the former problem allow us to overcome obstacles arising in tackling the latter one the results for the latter problem are a small gain condition and a formula of lyapunov functions which can be constructed for interconnections whenever the small gain condition holds it is demonstrated that for interconnections of partial differential equations the choice of a right state and input spaces is crucial in particular for iiss subsystems which are not iss as illustrative examples stability of two highly nonlinear reaction diffusion systems is established by the proposed small gain criterion

a review of goodness of fit tests for pareto distributions abstract pareto distributions are the most popular models in economics and finance hence it is essential to have a wide spectrum of tools for checking their goodness of fit to a given data set this paper provides the first review of known goodness of fit tests for pareto distributions over twenty tests are reviewed their powers are compared by simulation

use of two stage test statistic in the two period crossover trials for two period crossover trials where the residual carryover can only exist in the presence of treatment effect willan 1988 biometrics 44 211 218 recommended use of the maximum test statistic that chooses the analysis with the larger test statistic corresponding to the parallel analysis and the crossover analysis we construct two alternative two stage test procedures based on grizzle s approach that maintain the actual type i error rate at the desirable level the power accuracy and precision of the analysis based on the modified two stage procedures are compared to those based on the parallel analysis crossover analysis and the maximum test statistic

brief paper adaptive state feedback stabilization for a large class of high order stochastic nonlinear systems under the more general conditions on the power order and the nonlinear functions this paper investigates the problem of adaptive state feedback stabilization for a class of high order stochastic nonlinear systems with time varying control coefficients based on the backstepping design method and homogeneous domination technique the closed loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely the efficiency of the state feedback controller is demonstrated by a simulation example

design and analysis of intra subject variability in cross over experiments recently interest has grown in the development of inferential techniques to compare treatment variabilities in the setting of a cross over experiment in particular comparison of treatments with respect to intra subject variability has greater interest than has inter subject variability we begin with a presentation of a general approach for statistical inference within a cross over design we discuss three different statistical models where model choice depends on the design and assumptions about carry over effects each model incorporates t variate random subject effects where t is the number of treatments we develop maximum likelihood ml and restricted maximum likelihood reml approaches to derive parameter estimators and we consider a special case in which closed form expressions for the variance component estimators are available finally we illustrate the methodologies with the analysis of data from three examples

construction of lyapunov krasovskii functionals for networks of iiss retarded systems in small gain formulation this paper tackles a problem of verifying stability of retarded dynamical networks in a dissipative formulation subsystems are assumed to be integral input to state stable iiss time delays are allowed to reside in both subsystems and interconnection channels and may be both discrete and distributed no assumption is made on the interconnection topology a small gain methodology is developed for constructing a lyapunov krasovskii functional to establish iiss of such a network

estimation of variance components with high breakdown point and high efficiency summary for the one way random effects model three noniterative robust variance component estimators are investigated for these estimators block breakdown points measurement breakdown points and efficiency are derived it is shown that the block breakdown points are approximating 50 and that the measurement breakdown points are not smaller than 25 by deriving the asymptotic normal distribution of these estimators we show that two of the new estimators have an asymptotic efficiency greater than 82 and under certain circumstances up to 96 competing estimators have lower breakdown points and lower efficiencies a simulation study shows that the high efficiency also appears for finite samples the use of the estimators for interlaboratory tests is demonstrated in a practical example

is the simple carry over model useful it is argued that the models usually employed for carry over effects in cross over trials are not reasonable the example of a non linear dose response for a dose finding trial arranged in a williams square is developed to show that if carry over is present to any appreciable degree the usual statistical models provide no guaranteed protection against its effects it is concluded that the most reasonably defended assumption about carry over effects is that no important carry over has taken place and that where this assumption cannot be defended statistical models provide no satisfactory substitute for it

meta analysis combining parallel and cross over clinical trials i continuous outcomes among clinical trials assessing a given treatment often parallel and cross over designs are used together in the first paper of a series of three we explore two methods to pool continuous outcomes in a meta analysis combining parallel and cross over trial designs the weighted mean difference wmd and the standardized weighted mean difference swmd the combined design meta analytic formulae are based on a weighted average of the two design treatment estimates a random effects model can be implemented both wmd and swmd can be used the choice of the method is determined by the type of outcomes obtained in the trials compared to the number of included subjects the relative weight of the cross over design is large in combined design meta analysis differences in the weight estimation between wmd and swmd can also accentuate the relative weight of cross over trials which must be considered a case of design specific bias

on dynamic properties of singularity robust jacobian inverse kinematics in the technical note we examine dynamic properties of the singularity robust jacobian inverse kinematics algorithm for mobile manipulators by design this algorithm operates at regular as well as singular configurations the main result of the technical note consists in establishing the completeness of the singularity robust algorithm and in providing a condition for its convergence computer simulations illustrate the theory

brief paper a degree of flexibility in lyapunov inequalities for establishing input to state stability of interconnected systems in this paper a novel approach to constructing flexible lyapunov inequalities is developed for establishing input to state stability iss of interconnection of nonlinear time varying systems it aims at a useful tool for using nonlinear small gain conditions by allowing some flexibility in lyapunov inequalities each subsystem is to satisfy in the application of the iss small gain theorem achieving a lyapunov inequality conforming to a nonlinear small gain condition is not a straightforward task the proposed technique provides us with many lyapunov inequalities with which a single trade off condition between subsystems gains can establish the iss property of the interconnected system proofs are based on explicit construction of lyapunov functions

multiple lyapunov functions based small gain theorems for switched interconnected nonlinear systems multiple lyapunov functions mlfs based small gain theorems are presented for switched interconnected nonlinear systems with unstable subsystems which extend the small gain technique from its original non switched nonlinear version to a switched nonlinear version each low dimensional subsystem does not necessarily have the input to state stability iss property in the whole state space and it only has individual iss property in some subregions of the state space the novelty of this paper is that integral type mlfs and small gain techniques are utilized to establish some mlfs based small gain theorems for switched interconnected nonlinear systems which derive various stability results under some novel switching laws designed and construct integral type mlfs the small gain theorems proposed cover several recent results as special cases which also permit removal of a common restriction in which all low dimensional subsystems in switched interconnected systems are iss or only some are iss and others are not finally two illustrative examples are presented to demonstrate the effectiveness of the results provided

the analysis of data from 2 2 cross over trials with baseline measurements an account is given of the analysis of data from 2 x 2 cross over trials which include baseline measurements we show that most of the previously proposed methods can be incorporated into a general framework of least squares estimation with a simple linear model a simple analysis based on ordinary least squares estimators is described which can be used with either two sample t tests and confidence intervals or with the corresponding non parametric procedures it is shown how the use of generalized least squares estimators is equivalent to the use of covariance adjustment these methods require no assumptions about the covariance structure of the measurements from each subject the results of assessing the covariance structure present in examples of data from a number of trials are summarized these results suggest that previously proposed simple covariance structures are unlikely to be appropriate in general

strong iiss is preserved under cascade interconnection in a recent paper we have introduced the notion of strong iiss as a compromise between the strength of input to state stability iss and the generality of integral iss iiss in this note we continue the investigations around this property by studying its behavior in an interconnection context in particular we show that the cascade of strongly iiss systems is itself strongly iiss and we recall some useful tools to study strongly iiss systems in feedback interconnection

an iiss framework for stochastic robustness of interconnected nonlinear systems this paper addresses integral input to state stability iiss for stochastic nonlinear dynamical systems and develops lyapunov type criteria the developments offer an iiss small gain framework for verifying robustness of interconnected systems with respect to disturbances the framework not only includes input to state stability iss as a special case but also highlights fundamental differences between the stochastic and deterministic systems in particular dealing with nonlinearities in interconnection gives rise to a unique issue of degradation in the presence of stochastic noises this paper addresses this issue by coping judiciously with the effect of the gradient of lyapunov functions of subsystems through diffusion fields in composing a lyapunov function of the entire system this paper employs two types of robustness notions and demonstrates that the influence of the stochastic degradation on one notion is considerably different from the influence on the other notion in dealing with interconnected systems

brief paper small gain control method for stochastic nonlinear systems with stochastic iiss inverse dynamics this paper investigates the small gain type conditions on stochastic iiss siiss systems and makes full use of these conditions in the design and analysis of the controller the contributions are as follows 1 a new proof of the stochastic lasalle theorem is provided 2 the small gain type conditions on siiss are developed and their relationship is discussed 3 based on the stochastic lasalle theorem and siiss small gain type conditions the adaptive controllers are designed to guarantee that all of the closed loop signals are bounded almost surely and the stochastic closed loop systems are globally asymptotically stable in probability

connection between cooperative positive systems and integral input to state stability of large scale systems we consider a class of continuous time cooperative systems evolving on the positive orthant r n we show that if the origin is globally attractive then it is also globally stable and furthermore there exists an unbounded invariant manifold where trajectories strictly decay this leads to a small gain type condition which is sufficient for global asymptotic stability gas of the origin we establish the following connection to large scale interconnections of integral input to state stable iss subsystems if the cooperative system is integral iss and arises as a comparison system associated with a large scale interconnection of i iss systems then the composite nominal system is also i iss we provide a criterion in terms of a lyapunov function for integral input to state stability of the comparison system furthermore we show that if a small gain condition holds then the classes of systems participating in the large scale interconnection are restricted in the sense that certain iiss systems cannot occur moreover this small gain condition is essentially the same as the one obtained previously by dashkovskiy ruffer and wirth 2007 in press for large scale interconnections of iss systems

reduced order observer based output feedback regulation for a class of nonlinear systems with iiss inverse dynamics global asymptotic regulation via output feedback based on a reduced order observer is considered for a class of nonlinear systems with integral input to state stable iiss inverse dynamics the contributions are that 1 we further consider the conditions on changing supply rates in iiss systems and discuss the necessity of some conditions by constructing a counter example 2 for a more general class of nonlinear systems with iiss inverse dynamics a reduced order observer is introduced and by the combined approach of backstepping and changing iiss supply rates an output feedback controller is given to drive the output of system to the origin asymptotically and maintain other closed loop signals bounded

longcrisp a test for bump hunting in longitudinal data we propose an extension of the harezlak and heckman j comput graph statist 2001 10 4 713 729 test for detecting local extrema to the longitudinal data setting we use penalized spline regression techniques statist sci 1996 11 89 102 to provide a computationally efficient method of testing for relatively large data sets we estimate the p values of our test longcrisp with a smoothed bootstrap our simulation studies indicate that the test is generally conservative and has power exceeding 70 per cent at the alpha 0 1 nominal level in most considered settings finally we apply our testing procedure to the longitudinal measurements of body mass index of former prisoners of war in vietnam and conclude that the mean population curve exhibits non monotone behaviour

generalized s estimators abstract in this article we introduce a new type of positive breakdown regression method called a generalized s estimator or gs estimator based on the minimization of a generalized m estimator of residual scale we compare the class of gs estimators with the usual s estimators including least median of squares it turns out that gs estimators attain a much higher efficiency than s estimators at the cost of a slightly increased worst case bias we investigate the breakdown point the maxbias curve and the influence function of gs estimators we also give an algorithm for computing gs estimators and apply it to real and simulated data

the performance of the two stage analysis of two treatment two period crossover trials in the two treatment two period crossover trial patients are randomly allocated either to one group that receives treatment a followed by treatment b or to another group that receives the treatments in the reverse order grizzle first proposed a two stage procedure for analysing the data from such a trial this paper examines the long run sampling properties of this procedure in terms of mean square error of point estimates coverage probability of confidence intervals and actual significance level of hypothesis tests for the differences between the effects of the two treatments the advantages of incorporating baseline observations into the analysis are also explored because the preliminary test for carryover is highly correlated with the analysis of data from the first period only actual significance levels are higher than nominal levels even when there is no differential carryover when carryover is present the nominal level very seriously understates the actual level and this becomes even worse when baseline observations are ignored increasing sample size only exacerbates the problem since this adverse behaviour then occurs at smaller values of the carryover effect it is concluded that the two stage analysis is too potentially misleading to be of practical use

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

robust stability of networks of iiss systems construction of sum type lyapunov functions this paper gives a solution to the problem of verifying stability of networks consisting of integral input to state stable iiss subsystems the iiss small gain theorem developed recently has been restricted to interconnections of two subsystems for large scale systems stability criteria relying only on gain type information that were previously developed address only input to state stable iss subsystems to address the stability problem involving iiss subsystems interconnected in general structure this paper shows how to construct lyapunov functions of the network by means of a sum of nonlinearly rescaled individual lyapunov functions of subsystems under an appropriate small gain condition

estimating densities of functions of observations abstract density estimates such as histograms and more sophisticated versions are important in applied and theoretical statistics in applied statistics a density estimate gives the data analyst a graphical overview of the shape of the distribution this overview allows the data analyst to arrive immediately at a qualitative impression of the location scale and various aspects of the extremes of the distribution in theoretical statistics the shape of the density allows the researcher to link the data to families of curves perhaps indexed parametrically by estimating a density nonparametrically certain aspects of the data can be viewed without the restriction of a priori imposing limitations of a class of parametric curves in this article we introduce density estimation for functions of observations to motivate the study one type of function used is the interpoint distance between observations arising in spatial statistics from the fields of biometry and regional science a second type of func

invariance like theorems and lim inf convergence properties several theorems inspired by the krasovskii lasalle invariance principle to establish lim inf convergence results are presented in a unified framework these properties are useful to describe the oscillatory behavior of the solutions of dynamical systems the theorems resemble lim inf matrosov and small gain theorems and are based on a lim inf barbalat s lemma additional technical assumptions to have lim convergence are given the lim inf lim relation is discussed in depth and the role of some of the assumptions is illustrated by means of examples

the least trimmed differences regression estimator and alternatives abstract this article proposes and studies the performance in theory and practice of the least trimmed differences ltd linear regression estimator the estimator minimizes the sum of the smallest quartile of the squares of the differences in each pair of residuals we obtain the breakdown point maxbias curve and large sample properties of a class of estimators including the ltd as special case the ltd estimator has a 50 breakdown point and gaussian efficiency of 66 substantially higher than other common high breakdown estimators such as least median of squares and least trimmed squares the ltd estimator is difficult to compute but can be performed using a feasible solution algorithm half sample jackknifing is effective in producing standard errors in simulations we find the ltd to be more stable than other high breakdown estimators in an example the ltd still shows instability like other high breakdown estimators when there are small changes in the data

a generalization of the small gain theorem for nonlinear feedback systems abstract a generalization is given of the usual small gain theorem which allows greater flexibility in use of gain bounds for stability analysis of nonlinear feedback systems

extending a bayesian analysis of the two period crossover to allow for baseline measurements in the context of a two period crossover study with baseline measurements a graphical method is developed for displaying the dependence of posterior inferences concerning the treatment effect on unavoidable prior beliefs about the correct model the method is a generalization of the approach developed by grieve for the corresponding case without baselines

small gain type sufficient conditions for sampled data feedback stabilization for autonomous composite systems small gain type sufficient conditions are established guaranteeing weak global asymptotic stabilization for composite autonomous systems by means of a sampled data feedback our main result generalizes the well known small gain theorem for global asymptotic stability for composite systems with no controls under the presence of the input to state stability the sufficient conditions we propose enable us to derive a set of algebraic sufficient conditions for the existence of a sampled data feedback stabilizer with zero order hold the work is a continuation of author s work published in same journal

constrained motion planning of nonholonomic systems this paper addresses the constrained motion planning problem for nonholonomic systems represented by driftless control systems with output the problem consists in defining a control function driving the system output to a desirable point at a given time instant whereas state and control variables remain over the control horizon within prescribed bounds the state and control constraints are handled by extending the control system with a pair of state equations driven by the violation of constraints and adding regularizing perturbations for the regularized system a jacobian motion planning algorithm is designed called imbalanced solutions of example constrained motion planning problems for the rolling ball illustrate the theoretical concepts

glivenko cantelli properties of some generalized empirical df s and strong convergence of generalized l statistics we study a nonclassical form of empirical df hnwhich is of u statistic structure and extend to hnthe classical exponential probability inequalities and glivenko cantelli convergence properties known for the usual empirical df an important class of statistics is given byt hn where t is a generalized form of l functional for such statisticswe prove almost sure convergence using an approach which separates the functional analytic and stochastic components of the problem and handles the latter component by application of glivenko cantelli type properties classical results for u statistics and l statistics are obtained as special cases without addition of unnecessary restrictions many important new types of statistics of current interest are covered as well by our result

generalized l m and r statistics abstract a class of statisticss generalizing u statistics and l statistics and containing other varieties of statistics as well such as trimmed u statistics is studied using the differentiable statistical function approach differential approximations are obtained and the influence curves of these generalized l statistics are derived these results are employed to establish asymptotic normality for such statistics parallel generalizations of m and r statistics are noted strong convergence berry esseen rates and computational aspects are discussed

further results on global asymptotic regulation control for a class of nonlinear systems with iiss inverse dynamics this note studies the global asymptotic regulation problem for a class of nonlinear systems with integral input to state stable iiss inverse dynamics by output feedback it does not require a priori knowledge of the sign of the high frequency gain the considered system represents more general classes of nonlinear uncertain systems the novelty of this note lies in the observer whose gain comes from a time varying riccati differential equation

limit theorems for functionals of moving averages let x n i 1 a i e n 1 where the e i are i i d with mean 0 and finite second moment and the a i are either summable or regularly varying with index 1 1 2 the sequence x n has short memory in the former case and long memory in the latter for a large class of functions k a new approach is proposed to develop both central n rate and noncentral non n rate limit theorems for s n n 1 n k x n ek x n specifically we show that in the short memory case the central limit theorem holds for s n and in the long memory case s n can be decomposed into two asymptotically uncorrelated parts that follow a central limit and a non central limit theorem respectively further we write the noncentral part as an expansion of uncorrelated components that follow noncentral limit theorems connections with the usual hermite expansion in the gaussian setting are also explored

a region dependent gain condition for asymptotic stability a sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem roughly speaking to apply this theorem it is required that the gains composition is continuous increasing and upper bounded by the identity function in this work an alternative sufficient condition is presented for the case in which this criterion fails due to either lack of continuity or the bound of the composed gain is larger than the identity function more precisely the local resp non local asymptotic stability of the origin resp global attractivity of a compact set is ensured by a region dependent small gain condition under an additional condition that implies convergence of solutions for almost all initial conditions in a suitable domain the almost global asymptotic stability of the origin is ensured two examples illustrate and motivate this approach

stability of stochastic nonlinear systems in cascade with not necessarily unbounded decay rates this paper develops tools to verify stability and robustness of cascaded nonlinear stochastic systems based on lyapunov functions constituent systems are formulated in terms of integral input to state stability iiss and input to state stability iss which are popular notions for both stochastic and deterministic systems this paper highlights differences between the stochastic and the deterministic cases in contrast to deterministic systems it is demonstrated that assuming iss systems having unbounded decay rates in dissipation inequalities is restrictive taking this fact into account stability criteria are formulated without assuming unboundedness of decay rates so that iss systems with bounded decay rates and iiss systems which are not iss are covered in a unified manner stability criteria for stochastic cascades involve the growth rate conditions at connecting channels this paper clarifies how noise diffusion fields affect the growth rate conditions and the influence depends on definition of stochastic robustness

extending a bayesian analysis of the two period crossover to accommodate missing data summary a procedure is developed for performing a bayesian analysis of a simple two period crossover design when some observations are missing in one or both treatment periods the approach requires the numerical evaluation of a single integral to be performed for each posterior marginal distribution of interest the relative efficiency of this approach to one in which patients with missing data are excluded is investigated

forward and adjoint sensitivity analysis with continuous explicit runge kutta schemes abstract we study the numerical solution of tangent linear first and second order adjoint models with high order explicit continuous runge kutta pairs the approaches currently implemented in popular packages such as sundials or daspkadjoint are based on linear multistep methods for adaptive time integration of nonlinear models interpolation of the forward model solution is required during the adjoint model simulation we propose to use the dense output mechanism built in the continuous runge kutta schemes as a highly accurate and cost efficient interpolation method in the inverse problem run we implement our approach in a fortran library called denserks which is found to compare well to other similar software on a number of test problems