analysis of covariance using the rank transformation the rank transformation refers to the replacement of data by their ranks with a subsequent analysis using the usual normal theory procedure but calculated on the ranks rather than on the data rank transformation procedures have previously been shown by the authors to have properties of robustness and power in both regression and analysis of variance it seems natural to consider the use of the rank transformation in analysis of covariance which is a combination of regression and analysis of variance in this paper the rank transformation approach to analysis of covariance is presented and examined comparisons are made with the rank transformation procedure given by quade 1967 journal of the american statistical association 62 1187 1200 and some standard data sets are used to compare the results of these two procedures a monte carlo simulation study examines the behavior of these methods under the null hypothesis and under alternative hypotheses with both normal and nonnormal distributions all results are compared with the usual analysis of covariance procedure on the basis of robustness and power

assessing normality in random effects models when one uses the unbalanced mixed linear model mathbf y i mathbf x i mathbf alpha mathbf z i mathbf beta i varepsilon i i 1 cdots n to analyze data from longitudinal experiments with continuous outcomes it is customary to assume varepsilon i sim operatorname ind mathscr n mathbf 0 sigma 2 mathbf i i independent of mathbf beta i sim operatorname iid mathscr n mathbf 0 delta where sigma 2 and the elements of an arbitrary mathbf delta are unknown variance and covariance components in this paper we describe a method for checking model adequacy and in particular the distributional assumption on the random effects mathbf beta i we generalize the weighted normal plot to accommodate dependent nonidentically distributed observations subject to multiple random effects for each individual unit under study one can detect various departures from the normality assumption by comparing the expected and empirical cumulative distribution functions of standardized linear combinations of estimated residuals for each of the individual units through application of distributional results for a certain class of estimators to our context we adjust the estimated covariance of the empirical cumulative distribution function to account for estimation of unknown parameters several examples of our method demonstrate its usefulness in the analysis of longitudinal data

assessing cross sectional correlation in panel data abstract consider drawing a sample of n experimental units where each unit is observed over t time periods are the draws independent a test statistic introduced by breusch and pagan 1980 is one measure used to quantify the amount of cross sectional correlation it is effective when t is large relative to n and as shown by breusch and pagan has desirable asymptotic in t properties in this paper we consider the case often encountered in the analysis of panel data where n is large relative to t here the breusch and pagan statistic does not enjoy the same desirable asymptotic in n properties in fact we show that the asymptotic distribution depends on the parent population even under the hypothesis of no cross sectional correlations thus we introduce a distribution free statistic that does not have this drawback asymptotic properties of the new statistic are established when the data are drawn from identical distributions and when the statistic is evaluated using residuals from a complex model both the breusch and pagan statistic and the new statistic are shown to be members of a more general family by considering this generalization finite sample properties of members of the family are easily established further it turns out that a statistic introduced by friedman 1937 is another special case of this family

multiplicity of positive periodic solutions to superlinear repulsive singular equations abstract in this paper we study positive periodic solutions to the repulsive singular perturbations of the hill equations it is proved that such a perturbation problem has at least two positive periodic solutions when the anti maximum principle holds for the hill operator and the perturbation is superlinear at infinity the proof relies on a nonlinear alternative of leray schauder type and on krasnoselskii fixed point theorem on compression and expansion of cones

on the existence of periodic solutions of a neutral delay model of single species population growth abstract in this paper we employ some new techniques to study the existence of positive periodic solutions of the neutral delay model n t n t a t t n t b t n t t c t n t t our result gives a correct answer to the open problem 9 2 due to y kuang 1993 delay differential equations with applications in population dynamics academic press new york

on existence of positive solutions and bounded oscillations for neutral difference equations abstract a criterion for the existence of a positive solution for the first order difference equation xn cxn m pnxn k 0 pn 0 is established results are also obtained for the oscillation and nonoscillation of solutions of a second order difference equation 2 xn cxn m pnxn k where the pn are either of constant sign or are oscillatory some of the results are sharp

two periodic solutions of neutral difference systems depending on two parameters in this paper we establish existence multiplicity and nonexistence of periodic solutions for a class of first order neutral difference systems our approach is based on a fixed point theorem in cones as well as some analysis techniques

periodic solutions of linear and quasilinear neutral functional differential equations abstract in this paper we will use the fourier expansions to generalize hale s alternative results for the existence of periodic solutions of linear retarded functional differential equations to neutral equations using some a priori estimation and the leray schauder degree theory we will obtain some existence theorems of periodic solutions for a class of quasilinear neutral equations the results also generalize the works of hatvani and krisztin on retarded equations

the effects on convergence of substituting parameter estimates into u statistics and other families of statistics substituting an estimator in a statistic will often affect its limiting distribution sukhatme 1958 randles 1982 and pierce 1982 all consider the changes if any in the statistic s limiting normal distribution this paper gives conditions for a law of the iterated logarithm for u statistics which have a kernel with an estimator substituted into it it also gives conditions for both strong and weak convergence applications of the theory are illustrated by constructing a sequential test for scale differences with power one the theory also produces convergence results for adaptive m estimators and for cross validation assessment statistics in addition it is shown how to extend lil results to a broad class of statistics with estimators substituted into them by use of the differential in particular a law of the iterated logarithm is described for adaptive l statistics and is illustrated by an example of de wet and van wyk 1979

a test for asymmetry associated with the hodges lehmann estimator abstract one version of the hodges lehmann estimator median xi xj 2 1 i j n is also the minimum distance estimator derived from a particular cramer von mises distance this distance evaluated at that is the minimized distance provides a natural statistic for testing asymmetry of the underlying distribution

a lack of fit test for the mean function in a generalized linear model abstract a supremum type statistic based on partial sums of residuals is proposed to test the validity of the mean function of the response variable in a generalized linear model the proposed test does not need a partition of the space of covariates to handle the case of nonreplication the new test is consistent against the alternative under which the deterministic part of the model is not the one specified in the null hypothesis the asymptotic null distribution of the test statistic can be approximated through simulations this approximation is valid even if the variance of the response variable is misspecified in the model for practical sample sizes the adequacy of this large sample approximation to the null distribution of the test statistic is carefully examined power comparisons with other lack of fit tests are also performed to show the advantage of the test in particular we find that the new procedure is rather sensitive to detect a misspecified mean function if the assumed mean functio

permanence criteria for general delayed discrete nonautonomous n species kolmogorov systems and its applications in this paper the permanence for the general nonautonomous n species discrete kolmogorov systems with delays is studied by using the method of multiple discrete lyapunov like functionals a quite general sufficient condition is established as application of this result new sufficient conditions are obtained to ensure the permanence of all species for the discrete nonautonomous pure delayed n species lotka volterra competitive systems and food chain systems particularly as special cases a series of new sufficient conditions on the permanence for the discrete nonautonomous pure delayed lotka volterra two species competitive systems predator prey systems and three species food chain systems and the discrete autonomous pure delayed lotka volterra competition systems and food chain systems are obtained

smooth goodness of fit tests for composite hypothesis in hazard based models consider a counting process n t t j with compensator process a t t j where a t 0 t y s 0 s ds y t t j is an observable predictable process and 0 is an unknown hazard rate function a general procedure for extending neyman s smooth goodness of fit test for the composite null hypothesis h 0 0 c 0 r q is proposed and developed the extension is obtained by embedding c in the class a k whose members are of the form 0 exp t x r k where 1 k t is a vector of observable random processes satisfying certain regularity conditions the tests are based on quadratic forms of the statistic 0 t s dm s where m t n t 0 t y s 0 s ds and is a restricted maximum likelihood estimator of asymptotic properties of the test statistics are obtained under a sequence of local alternatives and the asymptotic local powers of the tests are examined the effect of estimating by is ascertained and the problem of choosing the process is discussed the procedure is illustrated by developing tests for testing that 0 belongs to i the class of constant hazard rates and ii the class of weibull hazard rates with particular emphasis on the random censorship model simulation results concerning the achieved levels and powers of the tests are presented and the procedures are applied to three data sets that have been considered in the literature

permanence for a discrete time lotka volterra type food chain model with delays abstract considered is a delayed discrete time lotka volterra type food chain model sufficient conditions are established for the permanence and the feasibility of the obtained results are illustrated with an example

on tests applied to residuals abstract the null distribution of a test statistic computed on residuals can be affected by the dependence among the residuals it might be expected however that the dependence decreases as the sample size increases so that the limiting null distribution is the same as if the test were based on independent observations the author investigates whether this large sample equivalence holds for tests of correlation scale difference regression and location difference particular emphasis is placed on showing when rank tests based on residuals have a strongly asymptotically distribution free property u statistic theorems are used to investigate these issues

positive periodic solutions of functional differential equations abstract we consider the existence multiplicity and nonexistence of positive periodic solutions for the periodic equation x t a t g x x t b t f x t t where a b c r 0 are periodic 0 a t dt 0 0 b t dt 0 f g c 0 0 and f u 0 for u 0 g x is bounded t is a continuous periodic function define f 0 lim u 0 f u u f lim u f u u i0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f we show that the equation has i0 or i positive periodic solution s for sufficiently large or small 0 respectively

uniform persistence in functional differential equations abstract in this paper we investigate the question of uniform persistence for retarded functional differential equations by utilizing liapunov like functions razumikhin techniques and differential inequalities we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations difference equations and reaction diffusion equations we apply these criteria to some well known biological models with delay our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence moreover these conditions are equivalent to uniform persistence for the cases without delay as well

smooth goodness of fit tests for the baseline hazard in cox s proportional hazards model abstract for the cox proportional hazards model the goodness of fit problem of testing whether the baseline hazard rate function equals some specified hazard rate function 0 in the presence of incomplete data is considered extending neyman s idea the goodness of fit tests are score tests obtained by embedding in a larger family of hazard rate functions developed through smooth and possibly random transformations of 0 but whereas their smooth alternatives were formulated through the density function my formulation is through the hazard rate function which is more natural in failure time models where model specification is now done through hazard rates furthermore my smooth alternatives are allowed to be data driven or dynamic through this machinery classes of omnibus as well as directional goodness of fit tests are obtained moreover this machinery provides a theoretically sound method for combining varied directional goodness of fit tests into omnibus tests some of the resul

memoryless stabilization of linear delay differential systems sufficient conditions for memoryless feedback stabilization of linear time invariant delay differential systems are derived for both constant and time dependent delays

misspecification tests in econometrics based on ranks abstract this paper introduces a class of rank statistics for use in testing econometric models for misspecification these statistics are ideally suited to survey data since endogenous and exogenous variables in econometric models may therefore be considered exchangeable thus residuals from a wide class of models e g linear regression non linear regression simultaneous equations etc are also exchangeable since rank statistics are distribution free when based on exchangeable data it follows the rank statistics based on these residuals are also distribution free simulation studies in the linear regression case suggest that they have good power characteristics and are distributionally robust in comparison to the usual classical procedures

robust stabilization of a class of singularly perturbed discrete bilinear systems this paper presents two kinds of robust controllers for stabilizing singularly perturbed discrete bilinear systems the first one is an spl epsi dependent controller that stabilizes the closed loop system for all spl epsi spl isin 0 spl epsi sub 0 where spl epsi sub 0 is the prespecified upper bound of the singular perturbation parameter the second one is an spl epsi independent controller which is able to stabilize the system in the entire state space for all spl epsi spl isin 0 spl epsi where spl epsi is the exact upper spl epsi bound the spl epsi can be calculated by the critical stability criterion once the robust controller is determined an example is presented to illustrate the proposed schemes

periodic solutions of neutral differential equation with multiple deviating arguments in this paper by means of an abstract continuous theorem of k set contractive operator and some analysis techniques the authors study the existence of periodic solution of the nonlinear neutral differential equation with multiple deviating argumentsddt x t cx email protected email protected i 1 email protected i t f x email protected i t email protected j 1 email protected j t g x email protected j t p t a new result is obtained

stabilizability conditions by memory less feedback for linear systems with time delay abstract sufficient conditions for the stabilization by a memoryless feedback of the system with time delay are derived the main results are as follows 1 if we can place the maximal eigenvalue of some matrix sufficiently left in the left hand plane the system with time delay can be stabilized by a memoryless feedback 2 if a certain dynamical system defined by the original system is minimum phase then stabilization by a memoryless feedback is possible

periodic solutions for some nonlinear differential equations of neutral type where f ir x ir ir is a caratheodory function f x is 2n periodic for every x ci e r and r e io 2n this problem has been studied by sadovskii in 151 by hale and mawhin in 6 in the case ial 1 to the previous one our interest is particularly motivated by the fact that represents a simple and meaningful model for a general phenomenon which often arises in the study of functional differential equations in fact as is well known in some cases a delayed differential equation can be seen as a perturbation of an ordinary differential equation in particular this occurs when the delayed term in the equation can be considered smaller than the ordinary one or dominated by it when such domination is available many good properties can be proved and several results such as those of 6 and 16 take advantage of this fact on the contrary when no domination is present the situation is much more complicated and in general very little is known in problem the delayed term can be considered dominated by the ordinary one whenever ial 1 as a matter of fact in this case one can prove the invertibility of the differential operator l x x a r ux the compactness of its inverse and even some a priori estimates for the solutions consequently one can reduce to a fixed point problem and solve it by means of some topological degree argument however when 11 1 so that the weight of the two terms x t and x t t is the same the above properties fail and moreover for some delays the kernel of the differential operator lx x a r is infinite dimensional therefore one must look for different methods problem is thus a simple but nevertheless significant example of the considerations illustrated by hale in 5 about the difficulty of undertaking a unified approach in the study of functional differential equations at the same time it provides an analogy between neutral equations and the wave equation in the line suggested by hale in 5

periodic solutions of difference equations with general periodicity abstract motivated by 1 we study the existence of periodic solutions of a perturbed continuous difference equation of first order without the assumptions of one periodicity moreover we generalize our results to the case of higher order difference equations we also give an algorithm to estimate the bound of the parameter for which periodic solutions exist

a discrete periodic lotka volterra system with delays in this paper we investigate the following discrete periodic lotka volterra system with delays x n 1 x n expb n i 1qai n x n ti j 1mcj n y n li y n 1 y n expr n i 1qdi n x n ki j 1mej n y n si the sufficient and realistic conditions are obtained for the existence of positive periodic solutions and the permanence for the above system

predictor based control of linear systems with large and variable measurement delays this paper concerns the problem of the control of linear systems by means of feedback from delayed output where the delay is known and time varying the main advantage of the approach is that it can be applied to systems with any delay bound i e not only small delays the predictor is based on a combination of finite dimensional elementary predictors whose number can be suitably chosen to compensate any delay the single predictor element is an original proposal and the class of delays to which the schema can be applied includes but it is not limited to continuous delay functions

memoryless stabilization of uncertain linear systems including time varying state delays the problem of stabilizing a class of uncertain time delay systems via memoryless linear feedback is examined the systems under consideration are linear systems with time varying state delays they also contain uncertain parameters possibly time varying whose values are known only to within a prescribed compact bounding set the main contribution given is to enlarge the class of time delay systems for which one can construct a stabilizing memoryless linear feedback controller within this framework a novel notion of robust memoryless stabilizability is first introduced via the method of lyapunov functionals then a sufficient condition for the stabilizability is proposed it is shown that solvability of a parameterized riccati equation can be used to determine whether the time delay system satisfies the sufficient condition if there exists a positive definite symmetric solution satisfying the riccati equation a suitable memoryless linear feedback law can be derived

two periodic solutions of n dimensional neutral functional difference systems in this paper we establish existence multiplicity and nonexistence of periodic solutions for a class of first order n dimensional neutral functional difference systems our approach requires the krasnoselskii fixed point theorem in cones

union intersection rank tests for ordered alternatives in anocova abstract for an analysis of covariance model pertaining to completely randomized as well as complete block designs based on the union intersection principle a general class of permutationally distribution free rank tests for the ordered alternative problem is considered the theory is supplemented by numerical studies

positive periodic solutions of nonlinear functional difference equations depending on a parameter in this paper we use the upper and lower solutions method to show that there existsa l such that the nonlinear functional difference equation of the form g n 1 a n g n lh n g n t n n e z has at least one positive t periodic solutions for l e 0 l and does not have any positive t periodic solutions for l l where a n h n and t n are t periodic functions

a geometric interpretation of inferences based on ranks in the linear model abstract four different approaches based on ranks to testing hypotheses are unified through the geometry of the linear model the various tests are identified with different but algebraically equivalent forms of the classical f test small sample differences are investigated via a monte carlo study using both rank and signed rank tests

observer based output feedback control of linear systems with input and output delays abstract this paper is concerned with observer based output feedback control of linear systems with both multiple input and output delays our recently developed truncated predictor feedback tpf approach for state feedback stabilization of time delay systems is generalized to the design of observers by imposing some restrictions on the open loop system two classes of observer based output feedback controllers one being finite dimensional and the other infinite dimensional are constructed it is further shown that the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time varying input and output delays it is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers but does not hold for the finite dimensional ones numerical examples are worked out to illustrate the effectiveness of the proposed approaches

a necessary and sufficient condition for permanence of a lotka volterra discrete system with delays abstract in this paper we consider the permanence of the following lotka volterra discrete competition system with delays k1 k2 l1 and l2 x n 1 x n exp r1 1 x n k1 1y n k2 y n 1 y n exp r2 1 2x n l1 y n l2 we show the system is permanent for all nonnegative integers k1 k2 l1 and l2 if and only if 1

detecting skewed errors from regression residuals symmetry of the error distribution is a common assumption in robust estimation of location and regression parameters tests for detecting asymmetry in the location problem are available but their performance in regression situations is unknown here two such tests are investigated and the evidence suggests two conclusions first the tests are valid when applied directly to either robust or least squares residuals as long as the number of parameters estimated is no more than a fourth of the sample size second the effect of the design matrix on power for detecting a skewed error distribution is roughly characterized by a third moment quantity based on least squares analysis