cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

misspecified proportional hazard models summary the properties of an estimator based on a proportional hazards model are investigated when the model is incorrect the estimator from the partial likelihood is shown to be consistent for a parameter that is defined implicitly the results are used to investigate the effects on estimation if the true model is accelerated failure time or if covariates are omitted from the proportional hazards model

goodness of fit test for monotone proportional subdistribution hazards assumptions based on weighted residuals recently goodness of fit tests have been proposed for checking the proportional subdistribution hazards assumptions in the fine and gray regression model zhou fine and laird proposed weighted schoenfeld type residuals tests derived under an assumed model with specific form of time varying regression coefficients li sheike and zhang proposed an omnibus test based on cumulative sums of schoenfeld type residuals in this article we extend the class of weighted residuals tests by allowing random weights of schoenfeld type residuals at ordered event times in particular it is demonstrated that weighted residuals tests using monotone weight functions of time are consistent against monotone proportional subdistribution hazards assumptions extensive monte carlo studies were conducted to evaluate the finite sample performance of recent goodness of fit tests results from simulation studies show that weighted residuals tests using monotone random weight functions commonly used in non proportional hazards regression settings tend to be more powerful for detecting monotone departures than other goodness of fit tests assuming no specific time varying effect or misspecified time varying effects two examples using real data are provided for illustrations copyright 2016 john wiley sons ltd

global exponential stability for complex valued recurrent neural networks with asynchronous time delays in this paper we investigate the global exponential stability for complex valued recurrent neural networks with asynchronous time delays by decomposing complex valued networks to real and imaginary parts and construct an equivalent real valued system the network model is described by a continuous time equation there are two main differences of this paper with previous works 1 time delays can be asynchronous i e delays between different nodes are different which make our model more general and 2 we prove the exponential convergence directly while the existence and uniqueness of the equilibrium point is just a direct consequence of the exponential convergence using three generalized norms we present some sufficient conditions for the uniqueness and global exponential stability of the equilibrium point for delayed complex valued neural networks these conditions in our results are less restrictive because of our consideration of the excitatory and inhibitory effects between neurons so previous works of other researchers can be extended finally some numerical simulations are given to demonstrate the correctness of our obtained results

on scalar extensions and spectral decompositions of complex symmetric operators abstract in this paper we prove that a complex symmetric operator with property is subscalar as a corollary we get that such operators with rich spectra have nontrivial invariant subspaces we also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints

multistability and convergence in delayed neural networks abstract we present the existence of 2 n stable stationary solutions for a general n dimensional delayed neural networks with several classes of activation functions the theory is obtained through formulating parameter conditions motivated by a geometrical observation positively invariant regions for the flows generated by the system and basins of attraction for these stationary solutions are established the theory is also extended to the existence of 2 n limit cycles for the n dimensional delayed neural networks with time periodic inputs it is further confirmed that quasiconvergence is generic for the networks through justifying the strongly order preserving property as the self feedback time lags are small for the neurons with negative self connection weights our theory on existence of multiple equilibria is then incorporated into this quasiconvergence for the network four numerical simulations are presented to illustrate our theory

some new classes of complex symmetric operators we say that an operator t e b h is complex symmetric if there exists a conjugate linear isometric involution c so that t ct c we prove that binormal operators operators that are algebraic of degree two including all idempotents and large classes of rank one perturbations of normal operators are complex symmetric from an abstract viewpoint these results explain why the compressed shift and volterra integration operator are complex symmetric finally we attempt to describe all complex symmetric partial isometries obtaining the sharpest possible statement given only the data dim ker t dim ker t

on an example of a complex symmetric composition operator on h2 d abstract in the article 8 an example of a composition operator c on the hardy space h 2 d is discovered that is claimed to be complex symmetric but not normal the purpose of this note is to highlight a mistake in the example that makes the result incorrect

stability analysis of continuous time and discrete time quaternion valued neural networks with linear threshold neurons this paper addresses the problem of stability for continuous time and discrete time quaternion valued neural networks qvnns with linear threshold neurons applying the semidiscretization technique to the continuous time qvnns the discrete time analogs are obtained which preserve the dynamical characteristics of their continuous time counterparts via the plural decomposition method of quaternion homeomorphic mapping theorem as well as lyapunov theorem some sufficient conditions on the existence uniqueness and global asymptotical stability of the equilibrium point are derived for the continuous time qvnns and their discrete time analogs respectively furthermore a uniform sufficient condition on the existence uniqueness and global asymptotical stability of the equilibrium point is obtained for both continuous time qvnns and their discrete time version finally two numerical examples are provided to substantiate the effectiveness of the proposed results

multistability of neural networks with time varying delays and concave convex characteristics in this paper stability of multiple equilibria of neural networks with time varying delays and concave convex characteristics is formulated and studied some sufficient conditions are obtained to ensure that an n neuron neural network with concave convex characteristics can have a fixed point located in the appointed region by means of an appropriate partition of the n dimensional state space when nonlinear activation functions of an n neuron neural network are concave or convex in 2k 2m 1 intervals this neural network can have 2k 2m 1 n equilibrium points this result can be applied to the multiobjective optimal control and associative memory in particular several succinct criteria are given to ascertain multistability of cellular neural networks these stability conditions are the improvement and extension of the existing stability results in the literature a numerical example is given to illustrate the theoretical findings via computer simulations

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

properties of proportional hazards score tests under misspecified regression models the effects are investigated of misspecifying a proportional hazards regression model on the associated partial likelihood score test for comparing two randomized treatments in the presence of covariates the asymptotic efficiency of the proportional hazards score test relative to the optimal partial likelihood test declines slowly as the hazard functions for the two treatments deviate from proportionality the efficiency can be very low when the hazard functions cross or differ only at large survival times misspecification of the functional form of the regression portion of a proportional hazards model introduces a quantitative treatment covariate interaction in the situations that we examine based on a binary covariate this misspecification usually results in only a minor drop in efficiency the omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test but can substantially reduce power when the covariate effect is strong the loss of power from mismodeling a balanced covariate is usually small

multistability analysis of quaternion valued neural networks with time delays this paper addresses the multistability issue for quaternion valued neural networks qvnns with time delays by using the inequality technique sufficient conditions are proposed for the boundedness and the global attractivity of delayed qvnns based on the geometrical properties of the activation functions several criteria are obtained to ensure the existence of 81 n equilibrium points 16 n of which are locally stable two numerical examples are provided to illustrate the effectiveness of the obtained results

global stability of complex valued recurrent neural networks with time delays since the last decade several complex valued neural networks have been developed and applied in various research areas as an extension of real valued recurrent neural networks complex valued recurrent neural networks use complex valued states connection weights or activation functions with much more complicated properties than real valued ones this paper presents several sufficient conditions derived to ascertain the existence of unique equilibrium global asymptotic stability and global exponential stability of delayed complex valued recurrent neural networks with two classes of complex valued activation functions simulation results of three numerical examples are also delineated to substantiate the effectiveness of the theoretical results

complex symmetric generators of c algebras abstract this paper gives necessary and sufficient conditions for an essentially normal operator t to have its c algebra c t generated by a complex symmetric operator also it is completely determined when c t is isomorphic to a c algebra singly generated by complex symmetric operators these both depend only on the singular part of t

stability analysis for neural networks with time varying delay based on quadratic convex combination in this paper a novel method is developed for the stability problem of a class of neural networks with time varying delay new delay dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time varying delay are derived by the newly proposed augmented simple lyapunov krasovski functional different from previous results by using the first order convex combination property our derivation applies the idea of second order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to jensen s inequality a numerical example is provided to verify the effectiveness and superiority of the presented results

quantifying the totality of treatment effect with multiple event time observations in the presence of a terminal event from a comparative clinical study to evaluate the totality of one treatment s benefit risk profile relative to an alternative treatment via a longitudinal comparative clinical study the timing and occurrence of multiple clinical events are typically collected during the patient s follow up these multiple observations reflect the patient s disease progression burden over time the standard practice is to create a composite endpoint from the multiple outcomes the timing of the occurrence of the first clinical event to evaluate the treatment via the standard survival analysis techniques by ignoring all events after the composite outcome this type of assessment may not be ideal various parametric or semiparametric procedures have been extensively discussed in the literature for the purposes of analyzing multiple event time data many existing methods were developed based on extensive model assumptions when the model assumptions are not plausible the resulting inferences for the treatment effect may be misleading in this article we propose a simple nonparametric inference procedure to quantify the treatment effect which has an intuitive clinically meaningful interpretation we use the data from a cardiovascular clinical trial for heart failure to illustrate the procedure a simulation study is also conducted to evaluate the performance of the new proposal

quasi synchronization and bifurcation results on fractional order quaternion valued neural networks in this article the quasi synchronization and hopf bifurcation issues are investigated for the fractional order quaternion valued neural networks qvnns with time delay in the presence of parameter mismatches on the basis of noncommutativity property of quaternion multiplication results the quaternion network has been split as four real valued networks a synchronization theorem for fractional order qvnns is derived by employing suitable lyapunov functional candidate furthermore the bifurcation behavior of the hub structured fractional order qvnns with time delay has been investigated finally two numerical examples are provided to demonstrate the effectiveness of the theoretical results

complex symmetric weighted composition operators in several variables abstract in this paper we study the complex symmetric weighted composition operators on the hilbert space h s of analytic functions over the open unit ball with reproducing kernels k w s z 1 z w s where s n we completely characterize complex symmetric weighted composition operators with respect to two important conjugations j v and j which include hermitian weighted composition operators and normal weighted composition operators appeared in 17 surprisingly they are essential representatives of general conjugations of the form c j where c is unitary and j symmetric indeed these complex symmetric weighted composition operators can only be divided into two classes the size estimates and some other properties of these complex symmetric weighted composition operators are obtained moreover involutive weighted composition operators are completely characterized too as an application we construct concrete conjugations for the involutive composition operators which solves a problem raised by garcia and hammond in a general case

estimation of the proportional hazard in two treatment group clinical trials two easily computed approximate methods of obtaining an estimate of the ratio of the hazard rates for two treatments in survival analysis are compared by simulation with the partial maximum likelihood cml estimator which assumes the cox model with no covariates the two methods studied are the mantel haenszel estimator and the o e method which employs the ratio of the relative death rates for the two treatments uncensored and censored cases are examined for both continuous and tied data with the assumption of either an underlying exponential distribution or a weibull distribution with shape parameter 2 the o e method is biased but within the range of values of the ratio of the hazard rates of interest in clinical trials it is more efficient in terms of mean square error than either cml or the mantel haenszel method for all but the largest trials the mantel haenszel method is minimally biased gives answers very close to those obtained using cml and may be used to provide satisfactory approximate confidence intervals

weyl s theorem for complex symmetric operators abstract an operator on hilbert space is complex symmetric if it can be represented as a symmetric matrix relative to some orthonormal basis of the space it is proved in this paper that each complex symmetric operator on a complex separable hilbert space has a compact perturbation being complex symmetric and satisfying weyl s theorem where the compact can be chosen with arbitrarily small norm

survival analysis 1982 1991 the second decade of the proportional hazards regression model a short review of the cox regression model and its development from publication to 1982 is given i discuss how the model is used and presented in medical journals and how improvement may be achieved finally some extensions of the model are outlined

on local spectral properties of complex symmetric operators abstract in this paper we study properties of complex symmetric operators in particular we prove that every complex symmetric operator having property or is decomposable moreover we show that complex symmetric operator t has dunford s property c and it satisfies weyl s theorem if and only if its adjoint does

global µ stability criteria for quaternion valued neural networks with unbounded time varying delays in this paper we first propose quaternion valued neural networks qvnns with unbounded time varying delays some sufficient conditions on the global stability in the form of both complex valued and real valued linear matrix inequalities lmis are provided by solving two difficulties one is decomposing the qvnn into two complex valued systems with the plural decomposition method of quaternion which can reduce the complexity of calculations by avoiding the non commutativity of quaternion multiplication the other is choosing the appropriate lyapunov krasovskii functional in the form of hermitian matrices which is a big challenge finally two numerical examples are provided to verify the effectiveness of the obtained results

unitary equivalence to a complex symmetric matrix low dimensions abstract a matrix t m n c is uecsm if it is unitarily equivalent to a complex symmetric i e self transpose matrix we develop several techniques for studying this property in dimensions three and four among other things we completely characterize 4 4 nilpotent matrices which are uecsm and we settle an open problem which has lingered in the 3 3 case we conclude with a discussion concerning a crucial difference which makes dimension three so different from dimensions four and above

multistability of recurrent neural networks with time varying delays and the piecewise linear activation function in this brief stability of multiple equilibria of recurrent neural networks with time varying delays and the piecewise linear activation function is studied a sufficient condition is obtained to ensure that n neuron recurrent neural networks can have 4k 1 n equilibrium points and 2k n of them are locally exponentially stable this condition improves and extends the existing stability results in the literature simulation results are also discussed in one illustrative example

complex symmetric monomial toeplitz operators on the unit ball abstract monomial toeplitz operators t z p z q on the weighted bergman space of the unit ball in c n are natural extension of the weighted shift operators in higher dimensions dim ker t z p z q may occur for non trivial case thus complex symmetric phenomena will appear in this paper we completely characterize when the monomial toeplitz operator t z p z q on the weighted bergman space is j a symmetric where j a f z f a z with the symmetric unitary n n matrix a moreover we also determine all possible forms of a such that t z p z q is j a symmetric as an application we construct the weakly closed unital commutative algebra generated by complex symmetric toeplitz operators

discrete time analogs for a class of continuous time recurrent neural networks this paper is concerned with the problem of local and global asymptotic stability for a class of discrete time recurrent neural networks which provide discrete time analogs to their continuous time counterparts i e continuous time recurrent neural networks with distributed delay some stability criteria which include some existing results as their special cases are derived a discussion about the dynamical consistence of discrete time neural networks versus their continuous time counterparts is provided an unconventional finite difference method is proposed and an example is also given to show the effectiveness of the method

a simple estimator for a shared frailty regression model summary we propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution inferences for the frailty parameter can be obtained by using output from cox regression analyses the computational burden is substantially less than that of the other approaches to estimation the large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes the methods are motivated by studies of familial associations in the natural history of diseases their practical utility is illustrated with sib pair data from beaver dam wisconsin

the impact of time dependent bias in proportional hazards modelling in the clinical literature time dependent exposure status has regularly been analysed as if known at time origin although statisticians agree that such an analysis yields biased results when analysing the effect on the time until some endpoint of interest this paper is the first to study in detail the bias arising in a proportional hazards analysis we show that the biased hazard ratio estimate will always be less than the unbiased one this leads to either an inflated or a damped effect of exposure depending on the sign of the correct log hazard ratio estimate we find an explicit formula of the asymptotic bias based on generalized rank estimators and we investigate the role of censoring which may prevent an individual from being considered as being baseline exposed in the biased analysis we illustrate our results with data on hospital infection status and different censoring patterns

dynamic analysis of fractional order quaternion valued fuzzy memristive neural networks vector ordering approach abstract this paper addresses the problems of stabilization and synchronization control of the fractional order quaternion valued fuzzy memristive neural networks by means of the contraction mapping theorem the corresponding conditions are established for the existence and uniqueness of the equilibrium point ep subsequently the corresponding stability analysis are proposed by two suitable controllers what should be mentioned is that a vector ordering approach is developed to determine the magnitude of two different quaternions as a result the closed convex hull proposed by quaternion connections can be easily derived finally two simulation examples are utilized to illustrate the effectiveness of the proposed control method

graphical representation of survival curves associated with a binary non reversible time dependent covariate the use of time dependent covariates has allowed for incorporation into analysis of survival data intervening events that are binary and non reversible for example heart transplant initial response to chemotherapy we can represent this type of intervening event as a three state stochastic process with a starting state s an intervening state i and an absorbing state d which usually represents death in this paper we present three procedures for calculating survivorship functions which attempt to display the prognostic significance of the time dependent covariate the first method compares survival from baseline for the two possible paths through the stochastic process the second method compares overall survival to survival with state i removed from the process and the third method compares survival for those already in state i at a landmark time x to those in state s at time x who will never enter state i we develop discrete hazard estimates for the survival curves associated with the three methods two examples illustrate how these methods can yield different results and in which situations one might employ each of the three methods extensions to applications with reversible binary time dependent covariates and models with both baseline and time dependent covariates are suggested

multistability of discrete time recurrent neural networks with unsaturating piecewise linear activation functions this paper studies the multistability of a class of discrete time recurrent neural networks with unsaturating piecewise linear activation functions it addresses the nondivergence global attractivity and complete stability of the networks using the local inhibition conditions for nondivergence are derived which not only guarantee nondivergence but also allow for the existence of multiequilibrium points under these nondivergence conditions global attractive compact sets are obtained complete stability is studied via constructing novel energy functions and using the well known cauchy convergence principle examples and simulation results are used to illustrate the theory

the mizon richard encompassing test for the cox and aalen additive hazards models summary the cox hazards model cox 1972 journal of the royal statistical society series b 34 187 220 for survival data is routinely used in many applied fields sometimes however with too little emphasis on the fit of the model a useful alternative to the cox model is the aalen additive hazards model aalen 1980 in lecture notes in statistics 2 1 25 that can easily accommodate time changing covariate effects it is of interest to decide which of the two models that are most appropriate to apply in a given application this is a nontrivial problem as these two classes of models are nonnested except only for special cases in this article we explore the mizon richard encompassing test for this particular problem it turns out that it corresponds to fitting of the aalen model to the martingale residuals obtained from the cox regression analysis we also consider a variant of this method which relates to the proportional excess model martinussen and scheike 2002 biometrika 89 283 298 large sample properties of the suggested methods under the two rival models are derived the finite sample properties of the proposed procedures are assessed through a simulation study the methods are further applied to the well known primary biliary cirrhosis data set

complex symmetric operators and applications ii a bounded linear operator t on a complex hilbert space h is called complex symmetric if t ct c where c is a conjugation an isometric antilinear involution of h we prove that t cj t where j is an auxiliary conjugation commuting with t t t we consider numerous examples including the poincare neumann singular integral bounded operator and the jordan model operator compressed shift the decomposition t cj t also extends to the class of unbounded c selfadjoint operators originally introduced by glazman in this context it provides a method for estimating the norms of the resolvents of certain unbounded operators

means of unitaries conjugations and the friedrichs operator abstract if c is a conjugation an isometric conjugate linear involution on a separable complex hilbert space h then t b h is called c symmetric if t c t c in this note we prove that each c symmetric contraction t is the mean of two c symmetric unitary operators we discuss several corollaries and an application to the friedrichs operator of a planar domain

complex symmetric weighted composition operators on h2 d abstract in this paper we study complex symmetric weighted composition operators on the hardy space we provide some characterizations of and when a weighted composition operator w is complex symmetric we investigate which combinations of weights and maps of the open unit disk give rise to complex symmetric weighted composition operators with a special conjugation as some applications we obtain several examples for nonnormal complex symmetric operators in addition we give spectral properties of complex symmetric weighted composition operators we examine eigenvalues and eigenvectors of such operators and find some conditions for which a complex symmetric weighted composition operator is hilbert schmidt finally we consider cyclicity hypercyclicity and the single valued extension property for complex symmetric weighted composition operators

on linear maps preserving complex symmetry abstract an operator t on a complex hilbert space h is said to be complex symmetric if there exists a conjugate linear isometric involution c h h so that c t c t this paper is devoted to describing which linear maps leave the class of complex symmetric operators invariant complete characterizations are obtained for several classes of linear maps including similarity transformations surjective linear isometries multiplication operators and certain completely positive maps

orthogonality of decision boundaries in complex valued neural networks this letter presents some results of an analysis on the decision boundaries of complex valued neural networks whose weights threshold values input and output signals are all complex numbers the main results may be summarized as follows 1 a decision boundary of a single complex valued neuron consists of two hypersurfaces that intersect orthogonally and divides a decision region into four equal sections the xor problem and the detection of symmetry problem that cannot be solved with two layered real valued neural networks can be solved by two layered complex valued neural networks with the orthogonal decision boundaries which reveals a potent computational power of complex valued neural nets furthermore the fading equalization problem can be successfully solved by the two layered complex valued neural network with the highest generalization ability 2 a decision boundary of a three layered complex valued neural network has the orthogonal property as a basic structure and its two hypersurfaces approach orthogonality as all the net inputs to each hidden neuron grow in particular most of the decision boundaries in the three layered complex valued neural network inetersect orthogonally when the network is trained using complex bp algorithm as a result the orthogonality of the decision boundaries improves its generalization ability 3 the average of the learning speed of the complex bp is several times faster than that of the real bp the standard deviation of the learning speed of the complex bp is smaller than that of the real bp it seems that the complex valued neural network and the related algorithm are natural for learning complex valued patterns for the above reasons

generalized martingale residual processes for goodness of fit inference in cox s type regression models in the paper a general class of stochastic processes based on the sums of weighted martingale transform residuals for goodness of fit inference in general cox s type regression models is studied their form makes the inference robust to covariate outliers a weak convergence result for such processes is obtained giving the possibility of establishing the randomness of their graphs together with the construction of the formal x 2 type goodness of fit tests by using the khmaladze innovation approach a modified version of the initial class of processes is also defined weak convergence results for the processes are derived this leads to the main application which concerns the formal construction of the kolmogorov smirnov and cramer von mises type goodness of fit tests this is done within the general situation considered

complex symmetric toeplitz operators on the dirichlet space abstract we study when a toeplitz operator t on the dirichlet space of the unit disk is complex symmetric with respect to a class of conjugations and find surprisingly that the case of complex symmetries of toeplitz operators according to these conjugations is very few we also show that if t is complex symmetric then the curve t t must be nowhere winding furthermore the spectrum and invertibility of complex symmetric toeplitz operators are described

complex symmetric partial isometries an operator t b h is complex symmetric if there exists a conjugate linear isometric involution c h h so that t ct c we provide a concrete description of all complex symmetric partial isometries in particular we prove that any partial isometry on a hilbert space of dimension 4 is complex symmetric

stability and stabilization of quaternion valued neural networks with uncertain time delayed impulses direct quaternion method abstract in this paper the exponential stability of impulsive quaternion valued neural networks iqvnns with time delays is investigated both the differential equation and impulses are affected by time varying delays which may be nonidentical uncertain parameters in impulses are also considered firstly the existence and uniqueness of the equilibrium of the iqvnns are discussed with the help of homeomorphic mapping theorem then by utilizing lyapunov functions and a newly developed inequality several sufficient criteria are established in the form of quaternion valued linear matrix inequalities lmis it should be noted that compared to most of existing results which are obtained by decomposing quaternion valued neural networks qvnns into four real valued neural networks rvnns or two complex valued neural networks cvnns our results are easier to be verified since the quaternion valued lmis exhibit lower dimensions then based on obtained results one impulsive controller is designed to realize the stabilization of delayed qvnns finally two numerical examples are presented to verify the effectiveness and merits of the theoretical analysis

global stability criterion for delayed complex valued recurrent neural networks the stability problem for delayed complex valued recurrent neural networks is considered in this paper by separating complex valued neural networks into real and imaginary parts forming an equivalent real valued system and constructing appropriate lyapunov functional a sufficient condition to ascertain the existence uniqueness and globally asymptotical stability of the equilibrium point of complex valued systems is provided in terms of linear matrix inequality meanwhile the errors in the recent work are pointed out and even if the result therein is correct it is shown that our result not only improves but also generalizes in that work numerical examples are given to show the effectiveness and merits of the present result

quaternion valued nonlinear adaptive filtering a class of nonlinear quaternion valued adaptive filtering algorithms is proposed based on locally analytic nonlinear activation functions to circumvent the stringent standard analyticity conditions which are prohibitive to the development of nonlinear adaptive quaternion valued estimation models we use the fact that stochastic gradient learning algorithms require only local analyticity at the operating point in the estimation space it is shown that the quaternion valued exponential function is locally analytic and since local analyticity extends to polynomials products and ratios we show that a class of transcendental nonlinear functions can serve as activation functions in nonlinear and neural adaptive models this provides a unifying framework for the derivation of gradient based learning algorithms in the quaternion domain and the derived algorithms are shown to have the same generic form as their real and complex valued counterparts to make such models second order optimal for the generality of quaternion signals both circular and noncircular we use recent developments in augmented quaternion statistics to introduce widely linear versions of the proposed nonlinear adaptive quaternion valued filters this allows full exploitation of second order information in the data contained both in the covariance and pseudocovariances to cater rigorously for second order noncircularity improperness and the corresponding power mismatch in the signal components simulations over a range of circular and noncircular synthetic processes and a real world 3 d noncircular wind signal support the approach

generating survival times to simulate cox proportional hazards models with time varying covariates simulations and monte carlo methods serve an important role in modern statistical research they allow for an examination of the performance of statistical procedures in settings in which analytic and mathematical derivations may not be feasible a key element in any statistical simulation is the existence of an appropriate data generating process one must be able to simulate data from a specified statistical model we describe data generating processes for the cox proportional hazards model with time varying covariates when event times follow an exponential weibull or gompertz distribution we consider three types of time varying covariates first a dichotomous time varying covariate that can change at most once from untreated to treated e g organ transplant second a continuous time varying covariate such as cumulative exposure at a constant dose to radiation or to a pharmaceutical agent used for a chronic condition third a dichotomous time varying covariate with a subject being able to move repeatedly between treatment states e g current compliance or use of a medication in each setting we derive closed form expressions that allow one to simulate survival times so that survival times are related to a vector of fixed or time invariant covariates and to a single time varying covariate we illustrate the utility of our closed form expressions for simulating event times by using monte carlo simulations to estimate the statistical power to detect as statistically significant the effect of different types of binary time varying covariates this is compared with the statistical power to detect as statistically significant a binary time invariant covariate copyright 2012 john wiley sons ltd

comparing nonnested cox models summary we derive the limiting distribution of the partial likelihood ratio under general conditions the multiplicative hazards models being fitted may be nonnested and misspecified the true model is not assumed to contain either model under consideration the null hypothesis is that the models are equidistant in kullback leibler metric applied to the rank likelihood the statistic is consistent for the model which is closer to the truth its distribution depends on the unknown data generating mechanism a sequential testing procedure is proposed for nonnested comparisons which is valid regardless of the true model this involves a novel statistic for the equality of the fitted models which is separate from the partial likelihood the methodology has important applications in model assessment simulations and a real example demonstrate its utility in selecting the functional forms of covariates and relative risks

a risk set calibration method for failure time regression by using a covariate reliability sample regression parameter estimation in the cox failure time model is considered when regression variables are subject to measurement error assuming that repeat regression vector measurements adhere to a classical measurement model we can consider an ordinary regression calibration approach in which the unobserved covariates are replaced by an estimate of their conditional expectation given available covariate measurements however since the rate of withdrawal from the risk set across the time axis due to failure or censoring will typically depend on covariates we may improve the regression parameter estimator by recalibrating within each risk set the asymptotic and small sample properties of such a risk set regression calibration estimator are studied a simple estimator based on a least squares calibration in each risk set appears able to eliminate much of the bias that attends the ordinary regression calibration estimator under extreme measurement error circumstances corresponding asymptotic distribution theory is developed small sample properties are studied using computer simulations and an illustration is provided

effect of misspecification of regression models in the analysis of survival data the accelerated life and proportional hazards families of models are widely used in the analysis of survival data we examine the question if interest lies in the qualitative effect on failure of various explanatory variables how critical is the choice of model family in assessing the relative importance of the explanatory variables we consider small effects when censoring is independent of the explanatory variables to first order the regression parameters are proportional under the alternative models this is not true when the censoring varies appreciably with the explanatory variables some higherorder theory is examined for the special case of the two sample problem

complex symmetric composition operators on the newton space abstract a conjecture posed by macdonald and rosenthal states the composition operator c acting on the newton space n 2 p induced by z m z m 1 2 is bounded where m 0 1 our first result is proving that the aforementioned conjecture holds we investigate complex symmetry of composition operators acting on the newton space which is different from that on the hardy space in addition normality and co isometry of composition operators are studied finally we consider complex symmetric weighted composition operators

dunnett type inference in the frailty cox model with covariates a frequent objective in medical research is the investigation of differences in patient survival between several experimental treatments and one standard treatment in order to assess these differences statistically we have to apply adjustments for multiple comparisons to prevent an increased number of false positive findings the most prominent procedure of this type is the bonferroni correction which maintains the error level but leads to conservative results on the basis of a general statistical framework for simultaneous inference we propose a new statistical procedure for many to one comparisons of treatments with adjustment for covariates for clustered survival data modeled by a frailty cox model in contrast to the bonferroni method dependencies between estimated effects are taken into account the resulting simultaneous confidence intervals for the hazard ratios of the experimental treatments compared with a control can be interpreted in terms of both statistical significance and clinical importance the quality of the new procedure is judged by the coverage probability for the simultaneous confidence intervals simulation results show an acceptable performance in balanced and various unbalanced designs the practical merits are demonstrated by a reanalysis of a chronic myelogeneous leukemia clinical trial the procedure presented here works well for multiple comparisons with a control with adjustment for covariates for survival data from multicenter clinical trials

two stage residual inclusion for survival data and competing risks an instrumental variable approach with application to seer medicare linked data instrumental variable is an essential tool for addressing unmeasured confounding in observational studies two stage predictor substitution 2sps estimator and two stage residual inclusion 2sri are two commonly used approaches in applying instrumental variables recently 2sps was studied under the additive hazards model in the presence of competing risks of time to events data where linearity was assumed for the relationship between the treatment and the instrument variable this assumption may not be the most appropriate when we have binary treatments in this paper we consider the 2sri estimator under the additive hazards model for general survival data and in the presence of competing risks which allows generalized linear models for the relation between the treatment and the instrumental variable we derive the asymptotic properties including a closed form asymptotic variance estimate for the 2sri estimator we carry out numerical studies in finite samples and apply our methodology to the linked surveillance epidemiology and end results seer medicare database comparing radical prostatectomy versus conservative treatment in early stage prostate cancer patients

complex symmetric composition operators on a hilbert space of dirichlet series abstract on the hilbert space of dirichlet series with square summable coefficients there are no non normal complex symmetric composition operators induced by non constant symbols this is in sharp contrast with the phenomenon on the classical hardy space over the unit disk

double robust semiparametric estimator for differences in restricted mean lifetimes in observational studies restricted mean lifetime is often of direct interest in epidemiologic studies involving censored survival times differences in this quantity can be used as a basis for comparing several groups for example transplant surgeons nephrologists and of course patients are interested in comparing posttransplant lifetimes among various types of kidney transplants to assist in clinical decision making as the factor of interest is not randomized covariate adjustment is needed to account for imbalances in confounding factors in this report we use semiparametric theory to develop an estimator for differences in restricted mean lifetimes although accounting for confounding factors the proposed method involves building working models for the time to event and coarsening mechanism i e group assignment and censoring we show that the proposed estimator possesses the double robust property i e when either the time to event or coarsening process is modeled correctly the estimator is consistent and asymptotically normal simulation studies are conducted to assess its finite sample performance and the method is applied to national kidney transplant data

robust alternatives to ancova for estimating the treatment effect via a randomized comparative study in comparing two treatments via a randomized clinical trial the analysis of covariance ancova technique is often utilized to estimate an overall treatment effect the ancova is generally perceiv

unitary equivalence to a complex symmetric matrix an algorithm abstract we present a necessary and sufficient condition for a 3 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries and an algorithm whereby an arbitrary 3 3 matrix can be tested this test generalizes to a necessary and sufficient condition that applies to almost every n n matrix the test is constructive in that it explicitly exhibits the unitary equivalence to a complex symmetric matrix

on the closure of the complex symmetric operators compact operators and weighted shifts abstract we study the closure cso of the set cso of all complex symmetric operators on a separable infinite dimensional complex hilbert space among other things we prove that every compact operator in cso is complex symmetric using a construction of kakutani as motivation we also describe many properties of weighted shifts in cso cso in particular we show that weighted shifts which demonstrate a type of approximate self similarity belong to cso cso as a byproduct of our treatment of weighted shifts we explain several ways in which our result on compact operators is optimal

stability analysis of quaternion valued neural networks with both discrete and distributed delays abstract the existence uniqueness and stability of the equilibrium of quaternion valued neural networks qvnns with both discrete and distributed delays are investigated in this paper the considered model is managed as a single entirety without decomposition based on homeomorphic mapping theorem and linear matrix inequality several sufficient criteria are derived to ascertain the aforementioned qvnns to be globally asymptotically stable and exponentially stable moreover provided criteria can be verified by the linear matrix inequality lmi toolbox in matlab finally one simulation example is demonstrated to verify the effectiveness of obtained results

asymptotically efficient two step estimators of the hazards ratio for follow up studies and survival data summary asymptotically efficient estimators of a common hazard rate ratio for follow up studies and the proportional hazards ratio for survival studies are obtained by a single iteration of the mantelhaenszel estimator appropriate for each setting estimators of their variance are also developed the two step estimator for survival data and its variance estimator are shown by simulation to be minimally biased and the estimator is shown to be efficient relative to the cox partial likelihood estimator in small samples

approximation of complex symmetric operators an operator t on a complex hilbert space mathcal h is called a complex symmetric operator if there exists a conjugate linear isometric involution c mathcal h rightarrow mathcal h so that ctc t in this paper we study the approximation of complex symmetric operators by virtue of an intensive analysis of compact operators in singly generated c algebras we obtain a complete characterization of norm limits of complex symmetric operators and provide a classification of complex symmetric operators up to approximate unitary equivalence this gives a general solution to the norm closure problem for complex symmetric operators as an application we provide a concrete description of partial isometries which are norm limits of complex symmetric operators

multistability analysis for recurrent neural networks with unsaturating piecewise linear transfer functions multistability is a property necessary in neural networks in order to enable certain applications e g decision making where monostable networks can be computationally restrictive this article focuses on the analysis of multistability for a class of recurrent neural networks with unsaturating piecewise linear transfer functions it deals fully with the three basic properties of a multistable network boundedness global attractivity and complete convergence this article makes the following contributions conditions based on local inhibition are derived that guarantee boundedness of some multistable networks conditions are established for global attractivity bounds on global attractive sets are obtained complete convergence conditions for the network are developed using novel energy like functions and simulation examples are employed to illustrate the theory thus developed

complex symmetry of invertible composition operators abstract a bounded operator t on a separable hilbert space h is said to be complex symmetric if there exists an orthonormal basis for h with respect to which t has a self transpose matrix representation in this paper we study the complex symmetry of composition operators c f f induced on the hardy space h 2 by holomorphic self maps of the open unit disk d for any holomorphic self map of d we establish that if c is complex symmetric then must fix a point in d thus among the automorphisms of d only the elliptic ones may induce complex symmetric composition operators for an elliptic automorphism we prove that if is not a rotation or of order 3 then c is complex symmetric if and only if z z 1 z for some d 0

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f