a nonparametric mixture model for cure rate estimation summary nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis in this paper we study a general nonparametric mixture model the proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured the em algorithm the marginal likelihood approach and multiple amputations are employed to estimate parameters of interest in the model this model extends models and improves estimation methods proposed by other researchers it also extends cox s proportional hazards regression model by allowing a proportion of event free patients and investigating covariate effects on that proportion the model and its estimation method are investigated by simulations an application to breast cancer data including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers confirms the conclusions from the parametric model but not those from the existing nonparametric model

a representation and the norm of toeplitz operators the toeplitz operator has been used in system and control theory for quite a long time recently it played a conspoicuous in h control theory one of the important properties of the toeplitz operator is that its norm is identical to the norm of the laurent operator with the same symbol the original proof of this property relies on some advanced tools in operator theory in this paper for toeplitz operators with symbols consisting of an infinite dimensional stable part and a finite dimensional unstable part an elementary and self contained proof of this property is given our proof is based on a representation of the toeplitz operator presented in this paper and the well known fact that an inner matrix defines an isometry the representation presented in this paper gives insight into the structure of the toeplitz operator a further application of this representation is also presented

an optimum strategy for detection in the presence of random transient disturbance and white gaussian noise detection of a deterministic signal is considered because of the presence of the transient disturbance the traditional totally probabilistic criteria are no longer appropriate since they cannot be related to the physical reality as in the case of stationary ergodic noise only a mixed strategy is proposed for the detection where the disturbance is treated as a semideterministic object while white gaussian noise is treated as a genuinely random object specifically the author uses as the detection statistic the log likelihood ratio of two conditional probability measures corresponding to the signal presence and the signal absence hypotheses given the disturbance in which the disturbance is replaced by its maximum a posteriori likelihood estimate the detection statistic takes the generalized in function space form of a soft limiter or a blanker followed by the matched filter it is an explicit detection algorithm though improvement in computational efficiency is much desired

locally optimum detection in moving average non gaussian noise detection algorithms that are locally optimum bayes and also asymptotically optimum are developed for both coherent and incoherent signaling for arbitrary interference and signal waveforms when the dependence in the noise samples is represented by a moving average model this leads to receiver structures which are prewhitened versions of the locally optimum detectors in the independent case a probability of error expression in the ideal observer symmetric case the processing gain and the minimum detectable signal are derived in both cases these demonstrate by means of an expression comparing performance between this and the independent case that for the same large sample size n 1 an improvement in performance is always achieved when the noise samples are dependent without any additional complexity in receiver structure

robust inference for multivariate survival data multivariate survival data arise when an individual records multiple survival events or when individuals recording single survival events are grouped into clusters in this paper we propose a new method for the analysis of multivariate survival data the technique is a synthesis of the poisson regression formulation for univariate censored survival analysis and the generalized estimating equation approach for obtaining valid variance estimates for generalized linear models in the presence of clustering when the survival data are clustered combining the methods provides not only valid estimates for the variances of regression parameters but also estimates of the dependence between survival times the approach entails specifying parametric models for the marginal hazards and a dependence structure but does not require specification of the joint multivariate survival distribution properties of the methodology are investigated by simulation and through an illustrative example

spread spectrum multiple access performance of orthogonal codes impulsive noise a direct sequence spread spectrum multiple access ssma communication system that assigned a set of m orthogonal sequences to each user is analyzed an accurate model is incorporated for the impulsive noise that characterizes the lf and mf bands so that the ssma receiver operates in a combination of multiple access interference and impulsive atmospheric noise the performance of a linear receiver operating in such an environment is analyzed and probability of error curves are presented the presence of impulsive noise motivates the derivation and analysis of a nonlinear receiver that use a variable gain stage to suppress noise impulses this receiver is effectively optimum when the signal amplitudes are below a certain bound and when the noise and interference samples are independent or nearly so however the gain stage of this nearly optimum receiver depends on the noise model parameters including the various user delays consequently a nonparametric receiver that incorporates a simple clipper is also analyzed the asymptotic relative efficiency of both receivers is determined

optimal and robust memoryless discrimination from dependent observations discrimination is considered between two possible sources based on dependent observations of their output the discrimination problem is modeled by means of a general binary hypothesis test the main emphasis being on situations that cannot be modeled as signals in additive noise the observations are modeled as stationary m dependent or rho mixing processes the structure of the discriminator is such that the observations are passed through a memoryless nonlinearity summed up to form a test statistic which is then compared to a threshold only fixed sample size tests are considered four different performance measures which resemble the signal to noise ratios encountered in the signal in additive noise problems are derived under different problem formulations the optimal nonlinearities for each of the performance measures are derived as solutions to various integral equations for three of the four performance measures the authors have successfully obtained robust nonlinearities for uncertainty in the marginal and the joint probability density functions of the observations computer simulation results that demonstrate the advantage of using these nonlinearities over the i i d nonlinearity under the probability of error criterion are presented

matched subspace detection with hypothesis dependent noise power we consider the problem of detecting a subspace signal in white gaussian noise when the noise power may be different under the null hypothesis where it is assumed to be known and the alternative hypothesis this situation occurs when the presence of the signal of interest soi triggers an increase in the noise power accordingly it may be relevant in the case of a mismatch between the actual soi subspace and its presumed value resulting in a modelling error we derive the generalized likelihood ratio test glrt for the problem at hand and contrast it with the glrt which assumes known and equal noise power under the two hypotheses a performance analysis is carried out and the distributions of the two test statistics are derived from this analysis we discuss the differences between the two detectors and provide explanations for the improved performance of the new detector numerical simulations attest to the validity of the analysis

sufficient conditions for robust bibo stabilization given by the gap metric a relation between coprime fractions and the gap metric is presented using this result we provide some sufficient conditions for robust bibo stabilization for a wide class of systems these conditions allow the plant and the compensator to be disturbed simultaneously

partial update lms algorithms partial updating of lms filter coefficients is an effective method for reducing computational load and power consumption in adaptive filter implementations this paper presents an analysis of convergence of the class of sequential partial update lms algorithms s lms under various assumptions and shows that divergence can be prevented by scheduling coefficient updates at random which we call the stochastic partial update lms algorithm spu lms specifically under the standard independence assumptions for wide sense stationary signals the s lms algorithm converges in the mean if the step size parameter spl mu is in the convergent range of ordinary lms relaxing the independence assumption it is shown that s lms and lms algorithms have the same sufficient conditions for exponential stability however there exist nonstationary signals for which the existing algorithms s lms included are unstable and do not converge for any value of spl mu on the other hand under broad conditions the spu lms algorithm remains stable for nonstationary signals expressions for convergence rate and steady state mean square error of spu lms are derived the theoretical results of this paper are validated and compared by simulation through numerical examples

robust detection of signals a large deviations approach robust detection of a signal is considered for the case of independent and identically distributed observations following an asymptotic but nonlocal approach the exponential rates of decrease of the error probabilities are considered as measure of performance under this measure a robust detection structure for the symmetric density case is derived this detection structure is a generalization of an existing result for the local case and is reduced to it when the signal magnitude tends to zero

a maximum variance model for robust detection and estimation with dependent data a model that accounts for uncertain data dependency is developed by generating a large class of stationary stochastic processes each with the same univariate distribution this class can be considered to be a contamination class about the nominal independent and identically distributed i i d process distribution the class is developed specifically for application to robust detector and estimator design based on asymptotic variance application of this dependency class leads to an intuitively pleasing result the minimax variance estimators and the maximin efficacy detectors are the same as obtained using i i d asymptotic estimation and detection theory thus our technique generalizes previously obtained robust design results for i i d data to this dependent data case

detection in impulsive noise based on robust whitening despite the widespread use of the additive gaussian noise model it has long been recognized that many important environments are distinctly nongaussian the authors present a detector which is designed to operate in a correlated plus impulsive noise environment the detector robustly whitens the data and then uses a two sided threshold test to determine the presence of impulsive samples the impulsive samples are discarded and the remaining samples are used to detect the presence or absence of a signal using a matched filter an approximate analysis is presented and simulations are used to demonstrate the effectiveness of this approach

robust large deviations performance analysis for large sample detectors large deviations theory is used to analyze the exponential rate of decrease of error probabilities for a sequence of decisions based on a test statistics sequence t sub n it is assumed that for a given statistical hypothesis the distributions of t sub n are determined by some unknown member of a class of probability distributions the worst case or least favorably exponential rate of error probability decrease over this class is sought it is shown that the legendre fenchel transform of the maximized cumulant function yields a lower bound for the minimized large deviations rate function and that in many cases this bound is tight application of the result is illustrated by a detailed consideration of i i d memoryless detection with an epsilon contamination distribution family

a nonlocal approach for asymptotic memoryless detection theory corresp previous literature on detector design has presented many tractable results using efficacy as a performance functional which is a small signal or local approach some nonlocal issues of memoryless detection are considered we argue that the asymptotic exponential rate of decrease of error probabilities or bayes risk provides the appropriate asymptotic measure of performance a main contribution is the development of an approximation for nonlocal design that retains the tractability of the efficacy approach we have proved the local consistency of our approximation also as a consequence of the analysis new proofs for pitman noether like theorems have been obtained

the general distance problem in h optimal control theory abstract the general distance problem that arises in h optimal control theory is considered transformations that reduce the general h problem to the general distance problem are reviewed and an iterative scheme called iteration is considered in which the general distance problem is reduced to a standard best approximation problem the iteration is viewed as a problem of finding the zero crossing of a function this function is shown to be continuous monotonically decreasing convex and bounded by some very simple functions these properties make it possible to obtain very rapid convergence of the iterative process the issues of model reduction and approximation in h synthesis will also be addressed

robust locally optimum detection of signals in dependent noise a robust locally optimum detector of a signal embedded in additive dependent nongaussian noise is presented the performance criterion is bayes risk the sample size is finite and the uncertainty class of multivariate inputs is the in contamination model the locally optimum detector is shown to be a censored version of the nominal likelihood ratio

insight into detection of deterministic and gaussian signals in correlated plus impulsive noise environments the authors present a different view of the discrete time detection problem in impulsive noise the approach used is to examine the geometry from a subspace viewpoint of two detectors the clairvoyant matched filter and the clairvoyant power detector they are clairvoyant in that the locations of the impulses in the received data sample are assumed known in the presence of impulses both detectors use this knowledge for properly weighting these samples to reduce the effects of the impulses unfortunately since it is never reasonable to assume that the impulse locations are known these are unrealizable detectors however these clairvoyant detectors provide insight into the problem of detection in an impulsive environment when the nominal component is correlated and suggest detectors which are realizable the results can be used as a theoretical justification of preprocessing the data to eliminate impulsive samples prior to detection

noise benefits to robust m estimation of location in dependent observations abstract in the presence of weakly dependent noise we analyze the asymptotic efficiency of robust maximum likelihood type estimators m estimators for location estimation we observe the noise enhanced asymptotic efficiency effect by tuning the background noise level for a single m estimator we also theoretically derive the asymptotic efficiency of a parallel array of m estimators and illustrate the possibility of the noise enhancement of the asymptotic efficiency by injecting extra additive noise components these obtained results enrich the research of noise benefits for the robust estimation of location from the dependent observations

mixtures of marginal models summary in this paper we adapt a mixture model originally developed for regression models with independent data for the more general case of correlated outcome data which includes longitudinal data as a special case the estimation is performed by a generalisation of the em algorithm which we call the expectation solution es algorithm in this es algorithm the m step of the em algorithm is replaced by a step requiring the solution of a series of generalised estimating equations the es algorithm a general algorithm for solving generalised estimating equations with incomplete data is then applied to the present problem of mixtures of marginal models in addition to allowing for correlation inherent in correlated outcome data the systematic component of this mixture of marginal models is more flexible than the conventional linear function the methodology is applied in the contexts of normal and poisson response data some theory regarding the es algorithm is presented

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

min max detection of weak signals in phi mixing noise detection of weak signals in a special varphi mixing noise class is considered the detector structure is restricted to sums of memoryless nonlinear transformations of the observations correlated with the data sequence and compared to a fixed threshold using the efficacy to measure performance the nonlinearity that has min max performance is derived

locally optimal detection in multivariate non gaussian noise the detection of a vanishingly small known signal in multi variate noise is considered efficacy is used as a criterion of detector performance and the locally optimal detector lod for multivariate noise is derived it is shown that this is a generalization of the well known lod for independent identically distributed i i d noise several characterizations of multivariate noise are used as examples these include specific examples and some general methods of density generation in particular the class of multivariate densities generated by a zero memory nonlinear transformation of a correlated gaussian source is discussed in some detail the detector structure is derived and practical aspects of obtaining detector subsystems are considered through the use of monte carlo simulations the performance of this system if compared to that of the matched filter and of the i i d lod finally the class of multivariate densities generated by a linear transformation of an i i d noise source is described and its lod is shown to be a form frequently suggested to deal with multivariate non gaussian noise a linear filter followed by a memoryless nonlinearity and a correlator

a semiparametric marginal mixture cure model for clustered survival data we consider a marginal model for the regression analysis of clustered failure time data with a cure fraction we propose to use novel generalized estimating equations in an expectation maximization algorithm to estimate regression parameters in a semiparametric proportional hazards mixture cure model the dependence among the cure statuses and among the survival times of uncured patients within clusters are modeled by working correlation matrices in the estimating equations we use a bootstrap method to obtain the variances of the estimates we report a simulation study to demonstrate a substantial efficiency gain of the proposed method over an existing marginal method finally we apply the model and the proposed method to a set of data from a multi institutional study of tonsil cancer patients treated with a radiation therapy

on signal detection in the presence of weakly correlated noise over fading channels in cognitive radio networks in order to avoid interference form secondary users to the primary license holders of the spectrum reliable spectrum sensing is necessary in scenarios where the noise samples are correlated the spectrum sensing methods optimized considering impairment by independent noise samples will not provide optimum performances to address this issue a locally optimum detection method for random signals under a weakly correlated noise model over fading channels is proposed the probabilities of false alarm and detection of the proposed detector in the low signal to noise ratio regime are analyzed the average probabilities are calculated over different channel gains numerical and simulation results demonstrate the superiority of the proposed method over the known energy detection method with comparable complexities furthermore we consider the scenario where the estimated correlation is different from the real correlation and investigate the effect of this correlation mismatch on the probabilities of false alarm and detection of the proposed method

robust detection of signals in dependent noise the robust detection of signals in additive dependent noise is considered the solution to the finite sample problem is obtained when the bayes risk is used as the performance measure for the multivariate densities involved we assume that they belong to an e contamination model the robust detection structure is shown to be optimum for the least favorable density and is a censored version of the nominal likelihood ratio

a bivariate cure mixture approach for modeling familial association in diseases summary for modeling correlation in familial diseases with variable ages at onset we propose a bivariate model that incorporates two types of pairwise association one between the lifetime risk or the overall susceptibility of two individuals and one between the ages at onset between two susceptible individuals for estimation we consider a two stage estimation procedure similar to that of shih 1998 biometrics 54 1115 1128 we evaluate the properties of the estimators through simulations and compare the performance with that from a bivariate survival model that allows correlation between ages at onset only we apply the methodology to breast cancer using the kinship data from the washington ashkenazi study we also discuss potential applications of the proposed method in the area of cure modeling

on the robust estimation of the autocorrelation coefficients of stationary sequences this paper discusses methods for the estimation of the autocorrelation coefficients of a finite dependent stationary random sequence three estimators are examined the sample average and two proposed approaches namely the pseudo maximum likelihood pseudo ml estimator and the pseudo m estimator the latter scheme is found as a solution of a fredholm integral equation all three estimators are first studied for specific distribution models then the existence of a minimax robust design is proved and a suboptimally robust scheme is proposed simulation results illustrate the theoretical foundations of the methods and indicate that the pseudo m estimator achieves significantly better performance than the other two schemes when tested against dependent data and in the presence of outliers finally the results may also be applied to the estimation of a location parameter of a dependent random sequence

signal detection in the presence of weakly dependent noise i optimum detection the problem of designing robust systems for detecting constant signals in the presence of weakly dependent noise with uncertain statistics is considered as in part i of this study which treated optimum detection in weakly dependent noise a moving average representation is used to model the dependence structure of the noise process with the degree of dependence being parameterized by the averaging weights weak dependence is then modeled as the situation in which quantities depending to second or higher order on the averaging weights can be considered to be negligible uncertainty in the noise statistics is introduced within this framework by allowing a general type of uncertainty in the univariate statistics of the independent sequence that drives the moving average to find robust detectors for signals in this type of weakly dependent noise environment related results concerning robust location estimation in an analogous dependent situation are applied to modify a robust detection system for the corresponding independent noise case it is argued here that a robust detector for this dependent noise model is characterized by a least favorable noise distribution which coincides with the distribution that is least favorable for the corresponding independent noise case however the resulting detector design for dependent noise differs from that for independent noise in particular the robust detector for dependent noise is based on a linearly corrected version of the influence curve that defines the independent noise robust detector the worst case performance of the proposed robust detector relative to that of the independent noise robust detector is also analyzed with the conclusion that the performance of the proposed technique is better to first order in the averaging weights in this respect a modification of this robust detector is also proposed which eliminates some practical disadvantages of this system while retaining equivalent performance to first order the specific situation of contaminated gaussian noise is treated in order to illustrate the analysis

the change of variance function for dependent data the infinitesimal stability of the asymptotic variance is considered form estimators of a location parameter when the nominal sample with i i d data is contaminated by a possibly dependent process it is shown that the resulting change of variance function can be expressed as a sum of two terms one corresponding contamination of the univariate distribution and one to contamination of the bivariate distributions a change of variance sensitivity is introduced the form of which is closely related to the average patch length of the outliers finally optimalv robust and mostv robust score functions are derived the resulting family of estimators is the same as for independent data in the general case but the truncation point approaches zero when dependency is accounted for for redescending score functions the family of estimators is changed

optimum detection of a weak signal with minimal knowledge of dependency the optimum nonlinearity is defined for detection of a weak signal when minimal knowledge of the dependency structure of the observations is available specifically it is assumed that the observations form a one dependent strictly stationary sequence of random variables and that only a finite number of moments of the marginal density and the correlation coefficient between consecutive observations are known it is assumed that the bivariate densities involved can be represented as diagonal series using orthonormal polynomials using efficacy as a performance measure the optimum nonlinearity is required to satisfy a saddle point condition over this class of bivariate densities

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

stability in linear detection the stability of linear detectors for signals nominally known except for amplitude in correlated nominally gaussian noise is considered stability is defined in terms of bounds on the distribution of the test statistic as the true probability measure on the observation space varies in a prokhorov neighborhood of the nominal the derived stability index is independent of the neighborhood size an optimization problem is formulated and solved to give the most stable linear detector meeting a constraint on the nominal level of detectability

on nonlinear direct sequence detectors in arbitrary power limited interference communication over a waveform channel corrupted by additive white gaussian noise and by an unknown and arbitrary interference of bounded power is considered for this channel an upper bound is presented for the worst case error probability of a communication system comprising a direct sequence spread spectrum modulator and a nonlinear correlation receiver it is shown that this bound is exponentially tight as the number of chips used in the modulator becomes large this bound is evaluated for several detector nonlinearities numerical examples and comparisons to the performance of a pure gaussian noise channel are also given