archimedean copula model selection under dependent truncation one sided truncated survival data arise when a pair of time to event variables x y is observed only when x y existing methods of analysis rely on the assumption of quasi independence between x and y recently lakhal chaieb et al biometrika 2006 93 655 669 modeled potential dependency between these random variables via a semi survival archimedean copula in this paper we present a model selection procedure to rank a set of semi survival archimedean copula families according to their ability to fit a given data set subject to dependent truncation the proposed procedure is based on a truncated version of kendall s tau j multivariate anal 1996 56 60 74 the performance of the proposal is illustrated through simulations and three real data sets

nonparametric tests of the markov model for survival data summary jones crowley 1989 introduced a general class of nonparametric statistics for right censored survival data that includes many of the existing procedures involving a single covariate this paper considers this class in the framework of a markov model and suggests some tests especially appropriate for the markov setting application to left truncated and right censored data is also given small sample properties and asymptotic relative efficiencies for several statistics of this class are investigated for both relative and excess risk models for the hazard

on scaling laws of diversity schemes in decentralized estimation this paper is concerned with decentralized estimation of a gaussian source using multiple sensors we consider a diversity scheme where only the sensor with the best channel sends their measurements over a fading channel to a fusion center using the analog amplify and forwarding technique the fusion centre reconstructs a minimum mean squared error mmse estimate of the source based on the received measurements a distributed version of the diversity scheme where sensors decide whether to transmit based only on their local channel information is also considered we derive asymptotic expressions for the expected distortion of the mmse estimate at the fusion centre of these schemes as the number of sensors becomes large for comparison asymptotic expressions for the expected distortion for a coherent multiaccess scheme and an orthogonal access scheme are derived it is seen that as opposed to the coherent multiaccess scheme and the orthogonal scheme where the expected distortion decays as 1 m m being the number of sensors the expected distortion decays only as 1 ln m for the diversity schemes this reduction of the decay rate can be seen as a tradeoff between the simplicity of the diversity schemes and the strict synchronization and large bandwidth requirements for the coherent multiaccess and the orthogonal schemes respectively we study for the diversity schemes the optimal power allocation for minimizing the expected distortion subject to average power constraints the effect of optimizing the probability of transmission on the expected distortion in the distributed scenario is also studied it is proved that for rayleigh fading optimal sensor transmit power allocation achieves the same asymptotic scaling law as the constant power allocation scheme whereas it is observed that optimizing the sensor transmission probability with or without optimal power allocation in the distributed case makes very little difference to the asymptotic scaling laws

regression analysis of doubly truncated data abstractdoubly truncated data are found in astronomy econometrics and survival analysis literature they arise when each observation is confined to an interval that is only those which fall wit

testing quasi independence of failure and truncation times via conditional kendall s tau truncated survival data arise when the failure time is observed only if it falls within a subject specific truncating set most analysis methods rely on the key assumption of quasi independence that is factorization of the joint density of failure and truncation times into a product proportional to the individual densities in the observable region unlike independence of failure time and censoring time quasi independence can be tested tests of quasi independence are available for one sided truncation and for truncation that depends on a measured covariate but not for more complex truncation schemes here tests of quasi independence based on a multivariate conditional kendall s tau are proposed for doubly truncated data bivariate left truncated data and other forms of truncated survival data that arise when initiating or terminating event times are interval censored asymptotic properties under the null are derived the tests are illustrated using several real datasets and evaluated via simulation

asymptotic properties of the product limit estimate under random truncation on donne une description precise du comportement asymptotique de l estimateur limite produit incluant une forme explicite simple de la structure de covariance asymptotique

the gaussian ceo problem for scalar sources with arbitrary memory in this paper we consider the achievable sum rate distortion tradeoff for the gaussian central estimation officer ceo problem with a scalar source having arbitrary memory we describe how the arbitrary memory problem can be fully characterized by using known results for the vector ceo problem and then we formulate the variational problem of minimizing the sum rate subject to a distortion constraint to solve the problem we extend the conventional lagrange method and show that if the solution exists it should consist of a zero part and a non zero part where the non zero part is determined by solving a set of euler equations by calculating the second variation of the min sum rate problem a sufficient condition is also found that can be used to determine if the necessary solution results in the minimal sum rate the special case of two terminals is examined in detail and it is shown that an analytical solution is possible in this case analysis and discussion with examples are provided to illustrate the theoretical results the general solution obtained in this paper is shown to be compatible with the previous results for cases such as the problem of rate evaluation for sources without memory

entanglement cost for sequences of arbitrary quantum states the entanglement cost of arbitrary sequences of bipartite states is shown to be expressible as the minimization of a conditional spectral entropy rate over sequences of separable extensions of the states in the sequence the expression is shown to reduce to the regularized entanglement of formation when the nth state in the sequence consists of n copies of a single bipartite state

multiterminal source channel communication over an orthogonal multiple access channel we consider the problem of multiterminal source channel communication where a number of distributed and possibly correlated sources are transmitted through an orthogonal multiple access channel to a common destination we provide a characterization of the optimal tradeoff between the transmission cost gamma and the distortion vector d as measured against individual sources our approach consists of two steps 1 a multiple letter characterization of the rate distortion region of the multiterminal source coding and 2 a source channel separation theorem ensuring that all achievable pairs of gamma d can be obtained by combining the rate distortion region and the orthogonal multiple access channel capacity region as a corollary we determine the optimal power and distortion tradeoff in a quadratic gaussian sensor network under orthogonal multiple access and show that separate source and channel coding strictly outperforms the uncoded amplify forward transmission and is in fact optimal in this case this result is in sharp contrast to the case of nonorthogonal multiple access for which separate source and channel coding is not only suboptimal but also strictly inferior to uncoded transmission

a posteriori error estimation for control constrained linear quadratic optimal control problems we derive a posteriori error estimates for control constrained linear quadratic optimal control problems the error is measured in a norm which is motivated by the objective our abstract error estimator is separated into three contributions the error in the variational inequality i e in the optimality condition for the control and the errors in the state and adjoint equation hence one can use well established estimators for the differential equations we show that the abstract error estimator is reliable and efficient if the utilized estimators for the differential equations have these properties we apply the error estimator to two distributed optimal control problems with distributed and boundary observation respectively numerical examples exhibit a good error reduction if we use the local error contributions for an adaptive mesh refinement

asymptotic performance of linear receivers in mimo fading channels linear receivers are an attractive low complexity alternative to optimal processing for multiple antenna multiple input multiple output mimo communications in this paper we characterize the information theoretic performance of mimo linear receivers in two different asymptotic regimes for fixed number of antennas we investigate the limit of error probability in the high signal to noise ratio snr regime in terms of the diversity multiplexing tradeoff dmt following this we characterize the error probability for fixed snr in the regime of large but finite number of antennas as far as the dmt is concerned we report a negative result we show that both linear zero forcing zf and linear minimum mean square error mmse receivers achieve the same dmt which is largely suboptimal even in the case where outer coding and deacircnot coding is performed across the antennas we also provide an apacircnot proximate quantitative analysis of the markedly different behavior of the mmse and zf receivers at finite rate and nonasymptotic snr and show that while the zf receiver achieves poor diversity at any finite rate the mmse receiver error curve slope flattens out progressively as the coding rate increases when snr is fixed and the number of antennas becomes large we show that the mutual information at the output of an mmse or zf linear receiver has fluctuations that converge in distribution to a gaussian random variable whose mean and variance can be characterized in closed form this analysis extends to the linear reacircnot ceiver case a well known result previously obtained for the optimal receiver simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas

fixed rate transmission over fading interference channels using point to point gaussian codes this paper investigates transmission schemes for fixed rate communications over a rayleigh block fading interference channel there are two source destination pairs where each source in the presence of a short term power constraint intends to communicate with its dedicated destination at a fixed data rate it encodes its messages using a point to point gaussian codebook the two users transmissions can be conducted orthogonally or non orthogonally in the latter case each destination performs either direct decoding by treating the interference as noise or successive interference cancellation sic to recover its desired message for each scheme we seek solutions of a power control problem to efficiently assign power to the sources such that the codewords can be successfully decoded at destinations however because of the random nature of fading the power control problem for some channel realizations may not have any feasible solution and the transmission will be in outage thus for each transmission scheme we first compute a lower bound and an upper bound on the outage probability next we use these results to find an outer bound and an inner bound on the epsilon outage achievable rate region i e the rate region in which the outage probability is below a certain value epsilon

meshless galerkin method using radial basis functions based on domain decomposition in this present paper we will give an overview about the combination of rbf meshless method with domain decomposition especially galerkin method based on the analysis for this method before we will consider the combination of projection domain decomposition method with radial basis function both of galerkin approximation and collocation method are discussed some examples are given to show the efficiency of this method

tests of independence for bivariate data with random censoring a contingency table approach procedures are proposed for testing the hypothesis of independence between two discrete or discretized random variables one or both of which may be randomly censored the censoring mechanisms can be either independent bivariate censoring or identical univariate censoring the proposed tests reduce to goodness of fit tests for log linear models applied to either complete or incomplete contingency tables three examples are analyzed for illustrative purposes

rate region of the quadratic gaussian two encoder source coding problem we determine the rate region of the quadratic gaussian two encoder source coding problem this rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression furthermore this architecture requires higher rates to send a gaussian source than it does to send any other source with the same covariance our techniques can also be used to determine the sum rate of some generalizations of this classical problem our approach involves coupling the problem to a quadratic gaussian ldquoceo problem rdquo

uncoded transmission is exactly optimal for a simple gaussian sensor network a single memoryless gaussian source is observed by many terminals subject to independent gaussian observation noises the terminals are linked to a fusion center via a standard gaussian multiple access channel the fusion center needs to recover the underlying gaussian source with respect to mean squared error in this correspondence a theorem of witsenhausen is shown to imply that an optimal communication strategy is uncoded transmission i e each terminal s channel input is merely a scaled version of its noisy observation

a concordance test for independence in the presence of censoring an extension of the definition of kendall s coefficient of concordance is proposed for testing independence in bivariate censored survival times the test statistic counts the number of known concordances minus the number of known discordances the variance of the statistic is calculated for an random censorship model which however does not require independence of the components of the censoring distribution two examples are given

testing the assumption of independence of truncation time and failure time summary for data subject to random censorship it is well known that the assumption of independence between censoring time and failure time cannot be tested nonparametrically for data subject to random truncation however it is possible to test independence of truncation time and failure time a statistic generalizing kendall s tau is proposed for testing the independence assumption and asymptotic properties under the null hypothesis are derived a conditional permutation test is also derived for small data sets generalization to allow right censoring and an application to truncated linear regression are also briefly discussed

multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes we study a multilevel preconditioner for the galerkin boundary element matrix arising from a symmetric positive definite bilinear form the associated energy norm is assumed to be equivalent to a sobolev norm of positive possibly fractional order m on a bounded open or closed surface of dimension d with 0 2m le d we consider piecewise linear approximation on triangular elements successive levels of the mesh are created by selectively subdividing elements within local refinement zones hanging nodes may be created and the global mesh ratio can grow exponentially with the number of levels the coarse grid correction consists of an exact solve and the correction on each finer grid amounts to a simple diagonal scaling involving only those degrees of freedom whose associated nodal basis functions overlap the refinement zone under appropriate assumptions on the choice of refinement zones the condition number of the preconditioned system is shown to be bounded by a constant independent of the number of degrees of freedom the number of levels and the global mesh ratio in addition to applying to galerkin discretisation of hypersingular boundary integral equations the theory covers finite element methods for positive definite self adjoint elliptic problems with dirichlet boundary conditions

multilevel preconditioning for the boundary concentrated hp fem abstract the boundary concentrated finite element method is a variant of the hp version of the finite element method that is particularly suited for the numerical treatment of elliptic boundary value problems with smooth coefficients and low regularity boundary conditions for this method we present two multilevel preconditioners that lead to preconditioned stiffness matrices with condition numbers that are bounded uniformly in the problem size n the cost of applying the preconditioners is o n numerical examples illustrate the efficiency of the algorithms

methods for bounding the marginal survival distribution for time to event data with many potential failure types one cannot uniquely determine the distribution of time to a specific event type or marginal survival distribution in the case where event types are mutually exclusive in this paper we discuss several methods for estimating functions that bound the non identifiable marginal survival distribution in the competing risks problem we compute and compare bounds for data simulated from two bivariate survival distributions results show that the methods provide a suitable estimate of the marginal survival probability when one has specified dependence correctly data from a large clinical trial for breast cancer illustrate the methods

nonparametric estimation for right censored length biased data a pseudo partial likelihood approach to estimate the lifetime distribution of right censored length biased data we propose a pseudo partial likelihood approach that allows us to derive two nonparametric estimators with its closed form estimators and explicit limiting variances this approach retains the simplicity of conditional analysis and has only a small efficiency loss compared with the unconditional analysis under some regularity conditions we show that the two estimators are uniformly consistent and converge weakly to gaussian processes a simulation study demonstrates that the proposed estimators have satisfactory finite sample performance application to an alzheimer s disease study is reported

the product moment correlation coefficient and linear regression for truncated data abstract the random truncation model has been considered extensively in the literature tsai has noted that many previous results hold under the weaker assumption of quasi independence between the failure time and the truncation time in the observable region of truncated data we generalize the pearson product moment correlation coefficient to measure the association between both time variables in the observable region we show that if the failure time and the truncation time follow a truncated bivariate normal distribution then a zero value of the generalized correlation coefficient is equivalent to the quasi independence we propose a corresponding sample correlation coefficient and consider its asymptotic behavior we also study an application of quasi independence to truncated linear regression with its asymptotic results the proposed estimator stemming directly from the least squares approach is computationally much simpler and has a natural extension to multiple linear regression a simulation s

estimation of the survival function with increasing failure rate based on left truncated and right censored data summary the maximum conditional likelihood estimator of the survival function with increasing hazard rate is derived based on left truncated and right censored data this estimator always exists whereas the fully nonparametric conditional maximum likelihood estimator may not exist a strong consistency theorem is established based on the total time on test transformation right censored survival observations arise naturally in biomedical studies of survival when some of the patients are not followed until death parametric and nonparametric methods for analysing such data have been considered by many authors in the single sample problem kaplan meier 1958 derived the nonparametric maximum likelihood estimator of the survival function based on right censored data in addition to right censoring data may be subject to left truncation this arises when the individuals enter the study at some known time after the time origin for example in studying the effects on mortality of occupational exposure to agents in a certain industry age would normally be taken as the primary time variable but observation on an individual would not commence until work in this industry started specifically we consider the following let x be a random variable representing lifetimes and let t c be the random variables describing the left truncation times and right censoring times respectively suppose that x follows the distribution f with associated survival function s 1 f we also assume that t c is independent of x and follows the joint distribution g with pr t c 1 the quantities observed are y min x c t and 8 where 8 1 if t x c and 8 0 if c x nothing is observed if x t in effect observations are made from the distribution of y t 8

nonparametric analysis of bivariate gap time with competing risks this article considers nonparametric methods for studying recurrent disease and death with competing risks we first point out that comparisons based on the well known cumulative incidence function can be confounded by different prevalence rates of the competing events and that comparisons of the conditional distribution of the survival time given the failure event type are more relevant for investigating the prognosis of different patterns of recurrence disease we then propose nonparametric estimators for the conditional cumulative incidence function as well as the conditional bivariate cumulative incidence function for the bivariate gap times that is the time to disease recurrence and the residual lifetime after recurrence to quantify the association between the two gap times in the competing risks setting a modified kendall s tau statistic is proposed the proposed estimators for the conditional bivariate cumulative incidence distribution and the association measure account for the induced dependent censoring for the second gap time uniform consistency and weak convergence of the proposed estimators are established hypothesis testing procedures for two sample comparisons are discussed numerical simulation studies with practical sample sizes are conducted to evaluate the performance of the proposed nonparametric estimators and tests an application to data from a pancreatic cancer study is presented to illustrate the methods developed in this article

inverse probability weighting methods for cox regression with right truncated data right truncated data arise when observations are ascertained retrospectively and only subjects who experience the event of interest by the time of sampling are selected such a selection scheme without adjustment leads to biased estimation of covariate effects in the cox proportional hazards model the existing methods for fitting the cox model to right truncated data which are based on the maximization of the likelihood or solving estimating equations with respect to both the baseline hazard function and the covariate effects are numerically challenging we consider two alternative simple methods based on inverse probability weighting ipw estimating equations which allow consistent estimation of covariate effects under a positivity assumption and avoid estimation of baseline hazards we discuss problems of identifiability and consistency that arise when positivity does not hold and show that although the partial tests for null effects based on these ipw methods can be used in some settings even in the absence of positivity they are not valid in general we propose adjusted estimating equations that incorporate the probability of observation when it is known from external sources which results in consistent estimation we compare the methods in simulations and apply them to the analyses of human immunodeficiency virus latency

testing the equality of two survival functions with right truncated data to compare the survival functions based on right truncated data lagakos et al proposed a weighted logrank test based on a reverse time scale this is in contrast to bilker and wang who suggested a semi parametric version of the mann whitney test by assuming that the distribution of truncation times is known or can be estimated parametrically the approach of lagakos et al is simple and elegant but the weight function in their method depends on the underlying cumulative hazard functions even under proportional hazards models on the other hand a semi parametric test may have better efficiency but it may be sensitive to misspecification of the distribution of truncation times therefore this paper proposes a non parametric test statistic based on the integrated weighted difference between two estimated survival functions in forward time the comparative results from a simulation study are presented and the implementation of these methods to a real data set is demonstrated

boundary concentrated finite element methods a method with optimal up to logarithmic terms complexity for solving elliptic problems is proposed the method relies on interior regularity but the solution may have globally low regularity due to rough boundary data or geometries elliptic regularity results high order approximation results and an efficient preconditioner are presented the method is utilized to realize with linear logarithmic complexity an accurate and data sparse approximation to the associated elliptic poincare steklov operators further applications include the treatment of exterior boundary value problems and the solution of problems in the framework of domain decomposition methods

semiparametric inferences for association with semi competing risks data in many biomedical studies it is of interest to assess dependence between bivariate failure time data we focus here on a special type of such data referred to as semi competing risks data in this article we develop methods for making inferences regarding dependence of semi competing risks data across strata of a discrete covariate z a class of rank statistics for testing constancy of association across strata are proposed its asymptotic properties are also derived we develop a novel resampling based technique for calculating the variances of the proposed test statistics in addition we develop methods for combining test statistics for assessing marginal effects of z on the dependent censoring variable as well as its effects on association the finite sample properties of the proposed methodology are assessed using simulation studies and they are applied to data from a leukaemia transplantation study copyright 2005 john wiley sons ltd

adaptive galerkin boundary element methods with panel clustering in this paper we will propose a boundary element method for solving classical boundary integral equations on complicated surfaces which possibly contain a large number of geometric details or even uncertainties in the given data the small size of such details is characterised by a small parameter varepsilon and the regularity of the solution is expected to be low in such zones on the surface which we call the wire basket zones we will propose the construction of an initial discretisation for such type of problems afterwards standard strategies for boundary element discretisations can be applied such as the h p and the adaptive hp version in a straightforward way for the classical boundary integral equations we will prove the optimal approximation results of our so called wire basket boundary element method and discuss the stability aspects then we construct the panel clustering and mathcal h matrix approximations to the corresponding galerkin bem stiffness matrix the method is shown to have an almost linear complexity with respect to the number of degrees of freedom located on the wire basket

a lower bound analysis of hamming distortion for a binary ceo problem with joint source channel coding a two node binary chief executive officer ceo problem is investigated noise corrupted versions of a binary sequence are forwarded by two nodes to a single destination node over orthogonal additive white gaussian noise awgn channels we first reduce the binary ceo problem to a binary multiterminal source coding problem of which an outer bound for the rate distortion region is derived the distortion function is then established by evaluating the relationship between the binary ceo and multiterminal source coding problems a lower bound approximation on the hamming distortion hd is obtained by minimizing a distortion function subject to constraints obtained based on the source channel separation theorem encoding decoding algorithms using concatenated convolutional codes and a joint decoding scheme are used to verify the lower bound on the hd it is found that the theoretical lower bounds on the hd and the computer simulation based bit error rate performance curves have the same tendencies the differences in the threshold signal to noise ratio between the theoretical lower bounds and those obtained by simulations are around 1 5 db in awgn channel the theoretical lower bound on the hd in block rayleigh fading channel is also evaluated by performing monte carlo simulation

new nonasymptotic channel coding theorems for structured codes new nonasymptotic random coding theorems with error probability epsilon and finite block length n based on gallager parity check ensemble and general parity check ensembles are derived in this paper the resulting nonasymptotic achievability bounds when combined with nonasymptotic equipartition properties developed in this paper can be easily computed analytically these nonasymptotic achievability bounds are shown to be asymptotically tight up to the second order of the coding rate as n goes to infinity with either constant or subexponentially decreasing epsilon in the case of gallager parity check ensemble and to imply that low density parity check ldpc codes be capacity achieving in the case of ldpc ensembles numerically they are also compared favorably for finite n and epsilon of practical interest with existing nonasymptotic achievability bounds in the literature

estimating survival under a dependent truncation summary the product limit estimator calculated from data subject to random left truncation relies on the testable assumption of quasi independence between the failure time and the truncation time in this paper we propose a model for a truncated sample of pairs xi y satisfying 1 xi a possible dependency between the truncation time and the variable of interest is modelled with a parametric family of copulas the model also features a distribution function fx and a survival distribution sy associated with the marginal behaviours of x and y in the observable region y x semiparametric estimators for these two functions are proposed they do not make any parametric assumption about either fx or sy we derive an estimator for the copula parameter cx based on the conditional kendall s tau we generalise the copula graphic estimators of zheng klein 1995 to truncated variables the asymptotic distributions of all these estimators are then investigated the methods are illustrated with a real dataset on hiv infection by transfusion and by simulations

power scheduling of universal decentralized estimation in sensor networks we consider the optimal power scheduling problem for the decentralized estimation of a noise corrupted deterministic signal in an inhomogeneous sensor network sensor observations are first quantized into discrete messages then transmitted to a fusion center where a final estimate is generated supposing that the sensors use a universal decentralized quantization estimation scheme and an uncoded quadrature amplitude modulated qam transmission strategy we determine the optimal quantization and transmit power levels at local sensors so as to minimize the total transmit power while ensuring a given mean squared error mse performance the proposed power scheduling scheme suggests that the sensors with bad channels or poor observation qualities should decrease their quantization resolutions or simply become inactive in order to save power for the remaining active sensors their optimal quantization and transmit power levels are determined jointly by individual channel path losses local observation noise variance and the targeted mse performance numerical examples show that in inhomogeneous sensing environment significant energy savings is possible when compared to the uniform quantization strategy

decentralized estimation in an inhomogeneous sensing environment we consider decentralized estimation of a noise corrupted deterministic parameter by a bandwidth constrained sensor network with a fusion center the sensor noises are assumed to be additive zero mean spatially uncorrelated but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment the classical best linear unbiased estimator blue linearly combines the real valued sensor observations to minimize the mean square error mse unfortunately such a scheme cannot be implemented in a practical bandwidth constrained sensor network due to its requirement to transmit real valued messages in this paper we construct a decentralized estimation scheme des where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal to noise ratio snr the resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter the proposed des is universal in the sense that each sensor compression scheme requires only the knowledge of local snr rather than the noise probability distribution functions pdf while the final fusion step is also independent of the local noise pdfs we show that the mse of the proposed des is within a constant factor of 25 8 of that achieved by the classical centralized blue estimator

unequal message protection asymptotic and non asymptotic tradeoffs we study a form of unequal error protection that we term unequal message protection ump the message set of a ump code is a union of m disjoint message classes each class has its own error protection requirement with some classes needing better error protection than others we analyze the tradeoff between rates of message classes and the levels of error protection our analysis reveals new tradeoffs which were not captured by prior works on ump codes to obtain our results we generalize finite block length achievability and converse bounds due to polyanskiy poor verdu we evaluate our bounds for the binary symmetric and binary erasure channels and analyze the asymptotic characteristic of the bounds in the fixed error and moderate deviations regimes in addition we consider two questions related to the practical construction of ump codes first we study a header construction that prefixes the message class into a header followed by data protection using a standard homogeneous classical code we show that in general this construction is not optimal at finite block lengths we further demonstrate that our main ump achievability bound can be obtained using coset codes which suggests a path to implementation of tractable ump codes

bivariate estimation with right truncated data abstract bivariate estimation with survival data has received considerable attention recently however most of the work has focused on random censoring models another common feature of survival data random truncation is considered in this study truncated data may arise if the time origin of the events under study precedes the observation period in a random right truncation model one observes the iid samples of y t only if y t where y is the variable of interest and t is an independent variable that prevents the complete observation of y suppose that y x is a bivariate vector of random variables where y is subject to right truncation in this study the bivariate reverse hazard vector is introduced and a nonparametric estimator is suggested an estimator for the bivariate survival function is also proposed weak convergence and strong consistency of this estimator are established via a representation by iid variables an expression for the limiting covariance function is provided and a

power constrained linear estimation in wireless sensor networks with correlated data and digital modulation we study the problem of joint quantization and power allocation in wireless sensor networks where spatially distributed sensors observe a gaussian random source quantize the resulting noisy observations and transmit over orthogonal fading channels to a remote fusion center fc the role of the fc is to reconstruct the source with minimal distortion using linear minimum mean square error estimation rule in this paper we undertake the design of joint quantization and power allocation based on the following optimization problem minimize the reconstruction distortion for a given total network power consumption to address this problem at each sensor node uniform scalar quantization is assumed moreover assuming pseudo quantization noise model we show that the problem can be solved using a block coordinate descent type algorithm which iteratively optimizes the quantization bits and the power allocations the algorithm takes into account the spatial correlation the observation noise and the channel quality of the sensors numerical and simulation examples corroborate the analytical results the examples illustrate that the proposed design holds a considerable performance gain compared to a quantization scheme based on uniform power allocation to the sensors

nonparametric estimation of the slope of a truncated regression a nonparametric estimate b is presented for the slope of a regression line y 83ox v subject to the truncation y c yo this model is relevant to a cosmological controversy which concerns hubble s law in astronomy the estimate 3 corresponds to the zero crossing of a random function s 3 which for each 8 is a mann whitney type of statistic designed to measure heterogeneity among the calculated residuals y 3x the asymptotic distribution of p is derived making extensive use of u statistics to show that sn 3o is asymptotically normal and then showing that s 3 behaves like sn 3o plus a deterministic term which is locally linear results on asymptotic efficiency are compared with finite sample size results by simulation

one shot classical quantum capacity and hypothesis testing the one shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold in this work we show that this capacity is well approximated by a relative entropy type measure defined via hypothesis testing combined with a quantum version of stein s lemma our results give a conceptually simple proof of the well known holevo schumacher westmoreland theorem for the capacity of memoryless channels more generally we obtain tight capacity formulas for arbitrary not necessarily memoryless channels

nonparametric inference on bivariate survival data with interval sampling association estimation and testing in many biomedical applications interest focuses on the occurrence of two or more consecutive failure events and the relationship between event times such as age of disease onset and residual lifetime bivariate survival data with interval sampling arise frequently when disease registries or surveillance systems collect data based on disease incidence occurring within a specific calendar time interval the initial event is then retrospectively confirmed and the subsequent failure event may be observed during follow up in life history studies the initial and two consecutive failure events could correspond to birth disease onset and death the statistical features and bias of observed data in relation to interval sampling were discussed by zhu wang 2012 here we propose nonparametric estimation of the association between bivariate failure times based on kendall s tau for data collected with interval sampling a nonparametric estimator is given where the contribution of each comparable and orderable pair is weighted by the inverse of the associated selection probability analysis methods for bivariate survival data with interval sampling rely on the assumption of quasi independence i e that bivariate failure times and the time of the initial event are independent in the observable region this paper develops a nonparametric test of quasi independence based on a bivariate conditional kendall s tau for such data simulation studies demonstrate that the association estimator and testing procedure perform well with moderate sample sizes illustrations with two real datasets are provided

optimality and approximate optimality of source channel separation in networks we consider the source channel separation architecture for lossy source coding in communication networks it is shown that the separation approach is optimal in two general scenarios and is approximately optimal in a third scenario the two scenarios for which separation is optimal complement each other the first is when the memoryless sources at source nodes are arbitrarily correlated each of which is to be reconstructed at possibly multiple destinations within certain distortions but the channels in this network are synchronized orthogonal and memoryless point to point channels the second is when the memoryless sources are mutually independent each of which is to be reconstructed only at one destination within a certain distortion but the channels are general including multi user channels such as multiple access broadcast interference and relay channels possibly with feedback the third scenario for which we demonstrate approximate optimality of source channel separation generalizes the second scenario by allowing each source to be reconstructed at multiple destinations with different distortions for this case the loss from optimality using the separation approach can be upper bounded when a difference distortion measure is taken and in the special case of quadratic distortion measure this leads to universal constant bounds

optimum estimation via gradients of partition functions and information measures a statistical mechanical perspective in continuation to a recent work on the statistical mechanical analysis of minimum mean square error mmse estimation in gaussian noise via its relation to the mutual information the i mmse relation here we propose a simple and more direct relationship between optimum estimation and certain information measures e g the information density and the fisher information which can be viewed as partition functions and hence are amenable to analysis using statistical mechanical techniques the proposed approach has several advantages most notably its applicability to general sources and channels as opposed to the i mmse relation and its variants which hold only for certain classes of channels e g additive white gaussian noise channels we then demonstrate the derivation of the conditional mean estimator and the mmse in a few examples two of these examples turn out to be generalizable to a fairly wide class of sources and channels for this class the proposed approach is shown to yield an approximate conditional mean estimator and an mmse formula that has the flavor of a single letter expression we also show how our approach can easily be generalized to situations of mismatched estimation

on the optimal power distortion tradeoff in asymmetric gaussian sensor network we present necessary and sufficient conditions similar to the recent results of gastpar 2007 for the achievability of all power distortion tuples p d p1 p2 middot middot middot pl d in an asymmetric gaussian sensor network where l distributed sensors transmit noisy observations of a gaussian source through a gaussian multiple access channel to a fusion center we show numerically that in general the gap between the provided upper bound and the lower bound of the distortion d is small we also provide an optimal power allocation that minimizes the total power consumption pmacr sigmai 1 l pi for uncoded transmission scheme while satisfying a given distortion constraint d numerical evaluations show that by applying the optimal power allocation uncoded transmission can perform nearly optimal in an asymmetric sensor network subject to a sum power constraint in the symmetric case both bounds agree and provide the optimal power distortion tradeoff p d this agrees with result of m gastpar 2007 thus in the sense of achieving the optimal p d tradeoff uncoded transmission is optimal in the symmetric case and can be nearly optimal in the asymmetric case

nonparametric analysis of truncated survival data with application to aids summary one source of data for the induction distribution of aids arises from persons infected by the aids virus from contaminated blood transfusions analyses of these data are complicated because the number of individuals infected by transfusion is unknown information is available only for those who are infected and develop aids within a certain chronologic time interval the statistical problem is one of making inferences about a stochastic process of infection and disease for which realizations are right truncated in chronologic time by considering the process in reverse time we transform the problem to one of analysing survival data that are left truncated in internal time we develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions of several groups an important feature of the natural history and population dynamics of aids is the induction period between infection with the aids virus and the onset of clinical aids this time is sometimes referred to as the latency period or incubation period follow up studies of individuals at risk of being infected will provide direct observations from the induction distribution but most of these studies will not be completed for several years one alternative source of information arises from persons infected with the aids virus from a contaminated blood transfusion of persons infected in this way only those who develop aids by a certain date can be identified the total number who are infected is not known a similar sampling distribution arises in the study of pediatric aids children who contract aids as a result of being infected in utero or at birth can be identified but the total number infected in this way is unknown the statistical problem is one of making inferences about a stochastic process of infection and subsequent disease in which realizations are right truncated in chronologic time by considering the process in reverse time the problem can be transformed to one of survival data that are left truncated in internal time we use this relationship to develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions for

the rate distortion function for the quadratic gaussian ceo problem a new multiterminal source coding problem called the ceo problem was presented and investigated by berger zhang and viswanathan recently viswanathan and berger have investigated an extension of the ceo problem to gaussian sources and call it the quadratic gaussian ceo problem they considered this problem from a statistical viewpoint deriving some interesting results in this paper we consider the quadratic gaussian ceo problem from a standpoint of multiterminal rate distortion theory we regard the ceo problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given this viewpoint leads us to a complete solution to the problem we determine the tradeoff between the total amount of rate and squared distortion deriving an explicit formula of the rate distortion function the derived function has the form of a sum of two nonnegative functions one is a classical rate distortion function for single gaussian source and the other is a new rate distortion function which dominates the performance of the system for a relatively small distortion it follows immediately from our result that the conjecture of viswanathan and berger on the asymptotic behavior of minimum squared distortion for large rates is true

in sample forecasting with local linear survival densities in this paper in sample forecasting is defined as forecasting a structured density to sets where it is unobserved the structured density consists of one dimensional in sample components that identify the density on such sets we focus on the multiplicative density structure which has recently been seen as the underlying structure of non life insurance forecasts in non life insurance the in sample area is defined as one triangle and the forecasting area as the triangle that 20 added to the first triangle produces a square recent approaches estimate two one dimensional components by projecting an unstructured two dimensional density estimator onto the space of multiplicatively separable functions we show that time reversal reduces the problem to two one dimensional problems where the one dimensional data are left truncated and a one dimensional survival density estimator is needed this paper then uses the local linear density smoother with 25 weighted cross validated and do validated bandwidth selectors full asymptotic theory is provided with and without time reversal finite sample studies and an application to non life insurance are included

testing goodness of fit of a uniform truncation model several goodness of fit tests of a lifetime distribution have been suggested in the literature many take into account censoring and or truncation of event times in some contexts a goodness of fit test for the truncation distribution is of interest in particular better estimates of the lifetime distribution can be obtained when knowledge of the truncation law is exploited in cross sectional sampling for example there are theoretical justifications for the assumption of a uniform truncation distribution and several studies have used it to improve the efficiency of their survival estimates the duality of lifetime and truncation in the absence of censoring enables methods for testing goodness of fit of the lifetime distribution to be used for testing goodness of fit of the truncation distribution however under random censoring this duality does not hold and different tests are required in this article we introduce several goodness of fit tests for the truncation distribution and investigate their performance in the presence of censored event times using simulation we demonstrate the use of our tests on two data sets

nonparametric methods for doubly truncated data abstract truncated data play an important role in the statistical analysis of astronomical observations as well as in survival analysis the motivating example for this article concerns a set of measurements on quasars in which there is double truncation that is the quasars are observed only if their luminosity occurs within a certain finite interval bounded at both ends with the interval varying for different observations nonparametric methods for the testing and estimation of doubly truncated data are developed these methods extend some known techniques for data that are truncated only on one side in particular lynden bell s estimator and the truncated version of kendall s tau statistic however the kind of hazard function arguments that underlie the one sided methods fail for two sided truncation bootstrap and markov chain monte carlo techniques are used here in their place finally we apply these techniques to the quasar data answering a question about their long term luminosity evolution

rate distortion theory for gaussian multiterminal source coding systems with several side informations at the decoder in this paper we consider the separate coding problem for l 1 correlated gaussian memoryless sources we deal with the case where l sources work as partial side information at the decoder for the reconstruction of the remaining source the determination problem of the rate distortion region for this system is the so called many help one problem and it has been known as a highly challenging problem for almost 20 years in this paper we give a partial solution to this problem we determine the rate distortion region in the case where the l sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given the additive white gaussian noise ceo problem is a special case of this we also discuss the relation of the result previous results of ours

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

estimating a distribution function with truncated data let mathscr p be a finite population with n geq 1 elements for each e in mathscr p let x e and y e be independent positive random variables with unknown distribution functions f and g and suppose that the pairs x e y e are i i d we consider the problem of estimating f g and n when the data consist of those pairs x e y e for which e in mathscr p and y e leq x e the nonparametric maximum likelihood estimators mles of f and g are described and their asymptotic properties as n rightarrow infty are derived it is shown that the mles are consistent against pairs f g for which f and g are continuous g 1 0 leq f 1 0 and g 1 1 leq f 1 1 sqrt n times estimation error for f converges in distribution to a gaussian process if int infty 0 1 g df infty but may fail to converge if this integral is infinite

nonidentifiability in the presence of factorization for truncated data a time to event formula see text is left truncated by formula see text if formula see text can be observed only if formula see text this often results in oversampling of large values of formula see text and necessitates adjustment of estimation procedures to avoid bias simple risk set adjustments can be made to standard risk set based estimators to accommodate left truncation when formula see text and formula see text are quasi independent we derive a weaker factorization condition for the conditional distribution of formula see text given formula see text in the observable region that permits risk set adjustment for estimation of the distribution of formula see text but not of the distribution of formula see text quasi independence results when the analogous factorization condition for formula see text given formula see text holds also in which case the distributions of formula see text and formula see text are easily estimated while we can test for factorization if the test does not reject we cannot identify which factorization condition holds or whether quasi independence holds hence we require an unverifiable assumption in order to estimate the distribution of formula see text or formula see text based on truncated data this contrasts with the common understanding that truncation is different from censoring in requiring no unverifiable assumptions for estimation we illustrate these concepts through a simulation of left truncated and right censored data

comparing estimation approaches for the illness death model under left truncation and right censoring left truncated data arise when lifetimes are observed only if they are larger than independent truncation times for example in a cross sectional sampling only individuals who live long enough to be present on the sampling day are observed there are several ways to perform statistical inference under this setting one can do the following i use an unconditional approach ii condition on the value of the truncation variable or iii condition on all the history up to the time of truncation the latter two approaches are equivalent when analyzing univariate survival outcomes but differ under the multi state framework in this paper we consider the illness death model and compare between the three estimation approaches in a parametric regression framework we show that approach ii is more efficient than the standard approach iii although it requires more computational effort approach i is the most efficient approach but it requires knowledge on the distribution of the truncation variable and hence is less robust the methods are compared using a theoretical example and simulations and are applied to intensive care units data collected in a cross sectional design where the illness state corresponds to a bloodstream infection

methods for testing the markov condition in the illness death model a comparative study markov three state progressive and illness death models are often used in biomedicine for describing survival data when an intermediate event of interest may be observed during the follow up however the usual estimators for markov models e g aalen johansen transition probabilities may be systematically biased in non markovian situations on the other hand despite non markovian estimators for transition probabilities and related curves are available including the markov information in the construction of the estimators allows for variance reduction therefore testing for the markov condition is a relevant issue in practice in this paper we discuss several characterizations of the markov condition with special focus on its equivalence with the quasi independence between left truncation and survival times in standard survival analysis new methods for testing the markovianity of an illness death model are proposed and compared with existing ones by means of an intensive simulation study we illustrate our findings through the analysis of a data set from stem cell transplant in leukemia copyright 2016 john wiley sons ltd

primal and dual interface concentrated iterative substructuring methods this paper is devoted to the fast solution of interface concentrated finite element equations the interface concentrated finite element schemes are constructed on the basis of a nonoverlapping domain decomposition where a conforming boundary concentrated finite element approximation is used in every subdomain similar to boundary element domain decomposition methods the total number of unknowns per subdomain behaves like o h h d 1 where h h and d denote the usual scaling parameter of the subdomains the average discretization parameter of the subdomain boundaries and the spatial dimension respectively we propose and analyze primal and dual substructuring iterative methods which asymptotically exhibit the same or at least almost the same complexity as the number of unknowns in particular the so called all floating finite element tearing and interconnecting solvers are highly parallel and very robust with respect to large coefficient jumps

exponential convergence of hp finite element discretization of optimal boundary control problems with elliptic partial differential equations we investigate the numerical solution of boundary control problems with elliptic partial differential equations by the hp finite element method we prove exponential convergence with respect to the number of unknowns for an a priori chosen discretization here we have to prove that derivatives of arbitrary order of the solution belong to suitably chosen weighted sobolev spaces this result relies on the assumption that the number of switching points of the optimal control is finite numerical experiments confirm the theoretical findings

the capacity of finite state markov channels with feedback we consider a class of finite state markov channels with feedback we first introduce a simplified equivalent channel model and then construct the optimal stationary and nonstationary input processes that maximize the long term directed mutual information furthermore we give a sufficient condition under which the channel s shannon capacity can be achieved by a stationary input process the corresponding converse coding theorem and direct coding theorem are proved

a linear program for the finite block length converse of polyanskiy poor verdu via nonsignaling codes motivated by recent work on entanglement assisted codes for sending messages over classical channels the larger easily characterized class of nonsignaling codes is defined analyzing the optimal performance of these codes yields an alternative proof of the finite block length converse of polyanskiy poor and verdu and shows that they achieve this converse this provides an explicit formulation of the converse as a linear program which has some useful features for discrete memoryless channels it is shown that nonsignaling codes attain the channel capacity with zero error probability if and only if the dispersion of the channel is zero

maximal lifetime power and rate allocation for wireless sensor systems with data distortion constraints we address a lifetime maximization problem for a single hop wireless sensor system also known as a gaussian sensor network where multiple sensors encode and communicate their measurements of a gaussian random source to a fusion center fc the fc is required to reconstruct the source within a prescribed distortion threshold the lifetime optimization problem is formulated as a joint power rate and timeslot for time division multiple access tdma allocation problem under the constraints of the well known rate distortion constraints for the gaussian ceo problem the capacity constraints of the wireless links the energy constraints of the sensor nodes and the strict delay constraint within which the encoded sensor data must arrive at the fc we study the performances of tdma and an interference limited nonorthogonal multiple access noma with single user decoding based protocols and compare them against recently reported simple uncoded amplify and forward schemes under a nonorthogonal multiple access channel with complete phase synchronization since computing the exact capacity region for correlated sources in a multiaccess channel is difficult we simply consider the gaussian multiaccess capacity constraints pretending that the sensor data are independent although they are clearly not we show that the optimal lifetime achieved under these capacity constraints provides an upper bound on the optimal lifetime achieved by the tdma and noma protocols while the constrained nonlinear optimization problems for the tdma and the gaussian multiaccess cases are convex the noma case results in a nonlinear nonconvex difference of convex functions d c programming problem we provide a simple successive convex approximation based algorithm for the noma case that converges fast to a suboptimal lifetime performance that compares favorably against the upper bound provided by the gaussian multiaccess case extensive numerical studies are presented for both static and slow fading wireless environments with full channel state information at the fusion center

epsilon capacity of binary symmetric averaged channels we consider the channel model obtained by averaging binary symmetric channel bsc components with respect to a weighting distribution a nonempty open interval a b is called a capacity gap for this channel model if no channel component has capacity in a b and this property fails for every open interval strictly containing a b for a fixed epsi 0 suppose one wishes to compute the epsi capacity of the channel which is the maximum asymptotic rate at which the channel can be encoded via a sequence of channel codes each achieving block error probability lesepsi in 1963 parthasarathy provided a formula for epsi capacity which is valid for all but at most countably many values of epsi when the formula fails there exists a unique capacity gap a b such that the epsi capacity lies in a b but one does not know precisely where via a coding theorem and converse we establish a formula for computing epsi capacity as a function of the endpoints a b of the associated capacity gap a b the formula holds whenever the capacity gap is sufficiently narrow in width

the ceo problem multiterminal source coding we consider a new problem in multiterminal source coding motivated by the following decentralized communication estimation task a firm s chief executive officer ceo is interested in the data sequence x t sub t 1 sup spl infin which cannot be observed directly perhaps because it represents tactical decisions by a competing firm the ceo deploys a team of l agents who observe independently corrupted versions of x t sub t 1 sup spl infin because x t is only one among many pressing matters to which the ceo must attend the combined data rate at which the agents may communicate information about their observations to the ceo is limited to say r bits per second if the agents were permitted to confer and pool their data then in the limit as l spl rarr spl infin they usually would be able to smooth out their independent observation noises entirely then they could use their r bits per second to provide the ceo with a representation of x t with fidelity d r where d spl middot is the distortion rate function of x t in particular with such data pooling d can be made arbitrarily small if r exceeds the entropy rate h of x t suppose however that the agents are not permitted to convene agent i having to send data based solely on his own noisy observations y sub i t we show that then there does not exist a finite value of r for which even infinitely many agents can make d arbitrarily small furthermore in this isolated agents case we determine the asymptotic behavior of the minimal error frequency in the limit as l and then r tend to infinity

a formula for the capacity of the general gel fand pinsker channel we consider the gel fand pinsker problem in which the channel and state are general i e possibly non stationary non memoryless and non ergodic using the information spectrum method and a non trivial modification of the piggyback coding lemma by wyner we prove that the capacity can be expressed as an optimization over the difference of a spectral inf and a spectral sup mutual information rate we consider various specializations including the case where the channel and the state are memoryless but not necessarily stationary

a lower bound on the probability of error in multihypothesis testing consider two random variables x and y where x is finitely or countably infinitely valued and where y is arbitrary let spl epsiv denote the minimum probability of error incurred in estimating x from y it is shown that spl epsiv spl ges sub 0 spl les spl alpha spl les 1 sup sup 1 spl alpha p spl pi x y spl les spl alpha where spl pi x y denotes the posterior probability of x given y this bound finds information theoretic applications in the proof of converse channel coding theorems it generalizes and strengthens previous lower bounds due to shannon and to verdu and han 1994