a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

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

a minimax approach to consistency and efficiency for estimating equations the consistency of estimating equations has been studied in the main along the lines of cramer s classical argument which only asserts the existence of consistent solutions the statement similar to that of doob and wald which identifies the consistent solutions has not yet been established the obstacle is that the solutions of estimating equations cannot in general be defined as the maximum of likelihood functions in this paper we demonstrate that the consistent solutions can be identified as the minimax of a function r whose properties resemble those of a log likelihood ratio but which exists in a much wider context furthermore since we do not need r to be differentiable the minimax is consistent even when the estimating equation does not exist in this respect the minimax is a new estimator we first convey the idea by focusing on the quasi likelihood estimate and then indicate its full generality by providing a set of sufficient conditions for consistency and studying a number of important cases efficiency will also be verified

efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors abstract let y x e where is unknown and e e x 0 with positive probability but there exist instrumental variables w such that e e w 0 w p 1 it is well known that such nonparametric regression models are generally ill posed in the sense that the map from the data to is not continuous in this paper we derive the efficiency bounds for estimating certain linear functionals of without assuming itself to be identified

adaptivity in space and time for reaction diffusion systems in electrocardiology the paper introduces and studies numerical methods that are fully adaptive in both three dimensional 3d space and time to challenging multiscale cardiac reaction diffusion models in these methods temporal adaptivity comes via stepsize control in function space oriented linearly implicit time integration while spatial adaptivity is realized within multilevel finite element methods controlled by a posteriori local error estimators in contrast to other recent adaptivity approaches to cardiac modeling that discretize first in space and then in time so called method of lines our method discretizes first in time and then in space so called rothe method an approach that has already proven to be highly efficient in a number of challenging multiscale problems in science and technology kardos code library with this method the evolution of a complete heartbeat from the excitation to the recovery phase is simulated both in the frame of the anisotropic monodomain models and in the more realistic anisotropic bidomain models coupled with either a variant of the simple fitzhugh nagumo model or the more complex phase i luo rudy ionic model the numerical results exhibit a rather satisfactory performance of our adaptive method for complex cardiac reaction diffusion models on 3d domains up to moderate sizes in particular the method accurately resolves the evolution of the intra and extracellular potentials gating variables and ion concentrations during the excitation plateau and recovery phases

partial likelihood for signal processing we present partial likelihood pl as an effective means for developing nonlinear techniques for signal processing posing signal processing problems in a likelihood setting provides a number of advantages such as allowing the use of powerful tools in statistics and easy incorporation of model order complexity selection into the problem by use of appropriate information theoretic criteria however likelihood formulations in most time series applications require a mechanism to discount the dependence structure of the data we address how pl bypasses this requirement and note that it might coincide with conditional likelihood in a number of cases we show that pl theory can also be used to establish the fundamental information theoretic connection to show the equivalence of likelihood maximization and relative entropy minimization without making the assumption of independent observations which is an unrealistic assumption for most signal processing applications we show that this equivalence is true for the basic class of probability models the exponential family which includes many important structures that can be used as nonlinear filters we conclude by giving examples of the application of pl theory

on tests against one sided hypotheses in some generalized linear models one sided hypotheses arise naturally in many situations when testing against such hypotheses it is desirable to take the available one sided information into account rather than simply applying a two sided test what we expect to gain by applying a one sided test instead of a two sided test is an increase in the power of the test we consider various tests of one sided hypotheses in a class of models that includes generalized linear and cox regression models the tests are likelihood ratio wald score generalized distance and a pearson chi square it is shown that these test statistics are asymptomatically equivalent in terms of local power this is a generalization of the well known corresponding result for two sided alternatives two examples are also discussed they are on 1 testing for interaction in binomial response models and 2 comparison of treatments with ordinal categorical responses

the effects of random and discrete sampling when estimating continuous time diffusions high frequency financial data are not only discretely sampled in time but the time separating successive observations is often random we analyze the consequences of this dual feature of the data when estimating a continuous time model in particular we measure the additional effects of the randomness of the sampling intervals over and beyond those due to the discreteness of the data we also examine the effect of simply ignoring the sampling randomness we find that in many situations the randomness of the sampling has a larger impact than the discreteness of the data

theory of partial likelihood a general asymptotic theory is developed for the maximum likelihood estimator based on a partial likelihood conditions are given for consistency and asymptotic normality and a method is provided for the calculation of the asymptotic efficiency of the estimator the implications of the general theory are examined in special cases such as inference in stochastic processes cox regression models and ar processes with missing segments

non causality in bivariate binary time series in this paper we develop a dynamic discrete time bivariate probit model in which the conditions for granger non causality can be represented and tested the conditions for simultaneous independence are also worked out the model is extended in order to allow for covariates representing individual as well as time heterogeneity the proposed model can be estimated by maximum likelihood granger non causality and simultaneous independence can be tested by likelihood ratio or wald tests a specialized version of the model aimed at testing granger non causality with bivariate discrete time survival data is also discussed the proposed tests are illustrated in two empirical applications

point process modelling for directed interaction networks abstract network data often take the form of repeated interactions between senders and receivers tabulated over time a primary question to ask of such data is which traits and behaviors are predictive of interaction to answer this question a model is introduced for treating directed interactions as a multivariate point process a cox multiplicative intensity model using covariates that depend on the history of the process consistency and asymptotic normality are proved for the resulting partial likelihood based estimators under suitable regularity conditions and an efficient fitting procedure is described multicast interactions those involving a single sender but multiple receivers are treated explicitly the resulting inferential framework is then employed to model message sending behavior in a corporate e mail network the analysis gives a precise quantification of which static shared traits and dynamic network effects are predictive of message recipient selection

robust estimation via minimum distance methods given a fixed parametric family p it is desired to estimate however due to contaminations of various sorts the data actually collected by the statistician follow a distribution that is close to but possibly distinct from thep s it is proved that under these conditions and in an appropriate asymptotic framework the minimum distance estimators of the cramer von mises type are robust specification of a cramer von mises weight functionh defines a notion of distance each such choice ofh then delineates the kind of contamination possible and leads to an estimator which defends optimally against it when the theory is specialized to location models various choices ofh lead to estimators asymptotically equivalent to such familiar ones as trimmed mean median hodges lehmann estimator and so forth the framework developed herein provides some guidelines for choosing among the possible estimators and suggests that the standard cramer von mises estimator of location is probably as good a robust estimator as any

a multiresolution stochastic process model for predicting basketball possession outcomes abstractbasketball games evolve continuously in space and time as players constantly interact with their teammates the opposing team and the ball however current analyses of basketball outcomes rely on discretized summaries of the game that reduce such interactions to tallies of points assists and similar events in this article we propose a framework for using optical player tracking data to estimate in real time the expected number of points obtained by the end of a possession this quantity called expected possession value epv derives from a stochastic process model for the evolution of a basketball possession we model this process at multiple levels of resolution differentiating between continuous infinitesimal movements of players and discrete events such as shot attempts and turnovers transition kernels are estimated using hierarchical spatiotemporal models that share information across players while remaining computationally tractable on very large data sets in addition to estima

consistency properties of least squares estimates of autoregressive parameters in arma models a unified treatment of the consistency properties of the ordinary least squares estimates in an autoregressive fitting of time series from nonstationary or stationary autoregressive moving average models is given for a given model the orders of autoregressions which produce consistent estimates are obtained and the limiting values hence the biases of the estimates of other autoregressions are investigated

polynomial acceleration of iterative schemes associated with subproper splittings a subproper splitting of a matrix a is a decomposition a b c such that the kernel of a includes that of b while the range of b includes that of a our purpose in the present work is to extend the convergence analysis of polynomial acceleration to the case of iterative schemes associated with subproper splittings in the case of hermitian matrices and consistent systems briefly stated our conclusions show that the regular theory extends to the subproper case provided that convergence to the solution of ax b is understood as convergence to a solution of ax b while b 1 a is understood as b a 0 where b is the moore penrose inverse of b

nonparametric maximum likelihood estimation of survival functions with a general stochastic ordering and its dual summary this paper discusses estimation of survival functions under an arbitrary partial stochas tic ordering of the underlying populations this technique is especially useful when data are not easily acquired from one or more of the populations but data from the other populations are available estimation of the ordered survival functions entails use of a fenchel duality theorem that results in an algorithm to identify and resolve violations of the underlying ordering the algorithm produces estimates which converge to the maximum likelihood estimates of the survival functions given the underlying ordering the method is illustrated by an example in life testing of components and in clinical trials estimation of a survival function p t is often of prime interest if the functional form of the survival function is unknown nonparametric methods such as the product limit estimator kaplan meier 1958 are needed johansen 1978 showed that the product limit estimator is a maximum likelihood estimator in the class of all distributions under a generalized maximum likelihood framework kiefer wolfowitz 1956 since the generalized maximum likelihood esti mates for continuous survival functions place probability only on those time points at which observations occur suppose however that one desires to estimate a number of survival functions when a partial stochastic ordering exists among them and under censoring for example in a clinical trial of two treatments for a rare debilitating disease let pi p2 and p3 be the survival functions respectively for the disease free group and for the disease groups under the two treatments the well documented survival function p1 can be used to generate better estimates for p2 and p3 by using the order restrictions pi t p2 t and pi t p3 t brunk et al 1966 developed the maximum likelihood estimators for two stochastically ordered distributions for uncensored independent random samples dykstra

p ary unified sequences p ary extended d form sequences with the ideal autocorrelation property in this paper for a prime number p a construction method to generate p ary d form sequences with the ideal autocorrelation property is proposed and using the ternary sequences found by helleseth kumar and martinsen 2000 ternary d form sequences with the ideal autocorrelation property are constructed by combining the methods for generating p ary extended sequences a special case of geometric sequences and p ary d form sequences a construction method of p ary unified extended d form sequences which also have the ideal autocorrelation property is proposed this is a very general class of p ary sequences including the binary and nonbinary extended sequences and the d form sequences from the ternary sequences by helleseth kumar and martinsen ternary unified sequences with the ideal autocorrelation property are also generated

semi implicit time discretization schemes for the bidomain model the bidomain model is a system of partial differential equations used to model the propagation of electrical potential waves in the myocardium it is composed of coupled parabolic and elliptic partial differential equations as well as at least one ordinary differential equation to model the ion activity through the cardiac cell membranes the purpose of this paper is to propose and analyze several implicit semi implicit and explicit time stepping methods to solve that model in particular to avoid the expensive resolution of a nonlinear system through the newton raphson method we identify necessary stability conditions on the time step delta t for the proposed methods through a theoretical analysis based on energy estimates we next compare the methods for one and two dimensional test cases in terms of both stability and accuracy of the numerical solutions the theoretical stability conditions are seen to be consistent with those observed in practice our analysis allows us to recommend using either the crank nicolson adams bashforth method or the second order semi implicit backward differention method these semi implicit methods produce a good numerical solution unlike the explicit methods their stability does not depend on the spatial grid size and unlike the implicit methods they do not require the resolution of a system of nonlinear equations

a lil type result for the product limit estimator let x1 x2 xn be i i d r v s with p x u f u and y1 y2 yn be i i d p y u g u where both f and g are unknown continuous survival functions for i 1 2 n set i 1 if xi yi and 0 if xi yi and zi min itxi yi one way to estimate f from the observations zi i i l n is by means of the product limit p l estimator fn kaplan meier 1958 6

strong approximations of some biometric estimates under random censorship the empirical distribution function has been widely used as an estimator for the distribution function of the elements of a random sample it is not however appropriate when the observations are incomplete this is the case for example when the observations have been randomly censored on the right in the latter case the so called product limit estimate of kaplan and meier 16 has been generally accepted as a substitute for the empirical distribution function and it possesses many of the same properties cf meier 19 developing the corresponding statement of efron 8 weak convergence over a finite interval of the kaplan meier product limit estimate to a gaussian process when there is censorship on the right has been obtained by breslow and crowley 3 cf also meier 19 breslow and crowley obtained their result via the limiting distribution of the closely related cumulative hazard process under random censorship a generalisation of the efron breslow crowley theorem was formulated by yang 24 for the case when censorship on the right is performed by more competing risks these results have numerous statistical applications in areas such as medical follow up studies life testing actuarial sciences and demography koziol and green 18 have computed tables for the limiting distribution of the cram6r von mises statistic based on the kaplan meier product limit estimate under a specific random censorship model a point will be stressed in this paper however that by a certain transformation which seems to have escaped many researchers attention and is due to efron 8 it is always possible to obtain the standard wiener process in the limit the distributions of many functionals of which are well known this transformation was only recently used in a stimulating note by gillespie and fisher 14 to construct asymptotic confidence bands for the unknown distribution function in the kaplan meier model a general scheme of random censorship can be defined in the following way let x be a real random variable with distribution function f t

character sum factorizations yield sequences with ideal two level autocorrelation we give a new existence criterion for p ary sequences which have ideal two level autocorrelation and we use it to obtain four general families of such sequences one for p 2 one for general odd primes p and two special ones for p 3 the binary family turns out to be equivalent to that discovered by dillon and dobbertin and published in 2004 the general p ary family is equivalent to that discovered by gong and helleseth by dillon and when p 3 by helleseth kumar and martinsen all of these p ary results were published in 2001 and 2002 the special ternary families are new and give as special cases the sequences conjectured by alfred lin in his 1998 ph d thesis as well as most of those conjectured in 2001 by ludkovski and gong our sequences may also be used to construct relative difference sets their corresponding block designs and generalized weighing matrices

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

a multilevel hybrid newton krylov schwarz method for the bidomain model of electrocardiology abstract a multilevel hybrid newton krylov schwarz nks method is constructed and studied numerically for implicit time discretizations of the bidomain reaction diffusion system in three dimensions this model describes the bioelectrical activity of the heart by coupling two degenerate parabolic equations with a stiff system of ordinary differential equations the nks bidomain solver employs an outer inexact newton iteration to solve the nonlinear finite element system originating at each time step of the implicit discretization the jacobian update during the newton iteration is solved by a krylov method employing a multilevel hybrid overlapping schwarz preconditioner additive within the levels and multiplicative among the levels several parallel tests on linux clusters are performed showing that the convergence of the method is independent of the number of subdomains scalability the discretization parameters and the number of levels optimality

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

new designs for signal sets with low cross correlation balance property and large linear span gf p case new designs for families of sequences over gf p with low cross correlation balance property and large linear span are presented the key idea of the new designs is to use short p ary sequences of period spl upsi with the two level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties the resulting sequences are interleaved sequences of period spl upsi sup 2 there are spl upsi cyclically shift distinct sequences in each family the maximal correlation value is 2 spl upsi 3 which is optimal with respect to the welch bound each sequence in the family is balanced and has large linear span in particular for binary case cross out of phase autocorrelation values belong to the set 1 spl upsi spl upsi 2 2 spl upsi 3 2 spl upsi 1 any sequence where the short sequences are quadratic residue sequences achieves the maximal linear span it is shown that some families of these sequences can be implemented efficiently in both hardware and software

partial likelihood estimation in categorical time series with stochastic covariates this paper presents an approach to statistical inference in markov regression models with stochastic covariates when the outcome variable is multivariate discrete the problem was motivated by an analysis of the influence of sea water density on plankton abundance the model is cast in semiparametric form so that only the regression function describing the dependence of outcomes on past observations and covariates is explicitly parameterised under general conditions maximum partial likelihood estimators of the regression coefficients are shown to be consistent and asymptotically gaussian

new families of codebooks achieving the levenstein bound in this paper a construction of codebooks based on a set of bent functions satisfying certain conditions is introduced it includes some earlier constructions of codebooks meeting the levenstein bound as special cases with this construction two new families of codebooks achieving the levenstein bound are obtained the codebooks constructed in this paper could have a very small alphabet size

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

bootstrapping the kaplan meier estimator abstract randomly censored data consist of iid pairs of observations xi i i 1 n if i 0 xi denotes a censored observation and if i 1 xi denotes an exact survival time which is the variable of interest for estimating the distribution f of the survival times the product limit estimator proposed by kaplan and meier 1958 has been studied extensively and it has been shown to enjoy a number of optimality properties wellner 1982 see gill 1980 chaps 1 4 1983 for a modern treatment and for references with censored data bootstrapping can be carried out using two different resampling plans introduced by efron 1981 and reid 1981 respectively with efron s plan one takes a random sample with replacement from x 1 xn n whereas with reid s plan one takes a random sample from the kaplan meier estimator the purpose of this article is to study the asymptotic behavior of the bootstrapped kaplan meier estimator with both resampling plans the approach adopted uses the

efficient estimation from right censored data when failure indicators are missing at random the kaplan meier estimator of a survival function is well known to be asymptotically efficient when cause of failure is always observed it has been an open problem however to find an efficient estimator when failure indicators are missing at random lo showed that nonparametric maximum likelihood estimators are inconsistent and this has led to several proposals of ad hoc estimators none of which are efficient we now introduce a sieved nonparametric maximum likelihood estimator and show that it is efficient our approach is related to the estimation of a bivariate survival function from bivariate right censored data 1 introduction suppose that we wish to estimate a survival distribution based on right censored data when cause of failure is always observed the method of nonparametric maximum likelihood leads to the well studied kaplan meier 1958 estimator which has many desirable properties including asymptotic efficiency wellner 1982 in this paper we address the problem of finding an asymptotically efficient estimator when cause of failure information is missing for some individuals

parametric models for response biased sampling summary suppose that subjects in a population follow the model f y lx 6 where y denotes a response x denotes a vector of covariates and 6 is the parameter to be estimated we consider response biased sampling in which a subject is observed with a probability which is a function of its response such response biased sampling frequently occurs in econometrics epidemiology and survey sampling the semiparametric maximum likelihood estimate of 6 is derived along with its asymptotic normality efficiency and variance estimates the estimate proposed can be used as a maximum partial likelihood estimate in stratified response selective sampling some computation algorithms are also provided

regression m estimators with doubly censored data the m estimators are proposed for the linear regression model with random design when the response observations are doubly censored the proposed estimators are constructed as some functional of a campbell type estimator f n for a bivariate distribution function based on data which are doubly censored in one coordinate we establish strong uniform consistency and asymptotic normality of f n and derive the asymptotic normality of the proposed regression m estimators through verifying their hadamard differentiability property as corollaries we show that our results on the proposed m estimators also apply to other types of data such as uncensored observations bivariate observations under univariate right censoring bivariate right censored observations and so on computation of the proposed regression m estimators is discussed and the method is applied to a doubly censored data set which was encountered in a recent study on the age dependent growth rate of primary breast cancer

adjustment for missingness using auxiliary information in semiparametric regression in this article we study the estimation of mean response and regression coefficient in semiparametric regression problems when response variable is subject to nonrandom missingness when the missingness is independent of the response conditional on high dimensional auxiliary information the parametric approach may misspecify the relationship between covariates and response while the nonparametric approach is infeasible because of the curse of dimensionality to overcome this we study a model based approach to condense the auxiliary information and estimate the parameters of interest nonparametrically on the condensed covariate space our estimators possess the double robustness property i e they are consistent whenever the model for the response given auxiliary covariates or the model for the missingness given auxiliary covariate is correct we conduct a number of simulations to compare the numerical performance between our estimators and other existing estimators in the current missing data literature including the propensity score approach and the inverse probability weighted estimating equation a set of real data is used to illustrate our approach

on the linear complexity of some new q ary sequences some new q ary sequences with period q 3 e k 1 q p m p an odd prime m e k integers are first constructed and then inspired by antweiler s method their linear complexity is examined the exact value of linear complexity k 6e w is determined when email protected i 1 wp e i furthermore an upper bound of the linear complexity is given for the other values of r our results show that this sequence has larger linear span than gmw sequence with the same parameters finally the results of a maple program are included to illustrate the validity of the results

minimum distance estimators of scale with censored data abstract this article examines how the level of censoring affects the performance of estimators of scale that minimize a weighted cramervon mises distance between the kaplan meier product limit estimator of the survival distribution function and an assumed model the article shows that under certain conditions these estimators are asymptotically normal if the survival function is a member of the assumed scale family weights that minimize the asymptotic variance under these conditions also are found under stronger conditions the minimum distance estimators mde s are asymptotically normal even if the survival function is not a member of the assumed scale family asymptotic coverage probabilities of confidence intervals are found for percentiles constructed from exponential mde s of scale under departures from the exponential distribution and what happens in the limiting cases of no censoring and complete censoring is examined using the asymptotic results and monte carlo experiments several exponenti

on estimation and adaptive estimation for locally asymptotically normal families locally asymptotically minimax lam estimates are constructed for locally asymptotically normal lan families under very mild additional assumptions adaptive estimation is also considered and a sufficient condition is given for an estimate to be locally asymptotically minimax adaptive incidently it is shown that a well known lower bound due to hajek 1972 for the local asymptotic minimax risk is not sharp

a new family of nonbinary sequences with three level correlation property and large linear span in this correspondence we present a new family of nonbinary sequences with three level nontrivial correlations and large linear complexity the sequences may be considered as nonlinear analogues of the well known sequences by trachtenberg and helleseth it is shown that the family is optimal with respect to the welch bound in terms of root mean square of all nontrivial correlations we also determine the correlation distribution of the new family

nearest neighbor estimation of a bivariate distribution under random censoring we consider the problem of estimating the bivariate distribution of the random vector x y when y may be subject to random censoring the censoring variable c is allowed to depend on x but it is assumed that y and c are conditionally independent given x x the estimate of the bivariate distribution is obtained by averaging estimates of the conditional distribution of y given x x over a range of values of x the weak convergence of the centered estimator multiplied by n 1 2 is obtained and a closed form expression for the covariance function of the limiting process is given it is shown that the proposed estimator is optimal in the beran sense this is similar to an optimality property the product limit estimator enjoys using the proposed estimator of the bivariate distribution an extension of the least squares estimator to censored data polynomial regression is obtained and its asymptotic normality established

the behavior of symmetric krylov subspace methods for solving mx m γi v abstract we analyze the behavior of krylov subspace methods for the solution of the symmetric system mx m i v when is close to some of the extreme eigenvalues of m we show that a stagnation phase may occur if the structure of the right hand side is not taken into account and we analyze the occurrence and persistence of such stagnation a natural alternative strategy is proposed and we show that the new approach provides a better approximation with the same number of matrix vector multiplications numerical experiments are also included

asymptotically optimal bandwidth selection for kernel density estimators from randomly right censored samples abstract this paper makes two important contributions to the theory of bandwidth selection for kernel density estimators under right censorship first an asymptotic representation of the integrated squared error into easily understood variance and squared bias components is given second it is shown that if the bandwidth is chosen by the data based method of least squares cross validation then it is asymptotically optimal in a compelling sense a by product of the first part is an interesting comparison of the two most popular kernel estimators keywords nonparametric density estimation smoothing parameter

local likelihood and local partial likelihood in hazard regression in survival analysis the relationship between a survival time and a covariate is conveniently modeled with the proportional hazards regression model this model usually assumes that the covariate has a log linear effect on the hazard function in this paper we consider the proportional hazards regression model with a nonparametric risk effect we discuss estimation of the risk function and its derivatives in two cases when the baseline hazard function is parametrized and when it is not parametrized in the case of a parametric baseline hazard function inference is based on a local version of the likelihood function while in the case of a nonparametric baseline hazard we use a local version of the partial likelihood this results in maximum local likelihood estimators and maximum local partial likelihood estimators respectively we establish the asymptotic normality of the estimators it turns out that both methods have the same asymptotic bias and variance in a common situation even though the local likelihood method uses information about the baseline hazard function

binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation generated by the polynomial z sup d z 1 sup d we present a construction for binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation property using the polynomial z sup d z 1 sup d we show that the sequence obtained from the polynomial becomes an m sequence for certain values of d we also find a few values of d which yield new binary sequences with ideal autocorrelation property when m is 3k spl plusmn 1 where k is a positive integer these new sequences are represented using a trace function and the results are tabulated

a model based block triangular preconditioner for the bidomain system in electrocardiology we introduce a preconditioner for the solution of the bidomain system governing the propagation of action potentials in the myocardial tissue the bidomain model is a degenerate parabolic set of nonlinear reaction diffusion equations the nonlinear term describes the ion flux at the cellular level the degenerate nature of the problem results in a severe ill conditioning of its discretization our preconditioning strategy is based on a suitable adaptation of the monodomain model a simplified version of the bidomain one which is by far simpler to solve nevertheless is unable to capture significant features of the action potential propagation the monodomain preconditioner application to a non symmetric formulation of the bidomain system results at the algebraic level in a lower block triangular preconditioner we prove optimality of the preconditioner with respect to the mesh size and corroborate our theoretical results with 3d numerical simulations both on idealized and real ventricle geometries

asymptotic optimality of the product limit estimator the product limit estimator due to kaplan and meier 1958 is well known to be the nonparametric maximum likelihood estimator of a distribution function based on censored data it is shown here that the product limit estimator is an asymptotically optimal estimator in two senses in the sense of a hajek beran type representation theorem for regular estimators and in an asymptotic minimax sense similar to the classical result for the uncensored case due to dvoretzky kiefer and wolfowitz 1956 the proofs rely on the methods of beran 1977 and millar 1979

binary time series modeling with application to adhesion frequency experiments repeated adhesion frequency assay is the only published method for measuring the kinetic rates of cell adhesion cell adhesion plays an important role in many physiological and pathological processes traditional analysis of adhesion frequency experiments assumes that the adhesion test cycles are independent bernoulli trials this assumption often can be violated in practice motivated by the analysis of repeated adhesion tests a binary time series model incorporating random effects is developed a goodness of fit statistic is introduced to assess the adequacy of distribution assumptions on the dependent binary data with random effects the asymptotic distribution of the goodness of fit statistic is derived and its finite sample performance is examined through a simulation study application of the proposed methodology to real data from a t cell experiment reveals some interesting information including the dependency between repeated adhesion tests

divisible difference sets relative difference sets and sequences with ideal autocorrelation abstract in this correspondence we consider the equivalent condition that a sequence possesses ideal autocorrelation function as we know for a binary sequence the equivalent condition is that the characteristic class of this sequence consists of two cyclic difference sets this paper proves that for a p ary sequence with d form property the equivalent condition is that its characteristic class consists of one cyclic divisible difference sets and p 1 relative difference sets moreover a new way to construct cyclic divisible difference sets is presented

some new classes of zero difference balanced functions zero difference balanced zdb functions were introduced recently by ding for the construction of optimal constant composition codes and optimal and perfect difference systems of sets they are closely related to partitioned difference families in this paper we present generic constructions of zdb functions from functions with difference balanced property in particular two classes of zdb functions with new and flexible parameters are reported employing these new zdb functions we obtain at the same time optimal 1 constant composition codes 2 constant weight codes and 3 perfect difference systems of sets all with new and flexible parameters

conditional score functions some optimality results summary the conditional score function has previously been shown to generate the optimal estimating equation for a parameter of interest when the conditioning statistic is complete and sufficient for the nuisance parameters godambe 1976 the present paper generalizes these results to partial likelihood factorizations and then examines the nature of the problem when the appropriate conditioning statistics depend on the parameter of interest in this case globally optimal estimating functions are impossible a weaker criterion of optimal weighting leads to a class of estimated conditional score functions which satisfy an information equality the purpose of this paper is to develop and justify an approach based on conditional likelihood to estimation in the presence of nuisance parameters the arguments focus on the case when there is a complete and sufficient statistic s 0 for the nuisance parameters when the parameter of interest 0 is fixed an extended notion of completeness will be presented in the context of partial likelihoods the problem takes on two separate natures depending on whether the statistic s 0 truly depends on 0 or not if s s 0 is free of 0 then the conditional likelihood of the data given s has been shown to generate optimal inferential procedures giving a best estimating equation godambe 1976 and a best asymptotically normal estimator in a mixture setting lindsay 1980 if s 0 depends on 0 then it will be shown that the best estimating equation also a conditional likelihood score will generally be only locally optimal leaving no single best strategy consideration of an optimal weighting strategy yields estimators which have second order properties similar to the conditional likelihoods of the first type

the convergence of linear stationary iterative processes for solving singular unstructured systems of linear equations this paper reviews the convergence properties of linear stationary iterative processes for solving large unstructured systems of linear equations special attention is given to the case where the system to be solved is singular and possibly inconsistent the review starts by investigating the iteration bf x k 1 h bf x k bf f k 0 1 2 cdots when the system i h bf x bf f is inconsistent in this case the sequence left bf x k right always diverges nevertheless when h is convergent there exists a vector bf q in text null i h such that the sequence hat bf x k bf x k k bf q converges the limit of this sequence hat bf x solves a certain least squares problem and the sequence of residual vectors bf r k i h bf x k bf f converges to i h hat bf x bf f furthermore if h is similar to a real diagonal matrix then the corresponding norms of bf r k and hat bf x k hat bf x decr

implicit explicit methods for time dependent partial differential equations implicit explicit imex schemes have been widely used especially in conjunction with spectral methods for the time integration of spatially discretized partial differential equations pdes of diffusion convection type typically an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection term reaction diffusion problems can also be approximated in this manner in this work we systematically analyze the performance of such schemes propose improved new schemes and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods for the prototype linear advection diffusion equation a stability analysis for first second third and fourth order multistep imex schemes is performed stable schemes permitting large time steps for a wide variety of problems and yielding appropriate decay of high frequency error modes are identified numerical experiments demonstrate that weak decay

efficient algebraic solution of reaction diffusion systems for the cardiac excitation process in this paper we deal with the problem of solving the large algebraic linear system arising in the numerical solution of a reaction diffusion r d system associated with myocardial excitation process modeling we show that an ad hoc preconditioning technique can be devised so as to efficiently and simultaneously handle the differential equations of the r d system with no additional memory requirements two different formulations are commonly considered for the theoretical and numerical analyses respectively we observe that the formulation employed for the theoretical analysis of the problem actually yields the best numerical performance when compared with the usual numerical scheme

projected partial likelihood and its application to longitudinal data summary an estimating equation which we call the projected partial score is introduced for longitudinal data analysis the estimating equation is obtained by projecting the partial likelihood score function onto the vector space spanned by a class of conditionally linear estimating equations we demonstrate that removing certain terms from the projection of the full likelihood score does not alter important inferential properties of the estimating equation and doing so is advantageous in handling missing data and time varying covariates within a prequential frame of reference it is shown that the estimating equation is optimal among the largest collection of estimating equations determined by the conditional moments furthermore the method possesses similar properties to generalised estimating equations in particular the correct conditional variance specification is necessary for efficiency but not for asymptotic consistency and distribution theory

binary pseudorandom sequences of period 2 sup n 1 with ideal autocorrelation in this correspondence we present five new classes of binary sequences of period 2 sup n 1 with ideal autocorrelation these sequences which correspond to new cyclic hadamard difference sets were found by extensive computer search conjectures on the general construction of these sequences are formulated

large sample study of empirical distributions in a random multiplicative censoring model consider an incomplete data problem with the following specifications there are three independent samples x 1 ldots x m z 1 ldots z n and u 1 ldots u n the first two samples are drawn from a common lifetime distribution function g while the third sample is drawn from the uniform distribution over the interval 0 1 in this paper we derive the large sample properties of hat g m n the nonparametric maximum likelihood estimate of g based on the observed data x 1 ldots x m and y 1 ldots y n where y i equiv z iu i i 1 ldots n the z s and u s are unobservable in particular we show that if m and n approach infinity at a suitable rate then sup t hat g m n t g t rightarrow 0 a s sqrt m n hat g m n g converges weakly to a gaussian process and the estimate hat g m n is asymptotically efficient in a nonparametric sense

profile likelihood and conditionally parametric models in this paper we outline a general approach to estimating the parametric component of a semiparametric model for the case of a scalar parametric component the method is based on the idea of first estimating a one dimensional subproblem of the original problem that is least favorable in the sense of stein the likelihood function for the scalar parameter along this estimated subproblem may be viewed as a generalization of the profile likelihood for the problem the scalar parameter is then estimated by maximizing this generalized profile likelihood this method of estimation is applied to a particular class of semiparametric models where it is shown that the resulting estimator is asymptotically efficient

non parametric maximum likelihood estimation of censored regression models abstract this paper presents a consistent estimator of a censored linear regression model which does not require knowledge of the distribution of the error term the estimator considered here applies duncan s 1982 suggestion that the likelihood function for the censored regression model be treated as a functional of both the unknown regression vector and the unknown error distribution our estimator is the majorizing regression vector for this non parametric likelihood functional we find conditions which ensure the consistency of the npmle the paper concludes with the results of monte carlo experiments which show the npmle to be more efficient than powell s least absolute deviations lad estimator particularly when the fraction of censored observations is large and the sample size is small

new nonbinary sequences with ideal two level autocorrelation we find new families of nonbinary sequences of period p sup n 1 with symbols from a finite field f sub p for any prime p spl ges 3 the sequences have two level ideal autocorrelation and are generalizations of previously found ternary sequences with ideal autocorrelation difference sets with parameters p sup n 1 p 1 p sup n 1 1 p 1 p sup n 2 1 p 1 can also be derived from these sequences in a natural way

a fully implicit finite element method for bidomain models of cardiac electromechanics we propose a novel monolithic and unconditionally stable finite element algorithm for the bidomainbased approach to cardiac electromechanics we introduce the transmembrane potential the extracellular potential and the displacement field as independent variables and extend the common two field bidomain formulation of electrophysiology to a three field formulation of electromechanics the intrinsic coupling arises from both excitation induced contraction of cardiac cells and the deformation induced generation of intra cellular currents the coupled reaction diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric galerkin approach as a novel aspect we propose a monolithic approach to solve the governing equations of excitation contraction coupling in a fully coupled implicit sense we demonstrate the consistent linearization of the resulting set of non linear residual equations to assess the algorithmic performance we illustrate characteristic features by means of representative three dimensional initial boundary value problems the proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes

nonparametric maximum likelihood estimation by the method of sieves maximum likelihood estimation often fails when the parameter takes values in an infinite dimensional space for example the maximum likelihood method cannot be applied to the completely nonparametric estimation of a density function from an operatorname iid sample the maximum of the likelihood is not attained by any density in this example as in many other examples the parameter space positive functions with area one is too big but the likelihood method can often be salvaged if we first maximize over a constrained subspace of the parameter space and then relax the constraint as the sample size grows this is grenander s method of sieves application of the method sometimes leads to new estimators for familiar problems or to a new motivation for an already well studied technique we will establish some general consistency results for the method and then we will focus on three applications

new cyclic relative difference sets constructed from d homogeneous functions with difference balanced property for a prime power q we show that a cyclic relative difference set with parameters q sup n 1 q 1 q 1 q sup n 1 q sup n 2 can be constructed from a d homogeneous function from f sub q sup n spl bsol 0 onto f sub q with difference balanced property where f sub q sup n is the finite field with q sup n elements this construction method enables us to construct several new cyclic relative difference sets with parameters p sup n 1 p sup l 1 p sup l 1 p sup n l p sup n 2l from p ary sequences of period p sup n 1 with ideal autocorrelation property introduced by helleseth and gong using a lifting idea other new cyclic relative difference sets can be constructed from the helleseth gong hg sequences also the 3 ranks and the trace representation of the characteristic sequences of cyclic relative difference sets from a specific class of ternary hg sequences and ternary lin sequences are derived

bpx preconditioners for the bidomain model of electrocardiology the aim of this work is to develop a bpx preconditioner for the bidomain model of electrocardiology this model describes the bioelectrical activity of the cardiac tissue and consists of a system of a non linear parabolic reaction diffusion partial differential equation pde and an elliptic linear pde modeling at macroscopic level the evolution of the transmembrane and extracellular electric potentials of the anisotropic cardiac tissue the evolution equation is coupled through the non linear reaction term with a stiff system of ordinary differential equations the so called membrane model describing the ionic currents through the cellular membrane the discretization of the coupled system by finite elements in space and semi implicit finite differences in time yields at each time step the solution of an ill conditioned linear system the goal of the present study is to construct analyze and numerically test a bpx preconditioner for the linear system arising from the discretization of the bidomain model optimal convergence rate estimates are established and verified by two and three dimensional numerical tests on both structured and unstructured meshes moreover in a full heartbeat simulation on a three dimensional wedge of ventricular tissue the bpx preconditioner is about 35 faster in terms of cpu times than ilu 0 and an algebraic multigrid preconditioner

efficient robust estimates in parametric models let p n an open subset ofr k be a regular parametric model for a sample ofn independent identically distributed observations this paper describes estimates t n n 1 of which are asymptotically efficient under the parametric model and are robust under small deviations from that model in essence the estimates are adaptively modified one step maximum likelihood estimates which adjust themselves according to how well the parametric model appears to fit the data when the fit seems poor t n discounts observations that would have large influence on the value of the usual one step mle the estimates t n are shown to be asymptotically minimax in the hajek lecam sense for a hellinger ball contamination model an alternative construction of robust asymptotically minimax estimates as modified mle s is described for canonical exponential families

a splitting preconditioner for a block two by two linear system with applications to the bidomain equations we construct an alternating splitting iteration scheme for solving and preconditioning a block two by two linear system arising from numerical discretizations of the bidomain equations the convergence theory of this class of splitting iteration methods is established and some useful properties of the preconditioned matrix are analyzed the potential of this approach is illustrated by numerical experiments

the proof of lin s conjecture via the decimation hadamard transform in 1998 lin presented a conjecture on a class of ternary sequences with ideal two level autocorrelation those sequences have a very simple structure i e their trace representation has two trace monomial terms in this paper we present a proof for the conjecture the mathematical tools employed are the second order multiplexing decimation hadamard transform stickelberger s theorem the teichmuller character and combinatorial techniques for enumerating the hamming weights of ternary numbers as a by product we also prove that the ternary sequences conjectured by lin are hadamard equivalent to ternary m sequences

new constructions for optimal sets of frequency hopping sequences in this paper two generic constructions of optimal frequency hopping sequence fhs sets employing d form functions with difference balanced property are presented they generalize the previous constructions of optimal fhs sets using m sequences and produce new optimal fhs sets that cannot be produced by the earlier constructions by choosing appropriate d form functions with difference balanced property both constructions lead to fhss with large linear complexity in addition one of the proposed constructions gives new optimal parameters of fhs sets

a three valued walsh transform from decimations of helleseth gong sequences the walsh transform of two level autocorrelation sequences has played an important role in the construction of the set of sequences in which any two sequences are orthogonal for p ary sequences there are only two basic classes of two level autocorrelation sequences with no subfield structures for an arbitrary odd prime p one is the class of p ary m sequences and the other is the class of p ary helleseth gong sequences in this paper the walsh transform of a subclass of p ary helleseth gong sequences and the walsh transform of their particular decimations are completely determined and are shown to be three valued

mixtures of experts of autoregressive time series asymptotic normality and model specification we consider a class of nonlinear models based on mixtures of local autoregressive time series at any given time point we have a certain number of linear models denoted as experts where the vector of covariates may include lags of the dependent variable additionally we assume the existence of a latent multinomial variable whose distribution depends on the same covariates as the experts that determines which linear process is observed this structure denoted as mixture of experts me is considerably flexible in modeling the conditional mean function as shown by jiang and tanner we present a formal treatment of conditions to guarantee the asymptotic normality of the maximum likelihood estimator mle under stationarity and nonstationarity and under correct model specification and model misspecification the performance of common model selection criteria in selecting the number of experts is explored via monte carlo simulations finally we present applications to simulated and real data sets to illustrate the ability of the proposed structure to model not only the conditional mean but also the whole conditional density

some results on cross correlation distribution between a p ary m sequence and its decimated sequences for an odd prime p and two positive integers m k such that m gcd k m 3 is odd let d be a positive integer satisfying d p k 1 2 mod p m 1 i n this paper the cross correlation between a p ary m sequence and its d decimated sequences is investigated and the cross correlation distribution is completely determined the relationship between the decimations d considered in this paper and some known ones is also studied this paper generalizes some previous results and also gives new decimations which lead to low cross correlation