vacuum expectation values of products of chiral currents in 3 1 dimensions an algebraic rule is presented for computing expectation values of products of local nonabelian charge operators for fermions coupled to an external vector potential in 3 1 space time dimensions the vacuum expectation value of a product of four operators is closely related to a cyclic cocycle in noncommutative geometry of alain connes the relevant representation of the current is constructed using kirillov s method of coadjoint orbits

universal schwinger cocycles of current algebras in d 1 dimensions geometry and physics we discuss the universal version of the schwinger terms of current algebra we call it the universal schwinger cocycle forp 3 herep denotes the class of the schatten ideali p which is related to the d 1 space time dimensions byp d 1 2 in detail and give a conjecture of the general form of the cocycle for anyp we also discuss the infinite charge renormalizations the highest weight vector and state vectors forp 3 last we give brief comments on the problems caused by the difficulties to construct the measure of infinite dimensional grassmann manifolds

estimating a treatment effect with repeated measurements accounting for varying effectiveness duration to assess treatment efficacy in clinical trials certain clinical outcomes are repeatedly measured over time for the same subject the difference in their means may characterize a treatment effect since treatment effectiveness lag and saturation times may exist erosion of treatment effect often occurs during the observation period instead of using models based on ad hoc parametric or purely nonparametric time varying coefficients we model the treatment effectiveness durations which are the time intervals between the lag and saturation times then we use some mean response models to include such treatment effectiveness durations our methodology is demonstrated by simulations and analysis of a landmark hiv aids clinical trial of short course nevirapine against mother to child hiv vertical transmission during labour and delivery

analysis of multi type recurrent events in longitudinal studies application to a skin cancer prevention trial we consider the statistical modeling and analysis of replicated multi type point process data with covariates such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types the underlying processes are modeled as nonhomogeneous mixed poisson processes with random subject and fixed covariate effects the method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients score tests and likelihood ratio statistics are used for covariate selection a graphical test of goodness of fit of the selected model is based on generalized residuals measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed an application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer

accuracy and cut off point selection in three class classification problems using a generalization of the youden index we study properties of the index j 3 defined as the accuracy or the maximum correct classification for a given three class classification problem specifically using j 3 one can assess the discrimination between the three distributions and obtain an optimal pair of cut off points c 1 c 2 in the sense that the sum of the correct classification proportions will be maximized it also serves as the generalization of the youden index in three class problems parametric and non parametric approaches for estimation and testing are considered and methods are applied to data from an mrs study on human immunodeficiency virus hiv patients

fractional loop group and twisted k theory we study the structure of abelian extensions of the group l q g of q differentiable loops in the sobolev sense generalizing from the case of the central extension of the smooth loop group this is motivated by the aim of understanding the problems with current algebras in higher dimensions highest weight modules are constructed for the lie algebra the construction is extended to the current algebra of the supersymmetric wess zumino witten model an application to the twisted k theory on g is discussed

likelihood ratio tests for a changepoint with survival data summary we consider the likelihood ratio test for a changepoint or lag of the effect of some covariates e g treatment in regression modelling of survival data subject to right censoring asymptotic distributions under null hypotheses are derived numerical examples are used to illustrate the implementation of the procedure finally we apply the theory to data from a large randomised cancer prevention trial

inference under right censoring for transformation models with a change point based on a covariate threshold we consider linear transformation models applied to right censored survival data with a change point in the regression coefficient based on a covariate threshold we establish consistency and weak convergence of the nonparametric maximum likelihood estimators the change point parameter is shown to be n consistent while the remaining parameters are shown to have the expected root n consistency we show that the procedure is adaptive in the sense that the nonthreshold parameters are estimable with the same precision as if the true threshold value were known we also develop monte carlo methods of inference for model parameters and score tests for the existence of a change point a key difficulty here is that some of the model parameters are not identifiable under the null hypothesis of no change point simulation studies establish the validity of the proposed score tests for finite sample sizes

approximating the distribution of maximally selected mcnemar s statistics summary it is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold with paired data and with a threshold chosen without reference to the outcomes mcnemar s test of marginal homogeneity may be applied to the resulting dichotomous pairs when testing for equality of the marginal distributions of the underlying continuous outcomes if the threshold is chosen to maximize the test statistic however referring the resulting test statistic to the nominal x2 distribution is incorrect instead the p value must be adjusted for the multiple comparisons here the distribution of a maximally selected mcnemar s statistic is derived and it is shown that an approximation due to durbin 1985 journal of applied probability22 99 122 may be used to estimate approximate p values the methodology is illustrated by an application to measurements of insulin like growth factor i igf i in matched prostate cancer cases and controls from the physicians health study the results of simulation experiments that assess the accuracy of the approximation in moderate sample sizes are reported

maximally selected chi square statistics two samples can be compared by selecting a cut point and then forming a 2 x 2 table of the numbers of observations above and below the cut point in each sample when the cut point is selected so as to maximize the standard chi square statistic the chi square percentile points are inappropriate actual significance levels are computed for large samples and correct percentile poillts are tabulated

group actions on c algebras 3 cocycles and quantum field theory we study group extensions where acts on a c algebraa given a twisted covariant representation v of the paira we construct 3 cocycles on with values in the centre of the group generated byv these 3 cocycles are obstructions to the existence of an extension of byv which acts ona compatibly with the main theorems of the paper introduce a subsidiary invariant which classifies actions of onv and in terms of which a necessary and sufficient condition for the the cohomology class of the 3 cocycle to be non trivial may be formulated examples are provided which show how non trivial 3 cocycles may be realised the framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories we show how to interpret our results in that setting in two ways one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups in order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a lie algebra version of the invariant and the 3 cocycle

maximally selected chi square statistics for small samples two samples can be compared by selecting a cut point and forming a 2 x 2 table of the numbers of observations above and below the cut point in each sample different cut points correspond to the maximum chi square statistic the maximum squared log odds ratio and the generalized kolmogorov smirnov statistic we simulated the small sample null distribution of these statistics the distributions of the maximally selected chi square statistic and the squared log odds ratio statistic are compared to each other and to the large sample results of miller and siegmund 1982 biometrics 38 1011 1016 the distributions of and agreement among the three cut points are also considered

on asymptotically optimal tests under loss of identifiability in semiparametric models we consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models where regularity conditions for profile likelihood theory fail exponential average tests based on integrated profile likelihood are constructed and shown to be asymptotically optimal under a weighted average power criterion with respect to a prior on the nonidentifiable aspect of the model these results extend existing results for parametric models which involve more restrictive assumptions on the form of the alternative than do our results moreover the proposed tests accommodate models with infinite dimensional nuisance parameters which either may not be identifiable or may not be estimable at the usual parametric rate examples include tests of the presence of a change point in the cox model with current status data and tests of regression parameters in odds rate models with right censored data optimal tests have not previously been studied for these scenarios we study the asymptotic distribution of the proposed tests under the null fixed contiguous alternatives and random contiguous alternatives we also propose a weighted bootstrap procedure for computing the critical values of the test statistics the optimal tests perform well in simulation studies where they may exhibit improved power over alternative tests

testing for change point in the covariate effects based on the cox regression model models with change point in covariates have wide applications in cancer research with the response being the time to a certain event a cox model with change point in covariate is considered at which the pattern of the change point effects can be flexibly specified to test for the existence of the change point effects three statistical tests namely the maximal score maximal normalized score and maximal wald tests are proposed the asymptotic properties of the test statistics are established monte carlo approaches to simulate the critical values are suggested a large scale simulation study is carried out to study the finite sample performance of the proposed test statistics under the null hypothesis of no change points and various alternative hypothesis settings each of the proposed methods provides a natural estimate for the location of the change point but it is found that the performance of the maximal score test can be sensitive to the true location of the change point in some cases while the performance of the maximal wald test is very satisfactory in general even in cases with moderate sample size for illustration the proposed methods are applied to two medical datasets concerning patients with primary biliary cirrhosis and breast cancer respectively

asymptotic score statistic processes and tests for constant hazard against a change point alternative the problem of testing for a constant failure rate against alternatives with failure rates involving a single change point is considered the asymptotic significance level for tests based on maximal score statistics are shown to involve the solution to a first passage time problem for an ornstein uhlenbeck process an example illustrates the methodology

multi threshold accelerated failure time model a two stage procedure for simultaneously detecting multiple thresholds and achieving model selection in the segmented accelerated failure time aft model is developed in this paper in the first stage we formulate the threshold problem as a group model selection problem so that a concave 2 norm group selection method can be applied in the second stage the thresholds are finalized via a refining method we establish the strong consistency of the threshold estimates and regression coefficient estimates under some mild technical conditions the proposed procedure performs satisfactorily in our simulation studies its real world applicability is demonstrated via analyzing a follicular lymphoma data

a comparison of algorithms for maximum likelihood estimation of choice models abstract maximum likelihood estimation mle is often avoided in econometric and other statistical applications due to computational considerations despite its strong theoretical appeal recent advances in non linear optimization provide feasible alternative methods for calculating mle s especially when special structure may be exploited as for example in probabilistic choice models this paper examines a range of quasi newton methods and gives numerical comparisons based on the multinomial logit model and a non independence of irrelevant alternative model among the issues considered are step determination and methods of approximating the hessian these include standard secant updates dfp and bfgs statistical approximations bhhh and recently developed approaches which use model switching

aalen additive hazards change point model we study a test comparing the full aalen additive hazards model and the change point model and suggest how to estimate the parameters of the change point model we also study a test for no change point effect both tests are provided with large sample properties and a resampling method is applied to obtain p values the finite sample properties of the proposed inference procedures and estimators are assessed through a simulation study the methods are further applied to a dataset concerning myocardial infarction

current algebras in d 1 dimensions and determinant bundles over infinite dimensional grassmannians we extend the methods of pressley and segal for constructing cocycle representations of the restricted general linear group in infinite dimensions to the case of a larger linear group modeled by schatten classes of rank 1 p an essential ingredient is the generalization of the determinant line bundle over an infinite dimensional grassmannian to the case of an arbitrary schatten rank p 1 the results are used to obtain highest weight representations of current algebras with the operator schwinger terms ind 1 dimensions when the space dimensiond is any odd number

weighted log rank type statistics for comparing survival curves when there is a time lag in the effectiveness of treatment summary in certain long term treatment trials one expects some lag period before the treatment is fully effective this paper presents two weighted log rank type statistics designed to have good efficiency over a wide range of lags a maximin efficiency robust statistic and a simplified version of this statistic both statistics can be computed as easily as the log rank statistic asymptotic efficiency calculations supported by small sample simulations show that the two proposed statistics are substantially more efficient than the conventional log rank statistic in certain lag situations with comparatively little efficiency loss relative to the log rank statistic when no lag exists we recommend the maximin statistic for situations where a lag is expected but cannot be specified precisely in advance

fermion current algebras and schwinger terms in 3 1 dimensions we discuss the restricted linear group in infinite dimensions modeled by the schatten class of rank 2p 4 which contains the 3 1 dimensional analogs of the loop groups and is closely related to yang mills theory with fermions in 3 1 dimensions we give an alternative to the construction of the highest weight representation of this group found by mickelsson and rajeev our approach is close to quantum field theory with the elements of this group regarded as bogoliubov transformations for fermions in an external yang mills field though these cannot be unitarily implemented in the physically relevant representation of the fermion field algebra we argue that they can be implemented by sesquilinear forms and that there is a regularized product of forms providing an appropriate group structure on the lie algebra level this gives an explicit non perturbative construction of fermion current algebras in 3 1 space time dimensions which explicity shows that the wave function renormalization required for a consistent definition of the currents and their lie bracket naturally leads to the schwinger term identical with the mickelsson rajeev cocycle though the explicit form of the schwinger term is given only for the casep 2 our arguments apply also to the restricted linear groups modeled by schatten classes of rank 2p 6 8 corresponding to current algebras in d 1 dimensions d 5 7

models for survival data from cancer prevention studies summary we propose a new parametric survival model for cancer prevention studies the formulation of the model is in the spirit of stochastic modelling of the occurrences of tumours through two stages initiation of an undetected tumour and promotion of the tumour to a detectable cancer several novel properties of the model proposed are derived in addition we examine the relationship of our model with the existing lagged regression model of zucker and lakatos also we bridge the difference between two distinct stochastic modelling methods for cancer data one used primarily for cancer therapeutic trials and the other used for cancer prevention trials

separable representations for automorphism groups of infinite symmetric spaces abstract in this paper we consider the separable unitary representations for the automorphism groups of the classical infinite rank finsler symmetric spaces defined by schatten p classes often referred to as restricted groups following earlier work of ol shanskii and voiculescu it is shown that the spherical representations are always type i the form of the irreducible spherical functions is determined and their analyticity established using an intuitive geometric argument it is shown that the real spherical functions extend to the hilbert schmidt limit and never beyond this yields a complete determination of the separable representations for groups corresponding to p classes with p 2

current algebra representation for the 3 1 dimensional dirac yang mills theory the structure of the current algebra representation in the state space of fermions in an external yang mills field in 3 1 space time dimensions is analyzed the topology of the vector space is determined by a countable family of semi definite inner products we show that there is no hermitian non trivial hilbert space representation such that the energy is bounded from below the structure of the hilbert space for the quantized coupled dirac yang mills system is discussed and the existence of the vacuum vector and the cancellation of commutator anomalies is described in terms of complex line bundles over infinite dimensional grassmannians

identifying optimal risk windows for self controlled case series studies of vaccine safety in vaccine safety studies subjects are considered at increased risk for adverse events for a period of time after vaccination known as risk window to our knowledge risk windows for vaccine safety studies have tended to be pre defined and not to use information from the current study inaccurate specification of the risk window can result in either including the true control period in the risk window or including some of the risk window in the control period which can introduce bias we propose a data based approach for identifying the optimal risk windows for self controlled case series studies of vaccine safety the approach involves fitting conditional poisson regression models to obtain incidence rate ratio estimates for different risk window lengths for a specified risk window length l the average time at risk t l is calculated when the specified risk window is shorter than the true the incidence rate ratio decreases with 1 t l increasing but there is no explicit relationship when the specified risk window is longer than the true the incidence rate ratio increases linearly with 1 t l increasing theoretically the risk window with the maximum incidence ratio is the optimal risk window because of sparse data problem we recommend using both the maximum incidence rate ratio and the linear relationship when the specified risk window is longer than the true to identify the optimal risk windows both simulation studies and vaccine safety data applications show that our proposed approach is effective in identifying medium and long risk windows

convergence theorems for least change secant update methods the purpose of this paper is to present a convergence analysis of least change secant methods in which part of the derivative matrix being approximated is computed by other means the theorems and proofs given here can be viewed as generalizations of those given by broyden dennis more j inst math appl 12 1973 pp 223 246 and by dennis more math comp 28 1974 pp 549 560 the analysis is done in the orthogonal projection setting of dennis schnabel siam rev 21 1980 pp 443 459 and many readers might feel that it is easier to understand the theorems here readily imply local and q superlinear convergence of all the standard methods in addition to proving these results for the first time for the sparse symmetric method of marwil and toint and the nonlinear least squares method of dennis gay welsch

on the mickelsson faddeev extension and unitary representations the mickelsson faddeev extension is a 3 space analogue of a kac moody group where the central charge is replaced by a space of functions of the gauge potential this extension is a pullback of a universal extension where the gauge potentials are replaced by operators in a schatten ideal as in non commutative differential geometry our main result is that the universal extension cannot be faithfully represented by unitary operators on a separable hilbert space we also examine potential consequences of the existence of unitary representations for the mickelsson faddeev extension

realizing 3 cocycles as obstructions the occurrence of a 3 cocycle in quantum mechanics or quantum field theory has been interpreted somewhat paradoxically as a breakdown of the jacobi identity the main result of this paper is that the 3 cocycle in chiral qcd arises as an obstruction which prevents the existence of a certain extension of one lie algebra by another this obstruction may be avoided by constructing a modified lie algebra extension consisting of derivations on the algebra generated by the fields however the 3 cocycle then appears when an attempt is made to implement these derivations by commutation with unbounded operators in the canonical equal time formalism assuming the existence of these unbounded operators is what leads to the violation of the jacobi identity

schwinger terms and cohomology of pseudodifferential operators we study the cohomology of the schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra we prove that for all pseudodifferential operators in 3 1 dimensions of this type the schwinger term is equivalent to the twisted radul cocycle a modified version of the radul cocycle arising in non commutative differential geometry in the process we also show how the ordinary radul cocycle for any pair of pseudodifferential operators in any dimension can be written as the phase space integral of the star commutator of their symbols projected to the appropriate asymptotic component

how bad are the bfgs and dfp methods when the objective function is quadratic we study the use of the bfgs and dfp algorithms with step lengths of one for minimizing quadratic functions of only two variables the updating formulae in this case imply nonlinear three term recurrence relations between the eigenvalues of consecutive second derivative approximations which are analysed in order to explain some gross inefficiencies that can occur specifically the bfgs algorithm may require more than 10 iterations to achieve the first decimal place of accuracy while the performance of the dfp method is far worse the results help to explain why the dfp method is often less suitable than the bfgs algorithm for general unconstrained optimization calculations and they show that quadratic functions provide much information about efficiency when the current vector of variables is too far from the solution for an asymptotic convergence analysis