local empirical likelihood inference for varying coefficient density ratio models based on case control data in this article we develop a varying coefficient density ratio model for case control studies the case and control samples come from two different distributions under the model assumption the ratio of the two densities is related to the linear combination of covariates with varying coefficients through a known function a special case is the exponential tilt model where the log ratio of the two densities is a linear function of covariates we propose a local empirical likelihood el approach to estimate the nonparametric coefficient functions under some regularity assumptions the proposed estimators are shown to be consistent and asymptotically normally distributed the sieve empirical likelihood ratio selr test statistic for detecting whether the varying coefficients are really constant and other related hypotheses is constructed and it follows approximately a chi squared distribution we introduce a modified bootstrap procedure to estimate the null distribution of the selr when sample size is s

inequalities and bounds for kernel length biased density estimation in this note non parametric estimates of the length biased probability density function and related reliability measures are presented non parametric estimates are also presented under random censoring inequalities and bounds for the error of kernel estimators used for the estimation of length biased probability densities are obtained non asymptotic bounds and stochastic convergence results are established inference for length biased energy functions is developed and implemented

subadditivity and additivity of the noncommutative yang mills action functional we formulate notions of subadditivity and additivity of the yang mills action functional in noncommutative geometry we identify a suitable hypothesis on spectral triples which proves that the yang mills functional is always subadditive the additivity property is stronger in the sense that it implies the subadditivity property under our hypothesis we also obtain a necessary and sufficient condition for the additivity of the yang mills functional an instance of additivity is shown for the case of noncommutative n tori we also investigate the behavior of critical points of the yang mills functional under additivity in the end we discuss examples involving compact spin manifolds matrix algebras noncommutative n torus and the quantum heisenberg manifolds to validate our hypothesis

the effect on the algebraic connectivity of a tree by grafting or collapsing of edges abstract let g v e be a tree on n 2 vertices and let v v let l g be the laplacian matrix of g and g be its algebraic connectivity let g k l be the graph obtained from g by attaching two new paths p vv 1 v 2 v k and q vu 1 u 2 u l of length k and l respectively at v we prove that if l k 1 then g k 1 l 1 g k l let v 1 v 2 be an edge of g let g be the tree obtained from g by deleting the edge v 1 v 2 and identifying the vertices v 1 and v 2 then we prove that g g as a corollary to the above results we obtain the celebrated theorem on algebraic connectivity which states that among all trees on n vertices the path has the smallest and the star has the largest algebraic connectivity

quantum heisenberg manifolds as twisted groupoid c algebras abstract the quantum heisenberg manifolds are noncommutative manifolds constructed by m rieffel as strict deformation quantizations of heisenberg manifolds and have been studied by various authors rieffel constructed the quantum heisenberg manifolds as the generalized fixed point algebras of certain crossed product c algebras and they also can be realized as crossed products of c t 2 by hilbert c bimodules in the sense of abadie et al in this paper we describe how the quantum heisenberg manifolds can also be realized as twisted groupoid c algebras in the final section for a transformation groupoid x z with x compact and e p x a locally trivial principal g bundle where g is a compact abelian group we form a groupoid that is a locally trivial principal g bundle over x z which reduces to the twist groupoid of the second author when g t

statistical models for intercepted data abstract consider a population of replaceable items of different ages and suppose that for each item there is a certain measurable attribute that is a monotone function perhaps random of the item s age to fix ideas we refer to this attribute as deterioration and we assume that as items age their level of deterioration increases we further assume that as the level of deterioration hits a certain threshold value perhaps unknown the item dies and disappears from the population so it is not available for sampling any more since items that deteriorate at a slower rate live longer any sample obtained over a short period of time would overrepresent slowly deteriorating items consequently under such circumstances longitudinal studies are often needed to statistically study deterioration as a function of age this article presents a statistical model that enables us to study the deterioration function from a single cross section snapshot of the population or some random parts of it specifically

an information matrix test for logistic regression models based on case control data summary we propose an information matrix based goodness of fit statistic to test the validity of the logistic regression model based on case control data by extending the information matrix test of white 1982 for detecting one sample parametric model misspecification to the semiparametric profile likelihood setting under a two sample semiparamnetric model which is equivalent to the assumed logistic regression model the proposed test statistic requires a high dimensional matrix inversion but is otherwise easily computed and has an asymptotic chi squared distribution this test statistic is an alternative to the kolmogorov smirnov type statistic of qin zhang 1997 and the chi squared type statistic of zhang 1999 and needs neither to employ a bootstrap method to evaluate its critical values nor to group the combined sample data into a finite number of mutually exclusive categories even when the underlying population distribution is continuous we demonstrate that the proposed test statistic and its asymptotic distribution may be obtained by fitting the prospective logistic regression model to case control data we present some results on simulation and on the analysis of three real datasets

non parametric tests for right censored data with biased sampling testing the equality of two survival distributions can be difficult in a prevalent cohort study when non random sampling of subjects is involved due to the biased sampling scheme independent censoring assumption is often violated although the issues about biased inference caused by length biased sampling have been widely recognized in statistical epidemiological and economical literature there is no satisfactory solution for efficient two sample testing we propose an asymptotic most efficient nonparametric test by properly adjusting for length biased sampling the test statistic is derived from a full likelihood function and can be generalized from the two sample test to a k sample test the asymptotic properties of the test statistic under the null hypothesis are derived using its asymptotic independent and identically distributed representation we conduct extensive monte carlo simulations to evaluate the performance of the proposed test statistics and compare them with the conditional test and the standard logrank test for different biased sampling schemes and right censoring mechanisms for length biased data empirical studies demonstrated that the proposed test is substantially more powerful than the existing methods for general left truncated data the proposed test is robust still maintains accurate control of type i error rate and is also more powerful than the existing methods if the truncation patterns and right censoring patterns are the same between the groups we illustrate the methods using two real data examples

empirical likelihood for right censored lifetime data abstractwhen the empirical likelihood el of a parameter is constructed with right censored data literature shows that 2log empirical likelihood ratio typically has an asymptotic scaled chi squared distribution where the scale parameter is a function of some unknown asymptotic variances therefore the el construction of confidence intervals for requires an additional estimation of the scale parameter additional estimation would reduce the coverage accuracy for by using a special influence function as an estimating function we prove that under very general conditions 2log empirical likelihood ratio has an asymptotic standard chi squared distribution with one degree of freedom this eliminates the need for estimating the scale parameter as well as eases some of the often demanding computations of the el method our estimating function yields a smaller asymptotic variance than those of wang and jing 2001 and qin and zhao 2007 thus it is not surprising that confidence intervals usi

the yang mills functional and laplace s equation on quantum heisenberg manifolds in this paper we discuss the yang mills functional and a certain family of its critical points on quantum heisenberg manifolds using noncommutative geometrical methods developed by a connes and m rieffel in our main result we construct a certain family of connections on a projective module over a quantum heisenberg manifold that gives rise to critical points of the yang mills functional moreover we show that there is a relationship between this particular family of critical points of the yang mills functional and laplace s equation on multiplication type skew symmetric elements of quantum heisenberg manifolds recall that laplacian is the leading term for the coupled set of equations making up the yang mills equation

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

yang mills connections on quantum heisenberg manifolds abstract we investigate critical points and minimizers of the yang mills functional ym on quantum heisenberg manifolds d c where the yang mills functional is defined on the set of all compatible linear connections on finitely generated projective modules over d c a compatible linear connection which is both a critical point and minimizer of ym is called a yang mills connection in this paper we investigate yang mills connections with constant curvature we are interested in yang mills connections on the following classes of modules over d c i abadie s module of trace 2 and its submodules ii modules of trace 2 iii tensor product modules of the form p e c where e c is morita equivalent to d c and p is a projection in e c we present a characterization of critical points and minimizers of ym and provide a class of new yang mills connections with constant curvature on over d c via concrete examples in particular we show that every yang mills connection on over d c with constant curvature should have a certain form of the curvature such as x y x z 0 and y z i id e also we show that these yang mills connections with constant curvature do not provide global minima but only local minima we do this by constructing a set of compatible connections that are not critical points but their values are smaller than those of yang mills connections with constant curvature our other results include i an example of a compatible linear connection with constant curvature on d c such that the corresponding connection on an isomorphic projective module does not have constant curvature and ii the construction of a compatible linear connection with constant curvature which neither attains its minimum nor is a critical point of ym on d c consequently the critical points and minimizers of ym depend crucially on the geometric structure of d c and of the projective modules over d c furthermore we construct the grassmannian connection on the projective modules with trace 2 over d c and compute its corresponding curvature finally we construct tensor product connections on p e c whose coupling constant is 2 and characterize the critical points of ym for this projective module

kernel density estimation for length biased data a new kernel density estimator for length biased data which derives from smoothing the nonparametric maximum likelihood estimator is proposed and investigated it has various advantages over an alternative method suggested by bhattacharyya franklin richardson 1988 it is necessarily a probability density it is particularly better behaved near zero it has better asymptotic mean integrated squared error properties and it is more readily extendable to related problems such as density derivative estimation

the algebraic connectivity of graphs under perturbation in this paper we investigate how the algebraic connectivity of a connected graph behaves when the graph is perturbed by separating or grafting an edge

yang mills on quantum heisenberg manifolds in the noncommutative geometry program of connes there are two variations of the concept of the yang mills action functional we show that for the quantum heisenberg manifolds for generic parameter values they agree

on the moduli space of a quantum heisenberg manifold we investigate the yang mills problem on a quantum heisenberg manifold d c in the setting of the non commutative differential geometry this problem was already studied by kang 2010 in 6 for a specific module over d c and kang obtained a family of connections which are critical points of the yang mills functional on but it turned out that they are neither minima nor maxima in this article we construct a connection 0 on and show that it is a minimum of the yang mills functional on the module moreover we give a certain family of minima including 0 and show that the moduli space for is non trivial

analysing bivariate survival data with interval sampling and application to cancer epidemiology in biomedical studies ordered bivariate survival data are frequently encountered when bivariate failure events are used as outcomes to identify the progression of a disease in cancer studies interest could be focused on bivariate failure times for example time from birth to cancer onset and time from cancer onset to death this paper considers a sampling scheme termed interval sampling in which the first failure event is identified within a calendar time interval the time of the initiating event can be retrospectively confirmed and the occurrence of the second failure event is observed subject to right censoring in a cancer data application the initiating first and second events could correspond to birth cancer onset and death the fact that the data are collected conditional on the first failure event occurring within a time interval induces bias interval sampling is widely used for collection of disease registry data by governments and medical institutions though the interval sampling bias is frequently overlooked by researchers this paper develops statistical methods for analysing such data semiparametric methods are proposed under semi stationarity and stationarity numerical studies demonstrate that the proposed estimation approaches perform well with moderate sample sizes we apply the proposed methods to ovarian cancer registry data

a theory of statistical models for monte carlo integration summary the task of estimating an integral by monte carlo methods is formulated as a statistical model using simulated observations as data the difficulty in this exercise is that we ordinarily have at our disposal all of the information required to compute integrals exactly by calculus or numerical integration but we choose to ignore some of the information for simplicity or computational feasibility our proposal is to use a semiparametric statistical model that makes explicit what information is ignored and what information is retained the parameter space in this model is a set of measures on the sample space which is ordinarily an infinite dimensional object none the less from simulated data the base line measure can be estimated by maximum likelihood and the required integrals computed by a simple formula previously derived by vardi and by lindsay in a closely related model for biased sampling the same formula was also suggested by geyer and by meng and wong using entirely different arguments by contrast with geyer s retrospective likelihood a correct estimate of simulation error is available directly from the fisher information the principal advantage of the semiparametric model is that variance reduction techniques are associated with submodels in which the maximum likelihood estimator in the submodel may have substantially smaller variance than the traditional estimator the method is applicable to markov chain and more general monte carlo sampling schemes with multiple samplers

ordering trees and graphs with few cycles by algebraic connectivity abstract several approaches for ordering graphs by spectral parameters are presented in the literature we can find graph orderings either by the greatest eigenvalue spectral radius or index or by the sum of the absolute values of the eigenvalues the energy of a graph or by the second smallest eigenvalue of the laplacian matrix the algebraic connectivity among others by considering the fact that the algebraic connectivity is related to the connectivity and shape of the graphs several structural properties of graphs relative to this parameter have been studied hence a large number of papers about ordering graphs by algebraic connectivity mainly about trees and graphs with few cycles have been published this paper surveys the significant results concerning these topics trying to focus on possible points to be investigated in order to understand the difficulties to obtain partial orderings via algebraic connectivity

estimation of incubation period and generation time based on observed length biased epidemic cohort with censoring for covid 19 outbreak in china the incubation period and generation time are key characteristics in the analysis of infectious diseases the commonly used contact tracing based estimation of incubation distribution is highly influenced by the individuals judgment on the possible date of exposure and might lead to significant errors on the other hand interval censoring based methods are able to utilize a much larger set of traveling data but may encounter biased sampling problems the distribution of generation time is usually approximated by observed serial intervals however it may result in a biased estimation of generation time especially when the disease is infectious during incubation in this paper the theory from renewal process is partially adopted by considering the incubation period as the interarrival time and the duration between departure from wuhan and onset of symptoms as the mixture of forward time and interarrival time with censored intervals in addition a consistent estimator for the distribution of generation time based on incubation period and serial interval is proposed for incubation infectious diseases a real case application to the current outbreak of covid 19 is implemented we find that the incubation period has a median of 8 50 days 95 confidence interval ci 7 22 9 15 the basic reproduction number in the early phase of covid 19 outbreak based on the proposed generation time estimation is estimated to be 2 96 95 ci 2 15 3 86

on the fiedler vectors of graphs that arise from trees by schur complementation of the laplacian abstract the utility of fiedler vectors in interrogating the structure of graphs has generated intense interest and motivated the pursuit of further theoretical results this paper focuses on how the fiedler vectors of one graph reveal structure in a second graph that is related to the first specifically we consider a point of articulation r in the graph g whose laplacian matrix is l and derive a related graph g r whose laplacian is the matrix obtained by taking the schur complement with respect to r in l we show how fiedler vectors of g r relate to the structure of g and we provide bounds for the algebraic connectivity of g r in terms of the connected components at r in g in the case where g is a tree with points of articulation r r we further consider the graph g r derived from g by taking the schur complement with respect to r in l we show that fiedler vectors of g r valuate the pendent vertices of g in a manner consistent with the structure of the tree

semiparametric model for bivariate survival data subject to biased sampling to better understand the relationship between patient characteristics and their residual survival after an intermediate event such as the local cancer recurrence it is of interest to identify patients with the intermediate event and then analyze their residual survival data one challenge in analyzing such data is that the observed residual survival times tend to be longer than those in the target population since patients who die before experiencing the intermediate event are excluded from the identified cohort we propose to jointly model the ordered bivariate survival data using a copula model and appropriately adjusting for the sampling bias we develop an estimating procedure to simultaneously estimate the parameters for the marginal survival functions and the association parameter in the copula model and use a two stage expectation maximization algorithm using empirical process theory we prove that the estimators have strong consistency and asymptotic normality we conduct simulations studies to evaluate the finite sample performance of the proposed method we apply the proposed method to two cohort studies to evaluate the association between patient characteristics and residual survival

maximum likelihood estimation under a successive sampling discovery model a common problem encountered in the analysis of discovery data is the size bias phenomenon in which the larger units tend to be discovered first one approach to account for this bias is to model the discovery process as sampling successively from a finite population without replacement and with probability proportional to size we consider in this article a generalized version of this model for analyzing multivariate data with any given measure of size we assume a superpopulation framework and develop procedures for maximum likelihood estimation of the parameters of the distribution the use of the em algorithm for computing the maximum likelihood estimates associated computational issues and relationships to regression estimators in survey sampling are discussed oil discovery data from the rimbey meadowbrook reef play are used to illustrate the techniques

analyzing length biased data with semiparametric transformation and accelerated failure time models right censored time to event data are often observed from a cohort of prevalent cases that are subject to length biased sampling informative right censoring of data from the prevalent cohort within the population often makes it difficult to model risk factors on the unbiased failure times for the general population because the observed failure times are length biased in this paper we consider two classes of flexible semiparametric models the transformation models and the accelerated failure time models to assess covariate effects on the population failure times by modeling the length biased times we develop unbiased estimating equation approaches to obtain the consistent estimators of the regression coefficients large sample properties for the estimators are derived the methods are confirmed through simulations and illustrated by application to data from a study of a prevalent cohort of dementia patients

low risk population size estimates in the presence of capture heterogeneity summary population estimation methods are used for estimating the size of a population from samples of individuals in many applications the probability of being observed in the sample varies across individuals resulting in sampling bias we show that in this setting estimators of the population size have high and sometimes infinite risk leading to large uncertainty in the population size as an alternative we propose estimating the population of individuals with observation probability exceeding a small threshold we show that estimators of this quantity have lower risk than estimators of the total population size the proposed approach is shown empirically to result in large reductions in mean squared error in a common model for capture recapture population estimation with heterogeneous capture probabilities

deformation quantization of heisenberg manifolds form a smooth manifold equipped with a poisson bracket we formulate ac algebra framework for deformation quantization including the possibility of invariance under a lie group of diffeomorphisms preserving the poisson bracket we then show that the much studied non commutative tori give examples of such deformation quantizations invariant under the usual action of ordinary tori going beyond this the main results of the paper provide a construction of invariant deformation quantizations for those poisson brackets on heisenberg manifolds which are invariant under the action of the heisenberg lie group and for various generalizations suggested by this class of examples interesting examples are obtained of simplec algebras on which the heisenberg group acts ergodically

empirical likelihood based inference in missing response problems and its application in observational studies summary the problem of missing response data is ubiquitous in medical and social science studies in the case of responses that are missing at random depending on some covariate information analyses focused only on the complete data may lead to biased results various debias methods have been extensively studied in the literature particularly the weighting method that was motivated by horvitz and thompson s estimators to improve efficiency robins rotnitzky and zhao proposed augmented estimating equations based on corrected complete case analyses a nice feature of the augmented method is its double robustness i e the estimator that is derived from the augmented method is asymptotically unbiased if either the underlying missing data mechanism or the underlying regression function is correctly specified furthermore the augmented estimator can achieve full efficiency if both the missing data mechanism and the regression function are correctly specified in general however it is very difficult to specify the regression function correctly especially when the dimension of covariates is high this is the so called curse of dimensionality problem the augmented estimator has much lower efficiency if the working regression model is not close to the true regression model in this paper the empirical likelihood method is employed to seek a constrained empirical likelihood estimation of mean response with the assumption that responses are missing at random the empirical likelihood based estimators enjoy the double robustness property moreover it is possible that the empirical likelihood based inference can produce asymptotically unbiased and efficient estimators even if the true regression function is not completely known simulation results indicate that the empirical likelihood based estimators are very robust to a misspecification of the propensity score and dominate other competitors in the sense of having smaller mean square errors methods that are developed in this paper have a nice application in observational causal inferences the propensity score is used to adjust for differences in pretreatment variables in the estimation of average treatment effects

merging information for semiparametric density estimation summary the density ratio model specifies that the likelihood ratio of m 1 probability density functions with respect to the mth is of known parametric form without reference to any parametric model we study the semiparametric inference problem that is related to the density ratio model by appealing to the methodology of empirical likelihood the combined data from all the samples leads to more efficient kernel density estimators for the unknown distributions we adopt variants of well established techniques to choose the smoothing parameter for the density estimators proposed