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

differential geometry palatini gravity and reduction the present article deals with a formulation of the so called vacuum palatini gravity as a general variational principle in order to accomplish this goal some geometrical tools related to the geometry of the bundle of connections of the frame bundle lm are used a generalization of lagrange poincare reduction scheme to these types of variational problems allows us to relate it with the einstein hilbert variational problem relations with some other variational problems for gravity found in the literature are discussed

dimension reduction in a semiparametric regression model with errors in covariates we consider a semiparametric estimation method for general regression models when some of the predictors are measured with error the technique relies on a kernel regression of the true covariate on all the observed covariates and surrogates this requires a nonparametric regression in as many dimensions as there are covariates and surrogates the usual theory copes with such higher dimensional problems by using higher order kernels but this is unrealistic for most problems we show that the usual theory is essentially as good as one can do with this technique instead of regression with higher order kernels we propose the use of dimension reduction techniques we assume that the true covariate depends only on a linear combination of the observed covariates and surrogates if this linear combination were known we could apply the one dimensional versions of the semiparametric problem for which standard kernels are applicable we show that if one can estimate the linear directions at the root n rate then asymptotically the resulting estimator of the parameters in the main regression model behaves as if the linear combination were known simulations lend some credence to the asymptotic results

conditional cumulant of exposure method in logistic missing covariate regression summary we consider estimation in logistic regression where some covariate variables may be missing at random satten and kupper 1993 journal of the american statistical association88 200 208 proposed estimating odds ratio parameters using methods based on the probability of exposure by approximating a partial likelihood we extend their idea and propose a method that estimates the cumulant generating function of the missing covariate given observed covariates and surrogates in the controls our proposed method first estimates some lower order cumulants of the conditional distribution of the unobserved data and then solves a resulting estimating equation for the logistic regression parameter a simple version of the proposed method is to replace a missing covariate by the summation of its conditional mean and conditional variance given observed data in the controls we note that one important property of the proposed method is that when the validation is only on controls a class of inverse selection probability weighted semiparametric estimators cannot be applied because selection probabilities on cases are zeros the proposed estimator performs well unless the relative risk parameters are large even though it is technically inconsistent small sample simulations are conducted we illustrate the method by an example of real data analysis

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

bias due to missing exposure data using complete case analysis in the proportional hazards regression model we studied bias due to missing exposure data in the proportional hazards regression model when using complete case analysis cca eleven missing data scenarios were considered one with missing completely at random mcar four missing at random mar and six non ignorable missingness scenarios with a variety of hazard ratios censoring fractions missingness fractions and sample sizes when missingness was mcar or dependent only on the exposure there was negligible bias 2 3 per cent that was similar to the difference between the estimate in the full data set with no missing data and the true parameter in contrast substantial bias occurred when missingness was dependent on outcome or both outcome and exposure for models with hazard ratio of 3 5 a sample size of 400 20 per cent censoring and 40 per cent missing data the relative bias for the hazard ratio ranged between 7 per cent and 64 per cent we observed important differences in the direction and magnitude of biases under the various missing data mechanisms for example in scenarios where missingness was associated with longer or shorter follow up the biases were notably different although both mechanisms are mar the hazard ratio was underestimated with larger bias when missingness was associated with longer follow up and overestimated with smaller bias when associated with shorter follow up if it is known that missingness is associated with a less frequently observed outcome or with both the outcome and exposure cca may result in an invalid inference and other methods for handling missing data should be considered

quantum and fisher information from the husimi and related distributions the two principal immediate influences which we seek to interrelate here upon the undertaking of this study are papers of yczkowski and slomczynski j phys a 34 6689 2001 and of petz and sudar j math phys 37 2262 1996 in the former work a metric the monge one specifically over generalized husimi distributions was employed to define a distance between two arbitrary density matrices in the petz sudar work completing a program of chentsov the quantum analog of the classically unique fisher information monotone metric of a probability simplex was extended to define an uncountable infinitude of riemannian also monotone metrics on the set of positive definite density matrices we pose here the questions of what is the specific unique fisher information metric for the classically defined husimi distributions and how does it relate to the infinitude of quantum metrics over the density matrices of petz and sudar we find a highly proximate small relative entropy relationship bet

a unified approach to regression analysis under double sampling designs we propose a unified approach to the estimation of regression parameters under double sampling designs in which a primary sample consisting of data on the rough or proxy measures for the response and or explanatory variables as well as a validation subsample consisting of data on the exact measurements are available we assume that the validation sample is a simple random subsample from the primary sample our proposal utilizes a specific parametric model to extract the partial information contained in the primary sample the resulting estimator is consistent even if such a model is misspecified and it achieves higher asymptotic efficiency than the estimator based only on the validation data specific cases are discussed to illustrate the application of the estimator proposed

semiparametric quasilikelihood and variance function estimation in measurement error models abstract we consider a quasilikelihood variance function model when a predictor x is measured with error and a surrogate w is observed when in addition to a primary data set containing y w a validation data set exists for which x w is observed we can i estimate the first and second moments of the response y given w by kernel regression ii use quasilikelihood and variance function techniques to estimate the regression parameters as well as variance structure parameters the estimators are shown to be asymptotically normally distributed with asymptotic variance depending on the size of the validation data set and not on the bandwith used in the kernel estimates a more refined analysis of the asymptotic covariance shows that the optimal bandwidth converges to zero at the rate n 1 3

regression analysis of doubly censored failure time data with applications to aids studies summary in many epidemiological studies the survival time of interest is the elapsed time between two related events the originating event and the failure event and the times of the occurrences of both events are right or interval censored we discuss the regression analysis of such studies and a simple estimating equation approach is proposed under the proportional hazards model the method can easily be implemented and does not involve any iteration among unknown parameters as full likelihood approaches proposed in the literature do the asymptotic properties of the proposed regression coefficient estimates are derived and an aids cohort study is analyzed to illustrate the proposed approach

further results on covariate measurement errors in cohort studies with time to response data the impact of covariate measurement errors on the estimation of relative risk regression parameters is discussed first the dependence of the induced relative risk process on the cumulative baseline failure rate function is noted next induced relative risk models under some specific failure time and measurement error models are described including the much simplified models that are appropriate under a rare disease assumption the presentation then turns to the joint estimation of relative risk parameters of primary interest along with measurement error parameters a partial likelihood product is proposed for such estimation and asymptotic properties are indicated guidance is also presented as to the appropriate size of a validation sample relative to the full cohort size finally some more general considerations are presented as to the usefulness and interpretation of deattenuated regression coefficients

missing data methods for generalized linear models a comparative review missing data is a major issue in many applied problems especially in the biomedical sciences we review four common approaches for inference in generalized linear models glms with missing covariate data maximum likelihood ml multiple imputation mi fully bayesian fb and weighted estimating equations wees there is considerable interest in how these four methodologies are related the properties of each approach the advantages and disadvantages of each methodology and computational implementation we examine data that are missing at random and nonignorable missing for ml we focus on techniques using the em algorithm and in particular discuss the em by the method of weights and related procedures as discussed by ibrahim for mi we examine the techniques developed by rubin for fb we review approaches considered by ibrahim et al for wee we focus on the techniques developed by robins et al we use a real dataset and a detailed simulation study to compare the four methods

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

logistic regression with incompletely observed categorical covariates a comparison of three approaches summary a logistic regression analysis based on the complete cases neglects the information due to subjects with missing values in at least one but not in all covariates three different approaches allowing the use of this information are compared maximum likelihood estimation pseudo maximum likelihood estimation and probability imputation the first two yield consistent estimates of the regression coefficients and asymptotic normality allows the construction of asymptotically valid confidence intervals the only necessary assumption is that the probability for the occurrence of missing values does not depend on the true value of the hidden covariates whereas there may be a dependence on completely observed covariates and on the outcome variable their relative efficiency and the gain relative to a complete case analysis is investigated comparison with imputation methods shows that imputation of conditional probabilities can be regarded as a close approximation to the pseudo maximum likelihood estimation whereas imputation of unconditional probabilities is associated with serious bias

comparing and combining biomarkers as principal surrogates for time to event clinical endpoints principal surrogate endpoints are useful as targets for phase i and ii trials in many recent trials multiple post randomization biomarkers are measured however few statistical methods exist for comparison of or combination of biomarkers as principal surrogates and none of these methods to our knowledge utilize time to event clinical endpoint information we propose a weibull model extension of the semi parametric estimated maximum likelihood method of huang and gilbert 1 that allows for the inclusion of multiple biomarkers in the same risk model as multivariate candidate principal surrogates we propose several methods for comparing candidate principal surrogates and evaluating multivariate principal surrogates these include the time dependent and surrogate dependent true and false positive fraction the time dependent and the integrated standardized total gain and the cumulative distribution function of the risk difference we illustrate the operating characteristics of our proposed methods in simulations and outline how these statistics can be used to evaluate and compare candidate principal surrogates we use these methods to investigate candidate surrogates in the diabetes control and complications trial

empirical likelihood inference in nonlinear errors in covariables models with validation data in this article we study inference in parametric nonparametric errors in covariables regression models using an empirical likelihood approach based on validation data it is shown that the asymptotic behavior of the proposed estimator depends on the ratio of the sizes of the primary sample and the validation sample respectively unlike cases without measurement errors the limit distribution of the estimator is no longer tractable and cannot be used for constructing confidence regions monte carlo approximations are employed to simulate the limit distribution to increase the coverage accuracy of confidence regions two adjusted empirical likelihood estimators are recommended which in the limit have a standard chi squared distribution a simulation study is carried out to compare the proposed methods with other existing methods the new methods outperform the least squares method and one of them works better than simulation extrapolation simex estimation even when the restrictive model assumptions n

an estimated likelihood method for continuous outcome regression models with outcome dependent sampling many biomedical observational studies attempt to relate a continuous outcome to an environmental exposure and other important covariates if the outcome is easier or cheaper to measure relative to the exposure of interest then the outcome may be observed for every member of a finite study population whereas exposure measurements may be obtained only for a relatively small subsample of this population rather than selecting a simple random subsample of individuals for exposure measurement investigators may attempt to enhance study efficiency by allowing the selection probabilities to depend on the observed outcomes we refer to such sampling schemes as outcome dependent sampling ods standard estimation methods that ignore the ods design will yield biased and inconsistent parameter estimates furthermore it is generally desirable to use estimators that incorporate all available data as analyses restricted to subjects with complete information are inefficient to this end we extend an estimated likel

reduction of poisson nijenhuis lie algebroids to symplectic nijenhuis lie algebroids with a nondegenerate nijenhuis tensor we show how to reduce under certain regularity conditions a poisson nijenhuis lie algebroid to a symplectic nijenhuis lie algebroid with a nondegenerate nijenhuis tensor we generalize the work done by magri and morosi for the reduction of poisson nijenhuis manifolds the choice of the more general framework of lie algebroids is motivated by the geometrical study of some reduced bi hamiltonian systems an explicit example of the reduction of a poisson nijenhuis lie algebroid is also provided

regression with missing x s a review abstract the literature of regression analysis with missing values of the independent variables is reviewed six classes of procedures are distinguished complete case analysis available case methods least squares on imputed data maximum likelihood bayesian methods and multiple imputation methods are compared and illustrated when missing data are confined to one independent variable and extensions to more general patterns are indicated attention is paid to the performance of methods when the missing data are not missing completely at random least squares methods that fill in missing x s using only data on the x s are contrasted with likelihood based methods that use data on the x s and y the latter approach is preferred and provides methods for elaboration of the basic normal linear regression model it is suggested that more widely distributed software is needed that advances beyond complete case analysis available case analysis and naive imputation methods bayesian simulation methods and mu

reduced classical field theories k cosymplectic formalism on lie algebroids in this paper we introduce a geometric description of lagrangian and hamiltonian classical field theories on lie algebroids in the framework of k cosymplectic geometry we discuss the relation between lagrangian and hamiltonian descriptions through a convenient notion of legendre transformation the theory is a natural generalization of the standard one in addition other interesting examples are studied mainly on reduction of classical field theories

nonparametric and semiparametric models for missing covariates in parametric regression robustness of covariate modeling for the missing covariate problem in parametric regression is studied under the missing at random assumption for a simple missing covariate pattern nonparametric covariate model is proposed and is shown to yield a consistent and semiparametrically efficient estimator for the regression parameter total robustness is achieved in this situation for more general missingcovariate patterns a novel semiparametric modeling approach is proposed for the covariates in this approach the covariate distribution is first decomposed into the product of a series of conditional distributions according to the overall missing data patterns and the conditional distributions are then represented in the general odds ratio form the general odds ratios are modeled parametrically and the other components of the covariate distribution are modeled nonparametrically maximum semiparametric likelihood is used to find the parameter estimates the proposed method yields a consistent estimator f

instrumental variable estimation in generalized linear measurement error models abstract instrumental variable estimation in generalized linear measurement error models are studied for models with canonical link functions unbiased estimating equations are derived the maximum likelihood estimator for the normal theory structural linear instrumental variable model is shown to be a solution to the estimating equations derived herein logistic regression is studied in detail an example is given and a simulation study described for the logistic model based on the framingham heart study data

pontryagin maximum principle on almost lie algebroids the fundamental theorem of the theory of optimal control the pontryagin maximum principle pmp is extended to the setting of almost lie al algebroids geometrical objects generalizing lie algebroids this formulation of the pmp yields in particular a scheme comprising reductions of optimal control problems similar to the reduction for the rigid body in analytical mechanics on the other hand in the presented approach the reduced and unreduced pmps are parts of the same universal formalism the framework is based on a very general concept of homotopy of measurable paths and the geometry of al algebroids

maximum likelihood inference on a mixed conditionally and marginally specified regression model for genetic epidemiologic studies with two phase sampling summary two phase stratified sampling designs can reduce the cost of genetic epidemiologic studies by limiting expensive ascertainments of genetic and environmental exposure to an efficiently selected subsample phase ii of the main study phase i family history and some covariate information which may be cheaply gathered for all subjects at phase i can be used for sampling of informative subjects at phase ii we develop alternative maximum likelihood methods for analysis of data from such studies by using a novel regression model that permits the estimation of marginal risk parameters that are associated with the genetic and environmental covariates of interest while simultaneously characterizing the conditional risk of the disease associated with family history after adjusting for the other covariates the methods and appropriate asymptotic theories are developed with and without an assumption of gene environment independence allowing the distribution of the environmental factors to remain non parametric the performance of the alternative methods and of sampling strategies is studied by using simulated data involving rare and common genetic variants an application of the methods proposed is illustrated by using a case control study of colorectal adenoma embedded within the prostate lung colorectal and ovarian cancer screening trial

k symplectic formalism on lie algebroids in this paper we introduce a geometric description of lagrangian and hamiltonian classical field theories on lie algebroids in the framework of k symplectic geometry we discuss the relation between the lagrangian and hamiltonian descriptions through a convenient notion of legendre transformation the theory is a natural generalization of the standard one in addition other interesting examples are studied in particular systems with symmetry and poisson sigma models

on surrogate dimension reduction for measurement error regression an invariance law we consider a general nonlinear regression problem where the predictors contain measurement error it has been recently discovered that several well known dimension reduction methods such as ols sir and phd can be performed on the surrogate regression problem to produce consistent estimates for the original regression problem involving the unobserved true predictor in this paper we establish a general invariance law between the surrogate and the original dimension reduction spaces which implies that at least at the population level the two dimension reduction problems are in fact equivalent consequently we can apply all existing dimension reduction methods to measurement error regression problems the equivalence holds exactly for multivariate normal predictors and approximately for arbitrary predictors we also characterize the rate of convergence for the surrogate dimension reduction estimators finally we apply several dimension reduction methods to real and simulated data sets involving measurement error to compare their performances

analysis of multivariate missing data with nonignorable nonresponse we consider multivariate regression analysis with missing data in the outcome variables when the nonresponse mechanism depends on the underlying values of the responses and hence is nonignorable related problems include response biased sampling where data are sampled with probability depending only on the univariate response our methods do not require specification of the form of the nonresponse mechanism we show that under certain regularity conditions all the regression parameters can be identified from a conditional likelihood based on the complete cases if the marginal distribution of the covariates is known if the marginal distribution of the covariates is estimated from the data then the regression parameters are identified from a pseudolikelihood resulting from substituting the estimated marginal distribution of the covariates in the above conditional likelihood simulation studies suggest that the pseudolikelihood method is approximately unbiased in order to identify the model parameters usually the dimension of the covariates and observed responses is required to be at least as large as the dimension of the missing responses the method can also be modified to handle partial information about the missing data mechanism we also consider the special case where the missing data have a monotone pattern where better use of the incomplete information can be made under certain assumptions

on the geometry of the hamilton jacobi equation and generating functions in this paper we develop a geometric version of the hamilton jacobi equation in the poisson setting specifically we geometrize what is usually called a complete solution of the hamilton jacobi equation we use some well known results about symplectic groupoids in particular cotangent groupoids as a keystone for the construction of our framework our methodology follows the ambitious program proposed by weinstein in mechanics day waterloo on 1992 volume 7 of fields institute communications american mathematical society providence 1996 in order to develop geometric formulations of the dynamical behavior of lagrangian and hamiltonian systems on lie algebroids and lie groupoids this procedure allows us to take symmetries into account and as a by product we recover results from channell and scovel phys d 50 1 80 88 1991 ge indiana univ math j 39 3 859 876 1990 ge and marsden phys lett a 133 3 134 139 1988 but even in these situations our approach is new a theory of generating functions for the poisson structures considered here is also developed following the same pattern solving a longstanding problem of the area how to obtain a generating function for the identity transformation and the nearby poisson automorphisms of poisson manifolds a direct application of our results gives the construction of a family of poisson integrators that is integrators that conserve the underlying poisson geometry these integrators are implemented in the paper in benchmark problems some conclusions current and future directions of research are shown at the end of the paper

causal inference in outcome dependent two phase sampling designs summary we consider estimation of the causal effect of a treatment on an outcome from observational data collected in two phases in the first phase a simple random sample of individuals is drawn from a population on these individuals information is obtained on treatment outcome and a few low dimensional covariates these individuals are then stratified according to these factors in the second phase a random subsample of individuals is drawn from each stratum with known stratum specific selection probabilities on these individuals a rich set of covariates is collected in this setting we introduce five estimators simple inverse weighted simple doubly robust enriched inverse weighted enriched doubly robust locally efficient we evaluate the finite sample performance of these estimators in a simulation study we also use our methodology to estimate the causal effect of trauma care on in hospital mortality by using data from the national study of cost and outcomes of trauma

random effects logistic regression analysis with auxiliary covariates summary we study a semiparametric estimation method for the random effects logistic regression when there is auxiliary covariate information about the main exposure variable we extend the semiparametric estimator of pepe and fleming 1991 journal of the american statistical association86 108 113 to the random effects model using the best linear unbiased prediction approach of henderson 1975 biometrics31 423 448 the method can be used to handle the missing covariate or mismeasured covariate data problems in a variety of real applications simulation study results show that the proposed method outperforms the existing methods we analyzed a data set from the collaborative perinatal project using the proposed method and found that the use of ddt increases the risk of preterm births among us children

classical field theory on lie algebroids variational aspects the variational formalism for classical field theories is extended to the setting of lie algebroids given a lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to being morphisms of lie algebroids in addition to the standard case our formalism includes as particular examples the case of systems with symmetry covariant euler poincare and lagrange poincare cases sigma models or chern simons theories

semiparametric methods for response selective and missing data problems in regression summary suppose that data are generated according to the model f ylx 0 g x where y is a response and x are covariates we derive and compare semiparametric likelihood and pseudolikelihood methods for estimating 0 for situations in which units generated are not fully observed and in which it is impossible or undesirable to model the covariate distribution the probability that a unit is fully observed may depend on y and there may be a subset of covariates which is observed only for a subsample of individuals our key assumptions are that the probability that a unit has missing data depends only on which of a finite number of strata that y x belongs to and that the stratum membership is observed for every unit applications include case control studies in epidemiology field reliability studies and broad classes of missing data and measurement error problems our results make fully efficient estimation of 0 feasible and they generalize and provide insight into a variety of methods that have been proposed for specific problems

weighted semiparametric estimation in regression analysis with missing covariate data abstract this article investigates estimation of the regression coefficients in an assumed mean function when covariates on some subjects are missing we examine the performance of a horvitz and thompson 1952 type weighted estimator by using different estimates of the selection probabilities which may be treated as nuisance parameters or a nuisance function in particular we investigate the properties of the estimate of the regression parameters when the selection probabilities are estimated by kernel smoothers we present large sample theory for the new estimator and conduct simulation studies comparing the proposed estimator to the maximum likelihood estimator and multiple imputation under various model assumptions and different missingness mechanisms in addition we provide two real examples that motivate this investigation

inferences about exposure disease associations using probability of exposure information unconditional and conditional likelihood methods are proposed for modeling odds and odds ratios relating a binary disease variable and an exposure variable that is only known probabilistically e g via measurement of a surrogate exposure variable while adjusting appropriately for a vector of covariables assuming nondifferential errors a probabilistic structure is developed that permits analysis of the marginal relation between disease and the surrogate while maintaining important properties of the marginal relation between disease and true exposure in particular analyses conditioned on marginal totals in surrogate disease tables remove the same nuisance parameters as are removed in a conditional analysis of true exposure disease tables in addition a relation between the probability of exposure poe in the disease and disease free groups is derived permitting the use of information about exposure from populations with structure different from the study population examples are presented illustr

lagrangian submanifolds and dynamics on lie algebroids in some previous papers a geometric description of lagrangian mechanics on lie algebroids has been developed in this topical review we give a hamiltonian description of mechanics on lie algebroids in addition we introduce the notion of a lagrangian submanifold of a symplectic lie algebroid and we prove that the lagrangian hamiltonian dynamics on lie algebroids may be described in terms of lagrangian submanifolds of symplectic lie algebroids the lagrangian hamiltonian formalism on lie algebroids permits us to deal with lagrangian hamiltonian functions not defined necessarily on tangent cotangent bundles thus we may apply our results to the projection of lagrangian hamiltonian functions which are invariant under the action of a symmetry lie group as a consequence we obtain that lagrange poincare hamilton poincare equations are the euler lagrange hamilton equations associated with the corresponding atiyah algebroid moreover we prove that lagrange poincare hamilton poincare equations are the local equations defining certain lagrangian submanifolds of symplectic atiyah algebroids

variational calculus with constraints on general algebroids variational calculus on a vector bundle e equipped with a structure of a general algebroid is developed together with the corresponding analogs of euler lagrange equations constrained systems are introduced in the variational and geometrical settings the constrained euler lagrange equations are derived for analogs of holonomic vakonomic and nonholonomic constraints this general model covers the majority of first order lagrangian systems which are present in the literature and reduces to the standard variational calculus and the euler lagrange equations in classical mechanics for e tm

renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems we discuss some properties of the generalized entropies called renyi entropies and their application to the case of continuous distributions in particular it is shown that these measures of complexity can be divergent however their differences are free from these divergences thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions we apply this formalism to the projection of wave functions onto the coherent state basis i e to the husimi representation we also show how the localization properties of the husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure i e no classical limit can be defined numerical simulations on a one dimensional disordered system corroborate our expectations

a semiparametric empirical likelihood method for biased sampling schemes with auxiliary covariates we consider a semiparametric inference procedure for data from epidemiologic studies conducted with a two component sampling scheme where both a simple random sample and multiple outcome or outcome auxiliary dependent samples are observed this sampling scheme allows the investigators to oversample certain subpopulations believed to have more information about the regression model while still gaining insights about the underlying population through the simple random sample we focus on settings where there is no additional information about the parent cohort and the sampling probability is nonidentifiable we motivate our problem with an ongoing study to assess the association between the mutation level of epidermal growth factor receptor egfr and the antitumor response to egfr targeted therapy among nonsmall cell lung cancer patients the proposed method applies to both binary and multicategorical outcome data and allows an arbitrary link function in the framework of generalized linear models simulation studies show that the proposed estimator has nice small sample properties the proposed method is illustrated with a data example

sieve maximum likelihood estimation for regression models with covariates missing at random missing covariates are common in regression problems we propose a new semiparametric method based on a fully nonparametric distribution for the missing covariates that are assumed to be missing at random the method of sieve maximum likelihood estimation is used to obtain the estimators of the regression coefficients these estimators are shown to be consistent and asymptotically normal with their asymptotic covariance matrix that achieves the semiparametric efficiency bound a bootstrap approach is used to estimate the asymptotic covariance matrix some practical modeling approaches for high dimensional covariates are proposed extensive simulation studies are conducted to examine the finite sample properties of the estimates and a real data set from a liver cancer clinical trial is analyzed using the proposed method

estimation of linear and nonlinear errors in variables models using validation data abstract consistent estimators for linear and nonlinear regression models with measurement errors in variables in the presence of validation data are proposed the estimation procedures are based on least squares methods with regression functions replaced by wide sense conditional expectation functions the methods do not depend on distributional assumptions and are robust against the misspecification of a measurement error model they are computationally and analytically simpler than semiparametric methods based on nonparametric regression or density functions

reduction in principal bundles covariant lagrange poincare equations a general reduction theory for field theoretical lagrangians on principal fiber bundles is presented the reduced variational problem as well as the associated equations are formulated the link between the solutions of the original problem and that of the reduced problem is discussed and an obstruction to the reconstruction of the solutions is isolated the important case of semidirect products is discussed in detail and several concrete examples are presented

prospective analysis of logistic case control studies abstract in a classical case control study prentice and pyke proposed to ignore the study design and instead base estimation and inference on a random sampling i e prospective formulation we generalize this prospective formulation of case control studies to include multiplicative models stratification missing data measurement error robustness and other examples the resulting estimators which ignore the case control study aspect and instead are based on a random sampling formulation are typically consistent for nonintercept parameters and are asymptotically normally distributed we derive the resulting asymptotic covariance matrix of the parameter estimates the covariance matrix obtained by ignoring the case control sampling scheme and using prospective formulas instead is shown to be at worst asymptotically conservative and asymptotically correct in a variety of problems a simple sufficient condition guaranteeing the latter is obtained

estimation from truncated lifetime data with supplementary information on covariates and censoring times summary in epidemiology reliability and other areas one encounters situations where response times and covariates for individuals in a population are observed only if the response time does not exceed an associated censoring time methods for obtaining supplementary information about covariates and censoring times for nonresponding individuals are considered estimation procedures are developed for the resulting combination of truncated data and supplementary data theoretical and simulation results are given and the methodology illustrated on some automobile failure data collected under a warranty plan

approximations for regression with covariate measurement error abstract the effect of covariate measurement error on maximum likelihood and maximum quasilikelihood estimates mle s or mqle s of regression parameters is considered the naive estimates obtained by ignoring error are modified to account for it the modified estimates can be computed explicitly from the naive ones and have less bias for small error they are particularly useful for berkson error models examples illustrate their application to linear and nonlinear regression errors in continuous covariates and misclassification of discrete covariates the estimates are applied to data relating air pollution to respiratory disease in children analytic methods and simulations are used to compare the estimates to others that have been proposed for dealing with covariate measurement errors the basic idea is that the mle or mqle of the parameter is a function of the size of the error when 0 and there is no error is the usual mle or mqle for small an improvement over is in many cases of

second moment of the husimi distribution as a measure of complexity of quantum states we propose the second moment of the husimi distribution as a measure of complexity of quantum states the inverse of this quantity represents the effective volume in phase space occupied by the husimi distribution and has a good correspondence with chaoticity of classical system its properties are similar to the classical entropy proposed by wehrl but it is much easier to calculate numerically we calculate this quantity in the quartic oscillator model and show that it works well as a measure of chaoticity of quantum states

semiparametric pseudoscore for regression with multidimensional but incompletely observed regressor we study the regression f y x z where y is the response z rd is a vector of fully observed regressors and x is the regressor with incomplete observation to handle missing data maximum likelihood estimation via expectation maximisation em is the most efficient but is sensitive to the specification of the distribution of x under a missing at random assumption we propose an em type estimation via a semiparametric pseudoscore like in em we derive the conditional expectation of the score function given y and z or the mean score over the incompletely observed units under a postulated distribution of x instead of directly using the mean score in estimating equation we use it as a working index to construct the semiparametric pseudoscore via nonparametric regression introduction of semiparametric pseudoscore into the em framework reduces sensitivity to the specified distribution of x it also avoids the curse of dimensionality when z is multidimensional the resulting regression estimator is more than doubly robust it is consistent if either the pattern of missingness in x is correctly specified or the working index is appropriately but not necessarily correctly specified it attains optimal efficiency when both conditions are satisfied numerical performance is explored by monte carlo simulations and a study on treating hepatitis c patients with hiv coinfection published 2017 this article is a u s government work and is in the public domain in the usa

semiparametric estimation in logistic measurement error models summary we describe semiparametric estimation and inference in a logistic regression model with measurement error in the predictors the particular measurement error model consists of a primary data set in which only the response y and a fallible surrogate w of the true predictor x are observed plus a smaller validation data set for which y x w are observed except for the underlying assumption of a logistic model in the true predictor no parametric distributional assumption is made about the true predictor or its surrogate we develop a semiparametric parameter estimate of the logistic regression parameter which is asymptotically normally distributed and computationally feasible the estimate relies on kernel regression techniques for scalar predictors by a detailed analysis of the mean squared error of the parameter estimate we obtain a representation for an optimal bandwidth

the berwald type linearization of generalized connections we study the existence of a natural linearization process for generalized connections on an affine bundle it is shown that this leads to an affine generalized connection over a prolonged bundle which is the analogue of what is called a connection of berwald type in the standard theory of connections various new insights are being obtained in the fine structure of affine bundles over an anchored vector bundle and affineness of generalized connections on such bundles

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

a path integral approach to the kontsevich quantization formula we give a quantum field theory interpretation of kontsevich s deformation quantization formula for poisson manifolds we show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory its batalin vilkovisky quantization yields a superconformal field theory the associativity of the star product and more generally the formality conjecture can then be understood by field theory methods as an application we compute the center of the deformed algebra in terms of the center of the poisson algebra

note on generalized connections and affine bundles we develop an alternative view on the concept of connections over a vector bundle map which consists of a horizontal lift procedure to a prolonged bundle we further focus on prolongations to an affine bundle and introduce the concept of affineness of a generalized connection

a maximum pseudo profile likelihood estimator for the cox model under length biased sampling this paper considers semiparametric estimation of the cox proportional hazards model for right censored and length biased data arising from prevalent sampling to exploit the special structure of length biased sampling we propose a maximum pseudo profile likelihood estimator which can handle time dependent covariates and is consistent under covariate dependent censoring simulation studies show that the proposed estimator is more efficient than its competitors a data analysis illustrates the methods and theory

modelling marginal hazards in multivariate failure time data we consider the problem of estimating relative risk parameters in the marginal distribution of failure times from a sample in which individuals are grouped into clusters and failure times for individuals within clusters may be dependent we assume that the marginal hazard of failure for individuals within a cluster is specified by a relative risk regression model and the structure of dependence between individuals within a cluster is left unspecified estimating equations for the regression parameters and an estimator for the cumulative base line marginal hazard are described

a semiparametric correction for attenuation abstract a correction method is proposed for models including the generalized linear model when the covariate is measured with error the method requires a separate validation data set that consists of the surrogate w and the true covariate x or an unbiased estimate x of x we do not require the classical additive measurement error model in which the surrogate is unbiased for the true covariates we first obtain an estimate of e x w by using nonparametric kernel regression of x or x on w based on the validation data then we perform a standard analysis with the unknown x replaced by the estimate of e x w the asymptotic distribution of the resulting regression parameter estimator is obtained generalizations to include components of x measured without error are also discussed

inference using surrogate outcome data and a validation sample summary in the context of estimating 3 from the regression model p yi x relating response y to covariates x suppose that only a surrogate response s is available for most study subjects suppose that for a random subsample of the study cohort termed the validation sample the true outcome y is available in addition to s we consider maximum likelihood estimation of 3 from such data and show that it is nonrobust to misspecification of the distribution relating the surrogate to the true outcome p s i y x an alternative semiparametric method is also considered which is nonparametric with respect to p s i y x large sample distribution theory for maximum estimated likelihood estimates is developed an illustrative example is presented

semiparametric estimation in generalized linear mixed models with auxiliary covariates a pairwise likelihood approach auxiliary covariates are often encountered in biomedical research settings where the primary exposure variable is measured only for a subgroup of study subjects this article is concerned with generalized linear mixed models in the presence of auxiliary covariate information for clustered data we propose a novel semiparametric estimation method based on a pairwise likelihood function and develop an estimating equation based inference procedure by treating both the error structure and random effects as nuisance parameters this method is robust against misspecification of either error structure or random effects distribution and allows for dependence between random effects and covariates we show that the resulting estimators are consistent and asymptotically normal extensive simulation studies evaluate the finite sample performance of the proposed estimators and demonstrate their advantage over the validation set based method and the existing method we illustrate the method with two real data examples

case control studies with errors in covariates we devise methods for estimating the parameters of a prospective logistic model with dichotomous response d and arbitrary covariates x from case control data when these covariates are measured with error we suppose that some fraction of the cases and controls provide only the error prone covariate measurements w the incomplete or reduced data whereas some of the cases and controls provide measurements on x and w the complete data we assume a measurement error density with a finite set of parameters namely fw xd w x d and nondifferential error is treated as a special case of this model fw x w x our algorithm estimates both the logistic parameters and from a pseudolikelihood because empirical distribution functions are used in place of needed distributions in the pseudolikelihoods the required asymptotic theory is more elaborate than for pseudolikelihoods based on substitution for a finite number of nuisance parameters we also examine computationally simpler methods under t

quasi coordinates from the point of view of lie algebroid structures a geometrical description of the lagrangian dynamics in quasi coordinates on the tangent bundle using the lie algebroid framework is given linear nonholonomic systems on lie algebroids are solved in local coordinates adapted to the constraints through lagrangian multipliers and gibbs appell generalized methods

gravity from lie algebroid morphisms inspired by the poisson sigma model and its relation to 2d gravity we consider models governing morphisms from t to any lie algebroid e where is regarded as a d dimensional spacetime manifold we address the question of minimal conditions to be placed on a bilinear expression in the 1 form fields sij x aiaj so as to permit an interpretation as a metric on this becomes a simple compatibility condition of the e tensor s with the chosen lie algebroid structure on e for the standard lie algebroid e tm the additional structure is identified with a riemannian foliation of m in the poisson case e t m with a sub riemannian structure which is poisson invariant with respect to its annihilator bundle for integrable image of s this means that the induced riemannian leaves should be invariant with respect to all hamiltonian vector fields of functions which are locally constant on this foliation this provides a huge class of new gravity models in d dimensions embedding known 2d and 3d models as particular examples

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

extended hamiltonian systems in multisymplectic field theories we consider hamiltonian systems in first order multisymplectic field theories we review the properties of hamiltonian systems in the so called restricted multimomentum bundle including the variational principle which leads to the hamiltonian field equations in an analogous way to how these systems are defined in the so called extended symplectic formulation of nonautonomous mechanics we introduce hamiltonian systems in the extended multimomentum bundle the geometric properties of these systems are studied the hamiltonian equations are analyzed using integrable multivector fields the corresponding variational principle is also stated and the relation between the extended and the restricted hamiltonian systems is established all these properties are also adapted to certain kinds of submanifolds of the multimomentum bundles in order to cover the case of almost regular field theories

auxiliary covariate data in failure time regression summary we consider the problem of missing covariate data in the context of censored failure time relative risk regression auxiliary covariate data which are considered informative about the missing data but which are not explicitly part of the relative risk regression model may be available full covariate information is available for a validation set an estimated partial likelihood method is proposed for estimating relative risk parameters this method is an extension of the estimated likelihood regression analysis method for uncensored data pepe 1992 pepe fleming 1991 a key feature of the method is that it is nonparametric with respect to the association between the missing and observed including auxiliary covariate components asymptotic distribution theory is derived for the proposed estimated partial likelihood estimator in the case where the auxiliary or mismeasured covariates are categorical asymptotic efficiencies are calculated for exponential failure times using an exponential relative risk model the estimated partial likelihood estimator compares favourably with a fully parametric maximum likelihood analysis comparisons are also made with a standard partial likelihood analysis which ignores the incomplete observations important efficiency gains can be made with the estimated partial likelihood method small sample properties are investigated through simulation studies

semiparametric efficient estimation of a conditional density with missing or mismeasured covariates summary pepe and fleming and carroll and wand have recently proposed estimators in a parametric model for the density of a random variable y conditional on a vector of covariates x v when data on one of the regressors x is missing for some study subjects we propose a new class of estimators that remains consistent and asymptotically normal even when the probability that x is missing depends on the observed v and y includes an estimator whose asymptotic variance attains the semiparametric variance bound for the model and when the data are missing completely at random includes an estimator that is asymptotically equivalent to the inefficient estimators proposed by pepe and fleming and by carroll and wand the optimal estimator in our class depends on the unknown probability law generating the data when the vector v of non missing regressors has at most two continuous components we propose an adaptive semiparametric efficient estimator and compare the performance of the proposed semiparametric efficient estimator with the estimators proposed by pepe and fleming and carroll and wand in a small simulation study when v has many continuous components we propose an alternative class of adaptive estimators that should have high efficiency

moments of generalized husimi distributions and complexity of many body quantum states we consider generalized husimi distributions for many body systems and show that their moments are good measures of complexity of many body quantum states our construction of the husimi distribution is based on the coherent state of the single particle transformation group then the coherent states are independent particle states and at the same time the most localized states in the husimi representation therefore delocalization of the husimi distribution which can be measured by the moments is a sign of many body correlation entanglement since the delocalization of the husimi distribution is also related to chaoticity of the dynamics it suggests a relation between entanglement and chaos our definition of the husimi distribution can be applied not only to systems of distinguishable particles but also to those of identical particles i e fermions and bosons we derive an algebraic formula to evaluate the moments of the husimi distribution

measurement error regression with unknown link dimension reduction and data visualization abstract a general nonlinear regression problem is considered with measurement error in the predictors we assume that the response is related to an unknown linear combination of a multidimensional predictor through an unknown link function instead of observing the predictor we instead observe a surrogate with the property that its expectation is linearly related to the true predictor with constant variance we identify an important transformation of the surrogate variable using this transformed variable we show that if one proceeds with the usual analysis ignoring measurement error then both ordinary least squares and sliced inverse regression yield estimates which consistently estimate the true regression parameter up to a constant of proportionality we derive the asymptotic distribution of the estimates a simulation study is conducted applying sliced inverse regression in this context

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

lie algebroid structures on a class of affine bundles we introduce the notion of a lie algebroid structure on an affine bundle whose base manifold is fibered over r it is argued that this is the framework which one needs for coming to a time dependent generalization of the theory of lagrangian systems on lie algebroids an extensive discussion is given of a way one can think of forms acting on sections of the affine bundle it is further shown that the affine lie algebroid structure gives rise to a coboundary operator on such forms the concept of admissible curves and dynamical systems whose integral curves are admissible brings an associated affine bundle into the picture on which one can define in a natural way a prolongation of the original affine lie algebroid structure

logistic regression with incompletely observed categorical covariates investigating the sensitivity against violation of the missing at random assumption missing values in the covariates are a widespread complication in the statistical inference of regression models the maximum likelihood principle requires specification of the distribution of the covariates at least in part for categorical covariates log linear models can be used additionally the missing at random assumption is necessary which excludes a dependence of the occurrence of missing values on the unobserved covariate values this assumption is often highly questionable we present a framework to specify alternative missing value mechanisms such that maximum likelihood estimation of the regression parameters under a specified alternative is possible this allows investigation of the sensitivity of a single estimate against violations of the missing at random assumption the possible results of a sensitivity analysis are illustrated by artificial examples the practical application is demonstrated by the analysis of two case control studies

a bayesian approach to prospective binary outcome studies with misclassification in a binary risk factor misclassification in a binary exposure variable within an unmatched prospective study may lead to a biased estimate of the disease exposure relationship it usually gives falsely small credible intervals because uncertainty in the recorded exposure is not taken into account when there are several other perfectly measured covariates interrelationships may introduce further potential for bias bayesian methods are proposed for analysing binary outcome studies in which an exposure variable is sometimes misclassified but its correct values have been validated for a random subsample of the subjects this bayesian approach can model relationships between explanatory variables and between exploratory variables and the probabilities of misclassification three logistic regressions are used to relate disease to true exposure misclassified exposure to true exposure and true exposure to other covariates credible intervals may be used to make decisions about whether certain parameters are unnecessary and hence whether the model can be reduced in complexity in the disease exposure model for parameters representing coefficients related to perfectly measured covariates the precision of posterior estimates is only slightly lower than would be found from data with no misclassification for the risk factor which has misclassification the estimates of model coefficients obtained are much less biased than those with misclassification ignored

analysis of censored survival data with intermittently observed time dependent binary covariates abstract in survival analyses that include a time dependent covariate the standard partial likelihood approach is often complicated by the fact that the necessary observations of the time dependent covariate are not always available for the subjects in each risk set in this article we consider the situation of a binary time dependent covariate we specify a longitudinal model for the binary covariate with missing observations and a proportional hazards model for survival time conditional on fixed covariates and the completed time dependent covariate history the joint posterior distribution of the missing covariates and the parameters in the covariate and hazard models is simulated using gibbs sampling the joint modeling approach allows the missing covariates to be generated using all of the observed covariates as well as the disease outcome and failure time information simulation studies show that this approach often leads to lower bias of relative risk estimates associated with the time dependent c

semiparametric estimation exploiting covariate independence in two phase randomized trials recent results for case control sampling suggest when the covariate distribution is constrained by gene environment independence semiparametric estimation exploiting such independence yields a great deal of efficiency gain we consider the efficient estimation of the treatment biomarker interaction in two phase sampling nested within randomized clinical trials incorporating the independence between a randomized treatment and the baseline markers we develop a newton raphson algorithm based on the profile likelihood to compute the semiparametric maximum likelihood estimate spmle our algorithm accommodates both continuous phase one outcomes and continuous phase two biomarkers the profile information matrix is computed explicitly via numerical differentiation in certain situations where computing the spmle is slow we propose a maximum estimated likelihood estimator mele which is also capable of incorporating the covariate independence this estimated likelihood approach uses a one step empirical covariate distribution thus is straightforward to maximize it offers a closed form variance estimate with limited increase in variance relative to the fully efficient spmle our results suggest exploiting the covariate independence in two phase sampling increases the efficiency substantially particularly for estimating treatment biomarker interactions

a mean score method for missing and auxiliary covariate data in regression models summary we consider regression analysis when incomplete or auxiliary covariate data are available for all study subjects and in addition for a subset called the validation sample true covariate data of interest have been ascertained the term auxiliary data refers to data not in the regression model but thought to be informative about the true missing covariate data of interest we discuss a method which is nonparametric with respect to the association between available and missing data allows missingness to depend on available response and covariate values and is applicable to both cohort and case control study designs the method previously proposed by flanders greenland 1991 and by zhao lipsitz 1992 is generalised and asymptotic theory is derived our expression for the asymptotic variance of the estimator provides intuition regarding performance of the method optimal sampling strategies for the validation set are also suggested by the asymptotic results