estimation of controlled direct effects when regression models adjust for mediators on the causal path from exposure to outcome the regression coefficient of exposure is commonly viewed as a measure of the direct exposure effect this interpretation can be misleading even with a randomly assigned exposure this is because adjustment for post exposure measurements introduces bias whenever their association with the outcome is confounded by more than just the exposure by the same token adjustment for such confounders stays problematic when these are themselves affected by the exposure robins accommodated this by introducing linear structural nested direct effect models with direct effect parameters that can be estimated by using inverse probability weighting by a conditional distribution of the mediator the resulting estimators are consistent but inefficient and can be extremely unstable when the mediator is absolutely continuous we develop direct effect estimators which are not only more efficient but also consistent under a less demanding model for a conditional expectation of the outcome we find that the one estimator which avoids inverse probability weighting altogether performs best this estimator is intuitive computationally straightforward and as demonstrated by simulation competes extremely well with ordinary least squares estimators in settings where standard regression is valid

matrices with prescribed lower triangular part abstract we give a necessary and sufficient condition for the existence of a square matrix with prescribed characteristic polynomial and prescribed entries on and below the main diagonal

bounded efficient and doubly robust estimation with inverse weighting consider estimating the mean of an outcome in the presence of missing data or estimating population average treatment effects in causal inference a doubly robust estimator remains consistent if an outcome regression model or a propensity score model is correctly specified we build on a previous nonparametric likelihood approach and propose new doubly robust estimators which have desirable properties in efficiency if the propensity score model is correctly specified and in boundedness even if the inverse probability weights are highly variable we compare the new and existing estimators in a simulation study and find that the robustified likelihood estimators yield overall the smallest mean squared errors

toward a curse of dimensionality appropriate coda asymptotic theory for semi parametric models we argue that due to the curse of dimensionality there are major difficulties with any pure or smoothed likelihood based method of inference in designed studies with randomly missing data when missingness depends on a high dimensional vector of variables we study in detail a semi parametric superpopulation version of continuously stratified random sampling we show that all estimators of the population mean that are uniformly consistent or that achieve an algebraic rate of convergence no matter how slow require the use of the selection randomization probabilities we argue that in contrast to likelihood methods which ignore these probabilities inverse selection probability weighted estimators continue to perform well achieving uniform n 1 2 rates of convergence we propose a curse of dimensionality appropriate coda asymptotic theory for inference in non and semi parametric models in an attempt to formalize our arguments we discuss whether our results constitute a fatal blow to the likelihood principle and study the attitude toward these that a committed subjective bayesian would adopt finally we apply our coda theory to analyse the effect of the curse of dimensionality in several interesting semi parametric models including a model for a two armed randomized trial with randomization probabilities depending on a vector of continuous pretreatment covariates x we provide substantive settings under which a subjective bayesian would ignore the randomization probabilities in analysing the trial data we then show that any statistician who ignores the randomization probabilities is unable to construct nominal 95 per cent confidence intervals for the true treatment effect that have both i an expected length which goes to zero with increasing sample size and ii a guaranteed expected actual coverage rate of at least 95 per cent over the ensemble of trials analysed by the statistician during his or her lifetime however we derive a new interval estimator depending on the randomization probabilities that satisfies i and ii

multiply robust estimation in regression analysis with missing data doubly robust estimators are widely used in missing data analysis they provide double protection on estimation consistency against model misspecifications however they allow only a single model for the missingness mechanism and a single model for the data distribution and the assumption that one of these two models is correctly specified is restrictive in practice for regression analysis with possibly missing outcome we propose an estimation method that allows multiple models for both the missingness mechanism and the data distribution the resulting estimator is consistent if any one of those multiple models is correctly specified and thus provides multiple protection on consistency this estimator is also robust against extreme values of the fitted missingness probability which for most doubly robust estimators can lead to erroneously large inverse probability weights that may jeopardize the numerical performance the numerical implementation of the proposed method through a modified newton ra

geometric multiplicities of completions of partial triangular matrices abstract a sufficient condition for a set of positive integers g 1 g 2 g n to be the geometric multiplicites of given eigenvalues for some strictly lower triangular completions of a partial matrix is given a method is proposed which allows one to reduce the investigation of geometric multiplicities of completed matrix with different eigenvalues to the nilpotent case

jordan forms of completions of partial upper triangular matrices abstract the possible jordan forms of completions of a matrix prescribed in its upper triangular part are studied it is shown that there always exists a nonderogatory completion for such a matrix jordan forms of nilpotent completions are considered as well

hyperbolicity of nodal hypersurfaces we show that a nodal hypersurface x in p3 of degree d with a sufficiently large number l of nodes l 8 3 d2 5 2 d is algebraically quasi hyperbolic i e x can only have finitely many rational and elliptic curves our results use the theory of symmetric differentials and algebraic foliations and give a very striking example of the jumping of the number of symmetric differentials in families

bias reduced doubly robust estimation over the past decade doubly robust estimators have been proposed for a variety of target parameters in causal inference and missing data models these are asymptotically unbiased when at least one of two nuisance working models is correctly specified regardless of which while their asymptotic distribution is not affected by the choice of root n consistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified this choice of estimators can have a dramatic impact under misspecification of at least one working model in this article we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models which is designed to improve the performance of the doubly robust estimator of interest relative to the default use of maximum likelihood estimators for the nuisance parameters the proposed approach locally minimizes the squared first order asymptotic bias of the doubly robust estim

the bogomolov miyaoka yau inequality for logarithmic surfaces in positive characteristic we generalize bogomolov s inequality for higgs sheaves and the bogomolov miyaoka yau inequality in positive characteristic to the logarithmic case we also generalize shepherd barron s results on bogomolov s inequality on surfaces of special type from rank 2 to the higher rank case we use these results to show some examples of smooth nonconnected curves on smooth rational surfaces that cannot be lifted modulo p2 these examples contradict some claims by xie

bounding singular surfaces via chern numbers we prove the existence of a bound on the number of steps of the minimal model program for singular surfaces in terms of discrepancies and chern numbers as an application we prove that given r in mathbb r 0 and epsilon in 0 1 the class mathcal f r epsilon of 2 dimensional pairs x d of general type with epsilon klt singularities d with standard coefficients and 4c 2 x d c 1 2 x d le r forms a bounded family

regression and weighting methods for causal inference using instrumental variables please see the supplementary material for a correction and a new result recent researches in econometrics and statistics have gained considerable insights into the use of instrumental variables ivs for causal inference a basic idea is that ivs serve as an experimental handle the turning of which may change each individual s treatment status and through and only through this effect also change observed outcome the average difference in observed outcome relative to that in treatment status gives the average treatment effect for those whose treatment status is changed in this hypothetical experiment we build on the modern iv framework and develop two estimation methods in parallel to regression adjustment and propensity score weighting in the case of treatment selection based on covariates the iv assumptions are made explicitly conditional on covariates to allow for the fact that instruments can be related to these background variables the regression method focuses on the relationship between respo

semiparametric theory for causal mediation analysis efficiency bounds multiple robustness and sensitivity analysis whilst estimation of the marginal total causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences in recent years investigators have also become increasingly interested in mediation analysis specifically upon evaluating the total effect of the exposure investigators routinely wish to make inferences about the direct or indirect pathways of the effect of the exposure not through or through a mediator variable that occurs subsequently to the exposure and prior to the outcome although powerful semiparametric methodologies have been developed to analyze observational studies that produce double robust and highly efficient estimates of the marginal total causal effect similar methods for mediation analysis are currently lacking thus this paper develops a general semiparametric framework for obtaining inferences about so called marginal natural direct and indirect causal effects while appropriately accounting for a large number of pre exposure confounding factors for the exposure and the mediator variables our analytic framework is particularly appealing because it gives new insights on issues of efficiency and robustness in the context of mediation analysis in particular we propose new multiply robust locally efficient estimators of the marginal natural indirect and direct causal effects and develop a novel double robust sensitivity analysis framework for the assumption of ignorability of the mediator variable

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

on the jordan form of completions of partial upper triangular matrices abstract rodman and shalom present in linear algebra appl 168 221 249 1992 two completion conjectures for partial upper triangular matrices in this paper we show that one of them is not true in general and we prove its validity for some particular cases we also prove the equivalence between the two conjectures in the case of partial hessenberg matrices

completions of partial jordan and hessenberg matrices abstract jordan forms of completions of partial jordan matrices are studied our approach is based on an algorithm for constructing completions of a given partial jordan matrix having prescribed eigenvalues and multiplicities an upper bound is given for the number of entries that must be made nonzero to produce such completions the algorithm is further interpreted in terms of the graph associated with a matrix some of the results are extended to a larger class of partial hessenberg matrices

chern classes of reflexive sheaves on normal surfaces we define chern classes of reflexive sheaves using wahl s relative local chern classes of vector bundles the main result of the paper bounds contributions of singularities of a sheaf to the riemann roch formula using it we are able to prove inequality in wahl s conjecture on relative asymptotic rr formula for rank 2 vector bundles moreover we prove that if wahl s conjecture is true for a singularity then it is true for any its quotient this implies wahl s conjecture for quotient singularities and for quotients of cones over elliptic curves

multiple robustness in factorized likelihood models we consider inference under a nonparametric or semiparametric model with likelihood that factorizes as the product of two or more variation independent factors we are interested in a finite dimensional parameter that depends on only one of the likelihood factors and whose estimation requires the auxiliary estimation of one or several nuisance functions we investigate general structures conducive to the construction of so called multiply robust estimating functions whose computation requires postulating several dimension reducing models but which have mean zero at the true parameter value provided one of these models is correct