mirror symmetry for the landau ginzburg a model m mathbb c n w z_ 1 cdots z_ n we calculate the category of branes in the landau ginzburg a model with background m cn and superpotential w z1 zn in the form of microlocal sheaves along a natural lagrangian skeleton our arguments employ the framework of perverse schobers and our results confirm expectations from mirror symmetry

oscillations of first order neutral delay differential equations abstract consider the neutral delay differential equation d dt y t py t qy t 0 t t 0 where q and are positive constants while p 1 0 for the case p 1 0 see ladas and sficas oscillations of neutral delay differential equations to appear the following results are then proved theorem 1 assume p and q 1 p 1 e then every solution of eq oscillates theorems 3 assume p 0 then every nonoscillatory solution y t of eq tends to zero as t theorem 4 assume p 0 then a necessary condition for all solutions of eq to oscillate is that theorem 5 assume p 0 and q 1 p 1 e then every solution of eq oscillates extensions of these results to equations with variable coefficients are also obtained

perverse sheaves of categories and some applications abstract we study perverse sheaves of categories their connections to classical algebraic geometry we show how perverse sheaves of categories encode naturally derived categories of coherent sheaves on p 1 bundles semiorthogonal decompositions and relate them to a recent proof of segal that all autoequivalences of triangulated categories are spherical twists furthermore we show that perverse sheaves of categories can be used to represent certain degenerate calabi yau varieties

necessary and sufficient conditions for oscillations of higher order delay differential equations we obtain necessary and sufficient conditions under which ail solutions of certain n th order delay differential equations oscillate when n is odd and necessary and sufficient conditions under which all bounded solutions oscillate when n is even the conditions derived involve the characteristic equation of the delay differential equation

exact lagrangian submanifolds in simply connected cotangent bundles we consider exact lagrangian submanifolds in cotangent bundles under certain additional restrictions triviality of the fundamental group of the cotangent bundle and of the maslov class and second stiefel whitney class of the lagrangian submanifold we prove such submanifolds are floer cohomologically indistinguishable from the zero section this implies strong restrictions on their topology an essentially equivalent result was recently proved independently by nadler 16 using a different approach

necessary and sufficient conditions for oscillations of second order neutral equations consider the neutral delay differential equation d2dt2 y t py t qy t 0 1 where p q r and r we proved that eq 1 oscillates if and only if the characteristic equation 2 2pe qe 0 has no real roots

a necessary and sufficient condition for the oscillation of neutral equations abstract consider the neutral differential equation d dt y t py t qy t 0 t t 0 where p q and are real numbers then a necessary and sufficient condition for the oscillation of is that the characteristic equation p e qe 0 has no real roots

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

finite volume flows and morse theory in this paper we present a new approach to morse theory based on the de rham federer theory of currents the full classical theory is derived in a transparent way the methods carry over uniformly to the equivariant and the holomorphic settings moreover the methods are substantially stronger than the classical ones and have interesting applications to geometry they lead for example to formulas relating characteristic forms and singularities of bundle maps

characteristic varieties and vanishing cycles on presente une etude systematique des varietes caracteristiques des systemes holonomes a singularites regulieres ce sont des sous varietes lagrangiennes coniques dans le fibre cotangent t x

a categorification of morelli s theorem we prove a theorem relating torus equivariant coherent sheaves on toric varieties to polyhedrally constructible sheaves on a vector space at the level of k theory the theorem recovers morelli s description of the k theory of a smooth projective toric variety morelli in adv math 100 2 154 182 1993 specifically let x be a proper toric variety of dimension n and let m mathbb r mathrm lie t mathbb r vee cong mathbb r n be the lie algebra of the compact dual real torus t mathbb r vee cong u 1 n then there is a corresponding conical lagrangian t m and an equivalence of triangulated dg categories mathcal p mathrm erf t x cong mathit sh cc m mathbb r lambda where mathcal p mathrm erf t x is the triangulated dg category of perfect complexes of torus equivariant coherent sheaves on x and shcc m is the triangulated dg category of complex of sheaves on m with compactly supported constructible cohomology whose singular support lies in this equivalence is monoidal it intertwines the tensor product of coherent sheaves on x with the convolution product of constructible sheaves on m

a cotangent fibre generates the fukaya category abstract we prove that the algebra of chains on the based loop space recovers the derived wrapped fukaya category of the cotangent bundle of a closed smooth oriented manifold the main new idea is the proof that a cotangent fibre generates the fukaya category using a version of the map from symplectic cohomology to the homology of the free loop space introduced by cieliebak and latschev

asymptotic and oscillatory behavior of solutions of first order nonlinear neutral delay differential equations the authors consider the first order nonlinear neutral delay differential equation e y t p t y t q t y t 0 where p q and are continuous q t 0 0 0 and u u 0 if u 0 they give sufficient conditions for all nonoscillatory solutions of e to converge to zero as t two oscillation theorems for equation e are also proved

a stable category of lagrangian cobordisms abstract given an exact symplectic manifold m and a support lagrangian m we construct an category lag m which we conjecture to be equivalent after specialization of the coefficients to the partially wrapped fukaya category of m relative to roughly speaking the objects of lag m are lagrangian branes inside of m t r n for large n and the morphisms are lagrangian cobordisms that are non characteristic with respect to the main theorem of this paper is that lag m is a stable category and in particular its homotopy category is triangulated with mapping cones given by an elementary construction the shift functor is equivalent to the familiar shift of grading for lagrangian branes

on the nature of the nonoscillatory solutions of a class of neutral delay differential equations consider the neutral delay differential equation ddt x t px t q x t 1 x t 2 0 e where p q 1 and 2 are nonnegative constants for 2 we prove that all nonoscillatory solutions of e are bounded if and only if c the characteristic equation p e q e 1 e 2 0 of e has no positive roots and zero is a simple root if we also prove that condition c is equivalent to 1 p q 1 2 if 2 moreover for the case where 2 we show that c is a necessary and sufficient condition for every nonoscillatory solution x of e to be bounded or such that 0 lim inft 1t 01 x s ds lim supt 1t 01 x s ds

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

an extension of the characterization of oscillations to arbitrary functional differential equations via the laplace transform in this paper we consider a functional differential equation of general form using the laplace transform we prove that such an equation has a nonoscillatory solution if and only if the characteristic equation has a real zero

oscillation theorems for second order neutral functional differential equations some new oscillation criteria are given for second order neutral functional differential equations of the form d 2dt 2 x t lx t t mx t s qx t a px t b 0 where l t m s p and q are real numbers and a and b are real positive constants

almost automorphic solutions of discrete delayed neutral system abstract we study almost automorphic solutions of the discrete delayed neutral dynamic system x t 1 a t x t q t x t g t g t x t x t g t by means of a fixed point theorem due to krasnoselskii using discrete variant of exponential dichotomy and proving uniqueness of projector of discrete exponential dichotomy we invert the equation and obtain some limit results leading to sufficient conditions for the existence of almost automorphic solutions of the neutral system unlike the existing literature we prove our existence results without assuming boundedness of inverse matrix a t 1 hence we significantly improve the results in the existing literature we provide two examples to illustrate effectiveness of our results finally we also provide an existence result for almost periodic solutions of the system

oscillation criteria for first order differential equations with deviating arguments abstract in this paper we study the oscillatory behavior of first order differential equations with deviating arguments of the general form x t 1 n p i x t i 0 where pi i 1 i n are constants necessary and sufficient conditions have been obtained to guarantee that eq is oscillatory and we also discuss the equivalence of two kinds of oscillation for equation is oscillatory if and only if the characteristic equation 1 n p i e i 0 has no real roots

existence and iterative approximations of nonoscillatory solutions of higher order nonlinear neutral delay differential equations this paper studies a few existence results of nonoscillatory solutions for the following higher order nonlinear neutral delay differential equation dndtnx t cx t 1 n i 1didtih t x h1 t x h2 t x hk t 1 n 1f t x f1 t x f2 t x fk t g t t t0 where n is a positive integer 0 i n 1 c r 1 0 h ci t0 rk r f c t0 rk r g c t0 r hl ci t0 r and fl c t0 r with limt hl t limt fl t l 1 k constructs several mann type iterative approximation sequences with errors for these nonoscillatory solutions and establish some error estimates between the approximate solutions and the nonoscillatory solutions in addition sufficient conditions for the existence of infinitely many nonoscillatory solutions for the above equation are given three nontrivial examples are given to illustrate the advantages of our results

hypertoric category o abstract we study the representation theory of the invariant subalgebra of the weyl algebra under a torus action which we call a hypertoric enveloping algebra we define an analogue of bgg category o for this algebra and identify it with a certain category of sheaves on a hypertoric variety we prove that a regular block of this category is highest weight and koszul identify its koszul dual compute its center and study its cell structure we also consider a collection of derived auto equivalences analogous to the shuffling and twisting functors for bgg category o

oscillations caused by several retarded and advanced arguments in this paper we study the oscillatory behavior of equations of the forms y t i 1npiy t i 0 and y t i 1npiy t i 0 where piand i i 1 2 n are positive constants we prove that each one of the following conditions 1 pi i1 e for some i i 1 2 n 2 i 1npi 1 e where min 1 2 n 3 i 1npi 1 n i 1n i 1 e or 4 1 n i 1n pi i 1 2 21 e implies that every solution of and oscillates a generalization in the case where the coefficientspi i 1 2 n are positive and continuous functions is also presented

necessary and sufficient conditions for oscillation of neutral equations with real coefficients abstract consider the neutral delay differential equation d dt y t py t q 1 y t 1 q 2 y t 2 0 where the coefficients p q1 q2 are real numbers and the delays 1 2 are nonnegative eal numbers we prove that every solution of eq 1 oscillates if and only if the characteristic equation pe q1e 1 q2e 2 0 has no real roots

oscillation criteria for forced first order neutral differential equations with variable coefficients abstract necessary and sufficient conditions are obtained so that every solution of y t p t y t q t g y t f t is oscillatory or tends to zero or to as t the problem is considered in various ranges for p t

a mixed neutral system on demontre des resultats d existence et d unicite pour le systeme d equations differentielles fonctionnelles suivant x t f t x j 1 m f j t x x t p j

necessary and sufficient conditions for oscillation of the solutions of linear functional differential equations of neutral type with distributed delay abstract for various classes of equations of the general form d dt x t 1 0 1 x t s dr 1 s 2 0 2 x t s dr 2 s 0 where 1 2 1 and r 1 r 2 are non decreasing functions necessary sufficient as well as necessary and sufficient conditions have been obtained for the oscillation of all nonvanishing solutions in terms of the properties of the roots of the respective characteristic or quasi characteristic equation

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

characteristic cycles of constructible sheaves in his paper k kashiwara introduced the notion of characteristic cycle for complexes of constructible sheaves on manifolds let x be a real analytic manifold and f a complex of sheaves of c vector spaces on x whose cohomology is constructible with respect to a subanalytic strati cation the characteristic cycle cc f is a subanalytic lagrangian cycle with in nite support and with values in the orientation sheaf of x in the cotangent bundle t x the de nition of cc f is morse theoretic heuristically cc f encodes the in nitesimal change of the euler characteristic of the stalks of f along the various directions in x it tends to be di cult in practice to calculate cc f explicitly for all but the simplest complexes f on the other hand the characteristic cycle construction has good functorial properties the behavior of cc f with respect to the operations of proper direct image verdier duality and non characteristic inverse image of f is well understood ks in this paper we describe the e ect of the operation of direct image by an open embedding combining our result with those that were previously known we obtain descriptions of cc rf f and cc f f analogous to those in ks for arbitrary morphisms f x y in the semi algebraic category and complexes f with semi algebraically constructible cohomology in e ect this provides an axiomatic characterization of the functor cc at least in the semi algebraic context our arguments do apply more generally in the subanalytic case but because statements become quite convoluted we shall not strive for the greatest degree of generality as a concrete application we consider the case of the ag manifold x of a complex semisimple lie algebra g here the weyl group w of g operates

oscillation and nonoscillation in first order neutral differential equations abstract verifiable sufficient conditions are obtained respectively for the oscillation and nonoscillation of the neutral differential equation x t cx t px t 0

a complete knot invariant from contact homology we construct an enhanced version of knot contact homology and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup in particular it completely determines a knot up to smooth isotopy the enhancement consists of the fully noncommutative legendrian contact homology associated to the union of the conormal torus of the knot and a disjoint cotangent fiber sphere along with a product on a filtered part of this homology as a corollary we obtain a new holomorphic curve proof of a result of the third author that the legendrian isotopy class of the conormal torus is a complete knot invariant

an oscillation test for a class of linear neutral differential equations where the following conditions are assumed to hold without further mention a h to co 0 co is continuous b t t cc p r is continuous increasing and satisfies lim oo r t cq c p cb co t 0 00 is continuous d g z co r is continuous and lim a g l cc in what follows by a solution of a or b we understand a continuous function x t co r such that x t h t x r t is continuously differentiable and satisfies a or b for all sufficiently large t 2 t as is customary we restrict our attention to those solutions x t of a or b which satisfy sup ix t t 2 t o

efficient restricted estimators for conditional mean models with missing data summary consider a conditional mean model with missing data on the response or explanatory variables due to two phase sampling or nonresponse robins et al 1994 introduced a class of augmented inverse probability weighted estimators depending on a vector of functions of explanatory variables and a vector of functions of coarsened data tsiatis 2006 studied two classes of restricted estimators class 1 with both vectors restricted to finite dimensional linear subspaces and class 2 with the first vector of functions restricted to a finite dimensional linear subspace we introduce a third class of restricted estimators class 3 with the second vector of functions restricted to a finite dimensional subspace we derive a new estimator which is asymptotically optimal in class 1 by the methods of nonparametric and empirical likelihood we propose a hybrid strategy to obtain estimators that are asymptotically optimal in class 1 and locally optimal in class 2 or class 3 the advantages of the hybrid likelihood estimator based on classes 1 and 3 are shown in a simulation study and a real data example

oscillation theorems for certain neutral functional differential equations in this paper we shall offer sufficient conditions for the oscillation of all solutions to neutral functional differential equations of mixed type of the form dndtn x t ax t bx t q t x t g p t x t h 0 1 here p and q are periodic functions

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

braid group actions on derived categories of coherent sheaves this paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety x the motivation for this is m kontsevich s homological mirror conjecture together with the occurrence of certain braid group actions in symplectic geometry one of the main results is that when dim x geq 2 our braid group actions are always faithful we describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities relations with the mckay correspondence and with exceptional sheaves on fano manifolds are given moreover the case of an elliptic curve is worked out in some detail

monodromy of monomially admissible fukaya seidel categories mirror to toric varieties abstract mirror symmetry for a toric variety involves laurent polynomials whose symplectic topology is related to the algebraic geometry of the toric variety we show that there is a monodromy action on the monomially admissible fukaya seidel categories of these laurent polynomials as the arguments of their coefficients vary that corresponds under homological mirror symmetry to tensoring by a line bundle naturally associated to the monomials whose coefficients are rotated in the process we introduce the monomially admissible fukaya seidel category as a new interpretation of the fukaya seidel category of a laurent polynomial on c n which has other potential applications and give evidence of homological mirror symmetry for non compact toric varieties

when all solutions of x qi t x t ti t oscillate abstract in this paper the long term behavior of solutions to the equation in the title are examined where q i t and t i t are positive in particular it is shown that if lim inf t i 1 n t i t q i t 1 e all solutions oscillate about 0 infinitely often

sufficient conditions for oscillation and nonoscillation of neutral equations received july 9 1986 consider the neutral delay differential equation x r p f x f r q t x r 0 o tat 1 where p q e c i co w and t d e iw we obtain sutlicient conditions for all solutions of eq 1 to oscillate our conditions are sharp in the sense than when the coefficients p and q are constants the conditions are also necessary we also obtain sufficient conditions for eq 1 to have a nonoscillatory solution when p r is a constant in the interval

smith theory and geometric hecke algebras in 1960 borel proved a localization result relating the rational cohomology of a topological space x to the rational cohomology of the fixed points for a torus action on x this result and its generalizations have many applications in lie theory in 1934 smith proved a similar localization result relating the mod p cohomology of x to the mod p cohomology of the fixed points for a mathbb z p action on x in this paper we study mathbb z p localization for constructible sheaves and functions we show that mathbb z p localization on loop groups is related via the geometric satake correspondence to some special homomorphisms that exist between algebraic groups defined over a field of small characteristic

necessary and sufficient conditions for oscillations of neutral equations with several coefficients consider the neutral equation with several positive and negative coefficients dd tx t ipix t i jrjx t j kqkx t k 0 1 where i j and k are initial segments of natural numbers pi i rj j qk are positive numbers and k 0 for i i j j and k k then a necessary and sufficient condition for the oscillation of all solutions of 1 is that its characteristic equation ipie i irje j kqke k 0 has no real roots

necessary and sufficient conditions for oscillations of neutral differential equations abstract consider the neutral delay differential equation x t px t qx t 0 t t 0 where q and are positive constants while p is a real parameter then a necessary and sufficient condition for all solutions of to oscillate is that the characteristic equation p e qe 0 of has no real roots

t duality and homological mirror symmetry for toric varieties abstract let x be a complete toric variety the coherent constructible correspondence of fang et al 2011 14 equates p erf t x with a subcategory sh c c m r of constructible sheaves on a vector space m r the microlocalization equivalence of nadler and zaslow 2009 27 and nadler 2009 25 relates these sheaves to a subcategory fuk t m r of the fukaya category of the cotangent t m r when x is nonsingular taking the derived category yields an equivariant version of homological mirror symmetry dcoh t x dfuk t m r which is an equivalence of triangulated tensor categories the nonequivariant coherent constructible correspondence of treumann preprint 33 embeds p erf x into a subcategory s h c t r of constructible sheaves on a compact torus t r when x is nonsingular the composition of and microlocalization yields a version of homological mirror symmetry dcoh x dfuk t t r which is a full embedding of triangulated tensor categories when x is nonsingular and projective the composition is compatible with t duality in the following sense an equivariant ample line bundle l has a hermitian metric invariant under the real torus whose connection defines a family of flat line bundles over the real torus orbits this data produces a t dual lagrangian brane l on the universal cover t m r of the dual real torus fibration we prove l l in fuk t m r thus equivariant homological mirror symmetry is determined by t duality

on level crossing in neutral integrodifferential equations necessary and sufficient conditions are obtained for all solutions of neutral integrodifferential equations of the formddt x t px t t rx t r a 0 k s x t s ds 0 t 0to have at least one zero on

a weighted estimating equation for missing covariate data with properties similar to maximum likelihood abstract in regression analysis missing covariate data occurs often a recent approach to analyzing such data is weighted estimating equations with weighted estimating equations the contribution to the estimating equation from a complete observation is weighted by the inverse probability of being observed in this article we propose a weighted estimating equation that is almost identical to the maximum likelihood estimating equations as such we propose an em type algorithm to solve these weighted estimating equations although the weighted estimating equations are a special case of those proposed earlier by robins et al our em type algorithm to solve them is new similar to robins and ritov we give the result that to obtain a consistent estimate of the regression parameters either the missing data mechanism or the distribution of the missing data given the observed data must be correctly specified we compare the weighted estimating equations to maximum likelihood via two examples a simulation a

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

dg quotients of dg categories abstract keller introduced a notion of quotient of a differential graded category modulo a full differential graded subcategory which agrees with verdier s notion of quotient of a triangulated category modulo a triangulated subcategory this work is an attempt to further develop his theory

sheaf quantization of hamiltonian isotopies and applications to nondisplaceability problems let i be an open interval m be a real manifold t m its cotangent bundle and phi phi t t in i a homogeneous hamiltonian isotopy of t m defined outside the zero section let lambda be the conic lagrangian submanifold associated with phi lambda is a subset of t m x t m x t i we prove the existence and unicity of a sheaf k on mxmxi whose microsupport is contained in the union of lambda and the zero section and whose restriction to t 0 is the constant sheaf on the diagonal of mxm we give applications of this result to problems of non displaceability in contact and symplectic topology in particular we prove that some strong morse inequalities are stable by hamiltonian isotopies and we also give results of non displaceability for positive isotopies in the contact setting in this new version we suppress one hypothesis in the main theorem and we extend the result of non displaceability for positive isotopies

representing the big tilting sheaves as holomorphic morse branes abstract we introduce morse branes in the fukaya category of a holomorphic symplectic manifold with the goal of constructing tilting objects in the category we give a construction of a class of morse branes in the cotangent bundles and apply it to give the holomorphic branes that represent the big tilting sheaves on flag varieties

local linear regression for generalized linear models with missing data fan heckman and wand proposed locally weighted kernel polynomial regression methods for generalized linear models and quasilikelihood functions when the covariate variables are missing at random we propose a weighted estimator based on the inverse selection probability weights distribution theory is derived when the selection probabilities are estimated nonparametrically we show that the asymptotic variance of the resulting nonparametric estimator of the mean function in the main regression model is the same as that when the selection probabilities are known while the biases are generally different this is different from results in parametric problems where it is known that estimating weights actually decreases asymptotic variance to reconcile the difference between the parametric and nonparametric problems we obtain a second order variance result for the nonparametric case we generalize this result to local estimating equations finite sample performance is examined via simulation studies the proposed method is demonstrated via an analysis of data from a case control study

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

legendrian knots and constructible sheaves we study the unwrapped fukaya category of lagrangian branes ending on a legendrian knot our knots live at contact infinity in the cotangent bundle of a surface the fukaya category of which is equivalent to the category of constructible sheaves on the surface itself consequently our category can be described as constructible sheaves with singular support controlled by the front projection of the knot we use a theorem of guillermou kashiwara schapira to show that the resulting category is invariant under legendrian isotopies a subsequent article establishes its equivalence to a category of representations of the chekanov eliashberg differential graded algebra we also find two connections to topological knot theory first drawing a positive braid closure on the annulus the moduli space of rank n objects maps to the space of local systems on a circle the second page of the spectral sequence associated to the weight filtration on the pushforward of the constant sheaf is the colored by n triply graded khovanov rozansky homology second drawing a positive braid closure in the plane the number of points of our moduli spaces over a finite field with q elements recovers the lowest coefficient in a of the homfly polynomial of the braid closure

semiparametric dimension reduction estimation for mean response with missing data model misspecification can be a concern for high dimensional data nonparametric regression obviates model specification but is impeded by the curse of dimensionality this paper focuses on the estimation of the marginal mean response when there is missingness in the response and multiple covariates are available we propose estimating the mean response through nonparametric functional estimation where the dimension is reduced by a parametric working index the proposed semiparametric estimator is robust to model misspecification it is consistent for any working index if the missing mechanism of the response is known or correctly specified up to unknown parameters even with misspecification in the missing mechanism it is consistent so long as the working index can recover e y x the conditional mean response given the covariates in addition when the missing mechanism is correctly specified the semiparametric estimator attains the optimal efficiency if e y x is recoverable through the working index robustness and efficiency of the proposed estimator is further investigated by simulations we apply the proposed method to a clinical trial for hiv

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