lie theory for nilpotent l algebras the deligne groupoid is a functor from nilpotent differential graded lie algebras concentrated in positive degrees to groupoids in the special case of lie algebras over a field of characteristic zero it gives the associated simply connected lie group we generalize the deligne groupoid to a functor from l algebras concentrated in degree n to n groupoids we actually construct the nerve of the n groupoid which is an enriched kan complex the construction of gamma is quite explicit it is based on dupont s proof of the de rham theorem and yields higher dimensional analogues of holonomy and of the campbell hausdorff formula in the case of abelian l algebras i e chain complexes the functor is the dold kan simplicial set

estimation of heterogeneous individual treatment effects with endogenous treatments this article estimates individual treatment effects ite and its probability distribution in a triangular model with binary valued endogenous treatments our estimation procedure takes two steps

instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings this paper reports estimates of the effects of jtpa training programs on the distribution of earnings the estimation uses a new instrumental variable iv method that measures program impacts on quantiles the quantile treatment effects qte estimator reduces to quantile regression when selection for treatment is exogenously determined qte can be computed as the solution to a convex linear programming problem although this requires first step estimation of a nuisance function we develop distribution theory for the case where the first step is estimated nonparametrically for women the empirical results show that the jtpa program had the largest proportional impact at low quantiles perhaps surprisingly however jtpa training raised the quantiles of earnings for men only in the upper half of the trainee earnings distribution

a method of centers based on barrier functions for solving optimal control problems with continuum state and control constraints this paper describes a method of centers based on barrier functions for solving optimal control problems with continuum inequality constraints on the state and control the method decomposes the original problem into a sequence of easily solved optimal control problems with control constraints only the method requires only approximate solution of these problems

formal completions and idempotent completions of triangulated categories of singularities abstract the main goal of this paper is to prove that the idempotent completions of triangulated categories of singularities of two schemes are equivalent if the formal completions of these schemes along singularities are isomorphic we also discuss thomason s theorem on dense subcategories and a relation to the negative k theory

lagrangian floer theory on compact toric manifolds i we introduced the notion of weakly unobstructed lagrangian submanifolds and constructed their potential function po purely in terms of a model data in fooo3 in this article we carry out explicit calculations involving po on toric manifolds and study the relationship between this class of lagrangian submanifolds with the earlier work of givental g1 which advocates that the quantum cohomology ring is isomorphic to the jacobian ring of a certain function called the landau ginzburg superpotential combining this study with the results from fooo3 we also apply the study to various examples to illustrate its implications to symplectic topology of lagrangian fibers of toric manifolds in particular we relate it to the hamiltonian displacement property of lagrangian fibers and to entov polterovich s symplectic quasi states

inference on counterfactual distributions counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics in this article we develop modeling and inference tools for counterfactual distributions based on regression methods the counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates for either of these scenarios we derive joint functional central limit theorems and bootstrap validity results for regression based estimators of the status quo and counterfactual outcome distributions these results allow us to construct simultaneous confidence sets for function valued effects of the counterfactual changes including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals these confidence sets can be used to test functional hypotheses such as no effect positive effect or stochastic dominance our theory applies to general counterfactual changes and covers the main regression methods including classical quantile duration and distribution regressions we illustrate the results with an empirical application to wage decompositions using data for the united states as a part of developing the main results we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution we show that distribution regression encompasses the cox duration regression and represents a useful alternative to quantile regression we establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals publication abstract

gross fibrations syz mirror symmetry and open gromov witten invariants for toric calabi yau orbifolds given a toric calabi yau orbifold x whose underlying toric variety is semi projective we construct and study a non toric lagrangian torus bration on x which we call the gross bration we apply the strominger yau zaslow recipe to the gross bration of a toric modication of x to construct its instanton corrected mirror where the instanton corrections come from genus 0 open orbifold gromov witten invariants which are virtual counts of holomorphic orbi disks inx bounded by bers of the gross bration we explicitly evaluate all these invariants by rst proving an open closed equality and then employing the toric mirror theorem for suitable toric parital compactications of x our calculations are then applied to 1 prove a conjecture of gross siebert on a relation between genus 0 open orbifold gromov witten invariants and mirror maps ofx this is called the open mirror theorem which leads to an enumerative meaning of mirror maps and 2 demonstrate how open orbifold gromov witten invariants for toric calabi yau orb ifolds change under toric crepant resolutions this is an open analogue of ruan s crepant resolution conjecture

a feasible directions algorithm for optimal control problems with state and control constraints convergence analysis in this paper we describe an optimization algorithm for the computation of solutions to optimal control problems with control state and terminal constraints inequality and equality constraints are dealt with by means of feasible directions and exact penalty approaches respectively we establish a general convergence property of the algorithm which makes no reference to the existence of accumulation points in this analysis the compactness of the space of relaxed controls is used only to guarantee boundedness of the sequence of penalty parameters we also demonstrate that relaxed accumulation points of sequences generated by the algorithm satisfy standard first order necessary conditions of optimality the algorithm contains a number of computation saving features including an varepsilon active strategy for dealing with the infinite dimensional inequality constraints our convergence analysis provides techniques for studying the convergence properties of related optimization algorithms in which direction finding subproblems involve the approximation of directional derivatives of the chebyshev functional associated with state constraints a companion paper provides details of implementation and numerical examples

efficient estimation of limited dependent variable models with endogenous explanatory variables abstract this paper discusses asymptotically efficient estimation of the parameters of limited dependent variable models with endogenous explanatory variables general results on asymptotic efficiency of two stage and amemiya gls estimators are derived and used to obtain a simple asymptotically efficient estimator of the structural coefficients this estimator can be calculated by applying gls to estimates of the reduced form coefficients that are obtained by using reduced form residuals as additional explanatory variables it is also shown that it is possible to obtain asymptotically efficient estimators of the other coefficients by a modified minimum chi square method

the extended bigraded toda hierarchy we generalize the toda lattice hierarchy by considering n m dependent variables we construct roots and logarithms of the lax operator which are uniquely defined operators with coefficients that are series of differential polynomials in the dependent variables and we use them to provide a lax pair definition of the extended bigraded toda hierarchy generalizing 4 using r matrix theory we give the bi hamiltonian formulation of this hierarchy and we prove the existence of a tau function for its solutions finally we study the dispersionless limit and its connection with a class of frobenius manifolds on the orbit space of the extended affine weyl groups of the a series defined by dubrovin and zhang 1998 compos math 111 167

brief paper optimal control problems with a continuous inequality constraint on the state and the control we consider an optimal control problem with a nonlinear continuous inequality constraint both the state and the control are allowed to appear explicitly in this constraint by discretizing the control space and applying a novel transformation a corresponding class of semi infinite programming problems is derived a solution of each problem in this class furnishes a suboptimal control for the original problem furthermore we show that such a solution can be computed efficiently using a penalty function method on the basis of these two ideas an algorithm that computes a sequence of suboptimal controls for the original problem is proposed our main result shows that the cost of these suboptimal controls converges to the minimum cost for illustration an example problem is solved

deformation theory of objects in homotopy and derived categories ii pro representability of the deformation functor abstract this is the second paper in a series in part i we developed deformation theory of objects in homotopy and derived categories of dg categories here we extend these derived deformation functors to an appropriate bicategory of artinian dg algebras and prove that these extended functors are pro representable in a strong sense

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

on the optimal control of systems described by evolution equations the authors present a mathematical foundation for the algorithmic solution of free and fixed time optimal control problems with evolution equation dynamics finite dimensional controls and constraints on the controls and end points in particular i expressions for the derivatives of the solutions of the evolution equations are developed with respect to controls in l m 2 0 1 and to the final time ii the solutions of the relaxed evolution equations are shown to have a certain kind of directional derivative iii algorithmic optimality conditions are developed with respect to both ordinary and relaxed controls and the final time and iv an approximation theory is presented that shows that finite dimensional minimax and methods of centers type algorithms can be used to obtain arbitrarily good approximations to stationary controls for optimal control problems with evolution equation dynamics and various constraints

treatment effects with censoring and endogeneity this article develops a nonparametric approach to identification and estimation of treatment effects on censored outcomes when treatment may be endogenous and have arbitrarily heterogenous effects identification is based on an instrumental variable that satisfies the exclusion and monotonicity conditions standard in the local average treatment effects framework the article proposes a censored quantile treatment effects estimator derives its asymptotic distribution and illustrates its performance using monte carlo simulations even in the exogenous case the estimator performs better in finite samples than existing censored quantile regression estimators and performs nearly as well as maximum likelihood estimators in cases where their distributional assumptions hold an empirical application to a subsidized job training program finds that participation significantly and dramatically reduced the duration of jobless spells especially at the right tail of the distribution

quantile regression with censoring and endogeneity in this paper we develop a new censored quantile instrumental variable cqiv estimator and describe its properties and computation the cqiv estimator combines powell 1986 censored quantile regression cqr to deal with censoring with a control variable approach to incorporate endogenous regressors the cqiv estimator is obtained in two stages that are nonadditive in the unobservables the first stage estimates a nonadditive model with infinite dimensional parameters for the control variable such as a quantile or distribution regression model the second stage estimates a nonadditive censored quantile regression model for the response variable of interest including the estimated control variable to deal with endogeneity for computation we extend the algorithm for cqr developed by chernozhukov and hong 2002 to incorporate the estimation of the control variable we give generic regularity conditions for asymptotic normality of the cqiv estimator and for the validity of resampling methods to approximate its asymptotic distribution we verify these conditions for quantile and distribution regression estimation of the control variable our analysis covers two stage uncensored quantile regression with nonadditive first stage as an important special case we illustrate the computation and applicability of the cqiv estimator with a monte carlo numerical example and an empirical application on estimation of engel curves for alcohol

resolutions in factorization categories building upon ideas of eisenbud buchweitz positselski and others we introduce the notion of a factorization category we then develop some essential tools for working with factorization categories including constructions of resolutions of factorizations from resolutions of their components and derived functors using these resolutions we lift fully faithfulness and equivalence statements from derived categories of abelian categories to derived categories of factorizations some immediate geometric consequences include a realization of the derived category of a projective hypersurface as matrix factorizations over a noncommutative algebra and recover of a theorem of baranovsky and pecharich

on the frobenius manifolds for cusp singularities abstract we show that the frobenius manifold associated to the pair of a cusp singularity and its canonical primitive form is isomorphic to the one constructed from the gromov witten theory for an orbifold projective line with at most three orbifold points we also calculate the intersection form of the frobenius manifold

the mckay correspondence as an equivalence of derived categories the classical mckay correspondence relates representations of a finite subgroup g sl 2 c to the cohomology of the well known minimal resolution of the kleinian singularity c2 g gonzalez sprinberg and verdier 10 interpreted the mckay correspondence as an isomorphism on k theory observing that the representation ring of g is equal to the g equivariant k theory of c2 more precisely they identify a basis of the k theory of the resolution consisting of the classes of certain tautological sheaves associated to the irreducible representations of g

iterative procedures for constrained and unilateral optimization problems we study an iterative procedure for determining an extremal of a nonconvex optimization problem with unilateral constraints patterned on the unilateral problems of optimal control we also investigate auxiliary procedures for determining inf alpha mid alpha 0 in a where a is a closed convex subset of a hilbert space mathbb r times h and for finding a point s q in a nearest some given point q

exterior powers of the adjoint representation and the weyl ring of e8 abstract i derive explicitly all polynomial relations in the character ring of e 8 of the form k e 8 p k 1 8 0 where k e 8 is an arbitrary exterior power of the adjoint representation and i is the ith fundamental character this has simultaneous implications for the theory of relativistic integrable systems seiberg witten theory quantum topology orbifold gromov witten theory and the arithmetic of elliptic curves the solution is obtained by reducing the problem to a large but finite dimensional linear problem which is amenable to an efficient solution via distributed computation

equivariant gw theory of stacky curves we extend okounkov and pandharipande s work on the equivariant gromov witten theory of mathbb p 1 to a class of stacky curves mathcal x our main result uses virtual localization and the orbifold elsv formula to express the tau function tau mathcal x as a vacuum expectation on a fock space

stokes matrices for the quantum cohomologies of a class of orbifold projective lines we prove the dubrovin s conjecture for the stokes matrices for the quantum cohomology of orbifold projective lines the conjecture states that the stokes matrix of the first structure connection of the frobenius manifold constructed from the gromov witten theory coincides with the euler matrix of a full exceptional collection of the bounded derived category of the coherent sheaves our proof is based on the homological mirror symmetry primitive forms of affine cusp polynomials and the picard lefschetz theory

chern characters and hirzebruch riemann roch formula for matrix factorizations we study the category of matrix factorizations for an isolated hypersurface singularity we compute the canonical bilinear form on the hochschild homology of this category we find explicit expressions for the chern character and the boundary bulk maps and derive an analogue of the hirzebruch riemann roch formula for the euler characteristic of the hom space between a pair of matrix factorizations we also establish g equivariant versions of these results

intersection theory on the moduli space of curves and the matrix airy function we show that two natural approaches to quantum gravity coincide this identity is nontrivial and relies on the equivalence of each approach to kdv equations we also investigate related mathematical problems

homological mirror symmetry for calabi yau hypersurfaces in projective space we prove homological mirror symmetry for a smooth d dimensional calabi yau hypersurface in projective space for any d 3 for example d 3 is the quintic threefold the main techniques involved in the proof are the construction of an immersed lagrangian sphere in the d dimensional pair of pants the introduction of the relative fukaya category and an understanding of its grading structure a description of the behaviour of this category with respect to branched covers via an orbifold fukaya cate gory a morse bott model for the relative fukaya category that allows one to make explicit computations and the introduction of certain graded categories of matrix factorizations mirror to the relative fukaya category

polynomial modular frobenius manifolds the moduli space of frobenius manifolds carries a natural involutive symmetry and a distinguished class so called modular frobenius manifolds lie at the fixed points of this symmetry in this paper a classification of semi simple modular frobenius manifolds which are polynomial in all but one of the variables is begun and completed for three and four dimensional manifolds the resulting examples may also be obtained from higher dimensional manifolds by a process of folding the relationship of these results with orbifold quantum cohomology is also discussed

localized mirror functor for lagrangian immersions and homological mirrorsymmetry for mathbb p 1_ a b c this paper gives a new way of constructing landau ginzburg mirrors using deformation theory of lagrangian immersions motivated by the works of seidel strominger yau zaslow and fukaya oh ohta ono moreover we construct a canonical functor from the fukaya category to the mirror category of matrix factorizations this functor derives homological mirror symmetry under some explicit assumptions as an application the construction is applied to spheres with three orbifold points to produce their quantum corrected mirrors and derive homological mirror symmetry furthermore we discover an enumerative meaning of the inverse mirror map for elliptic curve quotients

homological mirror symmetry for curves of higher genus abstract this paper is devoted to homological mirror symmetry conjecture for curves of higher genus it was proposed by katzarkov as a generalization of original kontsevich s conjecture a version of this conjecture in the case of the genus two curve was proved by seidel 25 based on the paper of seidel we prove the conjecture in the same version for curves of genus g 3 namely we relate the fukaya category of a genus g curve to the category of singularities of zero fiber in the mirror dual landau ginzburg model we also prove a kind of reconstruction theorem for hypersurface singularities namely formal type of hypersurface singularity i e a formal power series up to a formal change of variables can be reconstructed with some technical assumptions from its d z 2 g category of landau ginzburg branes the precise statement is theorem 1 2

enumerative meaning of mirror maps for toric calabi yau manifolds abstract we prove that the inverse of a mirror map for a toric calabi yau manifold of the form k y where y is a compact toric fano manifold can be expressed in terms of generating functions of genus 0 open gromov witten invariants defined by fukaya oh ohta ono 2010 15 such a relation between mirror maps and disk counting invariants was first conjectured by gross and siebert 2011 24 conjecture 0 2 and remark 5 1 as part of their program and was later formulated in terms of fukaya oh ohta ono s invariants in the toric calabi yau case in chan et al 2012 8 conjecture 1 1

an exact penalty function algorithm for control problems with state and control constraints this paper describes an exact penalty function algorithm for solving control problems with state control and terminal constraints and establishes its convergence properties a convex optimal control problem is defined whose solution yields a search direction which satisfies the control constraints and reduces a first order estimate of the exact penalty function step length is determined using an armijo like procedure an adaptive procedure for adjusting the penalty parameter completes the algorithm

inference in censored models with endogenous regressors this paper analyzes the linear regression model y x with a conditional median assumption med e z 0 where z is a vector of exogenous instrument random variables we study inference on the parameter when y is censored and x is endogenous we treat the censored model as a model with interval observation on an outcome thus obtaining an incomplete model with inequality restrictions on conditional median regressions we analyze the identified features of the model and provide sufficient conditions for point identification of the parameter we use a minimum distance estimator to consistently estimate the identified features of the model we show that under point identification conditions and additional regularity conditions the estimator based on inequality restrictions is n normal and we derive its asymptotic variance one can use our setup to treat the identification and estimation of endogenous linear median regression models with no censoring a monte carlo analysis illustrates our estimator in the censored and the uncensored case

homological mirror symmetry for punctured spheres we prove that the wrapped fukaya category of a punctured sphere s with an arbitrary number of points removed is equivalent to the triangulated category of singularities of a mirror landau ginzburg model proving one side of the homological mirror symmetry conjecture in this case by investigating fractional gradings on these categories we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the landau ginzburg model

censored regression quantiles with endogenous regressors this paper develops a semiparametric method for estimation of the censored regression model when some of the regressors are endogenous and continuously distributed and instrumental variables are available for them a distributional exclusion restriction is imposed on the unobservable errors whose conditional distribution is assumed to depend on the regressors and instruments only through a lower dimensional control variable here assumed to be the difference between the endogenous regressors and their conditional expectations given the instruments this assumption which implies a similar exclusion restriction for the conditional quantiles of the censored dependent variable is used to motivate a two stage estimator of the censored regression coefficients in the first stage the conditional quantile of the dependent variable given the instruments and the regressors is nonparametrically estimated as are the first stage reduced form residuals to be used as control variables the second stage estimator is a weighted least squares regression of pairwise differences in the estimated quantiles on the corresponding differences in regressors using only pairs of observations for which both estimated quantiles are positive i e in the uncensored region and the corresponding difference in estimated control variables is small the paper gives the form of the asymptotic distribution for the proposed estimator and discusses how it compares to similar estimators for alternative models

contraction algebra and singularity of three dimensional flopping contraction donovan and wemyss duke math j 165 8 1397 1474 2016 introduced the contraction algebra of flopping curves in threefold they conjectured that the contraction algebra determines the formal neighborhood of the underlying singularity of the contraction in this paper we prove that the contraction algebra together with its natural a infty structure constructed in hua and toda int math res not rnw333 2017 determine the formal neighborhood of the singularity

lagrangian floer potential of orbifold spheres abstract for each sphere with three orbifold points we construct an algorithm to compute the open gromov witten potential which serves as the quantum corrected landau ginzburg mirror and is an infinite series in general this gives the first class of general type geometries whose full potentials can be computed as a consequence we obtain an enumerative meaning of mirror maps for elliptic curve quotients furthermore we prove that the open gromov witten potential is convergent even in the general type cases and has an isolated singularity at the origin which is an important ingredient of proving homological mirror symmetry

gromov witten theory of orbicurves the space of tri polynomials and symplectic field theory of seifert fibrations we compute with symplectic field theory sft techniques the gromov witten theory of mathbb p 1 alpha 1 ldots alpha a i e the complex projective line with a orbifold points a natural subclass of these orbifolds the ones with polynomial quantum cohomology gives rise to a family of polynomial frobenius manifolds and integrable systems of hamiltonian pdes which extend the dispersionless bigraded toda hierarchy carlet the extended bigraded toda hierarchy arxiv preprint arxiv math ph 0604024 we then define a frobenius structure on the spaces of polynomials in three complex variables of the form f x y z xyz p1 x p2 y p3 z which contains as special cases the ones constructed on the space of laurent polynomials dubrovin geometry of 2d topologica field theories integrable systems and quantum groups springer lecture notes in mathematics 1620 120 348 1996 milanov and tseng the space of laurent polynomials mathbb p 1 orbifolds and integrable hierarchies preprint arxiv math 0607012v3 math ag we prove a mirror theorem stating that these frobenius structures are isomorphic to the ones found before for polynomial mathbb p 1 orbifolds finally we link rational sft of seifert fibrations over mathbb p 1 a b c with orbifold gromov witten invariants of the base extending a known result bourgeois a morse bott approach to contact homology ph d dissertation stanford university 2002 valid in the smooth case

conopt a grg code for large sparse dynamic nonlinear optimization problems the paper presents conopt an optimization system for static and dynamic large scale nonlinearly constrained optimization problems the system is based on the grg algorithm all computations involving the jacobian of the constraints use sparse matrix algorithm from linear programming modified to take optimal advantage of the nonlinearity the paper presents the main features of the system especially the inversion routines and their data structures the dynamic setting of tolerances in newton s algorithm and the user features in the overall packaging computational experience with some medium to large models is presented

quantile and probability curves without crossing this paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions also known as the quantile crossing problem bassett and koenker 1982 the method consists in sorting or monotone rearranging the original estimated non monotone curve into a monotone rearranged curve we show that the rearranged curve is closer to the true quantile curve than the original curve in finite samples establish a functional delta method for rearrangement related operators and derive functional limit theory for the entire rearranged curve and its functionals we also establish validity of the bootstrap for estimating the limit law of the entire rearranged curve and its functionals our limit results are generic in that they apply to every estimator of a monotone function provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions consequently our results apply to estimation of other econometric functions with monotonicity restrictions such as demand production distribution and structural distribution functions we illustrate the results with an application to estimation of structural distribution and quantile functions using data on vietnam veteran status and earnings

identification and estimation of local average treatment effects we investigate conditions sufficient for identification of average treatment effects using instrumental variables first we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect we then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument finally we derive the probability limit of the standard iv estimator under these conditions it is seen to be a weighted average of local average treatment effects this abstract was borrowed from another version of this item

quantile treatment effects in the regression discontinuity design abstract we introduce a nonparametric estimator for local quantile treatment effects in the regression discontinuity rd design the procedure uses local distribution regression to estimate the marginal distributions of the potential outcomes we illustrate the procedure through monte carlo simulations and an application on the distributional effects of a universal pre k program in oklahoma we find that participation in a pre k program significantly raises the lower end and the middle of the distribution of test scores

towards mirror symmetry for varieties of general type abstract the goal of this paper is to propose a theory of mirror symmetry for varieties of general type using landau ginzburg mirrors as motivation we describe the mirror of a hypersurface of general type and more generally varieties of non negative kodaira dimension as the critical locus of the zero fibre of a certain landau ginzburg potential the critical locus carries a perverse sheaf of vanishing cycles our main result shows that one obtains the interchange of hodge numbers expected in mirror symmetry this exchange is between the hodge numbers of the hypersurface and certain hodge numbers defined using a mixed hodge structure on the hypercohomology of the perverse sheaf

on the fukaya categories of higher genus surfaces abstract we construct the fukaya category of a closed surface equipped with an area form using only elementary essentially combinatorial methods we also compute the grothendieck group of its derived category

an alternative estimator for the censored quantile regression model the paper introduces an alternative estimator for the linear censored quantile regression model the objective function is globally convex and the estimator is a solution to a linear programming problem hence a global minimizer is obtained in a finite number of simplex iterations the suggested estimator also applies to the case where the censoring point is an unknown function of a set of regressors it is shown that under fairly weak conditions the estimator has a n convergence rate and is asymptotically normal in the case of a fixed censoring point its asymptotic property is nearly equivalent to that of the estimator suggested by powell 1984 1986a a monte carlo study performed shows that the suggested estimator has very desirable small sample properties it precisely corrects for the bias induced by censoring even when there is a large amount of censoring and for relatively small sample sizes

three step censored quantile regression and extramarital affairs this article suggests very simple three step estimators for censored quantile regression models with a separation restriction on the censoring probability the estimators are theoretically attractive i e asymptotically as efficient as the celebrated powell s censored least absolute deviation estimator at the same time they are conceptually simple and have trivial computational expenses they are especially useful in samples of small size or models with many regressors with desirable finite sample properties and small bias the separation restriction costs a small reduction of generality relative to the canonical censored regression quantile model yet its main plausible features remain intact the estimator can also be used to estimate a large class of traditional models including the normal amemiya tobin model and many accelerated failure and proportional hazard models we illustrate the approach with an extramarital affairs example and contrast our findings with those of fair

on the derived categories of degree d hypersurface fibrations we provide descriptions of the derived categories of degree d hypersurface fibrations which generalize a result of kuznetsov for quadric fibrations and give a relative version of a well known theorem of orlov using a local generator and morita theory we re interpret the resulting matrix factorization category as a derived equivalent sheaf of dg algebras on the base then applying homological perturbation methods we obtain a sheaf of a infty algebras which gives a new description of homological projective duals for relative d veronese embeddings recovering the sheaf of clifford algebras obtained by kuznetsov in the case when d 2