higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

tian s alpha _ m k hat k invariants on group compactifications in this paper we compute tian s alpha m k k times k invariant on a polarized g group compactification where k denotes a maximal compact subgroup of a connected complex reductive group g we prove that tian s conjecture see conjecture 1 1 below is true for alpha m k k times k invariant on such manifolds when k 1 but it fails in general by producing counter examples when k ge 2

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

least squares variogram fitting by spatial subsampling summary least squares methods are popular for fitting valid variogram models to spatial data the paper proposes a new least squares method based on spatial subsampling for variogram model fitting we show that the method proposed is statistically efficient among a class of least squares methods including the generalized least squares method further it is computationally much simpler than the generalized least squares method the method produces valid variogram estimators under very mild regularity conditions on the underlying random field and may be applied with different choices of the generic variogram estimator without analytical calculation an extension of the method proposed to a class of spatial regression models is illustrated with a real data example results from a simulation study on finite sample properties of the method are also reported

conservation laws for linear equations on braided linear spaces the properties of linear equations on braided linear spaces are investigated and conservation laws for them are derived the conserved currents are given in the explicit form the procedure is then applied to scalar wave equations on a quantum plane and on q minkowski space

on the second order properties of empirical likelihood with moment restrictions this paper considers the second order properties of empirical likelihood el for a parameter defined by moment restrictions which is the inferential framework of the generalized method of moments it is shown that the el defined for this general framework still admits the delicate second order property of bartlett correction this represents a substantial extension of all the established cases of bartlett correction for the el an empirical bartlett correction is proposed which is shown to work effectively in improving the coverage accuracy of confidence regions for the parameter

empirical likelihood based inference in conditional moment restriction models this paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions our estimator generalizes the maximum empirical likelihood estimator mele of qin and lawless 1994 using a kernel smoothing method we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood based procedure this yields a one step estimator which avoids estimating optimal instruments our likelihood ratio type statistic for parametric restrictions does not require the estimation of variance and achieves asymptotic pivotalness implicitly the estimation and testing procedures we propose are normalization invariant simulation results suggest that our new estimator works remarkably well in finite samples

free braided differential calculus braided binomial theorem and the braided exponential map braided differential operators i are obtained by differentiating the addition law on the braided covector spaces introduced previously such as the braided addition law on the quantum plane these are affiliated to a yang baxter matrix r the quantum eigenfunctions expr x v of the i braided plane waves are introduced in the free case where the position components xi are totally noncommuting a braided r binomial theorem and a braided taylor theorem expr a f x f a x are proven these various results precisely generalize to a generic r matrix and hence to n dimensions the well known properties of the usual one dimensional q differential and q exponential as a related application it is shown that the q heisenberg algebra px qxp 1 is a braided semidirect product c x c p of the braided line acting on itself a braided weyl algebra and similarly for its generalization to an arbitrary r matrix

q lorentz group and braided coaddition on q minkowski space we present a new version ofq minkowski space which has both a coaddition law and anslq 2 decomposition the additive structure forms a braided group rather than a quantum one in the process we obtain aq lorentz group which coacts covariantly on thisq minkowski space

quantum group gauge theory on quantum spaces we construct quantum group valued canonical connections on quantum homogeneous spaces including aq deformed dirac monopole on the quantum sphere of podles with quantum differential structure coming from the 3d calculus of woronowicz onsu q 2 the construction is presented within the setting of a general theory of quantum principal bundles with quantum group hopf algebra fibre associated quantum vector bundles and connection one forms both the base space spacetime and the total space are non commutative algebras quantum spaces

calibrated fibrations on noncompact manifolds via group actions in this paper we use lie group actions on noncompact riemannian manifolds with calibrations to construct calibrated submanifolds in particular if we have an n 1 torus acting on a noncompact calabi yau n fold with a trivial first cohomology then we have a special lagrangian fibration on that n fold we produce several families of examples for this construction and give some applications to special lagrangian geometry on compact almost calabi yau manifolds we also use group actions on noncompact g2 manifolds to construct coassociative submanifolds and we exhibit some new examples of coassociative submanifolds via this setup

on kahler einstein metrics on certain kahler manifolds with c1 m 0 on demontre qu il existe une metrique de kahler einstein sur une hypersurface de fermat a m dimensions de degre superieur a m 1

on bartlett correction of empirical likelihood in the presence of nuisance parameters summary lazar mykland 1999 showed that an empirical likelihood defined by two estimating equations with a nuisance parameter need not be bartlett correctable this paper shows that bartlett correction of empirical likelihood in the presence of a nuisance parameter depends critically on the way the nuisance parameter is removed when formulating the likelihood for the parameter of interest we establish in the broad framework of estimating functions that the empirical likelihood is still bartlett correctable if the nuisance parameter is profiled out given the value of the parameter of interest

large sample confidence regions based on subsamples under minimal assumptions in this article the construction of confidence regions by approximating the sampling distribution of some statistic is studied the true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data in the i i d context the method has been studied by wu in regular situations where the statistic is asymptotically normal the goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions essentially all that is required is that the statistic suitably normalized possesses a limit distribution under the true model unlike the bootstrap the convergence to the limit distribution need not be uniform in any sense the method is readily adapted to parameters of stationary time series or more generally homogeneous random fields for example an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field

hilbert series and obstructions to asymptotic semistability abstract given a polarized manifold there are obstructions for asymptotic chow semistability described as integral invariants which can be regarded as characters of the lie algebra of holomorphic vector fields in this paper we show that on toric fano manifolds the linear span of those lie algebra characters coincides with the derivatives of the laurent series of the hilbert series

braided geometry of the conformal algebra we show that the action of the special conformal transformations of the usual undeformed conformal group is the q 1 scaling limit of the braided adjoint action or r commutator of q minkowski space on itself we also describe the q deformed conformal algebra in r matrix form and its quasi structure

empirical likelihood for linear models empirical likelihood is a nonparametric method of inference it has sampling properties similar to the bootstrap but where the bootstrap uses resampling it profiles a multinomial likelihood supported on the sample its properties in i i d settings have been investigated in works by owen by hall and by diciccio hall and romano this article extends the method to regression problems fixed and random regressors are considered as are robust and heteroscedastic regressions to make the extension three variations on the original idea are considered it is shown that when some functionals of the distribution of the data are known one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization the result is first order equivalent to conditioning on a sample value of the known functional the use of a euclidean alternative to the likelihood function is investigated a triangular array version of the empirical likelihood theorem is given the one way anova and heteroscedastic regression models are considered in detail an example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model

alpha invariant and k stability of q fano varieties abstract we give a purely algebro geometric proof that if the invariant of a q fano variety x is greater than dim x dim x 1 then x o x k x is k stable the key of our proof is a relation among the seshadri constants the invariant and k stability it also gives applications concerning the automorphism group

braided momentum in the q poincare group the q poincare group of m schlieker et al z phys c 53 79 1992 is shown to have the structure of a semidirect product and coproduct b soq 1 3 where b is a braided quantum group structure on the q minkowski space of four momentum with braided coproduct p p 1 1 p here the necessary b is not a usual kind of quantum group but one with braid statistics similar braided vectors and covectors v r v r exist for a general r matrix the abstract structure of the q lorentz group is also studied

cross products by braided groups and bosonization let h be a braided cocommutative hopf algebra in a braided monoidal category c and b a hopf algebra in c on which h acts we construct a cross product hopf algebra b formula h in c as an application we show that every b in a certain class can be converted to an equivalent ordinary hopf algebra by a process of bosonization the class includes for example all super hopf algebras the constructions respect any quasitriangular structures on b as a corollary we show that if h r is an ordinary quasitriangular hopf algebra then the smash product by the adjoint action of h on itself had formula h can be given the structure of a hopf algebra we prove a similar result for any hopf algebra to which a quasitriangular hopf algebra maps

a construction of new families of minimal lagrangian submanifolds via torus actions in this paper we investigate connections between minimal lagrangian submanifolds and holomorphic vector fields in kahler manifolds our main result is let m2n n 2 be a kahler einstein manifold with positive scalar curvature with an effective structure preserving action by an n torus tn then precisely one regular orbit l of the tn action is a minimal lagrangian submanifold of m moreover there is an n 1 torus tn 1 tn and a sequence of non flat immersed minimal lagrangian tori lk in m such that all lk are invariant under tn 1 and lk locally converge to l in particular the supremum of the sectional curvatures of lk and the distance between l and lk go to 0 as k this result is new even for m pn for n 3

point and interval estimation of variogram models using spatial empirical likelihood we present a spatial blockwise empirical likelihood method for estimating variogram model parameters in the analysis of spatial data on a grid the method produces point estimators that require no spatial variance estimates to compute unlike least squares methods for variogram fitting but are as efficient as the best least squares estimator in large samples our approach also produces confidence regions for the variogram without requiring knowledge of the full joint distribution of the spatial data in addition the empirical likelihood formulation extends to spatial regression problems and allows simultaneous inference on both spatial trend and variogram parameters we examine the asymptotic behavior of the estimator analytically and investigate its behavior in finite samples through simulation studies

variance estimation for statistics computed from spatial lattice data summary a statistic s is computed on spatially indexed data x i e d where d is a finite subset of the integer lattice 22 we propose a method for estimating the variance and other moments of s by using only the data the set d may be irregularly shaped the statistic s may be arbitrarily complicated and no distributional assumptions marginal or joint are necessary the method uses the statistic computed on overlapping subshapes of d as replicates of s the estimator is simply the sample variance of the standardized replicates we demonstrate c2 consistency of the estimator under mild conditions on s and the strength of spatial dependence a rate of convergence is also given giving guidance into the appropriate choice of subshape size and the estimator is illustrated in two data examples

the existence of kahler einstein metrics on manifolds with positive anticanonical line bundle and a suitable finite symmetry group on utilise la methode de continuite pour demontrer l existence de metriques de kahler einstein pour des varietes de kahler de fibre linge positif anticanonique sous l hypothese additionnelle de l existence d un bon groupe de symetries fini ou compact

numerical kahler einstein metric on the third del pezzo the third del pezzo surface admits a unique kahler einstein metric which is not known in closed form the manifold s toric structure reduces the einstein equation to a single monge ampere equation in two real dimensions we numerically solve this nonlinear pde using three different algorithms and describe the resulting metric the first two algorithms involve simulation of ricci flow in complex and symplectic coordinates respectively the third algorithm involves turning the pde into an optimization problem on a certain space of metrics which are symplectic analogues of the algebraic metrics used in numerical work on calabi yau manifolds our algorithms should be applicable to general toric manifolds using our metric we compute various geometric quantities of interest including laplacian eigenvalues and a harmonic 1 1 form the metric and 1 1 form can be used to construct a klebanov tseytlin like supergravity solution

multiplier ideal sheaves and kahler einstein metrics of positive scalar curvature we present a method for proving the existence of kiihler einstein metrics of positive scalar curvature on certain compact complex manifolds and use the method to produce a large class of examples of compact kiihler einstein manifolds of positive scalar curvature suppose that m is a compact complex manifold of positive first chern class as is well known the existence of a kiihler einstein metric on m is equivalent to the existence of a solution to a certain complex monge ampere equation on m to solve this complex mongeampere equation by the method of continuity one needs only to establish the appropriate zeroth order a priori estimate suppose now that m does not admit a kiihler einstein metric so that the zeroth order a priori estimate fails to hold from this lack of an estimate we extract various global algebro geometric properties of m by introducing a coherent sheaf of ideals j on m called the multiplier ideal sheaf which carefully measures the extent to which the estimate fails the sheaf y is analogous to the subelliptic multiplier ideal sheaf that j j kohn introduced over a decade ago to obtain sufficient conditions for subellipticity of the d neumann problem now j is a global algebro geometric object on m and it so happens that j satisfies a number of highly nontrivial global algebro geometric conditions including a cohomology vanishing theorem in particular the complex analytic subspace v c m cut out by j is nonempty connected and has arithmetic genus zero if v is zero dimensional then it is a single reduced point while if v is one dimensional then its support is a tree of smooth rational curves the logarithmic geometric genus of m v always vanishes these considerations place nontrivial global algebro geometric restric

q euclidean space and quantum wick rotation by twisting the quantum matrix algebra r21x1x2 x2x1r is studied and proposed for the standard 2 2 case as the coordinates of q deformed euclidean space the algebra in this simplest case is isomorphic to the usual quantum matrices mq 2 but in a form which is naturally covariant under the euclidean rotations suq 2 suq 2 a quantum wick rotation is introduced that twists this system precisely into the approach to q minkowski space based on braided matrices and their associated spinorial q lorentz group

multiplier ideal sheaves and integral invariants on toric fano manifolds we extend nadel s results on some conditions for the multiplier ideal sheaves to satisfy which are described in terms of an obstruction defined by the first author applying our extension we can determine the multiplier ideal subvarieties on toric del pezzo surfaces which do not admit kahler einstein metrics we also show that one can define multiplier ideal sheaves for kahler ricci solitons and extend the result of nadel using the holomorphic invariant defined by tian and zhu

structures on braided spaces structures on quantum and braided spaces of the type defined via an r matrix are studied these include q minkowski and q euclidean spaces as additive braided groups the duality between the braided groups of vectors and covectors is proved and some first applications to braided geometry are made

a frequency domain empirical likelihood method for irregularly spaced spatial data this paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain unlike the frequency domain empirical likelihood fdel methodology for time series on a regular grid the formulation of the spatial fdel needs special care due to lack of the usual orthogonality properties of the discrete fourier transform for irregularly spaced data and due to presence of nontrivial bias in the periodogram under different spatial asymptotic structures a spatial fdel is formulated in the paper taking into account the effects of these factors the main results of the paper show that wilks phenomenon holds for a scaled version of the logarithm of the proposed empirical likelihood ratio statistic in the sense that it is asymptotically distribution free and has a chi squared limit as a result the proposed spatial fdel method can be used to build nonparametric asymptotically correct confidence regions and tests for covariance parameters that are defined through spectral estimating equations for irregularly spaced spatial data in comparison to the more common studentization approach a major advantage of our method is that it does not require explicit estimation of the standard error of an estimator which is itself a very difficult problem as the asymptotic variances of many common estimators depend on intricate interactions among several population quantities including the spectral density of the spatial process the spatial sampling density and the spatial asymptotic structure results from a numerical study are also reported to illustrate the methodology and its finite sample properties

examples of braided groups and braided matrices matrix braided groups are developed as an analog of the coordinate functions on a group or supergroup the 1 in the super case is replaced by braid statistics there are braided group analogs of all the classical simple lie groups as well as braided matrix groups and braided matrices b r for every regular solution r of the quantum yang baxter equations a direct verification of b r is provided and some of the simplest examples are computed in detail

kahler einstein metrics on complex surfaces with c 1 0 various estimates of the lower bound of the holomorphic invariant m defined in t are given here by using branched coverings potential estimates and lelong numbers of positive d closed 1 1 currents of certain type etc these estimates are then applied to produce kahler einstein metrics on complex surfaces withc1 0 in particular we prove that there are kahler einstein structures withc1 0 on any manifold of differential type cp 2 overline ncp 2 3 leqq n leqq 8

kahler einstein metrics with positive scalar curvature in this paper we prove that the existence of kahler einstein metrics implies the stability of the underlying kahler manifold in a suitable sense in particular this disproves a long standing conjecture that a compact kahler manifold admits kahler einstein metrics if it has positive first chern class and no nontrivial holomorphic vector fields we will also establish an analytic criterion for the existence of kahler einstein metrics our arguments also yield that the analytic criterion is satisfied on stable kahler manifolds provided that the partial c 0 estimate posed in t6 is true

empirical likelihood methods with weakly dependent processes this paper studies the method of empirical likelihood in models with weakly dependent processes in such cases if the likelihood function is formulated as if the data process were independent obviously empirical likelihood fails we propose to use empirical likelihood of blocks of observations to solve this problem in a nonparametric manner this method of blockwise empirical likelihood preserves the dependence of data and the resulting likelihood ratios can be used to construct asymptotically valid confidence intervals we consider general estimating equations for which an efficient estimator is derived by maximizing blockwise empirical likelihood we also introduce blocks of blocks empirical likelihood to conduct inference for parameters of the infinite dimensional joint distribution of data the smooth function model is used for such cases we show that blockwise empirical likelihood of the smooth function model with weakly dependent processes is bartlett correctable a wide variety of problems such as time series regressions and spectral densities can be treated using our methodology

empirical likelihood confidence regions in time series models summary this paper develops empirical likelihood in time series models by application of whittle s estimation method one obtains an m estimator of the parameter of a stationary time series from approximately independent observations the periodogram ordinates this estimator is used to obtain an empirical likelihood ratio which is asymptotically distributed as x2 and which can be used to construct confidence regions a procedure for the bartlett correction is also proposed finally small sample properties of the empirical likelihood confidence regions are explored through a simulation

conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces the conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived for discrete models the conserved charges are constructed explicitly the applications of the general method include equations on quantum plane supersymmetric equations for chiral and antichiral supermultiplets auxiliary equations of integrable models which means various cases of nonlinear toda lattice equations and anomalous diffusion equation

complete toric varieties with reductive automorphism group we give equivalent and sufficient criteria for the automorphism group of a complete toric variety respectively a gorenstein toric fano variety to be reductive in particular we show that the automorphism group of a gorenstein toric fano variety is reductive if the barycenter of the associated reflexive polytope is zero furthermore a sharp bound on the dimension of the reductive automorphism group of a complete toric variety is proven by studying the set of demazure roots

tapered block bootstrap summary we introduce and study tapered block bootstrap methodology that yields an improvement over the well known block bootstrap for time series of kiinsch 1989 the asymptotic validity and the favourable bias properties of the tapered block bootstrap are shown the important practical issues of optimally choosing the window shape and the block size are addressed in detail while some finite sample simulations are presented validating the good performance of the tapered block bootstrap