koszul duality of affine kac moody algebras and cyclotomic rational double affine hecke algebras abstract we give a proof of the parabolic singular koszul duality for the category o of affine kac moody algebras the main new tool is a relation between moment graphs and finite codimensional affine schubert varieties we apply this duality to q schur algebras and to cyclotomic rational double affine hecke algebras this yields a proof of a conjecture of chuang miyachi relating the level rank duality with the ringel koszul duality of cyclotomic rational double affine hecke algebras

syzygies of abelian varieties let a be an ample line bundle on an abelian variety x over an algebraically closed field a theorem of koizumi ko s developing mumford s ideas and results m states that if m 3 the line bundle l ao embeds x in projective space as a projectively normal variety moreover a celebrated theorem of mumford m2 slightly refined by kempf k4 asserts that the homogeneous ideal of x is generated by quadrics as soon as m 4 such results turn out to be particular cases of a statement conjectured by rob lazarsfeld concerning the minimal resolution of the graded algebra rl 0 ho x l h over the polynomial ring sl do symhho x l the purpose of this paper is to prove lazarsfeld s conjecture to put such matters into perspective it is useful to review the case of projective curves a classical theorem of castelnuovo states that a curve x embedded in projective space by a complete linear system ili is projectively normal as soon as deg l 2g x 1 and a theorem of mattuck fujita and saint donat states that if deg l 2g x 2 then the homogeneous ideal of x is generated by quadrics green g1 unified re interpreted and generalized these results to a statement about syzygies specifically given a smooth projective variety x and a very ample line bundle l on x a minimal resolution of rl as a graded sl module notation as above looks like

the subset argument and consistency of mle in glmm answer to an open problem and beyond we give answer to an open problem regarding consistency of the maximum likelihood estimators mles in generalized linear mixed models glmms involving crossed random effects the solution to the open problem introduces an interesting nonstandard approach to proving consistency of the mles in cases of dependent observations using the new technique we extend the results to mles under a general glmm an example is used to further illustrate the technique

estimation in generalized mixed models regression models containing fixed and random effects may have a response variable which is not normally distributed the generalized mixed model includes both discrete and continuous response variables and is developed here for problems in which the regression variables enter linearly into the model best linear unbiased predictor methods are extended to maximum likelihood and residual maximum likelihood estimation procedures applications in modelling discrete response variables and in survival analysis are discussed

projective normality and syzygies of algebraic surfaces in this work we develop new techniques to compute koszul cohomology groups for several classes of varieties as applications we prove results on projective normality and syzygies for algebraic surfaces from more general results we obtain in particular the following a mukai s conjecture and stronger variants of it regarding projective normality and normal presentation for surfaces with kodaira dimension 0 and uniform bounds for higher syzygies associated to adjoint linear series b effective bounds along the lines of mukai s conjecture regarding projective normality and normal presentation for surfaces of positive kodaira dimension and c results on projective normality for pluricanonical models of surfaces of general type recovering and strengthening results by ciliberto and generalizations of them to higher syzygies in addition we also extend the above results to singular surfaces

blocks of cyclotomic hecke algebras abstract this paper classifies the blocks of the cyclotomic hecke algebras of type g r 1 n over an arbitrary field rather than working with the hecke algebras directly we work instead with the cyclotomic schur algebras the advantage of these algebras is that the cyclotomic jantzen sum formula gives an easy combinatorial characterization of the blocks of the cyclotomic schur algebras we obtain an explicit description of the blocks by analyzing the combinatorics of jantzen equivalence we remark that a proof of the classification of the blocks of the cyclotomic hecke algebras was announced in 1999 unfortunately cox has discovered that this previous proof is incomplete

heisenberg algebras and rational double affine hecke algebras in this paper we categorify the heisenberg action on the fock space via the category o of cyclotomic rational double affine hecke algebras this permits us to relate the filtration by the support on the grothendieck group of o to a representation theoretic grading defined using the heisenberg action this implies a recent conjecture of etingof

log canonical singularities are du bois a recurring difficulty in the minimal model program mmp is that while log terminal singularities are quite well behaved for instance they are rational log canonical singularities are much more complicated they need not even be cohenmacaulay the aim of this paper is to prove that as conjectured in kol92 1 13 log canonical singularities are du bois the concept of du bois singularities abbreviated as db was introduced by steenbrink in ste83 as a weakening of rationality it is not clear how to define du bois singularities in positive characteristic so we work over a field of characteristic 0 throughout the paper the precise definition is rather involved see 1 10 but our main applications rely only on the following consequence

koszul duality and modular representations of semi simple lie algebras in this paper we prove that if g is a connected simply connected semi simple algebraic group over an algebraically closed field of sufficiently large characteristic then all the blocks of the restricted enveloping algebra of the lie algebra of g can be endowed with a koszul grading extending results of andersen jantzen soergel we also give information about the koszul dual rings in the case of the block associated to a regular character x of the harish chandra center the dual ring is related to modules over the enveloping algebra specialized at x with generalized trivial frobenius character our main tool is the localization theory developed by bezrukavnikov mirkovic rumynin

generalized linear models with random effects salamander mating revisited in recent years much effort has been devoted to extending regression methodology to non gaussian data where responses are not independent these methods for dependent responses are suitable for data from longitudinal studies or nested designs however use of these methods for crossed designs seems to have serious limitations due to the intensive computations involved because of the intractable nature of the joint distribution in this paper we cast the problem in a bayesian framework and use a monte carlo method the gibbs sampler to avoid current computational limitations the flexibility of this approach is illustrated by analyzing the interesting salamander mating data reported by mccullagh and nelder 1989 generalized linear models 2nd edition london chapman and hall

quadratic duals koszul dual functors and applications this paper studies quadratic and koszul duality for modules over positively graded categories typical examples are modules over a path algebra which is graded by the path length of a not necessarily finite quiver with relations we present a very general definition of quadratic and koszul duality functors backed up by explicit examples this generalizes the work of beilinson ginzburg and soergel 1996 in two substantial ways we work in the setup of graded categories i e we allow infinitely many idempotents and also de ne a koszul duality functor for not necessarily koszul categories as an illustration of the techniques we reprove the koszul duality ryom hansen 2004 of translation and zuckerman functors for the classical category o in a quite elementary and explicit way from this we deduce a conjecture of bernstein frenkel and khovanov 1999 as applications we propose a definition of a koszul dual category for integral blocks of harish chandra bimodules and for blocks outside the critical hyperplanes for the kac moody category o

global generation of pluricanonical and adjoint linear series on smooth projective threefolds the purpose of this paper is to show how the cohomological techniques developed by kawamata reid shokurov and others lead to some effective and practical results of reider type on freeness of linear series on smooth complex projective threefolds in recent years there has been a great deal of interest in the geometric properties of pluricanonical and adjoint linear systems on surfaces and higherdimensional varieties among other things one wants to understand as explicitly as possible when the systems in question are base point free or very ample modem work in this area goes back to kodaira kod and bombieri bmb who studied pluricanonical maps of surfaces of general type more recently many of their results have emerged as special cases of a celebrated theorem of reider rdr reider uses vector bundle techniques to show that if b is a nef line bundle on a surface x such that b2 5 then kx b is globally generated unless there exist certain special curves c c x such that b c 1 he also obtains analogous criteria for kx b to be very ample a cohomological approach to these theorems based on miyaoka s vanishing theorem for zariski decompositions was given by sakai sak2

the combinatorics of coxeter categories we present an alternative construction of soergel s category of bimodules associated to a reflection faithful representation of a coxeter system we show that its objects can be viewed as sheaves on the associated moment graph we introduce an exact structure and show that soergel s special bimodules are the projective objects then we construct the indecomposable projectives by both a global and a local method discuss a version of the kazhdan lusztig conjecture and prove it for universal coxeter systems

maximum likelihood variance components estimation for binary data abstract we consider a class of probit normal models for binary data and describe ml and reml estimation of variance components for that class as well as best prediction for the realized values of the random effects ml estimates are calculated using an em algorithm for complicated models em includes a gibbs step the computations are illustrated through two examples

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

neural networks for optimal approximation of smooth and analytic functions we prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives if the activation function evaluated by each principal element satisfies certain technical conditions under these conditions it is also possible to construct networks that provide a geometric order of approximation for analytic target functions the permissible activation functions include the squashing function 1 e x 1 as well as a variety of radial basis functions our proofs are constructive the weights and thresholds of our networks are chosen independently of the target function we give explicit formulas for the coefficients as simple continuous linear functionals of the target function

hierarchical mixtures of experts and the em algorithm we present a tree structured architecture for supervised learning the statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models glim s learning is treated as a maximum likelihood problem in particular we present an expectation maximization em algorithm for adjusting the parameters of the architecture we also develop an on line learning algorithm in which the parameters are updated incrementally comparative simulation results are presented in the robot dynamics domain

parabolic kazhdan lusztig polynomials and schubert varieties abstract we shall give a description of the intersection cohomology groups of the schubert varieties in partial flag manifolds over symmetrizable kac moody lie algebras in terms of parabolic kazhdan lusztig polynomials introduced by deodhar

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

bayesian inference in mixtures of experts and hierarchical mixtures of experts models with an application to speech recognition abstract machine classification of acoustic waveforms as speech events is often difficult due to context dependencies here a vowel recognition task with multiple speakers is studied via the use of a class of modular and hierarchical systems referred to as mixtures of experts and hierarchical mixtures of experts models the statistical model underlying the systems is a mixture model in which both the mixture coefficients and the mixture components are generalized linear models a full bayesian approach is used as a basis of inference and prediction computations are performed using markov chain monte carlo methods a key benefit of this approach is the ability to obtain a sample from the posterior distribution of any functional of the parameters of the given model in this way more information is obtained than can be provided by a point estimate also avoided is the need to rely on a normal approximation to the posterior as the basis of inference this is particularly important in cases where the posteri

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

on convergence rates of mixtures of polynomial experts in this letter we consider a mixture of experts structure where m experts are mixed with each expert being related to a polynomial regression model of order k we study the convergence rate of the maximum likelihood estimator in terms of how fast the hellinger distance of the estimated density converges to the true density when the sample size n increases the convergence rate is found to be dependent on both m and k while certain choices of m and k are found to produce near optimal convergence rates

adaptive regression by mixing adaptation over different procedures is of practical importance different procedures perform well under different conditions in many practical situations it is rather hard to assess which conditions are approximately satisfied so as to identify the best procedure for the data at hand thus automatic adaptation over various scenarios is desirable a practically feasible method named adaptive regression by mixing arm is proposed to convexly combine general candidate regression procedures under mild conditions the resulting estimator is theoretically shown to perform optimally in rates of convergence without knowing which of the original procedures work the best simulations are conducted in several settings including comparing a parametric model with nonparametric alternatives comparing a neural network with a projection pursuit in multidimensional regression and combining bandwidths in kernel regression the results clearly support the theoretical property of arm the arm algorithm assigns we

a note on the use of laplace s approximation for nonlinear mixed effects models the asymptotic properties of estimates obtained using laplace s approximation for nonlinear mixed effects models are investigated unlike the restricted maximum likelihood approach e g wolfinger 1993 here the laplace approximation is applied only to the random effects of the integrated likelihood this results in approximate maximum likelihood estimation the resulting estimates are shown to be consistent with the rate of convergence depending on both the number of individuals and the number of observations per individual conditions under which the leading term laplace approximation should be avoided are discussed

asymptotic properties and information criteria for misspecified generalized linear mixed models summary the problem of misspecification poses challenges in model selection the paper studies the asymptotic properties of estimators for generalized linear mixed models with misspecification under the framework of conditional kullback leibler divergence a conditional generalized information criterion is introduced and a model selection procedure is proposed by minimizing the criterion we prove that the model selection procedure proposed is asymptotically loss efficient when all the candidate models are misspecified the model selection consistency of the model selection procedure is also established when the true data generating procedure lies within the set of candidate models simulation experiments confirm the effectiveness of the method proposed the use of the criterion for model selection is illustrated through an analysis of the european currency opinion survey data

approximation of conditional densities by smooth mixtures of regressions this paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the kullback leibler distance by different specifications of finite mixtures of normal regressions in which normal means and variances and mixing probabilities can depend on variables in the conditioning set covariates these models are a special case of models known as mixtures of experts in statistics and computer science literature flexible specifications include models in which only mixing probabilities modeled by multinomial logit depend on the covariates and in the univariate case models in which only means of the mixed normals depend flexibly on the covariates modeling the variance of the mixed normals by flexible functions of the covariates can weaken restrictions on the class of the approximable densities obtained results can be generalized to mixtures of general location scale densities rates of convergence and easy to interpret bounds are also obtained for different model specifications these approximation results can be useful for proving consistency of bayesian and maximum likelihood density estimators based on these models the results also have interesting implications for applied researchers

inference for subgroup analysis with a structured logistic normal mixture model in this article we propose a statistical model for the purpose of identifying a subgroup that has an enhanced treatment effect as well as the variables that are predictive of the subgroup membership the need for such subgroup identification arises in clinical trials and in market segmentation analysis by using a structured logistic normal mixture model our proposed framework enables us to perform a confirmatory statistical test for the existence of subgroups and at the same time to construct predictive scores for the subgroup membership the inferential procedure proposed in the article is built on the recent literature on hypothesis testing for gaussian mixtures but the structured logistic normal mixture model enjoys some distinctive properties that are unavailable to the simpler gaussian mixture models with the bootstrap approximations the proposed tests are shown to be powerful and equally importantly insensitive to the choice of tuning parameters as an illustration we analyze a dataset fr

some results on rational surfaces and fano varieties this is the publisher s version also available electronically from http www degruyter com view j crll 2001 2001 issue 538 crll 2001 068 crll 2001 068 xml

a universal approximation theorem for mixture of experts models the mixture of experts moe model is a popular neural network architecture for nonlinear regression and classification the class of moe mean functions is known to be uniformly convergent to any unknown target function assuming that the target function is from a sobolev space that is sufficiently differentiable and that the domain of estimation is a compact unit hypercube we provide an alternative result which shows that the class of moe mean functions is dense in the class of all continuous functions over arbitrary compact domains of estimation our result can be viewed as a universal approximation theorem for moe models the theorem we present allows moe users to be confident in applying such models for estimation when data arise from nonlinear and nondifferentiable generative processes

small area inference for binary variables in the national health interview survey abstract the national health interview survey is designed to produce precise estimates of finite population parameters for the entire united states but not for small geographical areas or subpopulations our investigation concerns estimates of proportions such as the probability of at least one visit to a doctor within the past 12 months to include all sources of variation in the model we carry out a bayesian hierarchical analysis for the desired finite population quantities first for each cluster county a separate logistic regression relates the individual s probability of a doctor visit to his or her characteristics second a multivariate linear regression links cluster regression parameters to covariates measured at the cluster level we describe the numerical methods needed to obtain the desired posterior moments then we compare estimates produced using the exact numerical method with approximations finally we compare the hierarchical bayes estimates to empirical bayes estimates and to stand

sheaves on moment graphs and a localization of verma flags abstract to any moment graph g we assign a subcategory v of the category of sheaves on g together with an exact structure we show that in the case that the graph is associated to a non critical block of the equivariant category o over a symmetrizable kac moody algebra v is equivalent as an exact category to the subcategory of modules that admit a verma flag the projective modules correspond under this equivalence to the intersection cohomology sheaves on the graph and hence by a theorem of braden and macpherson to the equivariant intersection cohomologies of schubert varieties associated to kac moody groups

error bounds for functional approximation and estimation using mixtures of experts we examine some mathematical aspects of learning unknown mappings with the mixture of experts model mem specifically we observe that the mem is at least as powerful as a class of neural networks in a sense that will be made precise upper bounds on the approximation error are established for a wide class of target functions the general theorem states that spl par f f sub n spl par sub p spl les c n sup r d for f spl isin w sub p sup r l a sobolev class over 1 1 sup d and f sub n belongs to an n dimensional manifold of normalized ridge functions the same bound holds for the mem as a special case of the above the stochastic error in the context of learning from independent and identically distributed i i d examples is also examined an asymptotic analysis establishes the limiting behavior of this error in terms of certain pseudo information matrices these results substantiate the intuition behind the mem and motivate applications

nonparametric density estimation the l 1 view differentiation of integrals consistency lower bounds for rates of convergence rates of convergence in l1 the automatic kernel estimate l1 and pointwise convergence estimates related to the kernel estimate and the histogram estimate simulation inequalities and random variate generation the transformed kernel estimate applications in discrimination operations on density estimates estimators based on orthogonal series index

optimal model averaging estimation for generalized linear models and generalized linear mixed effects models abstractconsidering model averaging estimation in generalized linear models we propose a weight choice criterion based on the kullback leibler kl loss with a penalty term this criterion is different from that for continuous observations in principle but reduces to the mallows criterion in the situation we prove that the corresponding model averaging estimator is asymptotically optimal under certain assumptions we further extend our concern to the generalized linear mixed effects model framework and establish associated theory numerical experiments illustrate that the proposed method is promising

from moment graphs to intersection cohomology we describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori in terms of structure of the zero and one dimensional orbits the class of varieties to which our formula applies includes schubert varieties in flag varieties and affine flag varieties we also prove a monotonicity result on local intersection cohomology stalks

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

the stone weierstrass theorem and its application to neural networks the stone weierstrass theorem and its terminology are reviewed and neural network architectures based on this theorem are presented specifically exponential functions polynomials partial fractions and boolean functions are used to create networks capable of approximating arbitrary bounded measurable functions a modified logistic network satisfying the theorem is proposed as an alternative to commonly used networks based on logistic squashing functions

perverse sheaves and actions where t x denotes the action of t on x the set xw is known to be a locally closed c stable algebraic subvariety of x isomorphic to an affine space the pieces xw form a cell decomposition x uwewxw w e w the socalled bialynicki birula decomposition we assume this decomposition to be an algebraic stratification of x the closure of a cell may not be a union of cells in general let zw be the intersection cohomology complex on the closure of a cell xw extended by 0 to the whole of x the hypercohomology h 2w has a natural structure of a graded h x c module further for any x y e w there is a natural morphism of graded spaces

koszul duality patterns in representation theory the aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of koszul duality to repre sentation theory the paper consists of three parts relatively independent of each other the first part gives a reasonably selfcontained introduction to koszul rings and koszul duality koszul rings are certain z graded rings with particularly nice homological properties which involve a kind of duality thus to a koszul ring one associates naturally the dual koszul ring the second part is devoted to an application to representation theory of semisimple lie algebras we show license or copyright restrictions may apply to redistribution see http www ams org journal terms of use koszul duality patterns 527 that the block of the bernstein gelfand gelfand category o that corresponds to any fixed central character is governed by the koszul ring moreover the dual of that ring governs a certain subcategory of the category o again this generalizes the selfduality theorem conjectured by beilinson and ginsburg in 1986 and proved by soergel in 1990 in the third part we study certain cate gories of mixed perverse sheaves on a variety stratified by affine linear spaces we provide a general criterion for such a category to be governed by a koszul ring in the flag variety case this reduces to the setup of part two in the more general case of affine flag manifolds and affine grassmannians the criterion should yield interesting results about representations of quantum groups and affine lie algebras department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address sasha math mit edu department of mathematics the university of chicago chicago illinois 60637 e mail address ginzburg math uchicago edu max planck institut fur mathematik gottfried claren strase 26 d 53 bonn 3 germany current address mathematisches institut universitat freiburg albertstrase 23b d 79104 freiburg germany e mail address soergel sun1 mathematik uni freiburg de license or copyright restrictions may apply to redistribution see http www ams org journal terms of use

hierarchical mixtures of experts for exponential family regression models approximation and maximum likelihood estimation we consider hierarchical mixtures of experts hme models where exponential family regression models with generalized linear mean functions of the form x t are mixed here is the inverse link function suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form h x where h w 2 k0 a sobolev class over 0 1 s it is shown that the hme probability density functions can approximate the true density at a rate of o m 2 s in hellinger distance and at a rate of o m 4 s in kullback leibler divergence where m is the number of experts and s is the dimension of the predictor x we also provide conditions under which the mean square error of the estimated mean response obtained from the maximum likelihood method converges to zero as the sample size and the number of experts both increase

localization of g modules on the affine grassmannian we consider the category of modules over the affine kac moody algebra of critical level with regular central character in our previous paper we conjectured that this category is equivalent to the category of hecke eigen d modules on the affine grassmannian g t g t this conjecture was motivated by our proposal for a local geometric langlands correspondence in this paper we prove this conjecture for the corresponding i 0 equivariant categories where i 0 is the radical of the iwahori subgroup of g t our result may be viewed as an affine analogue of the equivalence of categories of g modules and d modules on the flag variety g b due to beilinson bernstein and brylinski kashiwara

mixtures of probabilistic principal component analyzers principal component analysis pca is one of the most popular techniques for processing compressing and visualizing data although its effectiveness is limited by its global linearity while nonlinear variants of pca have been proposed an alternative paradigm is to capture data complexity by a combination of local linear pca projections however conventional pca does not correspond to a probability density and so there is no unique way to combine pca models therefore previous attempts to formulate mixture models for pca have been ad hoc to some extent in this article pca is formulated within a maximum likelihood framework based on a specific form of gaussian latent variable model this leads to a well defined mixture model for probabilistic principal component analyzers whose parameters can be determined using an expectationmaximization algorithm we discuss the advantages of this model in the context of clustering density modeling and local dimensionality reduction and we demonstrate its application to image compression and handwritten digit recognition

consistent estimators in generalized linear mixed models abstract a simple method based on simulated moments is proposed for estimating the fixed effects and variance components in a generalized linear mixed model glmm it is shown that the method is not only computationally attractive but also leads to consistent estimators on the other hand simulation shows that the method can be quite inefficient

variable selection in finite mixture of regression models in the applications of finite mixture of regression fmr models often many covariates are used and their contributions to the response variable vary from one component to another of the mixture model this creates a complex variable selection problem existing methods such as the akaike information criterion and the bayes information criterion are computationally expensive as the number of covariates and components in the mixture model increases in this article we introduce a penalized likelihood approach for variable selection in fmr models the new method introduces penalties that depend on the size of the regression coefficients and the mixture structure the new method is shown to be consistent for variable selection a data adaptive method for selecting tuning parameters and an em algorithm for efficient numerical computations are developed simulations show that the method performs very well and requires much less computing power than existing methods the new method is illustrated by analyzin

asymptotically unbiased estimation in generalized linear models with random effects summary obtaining estimates that are nearly unbiased has proven to be difficult when random effects are incorporated into a generalized linear model in this paper we propose a general method of adjusting any conveniently defined initial estimates to result in estimates which are asymptotically unbiased and consistent the method is motivated by iterative bias correction and can be applied in principle to any parametric model a simulation based approach of implementing the method is described and the relationship of the method proposed with other sampling based methods is discussed results from a small scale simulation study show that the method proposed can lead to estimates which are nearly unbiased even for the variance components while the standard errors are only slightly inflated a new analysis of the famous salamander mating data is described which reveals previously undetected between animal variation among the male salamanders and results in better prediction of mating outcomes

normal presentation on elliptic ruled surfaces from the introduction let x be an irreducible projective variety and l a very ample lline bundle on x whose complete linear series defines l x p h0 l let s 1 m 0 smh0 x l and let r l l1 n 0 h0 x l n be the homogeneous coordinate ring associated to l then r is a finitely generated graded module over s so it has a minimal graded free resolution we say that the line bundle l is normally generated if the natural maps smh0 x l h0 x l m are surjective for all m 2 if l is normally generated then we say that l satisfies property np if the matrices in the free resolution of r over s have linear entries until the p th stage in particular property n1 says that the homogeneous ideal i of x in p h0 l is generated by quadrics a line bundle satisfying property n1 is also called normally presented let r kr1r2 be a graded algebra over a field k the algebra r is a koszul ring iff torri k k has pure degree i for all i in this article we determine exactly theorem 4 2 which line bundles on an elliptic ruled surface x are normally presented as a corollary we show that mukai s conjecture is true for the normal presentation of the adjoint linear series for an elliptic ruled surface in section 5 of this article we show that if l is normally presented on x then the homogeneous coordinate ring associated to l is koszul we also give a new proof of the following result due to butler if deg l 2g 2 on a curve x of genus g then l embeds x with koszul homogeneous coordinate ring

laplace approximation of high dimensional integrals summary it is shown that the usual laplace approximation is not a valid asymptotic approximation when the dimension of the integral is comparable with the limiting parameter n the formal laplace expansion for multidimensional integrals is given and used to construct asymptotic approximations for high dimensional integrals one example is considered in which the dimension of the integral is o n 1 2 and the relative error of the unmodified laplace approximation is 0 1 nevertheless it is possible to construct a valid asymptotic expansion by regrouping terms in the formal expansion according to asymptotic order in n

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

conditional inference functions for mixed effects models with unspecified random effects distribution in longitudinal studies mixed effects models are important for addressing subject specific effects however most existing approaches assume a normal distribution for the random effects and this could affect the bias and efficiency of the fixed effects estimator even in cases where the estimation of the fixed effects is robust with a misspecified distribution of the random effects the estimation of the random effects could be invalid we propose a new approach to estimate fixed and random effects using conditional quadratic inference functions qifs the new approach does not require the specification of likelihood functions or a normality assumption for random effects it can also accommodate serial correlation between observations within the same cluster in addition to mixed effects modeling other advantages include not requiring the estimation of the unknown variance components associated with the random effects or the nuisance parameters associated with the working correlations we establish a

maximum likelihood algorithms for generalized linear mixed models abstract maximum likelihood algorithms are described for generalized linear mixed models i show how to construct a monte carlo version of the em algorithm propose a monte carlo newton raphson algorithm and evaluate and improve the use of importance sampling ideas calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously i also use the newton raphson algorithm as a framework to compare maximum likelihood to the joint maximization or penalized quasi likelihood methods and explain why the latter can perform poorly

robust estimation in generalised linear mixed models summary we propose robust methods for estimation of parameters of interest in an extended generalised linear mixed model in which only the conditional means of the responses given the random effects are specified a first step estimator 0 of the vector 0 of parameters is obtained by solving a system of estimating equations it is shown that 9 is consistent if furthermore the conditional variances are correctly specified a second step estimator 0 can be obtained by solving a system of optimal estimating equations whose coefficients a are estimated by 0 it is shown that 0 maintains the asymptotic optimality simulations a also indicate solid improvement of 0 over 0 two examples involving real data analysis are considered the methods are developed under a more general framework so that they may be applied to more general estimation problems

on the asymptotic normality of hierarchical mixtures of experts for generalized linear models in the class of hierarchical mixtures of experts hme models experts in the exponential family with generalized linear mean functions of the form spl psi spl alpha x sup t spl beta are mixed according to a set of local weights called the gating functions depending on the predictor x here spl psi spl middot is the inverse link function we provide regularity conditions on the experts and on the gating functions under which the maximum likelihood method in the large sample limit produces a consistent and asymptotically normal estimator of the mean response the regularity conditions are validated for poisson gamma normal and binomial experts

cyclotomic double affine hecke algebras and affine parabolic category o using the orbifold kz connection we construct a functor from an affine parabolic category o of type a to the category o of a cyclotomic rational double affine hecke algebra h then we give several results concerning this functor

on the projective normality and normal presentation on higher dimensional varieties with nef canonical bundle abstract in this article we prove new results on projective normality and normal presentation of adjunction bundle associated to an ample and globally generated line bundle on higher dimensional smooth projective varieties with nef canonical bundle as one of the consequences of the main theorem we give bounds on very ampleness and projective normality of pluricanonical linear systems on varieties of general type in dimensions three four and five these improve known such results

on the approximation rate of hierarchical mixtures of experts for generalized linear models we investigate a class of hierarchical mixtures of experts hme models where generalized linear models with nonlinear mean functions of the form xt are mixed here is the inverse link function it is shown that mixtures of such mean functions can approximate a class of smooth functions of the form h x where h e w 2 k a sobolev class over 0 1 s as the number of experts m in the network increases an upper bound of the approximation rate is given as o m 2 s in lp norm this rate can be achieved within the family of hme structures with no more than s layers where s is the dimension of the predictor x

on consistency of bayesian inference with mixtures of logistic regression this is a theoretical study of the consistency properties of bayesian inference using mixtures of logistic regression models when standard logistic regression models are combined in a mixtures of experts setup a flexible model is formed to model the relationship between a binary yes no response y and a vector of predictors x bayesian inference conditional on the observed data can then be used for regression and classification this letter gives conditions on choosing the number of experts i e number of mixing components k or choosing a prior distribution for k so that bayesian inference is consistent in the sense of often approximating the underlying true relationship between y and x the resulting classification rule is also consistent in the sense of having near optimal performance in classification we show these desirable consistency properties with a nonstochastic k growing slowly with the sample size n of the observed data or with a random k that takes large values with nonzero but small probabilities

very ampleness and higher syzygies for calabi yau threefolds the authors prove various results concerning multiples of ample base point free linear systems on calabi yau threefolds suppose that b is an ample divisor on a calabi yau threefold x and that b has no base points then the authors prove that 3b is very ample and embeds x as a projectively normal variety if and only if b does not map x 2 1 onto p3 similarly they prove that 2b enjoys the same properties if and only if b does not map x onto a variety of minimal degree other than p3 nor maps x 2 1 onto p3 further results are proved giving conditions for when the linear system nb satisfies the condition np

bias correction in generalized linear mixed models with multiple components of dispersion abstract general formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi likelihood pql in generalized linear mixed models with canonical link function and multiple sets of independent random effects easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values both first order and second order correction procedures are developed for regression coefficients estimated by pql the methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects and their properties are evaluated in a simulation study

categorifications and cyclotomic rational double affine hecke algebras varagnolo and vasserot conjectured an equivalence between the category mathcal o for crdaha s and a subcategory of an affine parabolic category o of type a we prove this conjecture as applications we prove a conjecture of rouquier on the dimension of simple modules of crdaha s and a conjecture of chuang miyachi on the koszul duality for the category mathcal o of crdaha s