modified signed log likelihood ratio summary the signed log likelihood ratio r for a one dimensional interest parameter can be modified as r r r log u r so that r is asymptotically standard normally distributed with error of order o n 3 2 u being interpretable as a test statistic a new more direct derivation of this result is given which leads to a more explicit expression for u and provides a better handle on the error term the relation of the tail area approximation determined by r to a generalization of the lugannani rice approximation is discussed and the applicability of r to the analysis of residual variation is indicated

high order asymptotic expansions for robust tests summary this paper provides high order asymptotic expansions for the m ratio and the signedroot m ratio robust test statistics which allow one to compute accurate approximations to significance or critical values using the edgeworth approximation the bartlett correction the variance correction or the saddlepoint approximation specific results are obtained for the linear regression model with the huber m estimator a monte carlo study illustrates the numerical accuracy of these approximations with respect to the usual first order approximations

minimal resolutions of algebras abstract a method is described for constructing the minimal projective resolution of an algebra considered as a bimodule over itself the method applies to an algebra presented as the quotient of a tensor algebra over a separable algebra by an ideal of relations that is either homogeneous or admissible with some additional finiteness restrictions in the latter case in particular it applies to any finite dimensional algebra over an algebraically closed field the method is illustrated by a number of examples viz truncated algebras monomial algebras and koszul algebras with the aim of unifying existing treatments of these in the literature

going from cohomology to hochschild cohomology abstract the relation between ordinary cohomology and hochschild cohomology is investigated for quotients of quiver algebras which are either graded or finite dimensional it is shown that a resolution of the direct sum of the simple modules of the algebra can often be made two sided and yield a resolution of the algebra itself over its enveloping algebra the multiplicative structures of the cohomologies are shown to be related by a spectral sequence of algebras converging to the hochschild cohomology whose first term is given by a tensor product of the algebra itself with its cohomology algebra

robust bounded influence tests in general parametric models abstract we introduce robust tests for testing hypotheses in a general parametric model these are robust versions of the wald scores and likelihood ratio tests and are based on general m estimators their asymptotic properties and influence functions are derived it is shown that the stability of the level is obtained by bounding the self standardized sensitivity of the corresponding m estimator furthermore optimally bounded influence tests are derived for the wald and scores type tests applications to real and simulated data sets are given to illustrate the tests performance

nonsmooth analysis and frechet differentiability of m functionals abstract a necessary requirement for existence of the frechet derivative is that the defining psi function is uniformly bounded and this naturally excludes those nonrobust estimators such as the maximum likelihood estimator in normal parametric models in this paper the methods of nonsmooth analysis described in the book by f h clarke 1983 are introduced to the theory of statistical expansions and are used here in the proofs of weak continuity and frechet differentiability of m functionals subsequently the conditions for frechet differentiability given in clarke 1983 can be relaxed to include most popular m functionals additional keywords distribution functions m estimators robustness gross error sensitivity weak continuity asymptotic expansions asymptotic normality selection functional local uniqueness author

a general degree hybrid equilibrium finite element for kirchhoff plates summary we present a family of hybrid equilibrium finite elements for the quasistatic linear elastic analysis of plates governed by kirchhoff theory the moments are approximated by self balanced polynomial fields of general degree and in order to impose strong codiffusivity the normal boundary rotations are approximated with complete polynomials of the same degree whereas the transverse deflections use polynomials one degree lower furthermore it is also necessary to include an independent approximation of the vertex translations we show that the triangular form of this element is stable that is free from spurious kinematic modes and the formulation that we present allows these elements to be used as a standard displacement element examples of computed values and convergence of the solutions are presented which demonstrate the performance of these elements copyright 2013 john wiley sons ltd

the alternating syzygy behavior of monomial algebras abstract in this paper we present a minimal projective resolution of a monomial algebra over its enveloping algebra the syzygies for this resolution exhibit an alternating behavior which is explained by the construction of a special sequence of paths from the quiver of

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

homological invariants relating the super jordan plane to the virasoro algebra abstract nichols algebras are an important tool for the classification of hopf algebras within those with finite gk dimension we study homological invariants of the super jordan plane that is the nichols algebra a b v 1 2 these invariants are hochschild homology the hochschild cohomology algebra the lie structure of the first cohomology space which is a lie subalgebra of the virasoro algebra and its representations h n a a and also the yoneda algebra we prove that the algebra a is k 2 moreover we prove that the yoneda algebra of the bosonization a k z of a is also finitely generated but not k 2

general saddlepoint approximations of marginal densities and tail probabilities saddlepoint approximations of marginal densities and tail probabilities of general nonlinear statistics are derived these are based on the expansion of the statistic up to the second order their accuracy is shown in a variety of examples including logit and probit models and rank estimators for regression

hochschild homology and cohomology of down up algebras abstract we present a detailed computation of the cyclic and the hochschild homology and cohomology of generic and 3 calabi yau homogeneous down up algebras this family was defined by benkart and roby in 3 in their study of differential posets our calculations are completely explicit by making use of the koszul bimodule resolution and some arguments similar to those used in 13 to compute the hochschild cohomology of yang mills algebras

noncommutative mirror symmetry for punctured surfaces in 2013 abouzaid auroux efimov katzarkov and orlov showed that the wrapped fukaya categories of punctured spheres and finite unbranched covers of punctured spheres are derived equivalent to the categories of singularities of a superpotential on certain crepant resolutions of toric 3 dimensional singularities we generalize this result to other punctured riemann surfaces and reformulate it in terms of certain noncommutative algebras coming from dimer models in particular given any consistent dimer model we can look at a subcategory of noncommutative matrix factorizations and show that this category is mathtt a infty isomorphic to a subcategory of the wrapped fukaya category of a punctured riemann surface the connection between the dimer model and the punctured riemann surface then has a nice interpretation in terms of a duality on dimer models

uniqueness and frechet differentiability of functional solutions to maximum likelihood type equations solutions of simultaneous equations of the maximum likelihood type or m estimators can be represented as functionals existence and uniqueness of a root in a local region of the parameter space are proved under conditions that are easy to check if only one root of the equation exists the resulting statistical functional is frechet differentiable and robust when several solutions exists conditions on the loss criterion used to select the root for the statistic ensure frechet differentiability an interesting example of a frechet differentiable functional is the solution of the maximum likelihood equations for location and scale parameters in a cauchy distribution the estimator is robust and asymptotically efficient

general saddlepoint approximations with applications to l statistics abstract saddlepoint approximations are extended to general statistics the technique is applied to derive approximations to the density of linear combinations of order statistics including trimmed means a comparison with exact results shows the accuracy of these approximations even in very small sample sizes

projective resolutions of associative algebras and ambiguities abstract the aim of this article is to give a method to construct bimodule resolutions of associative algebras generalizing bardzell s well known resolution of monomial algebras we stress that this method leads to concrete computations providing thus a useful tool for computing invariants associated to the considered algebras we illustrate how to use it by giving several examples in the last section of the article in particular we give necessary and sufficient conditions for noetherian down up algebras to be 3 calabi yau

derived equivalences of gentle algebras via fukaya categories following the approach of haiden katzarkov kontsevich publ math inst hautes etudes sci 126 247 318 2017 to any homologically smooth mathbb z graded gentle algebra a we associate a triple sigma a lambda a eta a where sigma a is an oriented smooth surface with non empty boundary lambda a is a set of stops on partial sigma a and eta a is a line field on sigma a such that the derived category of perfect dg modules of a is equivalent to the partially wrapped fukaya category of sigma a lambda a eta a modifying arguments of johnson and kawazumi we classify the orbit decomposition of the action of the symplectic mapping class group of sigma a on the homotopy classes of line fields as a result we obtain a sufficient criterion for homologically smooth graded gentle algebras to be derived equivalent our criterion uses numerical invariants generalizing those given by avella alaminos geiss in avella et al j pure appl algebra 212 1 228 243 2008 as well as some other numerical invariants as an application we find many new cases when the aag invariants determine the derived morita class as another application we establish some derived equivalences between the stacky nodal curves considered in lekili and polishchuk j topology 11 615 444 2018

finiteness conditions on the ext algebra of a cycle algebra abstract let a be a finite dimensional algebra given by quiver and monomial relations in e l green d zacharia manuscripta math 85 1994 11 23 we see that the ext algebra of a is finitely generated only if all the ext algebras of certain cycle algebras overlying a are finitely generated here a cycle algebra is a finite dimensional algebra given by quiver and monomial relations where the quiver is an oriented cycle the main result of this paper gives necessary and sufficient conditions for the ext algebra of such a to be finitely generated this is achieved by defining a computable invariant of the smo tube we also give necessary and sufficient conditions for the ext algebra of to be noetherian

comparison morphisms and the hochschild cohomology ring of truncated quiver algebras abstract a main contribution of this paper is the explicit construction of comparison morphisms between the standard bar resolution and bardzell s minimal resolution for truncated quiver algebras over arbitrary fields tqa s as a direct application we describe explicitly the yoneda product and derive several results on the structure of the cohomology ring of tqa s over a field of characteristic zero for instance we show that the product of odd degree cohomology classes is always zero we prove that tqa s associated with quivers with no cycles or with neither sinks nor sources have trivial cohomology rings on the other side we exhibit a fundamental example of a tqa with nontrivial cohomology ring finally for truncated polynomial algebras in one variable we construct explicit cohomology classes in the bar resolution and give a full description of their cohomology ring

invariants and likelihood ratio statistics because the likelihood ratio statistic is invariant under reparameterization it is possible to make a large sample expansion of the statistic itself and of its expectation in terms of invariants in particular the bartlett adjustment factor can be expressed in terms of invariant combinations of cumulants of the first two log likelihood derivatives such expansions are given first for a scalar parameter and then for vector parameters geometrical interpretation is given where possible and some special cases discussed

rigidity of truncated quiver algebras a quiver q is a finite oriented graph which can contain more than one arrow between two vertices as well as loops and oriented cycles for n a positive integer q is the set of oriented paths of length n of q where the length is the number of arrows of the oriented path notice that q is the set of vertices and q the set of arrows let k be a field and kqo x st po ks be the commutative semi simple algebra with q0 as a k basis of idempotents for each arrow a e q with source vertex s a s and end vertex r u t the one dimensional vector space k has an evident kq bimodule structure for u e q we have au 6 sa and ua d a where 6 is the kronecker symbol in this way kq o ka is a kq bimodule and the quiver algebra kq is the tensor algebra over kqo of the kq bimodule kqt of course kq can also be described as the vector space kqo kql 0 kq 0 where the multiplication of e qj and ci e qi is 3 e qj if t a s p and 0 otherwise let now n be a finite dimensional k algebra we suppose that i is morita reduced and that the endomorphism ring of each simple n module is k this is equivalent to a r k x x k were r is the jacobson radical of i by definition the set of vertices of the gabriel s quiver q of i is the set of isomorphism classes of simple i modules if s and t are simple n modules the number of arrows from s to t is dim exti s t by an observation of gabriel 6 7 4 3 every k algebra n such that a r k x x k admits a presentation that is an algebra surjection cp kq a whose kernel z verifies f c zc f2 where f is the two sided ideal of kq generated by ql and m is some positive integer such ideals z of a quiver algebra are called admissible in general an algebra n has not a unique presentation that is two different admissible two sided ideals z and j of a quiver algebra kq can give isomorphic k algebras kq z and kq j by definition we say that a k algebra i is a truncated quiver algebra if

tools for the symbolic computation of asymptotic expansions summary this paper describes a collection of procedures for the systematic computation of asymptotic expansions that are common in statistical theory and practice expansions of functions of sums of independent and identically distributed random variables the procedures permit the expansion of maximum likelihood estimates the associated deviance or drop in likelihood and more general functions of random variables with distributions involving one or more parameters the procedures are illustrated with examples involving general and specific laws much of statistical theory and practice is based on asymptotic expansions many programs are available to assist in the numerical evaluation of such expansions but there is a need for computational tools to assist in their derivation and symbolic evaluation heller 1991 shows how symbolic calculation may be used in a wide variety of statistical problems kendall 1988 1990 gives procedures for the symbolic computation of expressions in the analysis of the diffusion of euclidean shape silverman and young 1987 use computer algebra to evaluate criteria on which the decision to smooth a bootstrap distribution is based young and daniels 1990 apply symbolic computation to evaluate expressions in the assessment of bootstrap bias venables 1985 utilizes symbolic computation heavily to obtain expansions of maximum marginal likelihood estimates most notably fisher s a statistic barndorff nielsen and blasild 1986 describe procedures for the numerical calculation of bartlett factors in cases where cumulants of the likelihood function may be specified most of these references involve the evaluation of complicated formulae in particular cases and not the derivation of the formulae themselves here we give general procedures for both the derivation of formulae and their evaluation in specific cases the derivation of asymptotic expansions is typically a simple but laborious task consider for example the calculation of the expectation of the likelihood ratio test statistic for a one parameter family to order 1 n this may be accomplished in general

on solvability of the first hochschild cohomology of a finite dimensional algebra for an arbitrary finite dimensional algebra a we introduce a general approach to determining when its first hochschild cohomology rm hh 1 a considered as a lie algebra is solvable if a is moreover of tame or finite representation type we are able to describe rm hh 1 a as the direct sum of a solvable lie algebra and a sum of copies of mathfrak sl 2 we proceed to determine the exact number of such copies and give an explicit formula for this number in terms of certain chains of kronecker subquivers of the quiver of a as a corollary we obtain a precise answer to a question posed by chaparro schroll and solotar

quivers from matrix factorizations we discuss how matrix factorizations offer a practical method of computing the quiver and associated superpotential for a hypersurface singularity this method also yields explicit geometrical interpretations of d branes i e quiver representations on a resolution given in terms of grassmannians as an example we analyze some non toric singularities which are resolved by a single mathbb p 1 but have length greater than one these examples have a much richer structure than conifolds a picture is proposed that relates matrix factorizations in landau ginzburg theories to the way that matrix factorizations are used in this paper to perform noncommutative resolutions

on parameter transformations and interval estimation summary parameterizations which reduce the asymptotic bias and skewness of various pivotal quantities arising in large sample theory are discussed for models depending on an unknown scalar parameter transformation formulae by which such parameterizations can be obtained are derived and these formulae extend those for one dimensional curved exponential families given by hougaard 1982 to assess the accuracy of normal approximations to the distributions of the pivots their second order properties are considered and comparisons with the signed square root of the likelihood ratio statistic are drawn

morse theory from an algebraic viewpoint forman s discrete morse theory is studied from an algebraic viewpoint and we show how this theory can be extended to chain complexes of modules over arbitrary rings as applications we compute the homologies of a certain family of nilpotent lie algebras and show how the algebraic morse theory can be used to derive the classical anick resolution as well as a new two sided anick resolution