a note on the regression analysis of censored data maximum likelihood estimates of the parameters in linear models with censored normal responses may be simply obtained using the em algorithm the iterative computations required for the regression coefficients are identical to those described by schmee and hahn for least squares estimates but those for the variance estimates are different the biases of the two variance estimates are discussed

linear free resolutions and minimal multiplicity let s k x x be a polynomial ring over a field and let a4 a m be a finitely generated graded module in the most interesting case a4 is an ideal of s for a given natural number p there is a great interest in the question can m be generated by homogeneous elements of degree p no simple answer say in terms of the local cohomology of m is known but somewhat surprisingly the stronger question can the jth syzygy of m be generated by elements of degree qp j for all j 0 l n does admit a simple response the following is neither new nor difficult to prove though it seems not well known

ideals with stable betti numbers componentwise linear ideals were introduced earlier to generalize the result that the stanley reisner ideal i of a simplicial complex has a linear resolution if and only if its alexander dual is cohen macaulay it turns out that i is componentwise linear if and only if is sequentially cohen macaulay in this paper we discuss betti number properties of componentwise linear ideals let i be a graded ideal of a polynomial ring s and gin i the generic initial ideal of i with respect to the reverse lexicographic term order on s our main result is that i and gin i admit the same graded betti numbers if and only if i is componentwise linear for the proof of this fact we describe some properties of the betti diagram of a generic initial ideal combinatorial implications for shifted complexes will also be discussed

two sided bounds on the rate of convergence to a stable law we derive necessary and sufficient conditions for several characterizations of the rate of convergence of a sum of independent variables to a stable law the technique used is to obtain upper and lower bounds on the rate in terms of functions depending in a very simple way on the common underlying distribution this permits a general approach to the problem of rates of convergence

computation of invariants for reductive groups abstract we will give an algorithm for computing generators of the invariant ring for a given representation of a linearly reductive group the algorithm basically consists of a single grobner basis computation we will also show a connection between some open conjectures in commutative algebra and finding good degree bounds for generating invariants

multigraded castelnuovo mumford regularity we develop a multigraded variant of castelnuovo mumford regularity motivated by toric geometry we work with modules over a polynomial ring graded by a finitely generated abelian group as in the standard graded case our definition of multigraded regularity involves the vanishing of graded components of local cohomology we establish the key properties of regularity its connection with the minimal generators of a module and its behavior in exact sequences for an ideal sheaf on a simplicial toric variety x we prove that its multigraded regularity bounds the equations that cut out the associated subvariety we also provide a criterion for testing if an ample line bundle on x gives a projectively normal embedding

castelnuovo mumford regularity by approximation abstract the castelnuovo mumford regularity of a module gives a rough measure of its complexity we bound the regularity of a module given a system of approximating modules whose regularities are known such approximations can arise naturally for modules constructed by inductive combinatorial means we apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the module of derivations of a hyperplane arrangement as well as to give degree bounds for invariants of finite groups

an econometric model of network formation with degree heterogeneity i introduce a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics homophily as well as unrestricted agent level heterogeneity in link surplus degree heterogeneity like in fixed effects panel data analyses the joint distribution of observed and unobserved agent level characteristics is left unrestricted two estimators for the common homophily parameter 0 are developed and their properties studied under an asymptotic sequence involving a single network growing large the first tetrad logit tl estimator conditions on a sufficient statistic for the degree heterogeneity the second joint maximum likelihood jml estimator treats the degree heterogeneity a i0 i 1 super n as additional incidental parameters to be estimated the tl estimate is consistent under both sparse and dense graph sequences whereas consistency of the jml estimate is shown only under dense graph sequences

generalized castelnuovo mumford regularity for affine kac moody algebras abstract the graded modules over noncommutative algebras often have minimal free resolutions of infinite length resulting in infinite castelnuovo mumford regularity in kang et al 2010 6 we introduced a generalized notion of castelnuovo mumford regularity to overcome this difficulty in this paper we compute the generalized castelnuovo mumford regularity for integrable highest weight representations of all affine kac moody algebras it is shown that the generalized regularity depends only on the type and rank of algebras and the level of representations

sharpening the generalized noether bound in the invariant theory of finite groups abstract we consider linear representations of a finite group g on a finite dimensional vector space over a field f in which g is invertible by a theorem due to e noether in char 0 and to fleischmann and fogarty in general the ring of invariants is generated by homogeneous elements of degree at most g schmid domokos and hegedus sharpened noether s bound when g is not cyclic and char f 0 we prove that the sharpened bound holds over general fields if g is not cyclic and g is invertible in f then the ring of invariants is generated by elements of degree at most 3 4 g if g is even and at most 5 8 g if g is odd

regression with censored data summary there are four regression techniques currently available for use with censored data which do not assume particular parametric families of survival distributions they are due to i cox 1972 ii miller 1976 iii buckley james 1979 and iv koul susarla van ryzin 1981 these four methods are described and their performances compared on the updated stanford heart transplant data conclusions on the usefulness of the four procedures are drawn

a diagonal bound for cohomological postulation numbers of projective schemes abstract let x be a projective scheme over a field k and let f be a coherent sheaf of o x modules we show that the cohomological postulation numbers f i of f e g the ultimate places at which the cohomological hilbert functions n dim k h i x f n h f i n start to be polynomial for n 0 are polynomially bounded in terms of the cohomology diagonal h f i i i 0 dim f of f as a consequence we obtain that there are only finitely many different cohomological hilbert functions h f i if f runs through all coherent sheaves of o x modules with fixed cohomology diagonal in order to prove these results we extend the regularity bound of bayer and mumford computational algebraic geometry and commutative algebra proc cortona 1991 cambridge univ press 1993 pp 1 48 from graded ideals to graded modules moreover we prove that the castelnuovo mumford regularity of the dual f of a coherent sheaf of o p k r modules f is polynomially bounded in terms of the cohomology diagonal of f

choice of time scale and its effect on significance of predictors in longitudinal studies time to event regression is a frequent tool in biomedical research in clinical trials this time is usually measured from the beginning of the study the same approach is often adopted in the analysis of longitudinal observational studies however in recent years there has appeared literature making a case for the use of the date of birth as a starting point and thus utilize age as the time to event in this paper we explore different types of age scale models and compare them with time on study models in terms of the estimated regression coefficients they produce we consider six proportional hazards regression models that differ in the choice of time scale and in the method of adjusting for the years before the study by considering the estimating equations of these models as well as numerical simulations we conclude that correct adjustment for the age at entry is crucial in reducing bias of the estimated coefficients the unadjusted age scale model is inferior to any of the five other models considered regardless of their choice of time scale additionally if adjustment for age at entry is made our analyses show very little to suggest that there exists any practically meaningful difference in the estimated regression coefficients depending on the choice of time scale these findings are supported by four practical examples from the framingham heart study

the information encoded in initial ideals we consider homogeneous ideals i and the initial ideal in i for the revlex order first we give a sequence of invariants computed from i giving better and better approximations to the initial ideal and ending in an equivalent description then we apply this to different settings in algebraic geometry to understand what information is encoded in the generic initial ideal of the ideal of a projective scheme we also consider the higher initial ideals as defined in a paper by fl0ystad in particular we show that giving the generic higher initial ideal of a space curve is equivalent to giving the generic initial ideal of a linked curve

recent improvements in the complexity of the effective nullstellensatz we bring up to date the estimates on the complexity of the effective nullstellensatz and the membership problem

a combinatorial proof of the eisenbud goto conjecture for monomial curves and some simplicial semigroup rings abstract we will give a pure combinatorial proof of the eisenbud goto conjecture for arbitrary monomial curves moreover we will show that the conjecture holds for certain simplicial affine semigroup rings

heat kernels for time dependent non symmetric stable like operators abstract when studying non symmetric nonlocal operators on r d l f x r d f x z f x f x z 1 z 1 x z z d d z where 0 2 d 1 and x z is a function on r d r d that is bounded between two positive constants it is customary to assume that x z is symmetric in z in this paper we study heat kernel of l and derive its two sided sharp bounds without the symmetric assumption x z x z in fact we allow the kernel to be time dependent and x t x z to be only locally holder continuous with holder constant possibly growing at a polynomial rate in z we also derive gradient estimate when 0 1 1 as well as fractional derivative estimate of order 0 2 for the heat kernel moreover when 1 2 drift perturbation of the time dependent non local operator l t with drift in kato s class is also studied in this paper as an application when x z z does not depend on x we show the boundedness of nonlocal riesz s transformation for any p 2 d d l 1 2 f p f 1 2 p where f 1 2 l f 2 f l f is the carre du champ operator associated with l and l 1 2 is the square root operator of l defined by using bochner s subordination here means that both sides are comparable up to a constant multiple

the freeness and minimal free resolutions of modules of differential operators of a generic hyperplane arrangement abstract let a be a generic hyperplane arrangement composed of r hyperplanes in an n dimensional vector space and s the polynomial ring in n variables we consider the s submodule d m a of the nth weyl algebra of homogeneous differential operators of order m preserving the defining ideal of a we prove that if n 3 r n m r n 1 then d m a is free holm s conjecture combining this with some results by holm we see that d m a is free unless n 3 r n m r n 1 in the remaining case we construct a minimal free resolution of d m a by generalizing yuzvinsky s construction for m 1 in addition we construct a minimal free resolution of the transpose of the m jet module which generalizes a result by rose and terao for m 1

saturation and castelnuovo mumford regularity abstract let i be a homogeneous ideal of the polynomial ring k x 0 x n where k is an arbitrary field avoiding the construction of a minimal graded free resolution of i we provide effective methods for computing the castelnuovo mumford regularity of i that also compute other cohomological invariants of k x 0 x n i

maximally selected chi square statistics two samples can be compared by selecting a cut point and then forming a 2 x 2 table of the numbers of observations above and below the cut point in each sample when the cut point is selected so as to maximize the standard chi square statistic the chi square percentile points are inappropriate actual significance levels are computed for large samples and correct percentile poillts are tabulated

cohomology of projective schemes from annihilators to vanishing we provide bounds on the castelnuovo mumford regularity in terms of defining equations by using elements that annihilates some cohomology modules inspired by works of miyazaki nagel schenzel and vogel the elements in these annihilators are provided either by liaison or by tight closure theories our results hold in any characteristic

applications of the lindeberg principle in communications and statistical learning we use a generalization of the lindeberg principle developed by s chatterjee to prove universality properties for various problems in communications statistical learning and random matrix theory we also show that these systems can be viewed as the limiting case of a properly defined sparse system the latter result is useful when the sparse systems are easier to analyze than their dense counterparts the list of problems we consider is by no means exhaustive we believe that the ideas can be used in many other problems relevant for information theory

the regularity of a toric variety abstract we give a method for computing the degrees of the minimal syzygies of a toric variety by means of combinatorial techniques indeed we complete the explicit description of the minimal free resolution of the associated semigroup algebra using the simplicial representation of koszul homology which appeared in a campillo and c marijuan 1991 sem theor nombres bordeaux3 249 260 as an application we obtain an algorithm for computing the castelnuovo mumford regularity of a projective toric variety this regularity is explicitly bounded by means of the semigroup generators which parametrize the variety

circuit complexity proof complexity and polynomial identity testing the ideal proof system we introduce a new and natural algebraic proof system whose complexity measure is essentially the algebraic circuit size of nullstellensatz certificates this enables us to exhibit close connections between effective nullstellensatze proof complexity and algebraic circuit complexity in particular we show that any super polynomial lower bound on any boolean tautology in our proof system implies that the permanent does not have polynomial size algebraic circuits vnp vp we also show that super polynomial lower bounds on the number of lines in polynomial calculus proofs imply the permanent versus determinant conjecture note that there was no proof system prior to ours for which lower bounds on an arbitrary tautology implied any complexity class lower bound our proof system helps clarify the relationships between previous algebraic proof systems in doing so we highlight the importance of polynomial identity testing pit in proof complexity in particular we use pit to illuminate ac0 p frege lower bounds which have been open for nearly 30 years with no satisfactory explanation as to their apparent difficulty finally we explain the obstacles that must be overcome in any attempt to extend techniques from algebraic circuit complexity to prove lower bounds in proof complexity using the algebraic structure of our proof system we propose a novel route to such lower bounds although such lower bounds remain elusive this proposal should be contrasted with the difficulty of extending ac0 p circuit lower bounds to ac0 p frege lower bounds

gaussian approximation of suprema of empirical processes we develop a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of gaussian processes without taking the route of approximating empirical processes themselves in the sup norm we prove an abstract approximation theorem that is applicable to a wide variety of problems primarily in statistics especially the bound in the main approximation theorem is non asymptotic and the theorem does not require uniform boundedness of the class of functions the proof of the approximation theorem builds on a new coupling inequality for maxima of sums of random vectors the proof of which depends on an effective use of stein s method for normal approximation and some new empirical processes techniques we study applications of this approximation theorem to local empirical processes and series estimation in nonparametric regression where the classes of functions change with the sample size and are not donsker type importantly our new technique is able to prove the gaussian approximation for the supremum type statistics under considerably weak regularity conditions especially concerning the bandwidth and the number of series functions in those examples

almost regular sequences and betti numbers let be a simplicial complex and s the shifted simplicial complex of as defined by kalai it is shown that the stanley reisner ideals i and i s have the same extremal betti numbers this theorem is the squarefree analogue of the corresponding result by bayer charalambous and popescu which asserts that a graded ideal and its generic ideal have the same extremal betti numbers our theorem implies well known results by kalai according to which and s have the same simplicial homology and is cohen macaulay if and only if its shifted complex is cohen macaulay

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

prediction in censored survival data a comparison of the proportional hazards and linear regression models although the analysis of censored survival data using the proportional hazards and linear regression models is common there has been little work examining the ability of these estimators to predict time to failure this is unfortunate since a predictive plot illustrating the relationship between time to failure and a continuous covariate can be far more informative regarding the risk associated with the covariate than a kaplan meier plot obtained by discretizing the variable in this paper the predictive power of the cox 1972 journal of the royal statistical society series b 34 187 202 proportional hazards estimator and the buckley james 1979 biometrika 66 429 436 censored regression estimator are compared using computer simulations and heuristic arguments it is shown that the choice of method depends on the censoring proportion strength of the regression the form of the censoring distribution and the form of the failure distribution several examples are provided to illustrate the usefulness of the methods

effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable we consider three commonly used statistical tests for assessing the association between an explanatory variable and a measured binary or survival time response variable and investigate the loss in efficiency from mismodelling or mismeasuring the explanatory variable with respect to mismodelling we examine the consequences of using an incorrect dose metameter in a test for trend of mismodelling a continuous explanatory variable and of discretizing a continuous explanatory variable we also examine the consequences of classification errors for a discrete explanatory variable and of measurement errors for a continuous explanatory variable for all three statistical tests the asymptotic relative efficiency are corresponding to each type of mis specification equals the square of the correlation between the correct and fitted form of the explanatory variable this result is evaluated numerically for the different types of mis specification to provide insight into the selection of tests the interpretation of results and the design of studies where the correct explanatory variable cannot be measured exactly

a kernel bound for non symmetric stable distribution and its applications abstract we generalize an inequality in 20 to the non symmetric stable distribution case with 1 2 and apply it to study the error of stable clt in wasserstein 1 distance note that this inequality has a similar form as the classical esseen s inequality

the noether bound in invariant theory of finite groups abstract let r be a commutative ring v a finitely generated free r module and g glr v a finite group acting naturally on the graded symmetric algebra a sym v let ag denote the minimal number m such that the ring ag of invariants can be generated by finitely many elements of degree at most m furthermore let h g be a normal subgroup such that the index g h is invertible in r in this paper we prove the inequality a g a h g h for h 1 and g invertible in r we obtain noether s bound ag g which so far had been shown for arbitrary groups only under the assumption that the factorial of the group order g is invertible in r

approximation to stable law by the lindeberg principle abstract by the lindeberg principle we develop in this paper an approximation to one dimensional possibly asymmetric stable distributions with 0 2 in the smooth wasserstein distance it is the first time that the general stable central limit theorem is proved by the lindeberg principle and that this theorem with 0 1 is proved by a new method other than fourier analysis our main tools are a taylor like expansion and a kolmogorov forward equation

central limit theorems and bootstrap in high dimensions this paper derives central limit and bootstrap theorems for probabilities that sums of centered high dimensional random vectors hit hyperrectangles and sparsely convex sets specifically we derive gaussian and bootstrap approximations for probabilities p n 1 2 ni 1xi a p n 1 2 i 1nxi a where x1 xnx1 xn are independent random vectors in rprp and aa is a hyperrectangle or more generally a sparsely convex set and show that the approximation error converges to zero even if p pn p pn as n n and p np n in particular pp can be as large as o ecnc o ecnc for some constants c c 0c c 0 the result holds uniformly over all hyperrectangles or more generally sparsely convex sets and does not require any restriction on the correlation structure among coordinates of xixi sparsely convex sets are sets that can be represented as intersections of many convex sets whose indicator functions depend only on a small subset of their arguments with hyperrectangles being a special case

rate of convergence to a stable law the rate of convergence to a stable law is determined for the probability density of the normalized sum of n independent identically distributed random variables as n rightarrow infty methods are given for using these results to fit data to such a law

choice of prediction estimator in censored regression models heller and simonoff 1992 biometrics 48 101 115 compared the accuracy of prediction of the cox 1972 journal of the royal statistical society series b 34 187 202 proportional hazards model and the buckley james 1979 biometrika 66 429 436 regression model for censored data they defined a measure of predictive accuracy which they applied to a simulation study to determine which model was better under a variety of different conditions we reanalyze their simulation results and show that they summarized their results incorrectly their suggested strategy for choice of model cox or buckley james is therefore inaccurate and we present an alternative

a sharp bound for the castelnuovo mumford regularity of subspace arrangements abstract we show that the ideal of an arrangement of d linear subspaces of projective space is d regular in the sense of castelnuovo and mumford answering a question of b sturmfels in particular this implies that the ideal of an arrangement of d subspaces is generated in degrees less than or equal to d

conditions for generic initial ideals to be almost reverse lexicographic abstract let i be a homogeneous artinian ideal in a polynomial ring r k x 1 x n over a field k of characteristic 0 we study an equivalent condition for the generic initial ideal gin i with respect to reverse lexicographic order to be almost reverse lexicographic as a result we show that the moreno socias conjecture implies the froberg conjecture and the pardue conjecture and for the case codim i 3 we show that r i has the strong lefschetz property if and only if gin i is almost reverse lexicographic finally we give a positive partial answer to the moreno socias conjecture and hence to the pardue conjecture

a stratification of the hilbert scheme of points in the projective plane this result is analogous to a theorem of iarrobino and brian on on the stratification of the punctual hilbert scheme where a different hilbert function defined by initial forms instead is used however cp i l thm 2 9 p 26 the proof essentially makes use of the smoothness of h a cp f p 517 and a general result of bialynicki birula on the action of the multiplicative group on a smooth projective scheme as already was done in a study of the homology of h a by ellingsrud and stromme this method is applied here to a study of h a around points which are invariant under the borel group in the appendix a method for computing the dimension of h is represented which rests on iarrobino s description of the tangent space to certain points of h a and the theorem of bialynicki birula finally i would like to mention that hirschowitz has outlined a general program for studying stratifications including those defined by hilbert functions cp h p 175 but the result obtained here can at best be regarded only as the most simple perhaps non trivial example

a generalization of the lindeberg principle we generalize lindeberg s proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables the result is applied to get a similar theorem for smooth functions of exchangeable random variables this theorem allows us to identify for the first time the limiting spectral distributions of wigner matrices with exchangeable entries

lefschetz properties and hyperplane arrangements abstract in this article we study the weak and strong lefschetz properties and the related notion of almost revlex ideal in the non artinian case proving that several results known in the artinian case hold also in this more general setting we then apply the obtained results to the study of the jacobian algebra of hyperplane arrangements

direct methods for primary decomposition leti be an ideal in a polynomial ring over a perfect field we given new methods for computing the equidimensional parts and radical ofi for localizingi with respect to another ideal and thus for finding the primary decomposition ofi our methods rest on modern ideas from commutative algebra and are direct in the sense that they avoid the generic projections used by hermann 1926 and all others until now

a free resolution of the module of logarithmic forms of a generic arrangement 1 1 the setup of this paper let v be an i dimensional vector space over a field k we assume that the characteristic of k is zero for the positive characteristic case see 4 6 let d be a generic arrangement of ii hyperplanes d is a finite family of one codimensional subspaces of v satisfying 1 n d 1 3 2 every 2 hyperplanes of d intersect only at the origin let s denote the symmetric algebra s v of the dual space v of v then 5 can be considered as the k algebra of all polynomial functions on v let 0 6 q 1 let 524 2 denote the s module of all regular q forms on v then each qq is a free s module of rank i for each he d choose cake v such that ker a h let

on the marcenko pastur law for linear time series institute of mathematical statistics 2015 this paper is concerned with extensions of the classical ma enko pastur law to time series specifically p dimensional linear processes are considered which are built from innovation vectors with independent identically distributed real or complex valued entries possessing zero mean unit variance and finite fourth moments the coefficient matrices of the linear process are assumed to be simultaneously diagonalizable in this setting the limiting behavior of the empirical spectral distribution of both sample covariance and symmetrized sample autocovariance matrices is determined in the high dimensional setting p n c 0 for which dimension p and sample size n diverge to infinity at the same rate the results extend existing contributions available in the literature for the covariance case and are one of the first of their kind for the autocovariance case

linear models random censoring and synthetic data summary estimators for the linear model in the presence of censoring are available a new extension of the least squares estimator to censored data is equivalent to applying the ordinary least squares estimator to synthetic times time constructed by magnifying the gaps between successive order statistics under suitable regularity conditions the synthetic data estimator is fisher consistent and asymptotically normal examples facilitate com parison of the synthetic data estimator with estimators proposed by buckley james 1979 and by koul susarla van ryzin 1981 the entire lifetime of a person a machine a plant or an animal is not always observable some lifetimes may be censored in that only a lower bound for the lifetime is recorded statisticians are often interested in modelling the distribution of the true lifetimes as a function of covariates when censoring is present a proportional hazards model is often used when there is no censoring linear models are often used for ad hoc modelling of dependent variables miller halpern 1982 survey the methods that have been proposed for the linear model in the presence of censoring this paper describes a closed form method which is consistent and asymptotically normal this method incorporates censor ing in a natural way section 2 formulates classical least squares estimation in a manner that generalizes to accommodate random right censoring section 3 gives some theoretical results for the simplest nontrivial linear model the two sample case section 4 contains examples and the final section discusses the role of this estimator the covariate vector of the ith person will be denoted by xi and usually includes one as the first component the true lifetime yi follows a linear model if its conditional distribution given xi is

a free resolution of the module of derivations for generic arrangements let y be an i dimensional vector space over an arbitrary field f and d an arrangement of n hyperplanes h i7 in v we always assume that n i 1 for each i 1 id 1 we fix once and forever aj e v such that ker cl hi the arrangement d is generic if its every i elements intersect only at 0 or equivalently every i functionals ai are linearly independent in v let s be the symmetric algebra of v and der s der s s the s module of derivations of s the following graded s module was introduced by h terao 4 and studied in many papers on arrangements d d d 0 e der s f3 ai e sa i 1 n at the nsf cbms conference on arrangements of hyperplanes in 1988 the author conjectured that for a generic arrangement with ii 1 we have hd d 1 2 soon after that l rose and h terao 2 proved this conjecture moreover they constructed minimal free resolutions of all modules of logarithmic forms with poles along d and used the fact that d is isomorphic to one of them the aim of the present paper is to give another somewhat more straightforward construction of a minimal free resolution of d more precisely we put do d d bedjo o and note that d does mo where t is the euler derivation defined by a ci for every ci e v then we construct a minimal free resolution of do which of course has the same length as a minimal free resolution of d the notation introduced above is used throughout the paper besides we denote by l the intersection lattice of including v as the unique minimal element of l put li x l dimx i and for every xel put cqzx xn hii x hi viewing it as an arrangement in x also for every xel we put l yel ycx l yel xc y and a x

asymptotic resurgences for ideals of positive dimensional subschemes of projective space abstract recent work of ein lazarsfeld smith and hochster huneke raised the containment problem of determining which symbolic powers of an ideal are contained in a given ordinary power of the ideal bocci harbourne defined a quantity called the resurgence to address this problem for homogeneous ideals in polynomial rings with a focus on zero dimensional subschemes of projective space here we take the first steps toward extending this work to higher dimensional subschemes we introduce new asymptotic versions of the resurgence and obtain upper and lower bounds on them for ideals i of smooth subschemes generalizing what is done in bocci and harbourne 2010 5 we apply these bounds to ideals of unions of general lines in p n we also pose a nagata type conjecture for symbolic powers of ideals of lines in p 3

a comparison of estimators for regression with a censored response variable summary several methods of estimating parameters in a linear regression when the response variable is censored are compared the estimator of buckley james 1979 is preferred further it is shown that the strength of the regression the support and distribution of the censoring variable and the magnitude of the slope all have an effect on the relative performance of the estimators

analysis of covariance and standardization as instances of prediction in this paper prediction provides the basis for unifying the procedures of covariances adjustment and standardization analysis of covariance is a method of forming predictions from a linear model it is used when qualitative effects are to be studied and the effects of continuous variables are to be adjusted for an essential feature is the division into effects of interest and effects for which adjustment is required covariates may also be qualitative as such they are used implicitly in experimental designs with blocks where treatment effects are adjusted for the effect of blocks the technique of standardization is well known in epidemiology and demography as a method of adjusting explicitly for qualitative effects the same division of effects applies when an analysis that uses generalized linear models is summarized two distinct types of prediction which give identical results in classical linear models are available prediction may be conditional on a fixed value of a covariate or marginal on a distribution of values such as the distribution in the set of data being analysed prediction methods are illustrated by the analysis of a table of proportions by use of a logit model

anisotropic local laws for random matrices we develop a new method for deriving local laws for a large class of random matrices it is applicable to many matrix models built from sums and products of deterministic or independent random matrices in particular it may be used to obtain local laws for matrix ensembles that are anisotropic in the sense that their resolvents are well approximated by deterministic matrices that are not multiples of the identity for definiteness we present the method for sample covariance matrices of the form open image in new window where t is deterministic and x is random with independent entries we prove that with high probability the resolvent of q is close to a deterministic matrix with an optimal error bound and down to optimal spectral scales as an application we prove the edge universality of q by establishing the tracy widom airy statistics of the eigenvalues of q near the soft edges this result applies in the single cut and multi cut cases further applications include the distribution of the eigenvectors and an analysis of the outliers and bbp type phase transitions in finite rank deformations they will appear elsewhere we also apply our method to wigner matrices whose entries have arbitrary expectation i e we consider w a where w is a wigner matrix and a a hermitian deterministic matrix we prove the anisotropic local law for w a and use it to establish edge universality

measures of dependence for censored survival data in the linear regression model with normal errors the squared product moment correlation provides the standard measure of dependence between the explanatory variable and the response variable using the concept of information gain a measure of dependence can also be defined for more general regression models used in survival analysis such as the weibull regression model or cox s proportional hazards model further this measure of dependence can be conveniently estimated even when the response variable is subject to censoring and a simple approximation is available

central limit theorems for supercritical branching nonsymmetric markov processes in this paper we establish a spatial central limit theorem for a large class of supercritical branching not necessarily symmetric markov processes with spatially dependent branching mechanisms satisfying a second moment condition this central limit theorem generalizes and unifies all the central limit theorems obtained recently in ren song and zhang j funct anal 266 2014 1716 1756 for supercritical branching symmetric markov processes to prove our central limit theorem we have to carefully develop the spectral theory of nonsymmetric strongly continuous semigroups which should be of independent interest

borel fixed ideals and reduction number abstract the aim of this paper is to study the relationship between the reduction number and borel fixed ideals in all characteristics especially it is shown that r r i r r i lex where i lex denotes the unique lex segment ideal whose hilbert function is equal to that of i this solves a recent question by conca