2d markov chains abstract the separation property that characterizes the dynamics of markov chains is extended to a class of discrete 2d models where the time support given by the discrete plane z z is partially ordered by the product of the orderings the paper analyzes the matrix representation structure of the probability transition map in a 2d markov chain and some properties of the associated characteristic polynomial in two variables these allow one to show how the long term behavior depends on the intersections between the variety of the characteristic polynomial and the distinguished boundary of the unit closed bidisk

complex representations of finite monoids ii highest weight categories and quivers abstract in this paper we continue our study of complex representations of finite monoids we begin by showing that the complex algebra of a finite regular monoid is a quasi hereditary algebra and we identify the standard and costandard modules we define the concept of a monoid quiver and compute it in terms of the group characters of the standard and costandard modules we use our results to determine the blocks of the complex algebra of the full transformation semigroup we show that there are only two blocks when the degree 3 we also show that when the degree 5 the complex algebra of the full transformation semigroup is not of finite representation type answering negatively a conjecture of ponizovskii

bootstrapping a regression equation some empirical results abstract the bootstrap like the jackknife is a technique for estimating standard errors the idea is to use monte carlo simulation based on a nonparametric estimate of the underlying error distribution the main object of this article is to present the bootstrap in the context of an econometric equation describing the demand for energy by industry as it turns out the conventional asymptotic formulas for estimating standard errors are too optimistic by factors of nearly three when applied to a particular finite sample problem in a simpler context this finding can be given a mathematical proof

robust estimation of mean squared error of small area estimators abstract a well known model due to fay and herriot for estimating small area domain means i is considered given i s it is assumed that the survey estimators y i are independent with means i and known variances di i 1 t further the i s are assumed to be independent with means x i and unknown variance a where x i is a vector of benchmark variables related to i and is a vector of regression parameters an empirical best linear unbiased prediction eblup estimator or an empirical linear bayes estimator t i y of i is obtained it is shown that an estimator of mean squared error mse of t t y derived by prasad and rao under normality of i and y i given i is robust with respect to nonnormality of the i s specifically it is shown that the prasad rao estimator of mse is correct to terms of order o t 1 for large t assuming only certain moment conditions on the i s and normally distributed survey errors results of a simulation study on the accur

symmetric algebras skew category algebras and inverse semigroups abstract we use results from the theory of inverse semigroups to identify and define a class of symmetric algebras which we call inverse symmetric algebras for a finite inverse category c we define the skew category algebra associated to a c algebra which satisfies some additional properties and we prove that remains inverse symmetric the classical examples of symmetric algebras matrix algebra iwahori hecke algebra and the twisted group algebra are inverse symmetric

maximal subgroups of free idempotent generated semigroups over the full linear monoid we show that the rank r component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of n times n matrices over a division ring q has maximal subgroup isomorphic to the general linear group gl r q where n and r are positive integers with r n 3

a comodule bialgebra structure for word series substitution and mould composition abstract an internal coproduct is described which is compatible with hoffman s quasi shuffle product hoffman s quasi shuffle hopf algebra with deconcatenation coproduct is a comodule hopf algebra over the bialgebra thus defined the relation with ecalle s mould calculus i e mould composition and contracting arborification is precised

jackknife variance estimators in linear models an alternative to the weighted jackknife variance estimator of wu 1986 is introduced motivated by the comments of efron 1986 ghosh 1986 and tibshirani 1986 the performance of wu s estimator is compared with the proposed estimator in terms of the average loss in some linear models some asymptotic properties of the proposed estimator are discussed

incorrect asymptotic size of subsampling procedures based on post consistent model selection estimators abstract subsampling and the m out of n bootstrap have been suggested in the literature as methods for carrying out inference based on post model selection estimators and shrinkage estimators in this paper we consider a subsampling confidence interval ci that is based on an estimator that can be viewed either as a post model selection estimator that employs a consistent model selection procedure or as a super efficient estimator we show that the subsampling ci of nominal level 1 for any 0 1 has asymptotic confidence size defined to be the limit of finite sample size equal to zero in a very simple regular model the same result holds for the m out of n bootstrap provided m 2 n 0 and the observations are i i d similar zero asymptotic confidence size results hold in more complicated models that are covered by the general results given in the paper and for super efficient and shrinkage estimators that are not post model selection estimators based on these results subsampling and the m out of n bootstrap are not recommended for obtaining inference based on post consistent model selection or shrinkage estimators

representation theory of finite semigroups semigroup radicals and formal language theory in this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field generalizing results of rhodes for the field of complex numbers applications are given to obtain many new results as well as easier proofs of several results in the literature involving triangularizability of finite semigroups which semigroups have split basic semigroup algebras two sided semidirect product decompositions of finite monoids unambiguous products of rational languages products of rational languages with counter and cerny s conjecture for an important class of automata

censored quantile regression with partially functional effects quantile regression offers a flexible approach to analyzing survival data allowing each covariate effect to vary with quantiles in practice constancy is often found to be adequate for some covariates in this paper we study censored quantile regression tailored to the partially functional effect setting with a mixture of varying and constant effects such a model can offer a simpler view regarding covariate survival association and moreover can enable improvement in estimation efficiency we propose profile estimating equations and present an iterative algorithm that can be readily and stably implemented asymptotic properties of the resultant estimators are established a simple resampling based inference procedure is developed and justified extensive simulation studies demonstrate efficiency gains of the proposed method over a naive two stage procedure the proposed method is illustrated via an application to a recent renal dialysis study

bootstrapping realized volatility we propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases we consider the independent and identically distributed i i d bootstrap and the wild bootstrap wb and prove their first order asymptotic validity under general assumptions on the log price process that allow for drift and leverage effects we derive edgeworth expansions in a simpler model that rules out these effects the i i d bootstrap provides a second order asymptotic refinement when volatility is constant but not otherwise the wb yields a second order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the wb data appropriately none of these methods provides third order asymptotic refinements both methods improve upon the first order asymptotic theory in finite samples

a bootstrapped spectral test for adequacy in weak arma models this paper proposes a cramer von mises cm test statistic to check the adequacy of weak arma models without posing a martingale difference assumption on the error terms the asymptotic null distribution of the cm test is obtained moreover this cm test is consistent and has nontrivial power against the local alternative of order n 1 2 due to the unknown dependence of error terms and the estimation effects a new block wise random weighting method is constructed to bootstrap the critical values of the test statistic the new method is easy to implement and its validity is justified the theory is illustrated by a small simulation study and an application to s p 500 stock index

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

static spherically symmetric solutions of the einstein yang mills equations we study the global behaviour of static spherically symmetric solutions of the einstein yang mills equations with gauge groupsu 2 our analysis results in three disjoint classes of solutions with a regular origin or a horizon the 3 spaces t const of the first generic class are compact and singular the second class consists of an infinite family of globally regular resp black hole solutions the third type is an oscillating solution which although regular is not asymptotically flat

generalized bootstrap for estimating equations we introduce a generalized bootstrap technique for estimators obtained by solving estimating equations some special cases of this generalized bootstrap are the classical bootstrap of efron the delete d jackknife and variations of the bayesian bootstrap the use of the proposed technique is discussed in some examples distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained

the representation theory of the monoid of all partial functions on a set and related monoids as ei category algebras the ordinary quiver of an algebra a is a graph that contains information about the algebra s representations we give a description of the quiver of cptn the algebra of the monoid of all partial functions on n elements our description uses an isomorphism between cptn and the algebra of the epimorphism category en whose objects are the subsets of 1 n and morphism are all total epimorphisms this is an extension of a well known isomorphism of the algebra of isn the monoid of all partial injective maps on n elements and the algebra of the groupoid of all bijections between subsets of an n element set the quiver of the category algebra is described using results of margolis steinberg and li on the quiver of ei categories we use the same technique to compute the quiver of other natural transformation monoids we also show that the algebra cptn has three blocks for n 1 and we give a natural description of the descending loewy series of cptn in the category form

information ratio test for model misspecification in quasi likelihood inference in this article we focus on the circumstances in quasi likelihood inference that the estimation accuracy of mean structure parameters is guaranteed by correct specification of the first moment but the estimation efficiency could be diminished due to misspecification of the second moment we propose an information ratio ir statistic to test for model misspecification of the variance covariance structure through a comparison between two forms of information matrix the negative sensitivity matrix and the variability matrix we establish asymptotic distributions of the proposed ir test statistics we also suggest an approximation to the asymptotic distribution of the ir statistic via a perturbation resampling method moreover we propose a selection criterion based on the ir test to select the best fitting variance covariance structure from a class of candidates through simulation studies it is shown that the ir statistic provides a powerful statistical tool to detect different scenarios of misspecific

a generalization of the schutzenberger product of finite monoids for each n 1 an n ary product on finite monoids is constructed this product has the following property let be a finite alphabet and the free monoid generated by for i 1 n let ai be a recognizable subset of m ai the syntactic monoid of an and m a1 an the syntactic monoid of the concatenation product a1 an then m a1 an m a1 m an the case n 2 was studied by schutzenberger as an application of the generalized product i prove the theorem of brzozowski and knast that the dot depth hierarchy of star free sets is infinite

a generalized birkhoff theorem for the einstein yang mills system some results of a systematic study of the coupled einstein yang mills eym equations for arbitrary gauge groups are presented herein in a first step a group theoretical analysis of spherically symmetric eym fields is given this will lead to a concise description of a large class of principal bundles for which the spherically symmetric solutions of the eym equations have to be static generalized birkhoff theorem and the metric must be of the reissner nordstro m type

conjugacy classes of renner monoids abstract in this paper we describe conjugacy classes of a renner monoid r with unit group w the weyl group we show that every element in r is conjugate to an element ue where u w and e is an idempotent in a cross section lattice denote by w e and w e the centralizer and stabilizer of e in w respectively let w e act by conjugation on the set of left cosets of w e in w we find that ue and ve u v w are conjugate if and only if u w e and v w e are in the same orbit as consequences there is a one to one correspondence between the conjugacy classes of r and the orbits of this action we then obtain a formula for calculating the number of conjugacy classes of r and describe in detail the conjugacy classes of the renner monoid of some j irreducible monoids we then generalize munn conjugacy on a rook monoid to any renner monoid and show that munn conjugacy coincides with semigroup conjugacy action conjugacy and character conjugacy we also show that the number of inequivalent irreducible representations of r over an algebraically closed field of characteristic zero equals the number of munn conjugacy classes in r

an alternative approach to obtaining nagar type moment approximations in simultaneous equation models this paper examines asymptotic expansions for estimation errors expressed explicitly as functions of underlying random variables taylor series expansions are obtained from which first and second moment approximations are derived while the expansions are essentially equivalent to the traditional nagar type the terms are expressed in a form which enables moment approximations to be obtained in a particularly straightforward way once the partial derivatives have been found the approach is illustrated by considering the k class estimators in a static simultaneous equation model where the disturbances are non spherical

analysis of the static spherically symmetric su n einstein yang mills equations the singular boundary value problem that arises for the static spherically symmetricsu n einstein yang mills equations in the so called magnetic case is analyzed among the possible actions ofsu 2 on asu n principal bundles over space time there is one which appears to be the most natural if one assumes that no electrostatic type component is present in the yang mills fields and the gauge is suitably fixed a set ofn 1 second order and two first order differential equations is obtained forn 1 gauge potentials and two metric components as functions of the radial distance this system generalizes the one for the casen 2 that leads to the discrete series of the bartnick mckinnon and the corresponding black hole solutions it is highly nonlinear and singular atr and atr 0 or at the black hole horizon but it is known to admit at least one series of discrete solutions which are scaled versions of then 2 case in this paper local existence and uniqueness of solutions near these singular points is established which turns out to be a nontrivial problem for generaln moreover a number of new numerical soliton i e globally regular numerical solutions of thesu 3 eym equations are found that are not scaledn 2 solutions

turing machines and bimachines we associate the iterated block product of a bimachine with a deterministic turing machine this allows us to introduce new algebraic notions to study the behavior of the turing machine namely we introduce double semidirect products through matrix multiplication of upper triangular matrices with coefficients in certain semigroups which leads in turn to the study of the iterations of bimachines by passing to the profinite or projective limit we obtain an algebraic profinite description of the limit behavior of the turing machine finally we analyze the proof that all languages in np can be reduced to circuit sat from this viewpoint

character theory of monoids over an arbitrary field abstract the basic character theory of finite monoids over the complex numbers was developed in the sixties and seventies based on work of munn ponizovski mcalister rhodes and zalcstein in particular mcalister determined the space of functions spanned by the irreducible characters of a finite monoid over c and the ring of virtual characters in this paper we present the corresponding results over an arbitrary field as a consequence we obtain a quick proof of the theorem of berstel and reutenauer that the characteristic function of a regular cyclic language is a virtual character of the free monoid this is a crucial ingredient in their proof of the rationality of the zeta function of a sofic shift in symbolic dynamics

fast fourier transforms for finite inverse semigroups abstract we extend the theory of fast fourier transforms on finite groups to finite inverse semigroups we use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its fourier transform to the problems of computing fourier transforms on its maximal subgroups and a fast zeta transform on its poset structure we then exhibit explicit fast algorithms for particular inverse semigroups of interest specifically for the rook monoid and its wreath products by arbitrary finite groups

transformations to symmetry and homoscedasticity abstract this article considers transformations in regression to eliminate skewness and heteroscedasticity of the response we work with the transform both sides model where the relationship between the median response and the independent variables has been identified at least tentatively to preserve this relationship the response and the regression model are transformed in the same way extending the work of others for the location parameter case we propose an estimator that eliminates skewness we also develop an estimator to eliminate heteroscedasticity and an estimator that attempts to induce both symmetry and homoscedasticity both and appear new by comparing and we develop a test of the null hypothesis that there exists a transformation to both symmetry and homoscedasticity we study the question when does the estimator of behave in terms of asymptotic variance as if the regression parameter were known and vice versa the results are of use for telling when the optimal estimator of do

estimation and inference in two stage semi parametric models of production processes many papers have regressed non parametric estimates of productive efficiency on environmental variables in two stage procedures to account for exogenous factors that might affect firms performance none of these have described a coherent data generating process dgp moreover conventional approaches to inference employed in these papers are invalid due to complicated unknown serial correlation among the estimated efficiencies we first describe a sensible dgp for such models we propose single and double bootstrap procedures both permit valid inference and the double bootstrap procedure improves statistical efficiency in the second stage regression we examine the statistical performance of our estimators using monte carlo experiments

a groupoid approach to discrete inverse semigroup algebras abstract let k be a commutative ring with unit and s an inverse semigroup we show that the semigroup algebra ks can be described as a convolution algebra of functions on the universal etale groupoid associated to s by paterson this result is a simultaneous generalization of the author s earlier work on finite inverse semigroups and paterson s theorem for the universal c algebra it provides a convenient topological framework for understanding the structure of ks including the center and when it has a unit in this theory the role of gelfand duality is replaced by stone duality using this approach we construct the finite dimensional irreducible representations of an inverse semigroup over an arbitrary field as induced representations from associated groups generalizing the case of an inverse semigroup with finitely many idempotents more generally we describe the irreducible representations of an inverse semigroup s that can be induced from associated groups as precisely those satisfying a certain finiteness condition this finiteness condition is satisfied for instance by all representations of an inverse semigroup whose image contains a primitive idempotent

slowly synchronizing automata with fixed alphabet size abstract it was conjectured by cern in 1964 that a synchronizing dfa on n states always has a shortest synchronizing word of length at most n 1 2 and he gave a sequence of dfas reaching this bound in this paper we investigate the role of the alphabet size for each possible alphabet size we count dfas on n 6 states which synchronize in n 1 2 e steps for all e 2 n 2 furthermore we give constructions of automata with any number of states and 3 4 or 5 symbols which synchronize slowly namely in n 2 3 n o 1 steps in addition our results prove cern s conjecture for n 6 our computations lead to 31 dfas on 3 4 5 or 6 states which synchronize in n 1 2 steps of these dfa s 19 are new the remaining 12 which were already known are exactly the minimal ones the 19 new dfas are extensions of automata which were already known but for n 3 we prove that the cern automaton on n states does not admit non trivial extensions with the same smallest synchronizing word length n 1 2

static spherically symmetric solutions of the so 5 einstein yang mills equations globally regular ie asymptotically flat and regular interior spher ically symmetric and localised particle like solutions of the coupled ein stein yang mills eym equations with gauge group su 2 have been known for more than 20 years yet their properties are still not well understood spher ically symmetric yang mills fields are classified by a choice of isotropy genera tor and so 5 is distinguished as the simplest model with a non abelian resid ual little group su 2 u 1 and which admits globally regular particle like solutions we exhibit an algebraic gauge condition which normalises the resid ual gauge freedom to a finite number of discrete symmetries this generalises the well known reduction to the real magnetic potential w r t in the original su 2 ym model reformulating using gauge invariant polynomials dramat ically simplifies the system and makes numerical search techniques feasible we find three families of embedded su 2 eym equations within the so 5 system one of which was first detected only within the gauge invariant polyno mial reduced system numerical solutions representing mixtures of the three su 2 sub systems are found classified by a pair of positive integers

asymptotic theory in generalized ilinear models with nuisance scale parameters this paper establishes the asymptotic normality and the consistencyrobustness of the weighted least squares estimator wlse in the generalized linear models with multiple nuisance scale parameters in addition noting that the asymptotic robust statistical inference in presence of nuisance scale parameters requires a consistency robust estimator of the asymptotic covariance matrix of the wlse this paper derives a class of covariance estimators and proves their consistency robustness

a comparison of the variance estimation methods for heteroscedastic nonlinear models heteroscedasticity is commonly encountered when fitting nonlinear regression models in practice we discuss eight different variance estimation methods for nonlinear regression models with heterogeneous response variances and present a simulation study to compare the performance of the eight methods in terms of estimating the standard errors of the fitted model parameters the simulation study suggests that when the true variance is a function of the mean model the power of the mean variance function estimation method and the transform both sides method are the best choices for estimating the standard errors of the estimated model parameters in general the wild bootstrap estimator and two modified versions of the standard sandwich variance estimator are reasonably accurate with relatively small bias especially when the heterogeneity is nonsystematic across values of the covariate furthermore we note that the two modified sandwich estimators are appealing choices in practice considering the computational advantage of these two estimation methods relative to the variance function estimation method and the transform both sides approach copyright 2016 john wiley sons ltd

some contributions to the theory of transformation monoids abstract the aim of this paper is to present some contributions to the theory of finite transformation monoids the dominating influence that permutation groups have on transformation monoids is used to describe and characterise transitive transformation monoids and primitive transitive transformation monoids we develop a theory that not only includes the analogs of several important theorems of the classical theory of permutation groups but also contains substantial information about the algebraic structure of the transformation monoids open questions naturally arising from the substantial paper of steinberg 2010 11 have been answered our results can also be considered as a further development in the hunt for a solution of the cern conjecture

calibrating confidence coefficients abstract two approaches for dealing with the problem of poor coverage probabilities of certain standard confidence intervals are proposed the first is a recommendation that the actual coverage be estimated directly from the data and its value reported in addition to the nominal level this is achieved through a combination of computer simulation and density estimation the asymptotic validity of the procedure is proved for a number of common situations a classical example is the nonparametric estimation of the variance of a population using the normal theory interval here it is shown that the estimated coverage probability consistently estimates the true coverage probability if the population distribution possesses a finite sixth moment the second approach is more traditional it is a procedure for modifying an interval to yield improved coverage properties given a confidence interval its estimated coverage probability obtained in the first approach is used to alter the nominal level of the interval

bootstrap confidence intervals for a class of parametric problems summary we consider the following class of problems having observed a multivariate normal data vector y with unknown mean vector q covariance matrix the identity find an approximate confidence interval for 0 t q a real valued function of q a simple geometric construction is given which leads to highly accurate solutions this construction shows that the standard approximation based on maximum likelihood theory 04 cz00 can be quite misleading when 0 is nonlinear in q we discuss bootstrap based confidence intervals which remove most of the error in the standard approximation at the expense of considerably more calculation the bootstrap intervals are invariant under transformation of both y and i and so they automatically produce accurate solutions in problems which can be transformed to multivariate normality without requiring knowledge of the normalizing transformation

a heteroskedasticity robust breusch pagan test for contemporaneous correlation in dynamic panel data models abstract this paper proposes a heteroskedasticity robust breusch pagan test of the null hypothesis of zero cross section or contemporaneous correlation in linear panel data models without necessarily assuming independence of the cross sections the procedure allows for either fixed strictly exogenous and or lagged dependent regressor variables as well as quite general forms of both non normality and heteroskedasticity in the error distribution the asymptotic validity of the test procedure is predicated on the number of time series observations t being large relative to the number of cross section units n in that either i n is fixed as t or ii n 2 t 0 as both t and n diverge jointly to infinity given this it is not expected that asymptotic theory would necessarily provide an adequate guide to finite sample performance when t n is small because of this we also propose and establish asymptotic validity of a number of wild bootstrap schemes designed to provide improved inference when t n is small across a variety of experimental designs a monte carlo study suggests that the predictions from asymptotic theory do in fact provide a good guide to the finite sample behaviour of the test when t is large relative to n however when t and n are of similar orders of magnitude discrepancies between the nominal and empirical significance levels occur as predicted by the first order asymptotic analysis on the other hand for all the experimental designs the proposed wild bootstrap approximations do improve agreement between nominal and empirical significance levels when t n is small with a recursive design wild bootstrap scheme performing best in general and providing quite close agreement between the nominal and empirical significance levels of the test even when t and n are of similar size moreover in comparison with the wild bootstrap version of the original breusch pagan test godfrey and yamagata 2011 our experiments indicate that the corresponding version of the heteroskedasticity robust breusch pagan test appears reliable as an illustration the proposed tests are applied to a dynamic growth model for a panel of 20 oecd countries

statistics of biophysical signal characteristics and state specificity of the human eeg abstract the analysis of records of biophysical signals like eeg have become increasingly interesting to physicists since the development of new algorithms for time series analysis this analysis however requires both an adequate methodology assessing the time series characteristics and an appropriate statistical assessment of the measures resulting from these algorithms the latter should separate inherent effects from those appearing only by chance e g in terms of an appropriate test statistics as a step towards such a statistical assessment we present here a data resampling approach data resampling techniques allow for the estimation of the variance of an f value as obtained through variance analysis a test statistics based on the so called f ratio 2 f f 2 is derived and the simulation of outcomes allows for the determination of its quantiles a multivariate formulation allows for the simultaneous inclusion of linear and nonlinear time series measures into the analysis we applied these concepts to the problem of distinguishing eeg of healthy probands from the eeg of patients diagnosed as schizophrenic together with an approach involving bayes formula to weight the variables it reveals a reliable discriminance performance of 81 when the nonlinear measure and the linear measures and power are included

the structure of spherically symmetric su n yang mills fields we summarize the algebraic structure of spherically symmetric yang mills potentials for a general compact gauge group and investigate the particular case of gauge groups with lie algebra su n in detail we develop techniques that lead to a complete classification of the possible spherical symmetry ansatze including descriptions of the reduced gauge group z the space of magnetic potentials h and for those ansatze that admit extensions across the symmetry axis a description of the space of vacuum potentials h0 and its little group z0 these results are illustrated by listing all irreducible models for su n n 6

mobius functions and semigroup representation theory ii character formulas and multiplicities abstract we generalize the character formulas for multiplicities of irreducible constituents from group theory to semigroup theory using rota s theory of mobius inversion the technique works for a large class of semigroups including inverse semigroups semigroups with commuting idempotents idempotent semigroups and semigroups with basic algebras using these tools we are able to give a complete description of the spectra of random walks on finite semigroups admitting a faithful representation by upper triangular matrices over the complex numbers these include the random walks on chambers of hyperplane arrangements studied by bidigare hanlon rockmore brown and diaconis applications are also given to decomposing tensor powers and exterior products of rook matrix representations of inverse semigroups generalizing and simplifying earlier results of solomon for the rook monoid

the cerný conjecture for one cluster automata with prime length cycle abstract we prove the cern conjecture for one cluster automata with prime length cycle consequences are given for the hybrid road coloring cern conjecture for strongly connected aperiodic digraphs with a proper cycle of prime length

inference from stratified samples second order analysis of three methods for nonlinear statistics abstract for stratified samples and nonlinear statistics that can be expressed as functions of estimated totals second order asymptotic expansions of the linearization jackknife and balanced repeated replication variance estimators are obtained based on these comparisons are made in terms of their biases some higher order asymptotic equivalence results are also established the special case of a combined ratio estimator is investigated in detail some results on bias reduction achieved by the jack knife and balanced repeated replication estimators of a nonlinear function of totals are also given

synchronizing groups and automata pin showed that every p state automaton p a prime containing a cyclic permutation and a non permutation has a synchronizing word of length at most p 1 2 in this paper we consider permutation automata with the property that adding any nonpermutation will lead to a synchronizing word and establish bounds on the lengths of such synchronizing words in particular we show that permutation groups whose permutation character over the rationals splits into a sum of only two irreducible characters have the desired property

robust permutation tests for correlation and regression coefficients abstractgiven a sample from a bivariate distribution consider the problem of testing independence a permutation test based on the sample correlation is known to be an exact level test however when used to test the null hypothesis that the samples are uncorrelated the permutation test can have rejection probability that is far from the nominal level further the permutation test can have a large type 3 directional error rate whereby there can be a large probability that the permutation test rejects because the sample correlation is a large positive value when in fact the true correlation is negative it will be shown that studentizing the sample correlation leads to a permutation test which is exact under independence and asymptotically controls the probability of type 1 or type 3 errors these conclusions are based on our results describing the almost sure limiting behavior of the randomization distribution we will also present asymptotically robust randomization tests for regression coeffi

a bootstrap comparison of genetic covariance matrices summary an important problem in evolutionary biology is how population bottlenecks affect additive genetic variance va when only additive effects are present a decrease in va is predicted whereas with many forms of nonadditive interactions an increase is predicted we present an analysis of the changes in variance that occur as a result of a bottleneck in a population of the red flour beetle tribolium castaneum in this experiment the additive genetic covariance matrix for four traits in two sexes was measured in the ancestral population the population then went through a bottleneck and the genetic covariance matrix was again measured these data were analyzed by first examining the univariate estimates for va and second examining the covariance matrices for the univariate measures the statistic we used was the change in va for the multivariate comparisons we used three measures the difference in rank the difference in the number of positive eigenvalues to test changes in the number of heritable traits a multivariate equivalent of bartlett s statistic to test changes in the size of the matrices and a modification of mantel s correlation to test for changes in the correlation structure of the matrices because the distribution of all of these measures is complex and dependent on the specifics of the particular matrices being compared we chose to use a bootstrap analysis to test for significance for females we found that following the population bottleneck va was significantly decreased and that the correlation structure of the matrix was significantly changed for males we found that following the population bottleneck va significantly increased but that the correlation structure was unchanged

an assumption free exact test for fixed design linear models with exchangeable errors we propose the cyclic permutation test cpt to test general linear hypotheses for linear models this test is non randomized and valid in finite samples with exact type i error alpha for an arbitrary fixed design matrix and arbitrary exchangeable errors whenever 1 alpha is an integer and n p ge 1 alpha 1 the test involves applying the marginal rank test to 1 alpha linear statistics of the outcome vector where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a non standard cyclic permutation group under the null hypothesis the power can be further enhanced by solving a secondary non linear travelling salesman problem for which the genetic algorithm can find a reasonably good solution extensive simulation studies show that the cpt has comparable power to existing tests when testing for a single contrast of coefficients an exact confidence interval can be obtained by inverting the test furthermore we provide a selective yet extensive literature review of the century long efforts on this problem highlighting the novelty of our test

jackknifing in the presence of inhomogeneity under the classical assumption that data are a random sample from a distribution with cumulative distribution function f the jackknife generally yields bias reduction an asymptotically pivotal statistic and a variance estimator for an estimator of an unknown parameter f in this article the classical assumption is relaxed to allow for inhomogeneous subpopulations the jackknife is been to account for these inhomogeneities automatically and so is valid in a class of problems much larger than that for which it was originally intended data from experiments to determine the acceleration of gravity at washington d c are analyzed a family of weighted mean estimators is considered and recommendations are made regarding which estimators yield both valid and efficient jackknife based inferences

heteroscedasticity robustness of jackknife variance estimators in linear models on etudie l absence de biais et la consistance asymptotiques de trois types d estimateurs de variance du jackknife en presence d heteroscedasticite de la variance de l erreur dans les modeles lineaires

bootstrap and wild bootstrap for high dimensional linear models in this paper two bootstrap procedures are considered for the estimation of the distribution of linear contrasts and of f test statistics in high dimensional linear models an asymptotic approach will be chosen where the dimension p of the model may increase for sample size n rightarrow infty the range of validity will be compared for the normal approximation and for the bootstrap procedures furthermore it will be argued that the rates of convergence are different for the bootstrap procedures in this asymptotic framework this is in contrast to the usual asymptotic approach where p is fixed

on resampling methods for variance and bias estimation in linear models let g be a nonlinear function of the regression parameters beta in a heteroscedastic linear model and hat beta be the least squares estimator of beta we consider the estimation of the variance and bias of g hat beta as an estimator of g beta by using three resampling methods the weighted jackknife the unweighted jackknife and the bootstrap the asymptotic orders of the mean squared errors and biases of the resampling variance and bias estimators are given in terms of an imbalance measure of the model consistency of the resampling estimators is also studied the results indicate that the weighted jackknife variance and bias estimators are asymptotically unbiased and consistent and their mean squared errors are of order o n 2 if the imbalance measure converges to zero as the sample size n rightarrow infty furthermore based on large sample properties the weighted jackknife is better than the unweighted jackknife the bootstrap method is shown to be asymptotically correct only under a homoscedastic error model bias reduction a closely related problem is also discussed

spherically symmetric einstein yang mills higgs fields for general compact gauge groups abstract we discuss and classify the einstein yang mills higgs eymh fields that are invariant under arbitrary actions of a symmetry group by automorphisms on principal bundles with arbitrary compact gauge groups that project onto the isometries of space time in particular we apply this result to the systematic construction of spherically symmetric eymh fields in this general setting physically reasonable boundary conditions at infinity and or at the center have been shown to considerably restrict the possible yang mills connections here we investigate for which representations of the gauge group higgs fields may be spherically symmetric or may at least contribute to a spherically symmetric stress energy tensor

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

directed nonabelian sandpile models on trees we define two general classes of nonabelian sandpile models on directed trees or arborescences as models of nonequilibrium statistical physics unlike usual applications of the well known abelian sandpile model these models have the property that sand grains can enter only through specified reservoirs

fast fourier transforms for the rook monoid we define the notion of the fourier transform for the rook monoid also called the symmetric inverse semigroup and provide two efficient divide and conquer algorithms fast fourier transforms or ffts for computing it this paper marks the first extension of group ffts to nongroup semigroups

primitive orthogonal idempotents for r trivial monoids we construct a recursive formula for a complete system of primitive orthogonal idempotents for any r trivial monoid this uses the newly proved equivalence between the notions of r trivial monoid and weakly ordered monoid

local existence proofs for the boundary value problem for static spherically symmetric einstein yang mills fields with compact gauge groups we prove local existence and uniqueness of static spherically symmetric solutions of the einstein yang mills eym equations for an arbitrary compact semisimple gauge group in the so called regular case by this we mean the equations obtained when the rotation group acts on the principal bundle on which the yang mills connection takes its values in a particularly simple way the only one ever considered in the literature the boundary value problem that results for possible asymptotically flat soliton or black hole solutions is very singular and just establishing that local power series solutions exist at the center and asymptotic solutions at infinity amounts to a nontrivial algebraic problem we discuss the possible field equations obtained for different group actions and solve the algebraic problem on how the local solutions depend on initial data at the center and at infinity

jackknife estimation of stationary autoregressive models abstract this paper explores the properties of jackknife methods of estimation in stationary autoregressive models some general results concerning the correct weights for bias reduction under various sampling schemes are provided and the asymptotic properties of a jackknife estimator based on non overlapping sub samples are derived for the case of a stationary autoregression of order p when the number of sub samples is either fixed or increases with the sample size at an appropriate rate the results of a detailed investigation into the finite sample properties of various jackknife and alternative estimators are reported and it is found that the jackknife can deliver substantial reductions in bias in autoregressive models this finding is robust to departures from normality arch effects and misspecification the median unbiasedness and mean squared error properties are also investigated and compared with alternative methods as are the coverage rates of jackknife based confidence intervals

unified theory for finite markov chains abstract we provide a unified framework to compute the stationary distribution of any finite irreducible markov chain or equivalently of any irreducible random walk on a finite semigroup s our methods use geometric finite semigroup theory via the karnofsky rhodes and the mccammond expansions of finite semigroups with specified generators this does not involve any linear algebra the original tsetlin library is obtained by applying the expansions to p n the set of all subsets of an n element set our set up generalizes previous groundbreaking work involving left regular bands or r trivial bands by brown and diaconis extensions to r trivial semigroups by ayyer steinberg thiery and the second author and important recent work by chung and graham the karnofsky rhodes expansion of the right cayley graph of s in terms of generators yields again a right cayley graph the mccammond expansion provides normal forms for elements in the expanded s using our previous results with silva based on work by berstel perrin reutenauer we construct infinite semaphore codes on which we can define markov chains these semaphore codes can be lumped using geometric semigroup theory using normal forms and associated kleene expressions they yield formulas for the stationary distribution of the finite markov chain of the expanded s and the original s analyzing the normal forms also provides an estimate on the mixing time

inference in linear regression models with many covariates and heteroskedasticity the linear regression model is widely used in empirical work in economics statistics and many other disciplines researchers often include many covariates in their linear model specification in a