the entries of circular orthogonal ensembles let v vij n n be a circular orthogonal ensemble in this paper for 1 m o n log n we give a bound for the tail probability of max1 i j m vij 1 n yi yj where y y1 yn is a certain n n matrix whose entries are independent and identically distributed random variables with the standard complex normal distribution cn 0 1 in particular this implies that for a sequence of such matrices vn vij n n n n 1 as n nvij n converges in distribution to cn 0 1 for any i 1 j 1 with i j and nvii n converges in distribution to 2 cn 0 1 for any i 1

existence and exponential stability of piecewise mean square almost periodic solutions for impulsive stochastic nicholson s blowflies model on time scales the concept of piecewise mean square almost periodic stochastic process is introduced a new impulsive stochastic nicholsons blowflies model is introduced and studied on time scales the first results of the piecewise mean square almost periodic solutions for the model are obtained in this paper a class of impulsive stochastic nicholson s blowflies model with patch structure and nonlinear harvesting terms is introduced and studied on time scales by using contraction mapping principal and gronwall bellman inequality technique some sufficient conditions for the existence and exponential stability of piecewise mean square almost periodic solutions for the model with infinite delays are established on time scales finally an example is given to demonstrate the validity of the conditions of the main theorem

circular law and arc law for truncation of random unitary matrix let v be the m m upper left corner of an n n haar invariant unitary matrix let 1 m be the eigenvalues of v we prove that the empirical distribution of a normalization of 1 m goes to the circular law that is the uniform distribution on z c z 1 as m with m n 0 we also prove that the empirical distribution of 1 m goes to the arc law that is the uniform distribution on z c z 1 as m n 1 these explain two observations by yczkowski and sommers 2000

how many entries of a typical orthogonal matrix can be approximated by independent normals we solve an open problem of diaconis that asks what are the largest orders of p n and q n such that z n the p n x q n upper left block of a random matrix r n which is uniformly distributed on the orthogonal group o n can be approximated by independent standard normals this problem is solved by two different approximation methods first we show that the variation distance between the joint distribution of entries of z n and that of p n q n independent standard normals goes to zero provided p n o n and q n o n we also show that the above variation distance does not go to zero if p n x n and q n y n for any positive numbers x and y this says that the largest orders of p n and q n are o n 1 2 in the sense of the above approximation second suppose n ij n n is generated by performing the gram schmidt algorithm on the columns of y n y ij n n where y ij 1 i j n are i i d standard normals we show that e n m max 1 i n 1 j m n ij y ij goes to zero in probability as long as m m n o n log n we also prove that e n m n 2 in probability when m n n logn for any a 0 this says that m n o n log n is the largest order such that the entries of the first m n columns of n can be approximated simultaneously by independent standard normals

i optimal curve for impulsive lotka volterra predator prey model abstract for the classical lotka volterra predator prey system new notion i optimal curve i is introduced this curve is disposed in the phase space of the system the curve i intersects each trajectory c of lotka volterra system at least once the points of i possess the following optimal property if m m i c0 then after a jump with magnitude i to the origin of coordinates it hits a trajectory c1 and c 1 is minimal i e c 1 is the nearest to the stable centre the minimality concerns the rest points of initial trajectory c 0 from which the impulsive jumps subtractings with magnitude i to 0 0 are realized the monotonicity continuity and linear asymptotical behaviour of i curve are proved

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

on random matrices from the compact classical groups if m is a matrix taken randomly with respect to normalized haar measure on u n o n or sp n then the real and imaginary parts of the random variables tr mk k 1 converge to independent normal random variables with mean zero and variance k 2 as the size n of the matrix goes to infinity for the unitary group this is a direct consequence of the strong szeg6 theorem for toeplitz determinants we will prove a conjecture of diaconis

bayesian estimation of the average treatment effect on the treated using inverse weighting we develop a bayesian approach to estimate the average treatment effect on the treated in the presence of confounding the approach builds on developments proposed by saarela et al in the context of marginal structural models using importance sampling weights to adjust for confounding and estimate a causal effect the bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in bayesian causal estimation relying on a joint likelihood we present results from simulation studies to estimate the average treatment effect on the treated evaluating the impact of sample size and the strength of confounding on estimation we illustrate our approach using the classic right heart catheterization data set and find a negative causal effect of the exposure on 30 day survival in accordance with previous analyses of these data we also apply our approach to the data set of the national center for health statistics birth data and obtain a negative effect of maternal smoking during pregnancy on birth weight

negative association of random variables with applications random variables x 1 cdots x k are said to be negatively associated na if for every pair of disjoint subsets a 1 a 2 of 1 2 cdots k operatorname cov lbrack f x 1 i in a 1 g x j j in a 2 rbrack leq 0 for all nondecreasing functions f g the basic properties of negative association are derived especially useful is the property that nondecreasing functions of mutually exclusive subsets of na random variables are na this property is shown not to hold for several other types of negative dependence recently proposed one consequence is the inequality p x i leq x i i 1 cdots k leq prod k 1p x i leq x i for na random variables x 1 cdots x k and the dual inequality resulting from reversing the inequalities inside the square brackets in another application it is shown that negatively correlated normal random variables are na other na distributions are the a multinomial b convolution of unlike multinomials c multivariate hypergeometric d dirichlet and e dirichlet compound multinomial negative association is shown to arise in situations where the probability measure is permutation invariant applications of this are considered for sampling without replacement as well as for certain multiple ranking and selection procedures in a somewhat striking example na and positive association representing quite strong opposing types of dependence are shown to exist side by side in models of categorical data analysis

the performance of estimators based on the propensity score we investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required like inverse probability weighting kernel and other variants of matching as well as different parametric models the simulation design used is based on real data usually employed for the evaluation of labour market programmes in germany we vary several dimensions of the design that are of practical importance like sample size the type of the outcome variable and aspects of the selection process we find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators a conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property

global attractivity in a food limited population model with impulsive effects abstract sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay logistic equation with impulsive effect n t r t n t k n p t k c t n p t n k n k exp i k ln n k k p where r t c t are continuous functions p k are positive constants and k k 1 denotes the sequence of impulsive time which assumed to be strictly increasing some special cases are also considered

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

large sample properties of matching estimators for average treatment effects matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases the absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data in this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results we focus on matching with replacement with a fixed number of matches first we show that matching estimators are not n 1 2 consistent in general and describe conditions under which matching estimators do attain n 1 2 consistency second we show that even in settings where matching estimators are n 1 2 consistent simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound third we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions software for implementing these methods is available in matlab stata and r

less conservative conditions for asymptotic stability of impulsive control systems this note studies the stability of impulsive control systems a new comparison theorem for asymptotic stability of impulsive differential system is presented based on the new result we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also enlarged

high powers of random elements of compact lie groups if a random unitary matrix u is raised to a sufficiently high power its eigenvalues are exactly distributed as independent uniform phases we prove this result and apply it to give exact asymptotics of the variance of the number of eigenvalues of u falling in a given arc as the dimension of u tends to infinity the independence result it turns out extends to arbitrary representations of arbitrary compact lie groups we state and prove this more general theorem paying special attention to the compact classical groups and to wreath products this paper is excerpted from the author s doctoral thesis 9

perron s theorem for linear impulsive differential equations with distributed delay in this paper it is shown that under a perron condition trivial solution of linear impulsive differential equation with distributed delay is uniformly asymptotically stable

on the failure of the bootstrap for matching estimators matching estimators are widely used in empirical economics for the evaluation of programs or treatments researchers using matching methods often apply the bootstrap to calculate the standard errors however no formal justification has been provided for the use of the bootstrap in this setting in this article we show that the standard bootstrap is in general not valid for matching estimators even in the simple case with a single continuous covariate where the estimator is root n consistent and asymptotically normally distributed with zero asymptotic bias valid inferential methods in this setting are the analytic asymptotic variance estimator of abadie and imbens 2006a as well as certain modifications of the standard bootstrap like the subsampling methods in politis and romano 1994

on some properties of orthogonal weingarten functions we give a fourier type formula for computing the orthogonal weingarten formula the weingarten calculus was introduced as a systematic method to compute integrals of polynomials with respect to haar measure over classical groups although a fourier type formula was known in the unitary case the orthogonal counterpart was not known it relies on the jack polynomial generalization of both schur and zonal polynomials this formula substantially reduces the complexity involved in the computation of weingarten formulas we also describe a few more new properties of the weingarten formula state a conjecture and give a table of values

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

on the moments of traces of matrices of classical groups we consider random matrices belonging to the groups u n o n so n and sp n and distributed according to the corresponding unit haar measure we prove that the moments of traces of powers of the matrices coincide with the moments of certain gaussian random variables if the order of moments is low enough corresponding formulas proved partly before by various methods are obtained here in the framework of a unique method reminiscent of the method of correlation equations of statistical mechanics the equations are derived by using a version of the integration by parts

the importance of the selberg integral it has been remarked that a fair measure of the impact of atle selberg s work is the number of mathematical terms that bear his name one of these is the selberg integral an n dimensional generalization of the euler beta integral we trace its sudden rise to prominence initiated by a question to selberg from enrico bombieri more than thirty years after its initial publication in quick succession the selberg integral was used to prove an outstanding conjecture in random matrix theory and cases of the macdonald conjectures it further initiated the study of q analogues which in turn enriched the macdonald conjectures we review these developments and proceed to exhibit the sustained prominence of the selberg integral as evidenced by its central role in random matrix theory calogero sutherland quantum many body systems knizhnik zamolodchikov equations and multivariable orthogonal polynomial theory

moments of traces of circular beta ensembles let 1 n be random variables from dyson s circular ensemble with probability density function constq 1 j kn je i j e i k

on existence of a globally attractive periodic solution of impulsive delay logarithmic population model in this paper it is shown that a logarithmic population model which is governed by impulsive delay differential equation has a globally attractive periodic solution

matching and semi parametric iv estimation a distance based measure of migration and the wages of young men abstract our paper estimates the effect of us internal migration on wage growth for young men between their first and second job our analysis of migration extends previous research by i exploiting the distance based measures of migration in the national longitudinal surveys of youth 1979 nlsy79 ii allowing the effect of migration to differ by schooling level and iii using propensity score matching to estimate the average treatment effect on the treated atet for movers and iv using local average treatment effect late estimators with covariates to estimate the average treatment effect ate and atet for compliers we believe the conditional independence assumption cia is reasonable for our matching estimators since the nlsy79 provides a relatively rich array of variables on which to match our matching methods are based on local linear local cubic and local linear ridge regressions local linear and local ridge regression matching produce relatively similar point estimates and standard errors while local cubic regression matching badly over fits the data and provides very noisy estimates we use the bootstrap to calculate standard errors since the validity of the bootstrap has not been investigated for the matching estimators we use and has been shown to be invalid for nearest neighbor matching estimators we conduct a monte carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching the data generating processes in our monte carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values the estimated standard errors from the bootstrap are very close to those from the monte carlo experiments which lends support to our using the bootstrap to calculate standard errors in our setting from the matching estimators we find a significant positive effect of migration on the wage growth of college graduates and a marginally significant negative effect for high school dropouts we do not find any significant effects for other educational groups or for the overall sample our results are generally robust to changes in the model specification and changes in our distance based measure of migration we find that better data matters if we use a measure of migration based on moving across county lines we overstate the number of moves while if we use a measure based on moving across state lines we understate the number of moves further using either the county or state measures leads to much less precise estimates we also consider semi parametric late estimators with covariates frolich 2007 using two sets of instrumental variables we precisely estimate the proportion of compliers in our data but because we have a small number of compliers we cannot obtain precise late estimates

boundedness for impulsive delay differential equations and applications to population growth models abstract in this paper criteria on uniform ultimate boundedness are derived for impulsive delay differential equations using lyapunov functions and razumikhin techniques it should be noted that the boundedness criteria establish global existence of solutions as well as boundedness without assuming a priori that solutions can necessarily be continued to infinity those criteria are then used to obtain permanence results for population growth models some examples are discussed to illustrate the theorems

bootstrap of the mean in the infinite variance case on montre que la version bootstrap de la moyenne normalisee a une distribution aleatoire dont la limite est aussi une distribution aleatoire impliquant que le bootstrap naif puisse etre defaillant dans le cas de queue chargee

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