closed subsets in duals of commutative table algebras a lower bound on the number of elements outside a closed subset of a c basis of a commutative c algebra with dual a table algebra is derived as is an equivalent condition for when the lower bound is met as corollaries lower bounds are obtained on the number of primitive idempotent matrices of rank greater than 1 in the adjacency algebra of a commutative imprimitive association scheme and for a given normal subgroup n of a finite group g on the number of irreducible characters of g whose kernels do not contain n and on the number of conjugacy classes of g not contained in n also found are equivalent conditions for when these lower bounds are met

the p cover problem abstract the modified p center called here p cover problem was discussed recently in several papers a practical and effective procedure to solving it is presented in this note

distribution theory for the studentized mean for long short and negative memory time series abstract we consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory short memory negative intermediate memory or is the first difference of such a process the rate of growth of this variance depends crucially on the type of memory and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically we also present asymptotic results for the case that the bandwidth is a fixed proportion of sample size extending known results to the case of flat top tapers we adopt the fixed proportion bandwidth perspective in our empirical section presenting two methods for estimating the limiting critical values both the subsampling method and a plug in approach simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean both methods perform well although the subsampling method appears to be better sized and provide a viable framework for conducting inference for the mean in summary we supply a unified asymptotic theory that covers all different types of memory under a single umbrella

testing optimal kernel choice in har inference abstract the paper investigates the optimal kernel choice in heteroskedasticity and autocorrelation robust tests based on the fixed b asymptotics in parallel with the optimality of the quadratic spectral kernel under the asymptotic mean squared error criterion of the point estimator of the long run variance as considered in andrews 1991 we show that the optimality of the quadratic spectral kernel continues to hold under the testing oriented criterion of sun philips and jin 2008 which takes a weighted average of the probabilities of type i and type ii errors of the fixed b asymptotic test

the error in rejection probability of simple autocorrelation robust tests a new class of autocorrelation robust test statistics is introduced the class of tests generalizes the kiefer vogelsang and bunzel 2000 test in a manner analogous to anderson and darling s 1952 generalization of the cramer von mises goodness of fit test in a gaussian location model the error in rejection probability of the new tests is found to be o t 1 log t where t denotes the sample size

asymptotic f and t tests in an efficient gmm setting abstract this paper considers two step efficient gmm estimation and inference where the weighting matrix and asymptotic variance matrix are based on the series long run variance estimator we propose a simple and easy to implement modification to the trinity of test statistics in the two step efficient gmm setting and show that the modified test statistics are all asymptotically f distributed under the so called fixed smoothing asymptotics the modification is multiplicative and involves the j statistic for testing over identifying restrictions this leads to convenient asymptotic f tests whose critical values i e the standard f critical values are readily available from standard statistical tables and programming environments for testing a single restriction with a one sided alternative an asymptotic t test theory using the standard t distribution as the reference distribution is also developed

permutation modules over table algebras and applications to association schemes abstract inspired by the notion of an action of a finite hypergroup on a finite set we introduce the more general concept of a permutation module over a table algebra it is easy to see that each permutation module over a table algebra is a direct sum of transitive permutation modules among the transitive permutation modules the w maximal and the maximal permutation modules are the most interesting ones we give various characterizations of these modules and we shall see that a standard table algebra admits a maximal transitive permutation module if and only if it arises from a finite association scheme we also show that the regular module of a standard table algebra is isomorphic to a direct summand of each w maximal transitive permutation module as a consequence one obtains 1 m for any irreducible character of the bose mesner algebra of a finite association scheme and its multiplicity m

testing dependence among serially correlated multicategory variables the contingency table literature on tests for dependence among discrete multicategory variables is extensive standard tests assume however that draws are independent and only limited results exist on the effect of serial dependency a problem that is important in areas such as economics finance medical trials and meteorology this article proposes new tests of independence based on canonical correlations from dynamically augmented reduced rank regressions the tests allow for an arbitrary number of categories as well as multiway tables of arbitrary dimension and are robust in the presence of serial dependencies that take the form of finite order markov processes for three way or higher order tables we propose new tests of joint and marginal independence monte carlo experiments show that the proposed tests have good finite sample properties an empirical application to microeconomic survey data on firms forecasts of changes to their production and prices demonstrates the importance of correcting fo

simple and powerful gmm over identification tests with accurate size abstract based on the series long run variance estimator we propose a new class of over identification tests that are robust to heteroscedasticity and autocorrelation of unknown forms we show that when the number of terms used in the series long run variance estimator is fixed the conventional j statistic after a simple correction is asymptotically f distributed we apply the idea of the f approximation to the conventional kernel based j tests simulations show that the j tests based on the finite sample corrected j statistic and the f approximation have virtually no size distortion and yet are as powerful as the standard j tests

noncommutative standard table algebras with at most one nontrivial multiplicity abstract standard table algebras that have an irreducible character of degree two and with all other irreducible characters of multiplicity one are classified to exact isomorphism

fixed smoothing asymptotics for time series 1 in this paper we derive higher order edgeworth expansions for the finite sample distributions of the subsampling based t statistic and the wald statistic in the gaussian location model under the so called fixed smoothing paradigm in particular we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions the results are used to justify the second order correctness of a new bootstrap method the gaussian dependent bootstrap in the context of gaussian location model 1 introduction many economic and financial applications involve time series data with autocorrelation and heteroskedasticity properties often the unknown dependence structure is not the chief object of interest but the inference on the parameter of interest involves the estimation of unknown dependence in stationary time series models estimated by generalized method of moments gmm robust inference is typically accomplished by consistently estimating the asymptotic covariance matrix which is proportional to the long run variance lrv matrix of the estimating equations or moment conditions defining the estimator using a kernel smoothing method in the econometrics and statistics literature the bandwidth parameter truncation lag involved in the kernel smoothing method is assumed to grow slowly with sample size in order to achieve consistency the inference is conducted by plugging in a covariance matrix estimator that is consistent under heteroskedasticity and autocorrelation this approach dates back to newey and west 25 and andrews 1 recently kiefer and vogelsang 13 kv hereafter developed an alternative first order asymptotic theory for the hac heteroskedasticity and autocorrelation consistent based robust inference where the proportion of the bandwidth involved in the hac estimator to the sample size t denoted as b is held fixed in the asymptotics under the fixed b asymptotics the hac estimator converges to a nondegenerate yet nonstandard limiting distribution the tests based on the fi xed b asymptotic approximation were shown to enjoy better finite sample properties than the tests based on the small b asymptotic theory

robust m tests without consistent estimation of the asymptotic covariance matrix we extend the kvb approach of kiefer vogelsang and bunzel 2000 to constructing robust m tests without consistent estimation of the asymptotic covariance matrix we demonstrate that when model parameters have to be estimated the normalizing matrix computed using a full sample estimator is able to eliminate the nuisance parameters when there is no estimation effect but not otherwise to circumvent the problem of estimation effect we propose using recursive estimators to compute the normalizing matrix and show that the resulting m test is asymptotically pivotal this m test is thus robust not only to heteroscedasticity and serial correlations of unknown form but also to the presence of an estimation effect as examples we consider robust tests for serial correlations and robust information matrix tests the former tests extend that of lobato 2001 and are applicable to model residuals for testing higher order moments we find that the latter tests are also robust when a lower order moment is miss

estimation and inference in semiparametric quantile factor models we propose an estimation methodology for a semiparametric quantile factor panel model we provide tools for inference that are robust to the existence of moments and to the form of weak cross sectional dependence in the idiosyncratic error term we apply our method to crsp daily data

measurement error in linear autoregressive models time series data are often subject to measurement error usually the result of needing to estimate the variable of interest although it is often reasonable to assume that the measurement error is additive i e the estimator is conditionally unbiased for the missing true value the measurement error variances often vary as a result of changes in the population process over time and or changes in sampling effort in this article we address estimation of the parameters in linear autoregressive models in the presence of additive and uncorrelated measurement errors allowing heteroscedasticity in the measurement error variances we establish the asymptotic properties of naive estimators that ignore measurement error and propose an estimator based on correcting the yule walker estimating equations we also examine a pseudo likelihood method based on normality assumptions and computed using the kalman filter we review other techniques that have been proposed including two that require no information about

a simple and trustworthy asymptotic t test in difference in differences regressions abstract we propose an asymptotically valid t test that uses student s t distribution as the reference distribution in a difference in differences regression for the asymptotic variance estimation we adopt the clustering by time approach to accommodate cross sectional dependence this approach often assumes the clusters to be independent across time but we allow them to be temporally dependent the proposed t test is based on a special heteroscedasticity and autocorrelation robust har variance estimator we target the type i and type ii errors and develop a testing oriented method to select the underlying smoothing parameter by capturing the estimation uncertainty of the har variance estimator the t test has more accurate size than the corresponding normal test and is just as powerful as the latter compared to the nonstandard test developed in the literature the standard t test is just as accurate but much more convenient to use model based and empirical data based monte carlo simulations show that the t test works quite well in finite samples

complexity of product positioning and ball intersection problems the product positioning problem consists in choosing the attributes of a new product in such a way as to maximize its market share i e to attract a maximum number of customers mathematically the problem can be formulated as follows given a set of balls with respect to some norm and a weight associated to each ball find a point which maximizes the sum of the weights of the balls containing it the complexity of this problem is investigated in the case of the l and of the euclidean norms in both cases the problem is proved to be np hard but to be polynomially solvable when the dimension of the space is fixed

optimal location and design of a competitive facility a single facility has to be located in competition with fixed existing facilities of similar type demand is supposed to be concentrated at a finite number of points and consumers patronise the facility to which they are attracted most attraction is expressed by some function of the quality of the facility and its distance to demand for existing facilities quality is fixed while quality of the new facility may be freely chosen at known costs the total demand captured by the new facility generates income the question is to find that location and quality for the new facility which maximises the resulting profits it is shown that this problem is well posed as soon as consumers are novelty oriented i e attraction ties are resolved in favour of the new facility solution of the problem then may be reduced to a bicriterion maxcovering minquantile problem for which solution methods are known in the planar case with euclidean distances and a variety of attraction functions this leads to a finite algorithm polynomial in the number of consumers whereas for more general instances the search of a maximal profit solution is reduced to solving a series of small scale nonlinear optimisation problems alternative tie resolution rules are finally shown to result in problems in which optimal solutions might not exist

testing for common deterministic trend slopes we propose tests for hypotheses on the parameters for deterministic trends the model framework assumes a multivariate structure for trend stationary time series variables we derive the asymptotic theory and provide some relevant critical values monte carlo simulations suggest which tests are more useful in practice than others we apply our tests to examine real gdp convergence for a sample of seven european countries

on structures of quasi thin table algebras and applications to association schemes abstract in this paper we develop a structure theory for a class of table algebras i e the so called quasi thin table algebras they are direct generalizations of quasi thin association schemes although this class of table algebras is rather close to finite groups its structural properties are quite different from those of finite groups the thin radical and thin residue give rise to two group structures for every table algebra they play the central role in our discussions applications to association schemes are also discussed and some new results about quasi thin association schemes are obtained in particular we will give necessary and sufficient conditions under which a commutative quasi thin association scheme has multiplicities 1 or 2 we will need these results in the study of the characterization and classification of double quasi thin association schemes in 22

a generalization of sylow s theorems on finite groups to association schemes let x g denote an association scheme or briefly a scheme in the sense of 5 and let p denote a prime number an element g in g will be called p valenced if ng is a power of p a subset of g will be called p valenced if each of its elements is p valenced a p valenced subset f of g will be called a p subset if nf is a power of p let us assume x g to be finite then by definition ng is finite we shall denote by sylp g the set of all closed p subsets h of g such that p does not divide ng h it is the purpose of the present note to prove the following theorem

on morphisms of association schemes abstract in this paper we present a necessary and sufficient condition under which a combinatorial morphism between association schemes induces an algebra homomorphism between their scheme rings we will also discuss scheme ring homomorphisms of naturally valenced association schemes

nonparametric stochastic discount factor decomposition stochastic discount factor sdf processes in dynamic economies admit a permanent transitory decomposition in which the permanent component characterizes pricing over long investment horizons this paper introduces an empirical framework to analyze the permanent transitory decomposition of sdf processes specifically we show how to estimate nonparametrically the solution to the perron frobenius eigenfunction problem of hansen and scheinkman 2009 our empirical framework allows researchers to i construct time series of the estimated permanent and transitory components and ii estimate the yield and the change of measure which characterize pricing over long investment horizons we also introduce nonparametric estimators of the continuation value function in a class of models with recursive preferences by reinterpreting the value function recursion as a nonlinear perron frobenius problem we establish consistency and convergence rates of the eigenfunction estimators and asymptotic normality of the eigenvalue estimator and estimators of related functionals as an application we study an economy where the representative agent is endowed with recursive preferences allowing for general nonlinear consumption and earnings growth dynamics

fixed smoothing asymptotics in a two step generalized method of moments framework fixed smoothing asymptotics this paper develops the fixed smoothing asymptotics in a two step generalized method of moments gmm framework under this type of asymptotics the weighting matrix in the second step gmm criterion function converges weakly to a random matrix and the two step gmm estimator is asymptotically mixed normal nevertheless the wald statistic the gmm criterion function statistic and the lagrange multiplier statistic remain asymptotically pivotal it is shown that critical values from the fixed smoothing asymptotic distribution are high order correct under the conventional increasing smoothing asymptotics when an orthonormal series covariance estimator is used the critical values can be approximated very well by the quantiles of a noncentral f distribution a simulation study shows that statistical tests based on the new fixed smoothing approximation are much more accurate in size than existing tests

second order correctness of the blockwise bootstrap for stationary observations we show that the blockwise bootstrap approximation for the distribution of a studentized statistic computed from dependent data is second order correct provided we choose an appropriate variance estimator we also show how to adapt the bc a confidence interval of efron to the dependent case for the proofs we extend the results of gotze and hipp on the validity of the formal edgeworth expansion for a sum to the studentized mean

on the effect of bias estimation on coverage accuracy in nonparametric inference abstractnonparametric methods play a central role in modern empirical work while they provide inference procedures that are more robust to parametric misspecification bias they may be quite sensitive to tuning parameter choices we study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice this is achieved using a novel yet simple studentization which leads to a new way of constructing kernel based bias corrected confidence intervals in addition for practical cases we derive coverage error optimal bandwidths and discuss easy to implement bandwidth selectors for interior points we show that the mse optimal bandwidth for the original point estimator before bias correction delivers the fastest coverage error decay rate after bias correction when second order equi

note on a modified one center model the objective of the one center model single facility minimax location in the plane is changed to be the maximum weighted number of demand points within a given weighted distance from the facility the paper presents an on2 log n algorithm for the model along with some computational experience

morphisms of naturally valenced association schemes and quotient schemes abstract let s and s be naturally valenced association schemes on sets x and x respectively and let be a combinatorial morphism from x s to x s in xu 2009 x2 a necessary and sufficient condition was given for to induce an algebra homomorphism from the scheme ring c s to the scheme ring c s the present paper provides new techniques with which this result can be proved without assuming ker to be finite to do this we will first need to prove that for any normal closed subset t of s whether t is finite or infinite the quotient s t is a naturally valenced association scheme on the set x t we will also need to discuss scheme ring homomorphisms of naturally valenced association schemes and prove some isomorphism theorems without assuming the kernels of the scheme ring homomorphisms to be finite as a direct consequence for a naturally valenced commutative association scheme s on a set x and any closed subset t of s the quotient s t is a naturally valenced commutative association scheme on the set x t the approach in this paper is different from xu 2009 x2 and quasi algebraic morphisms of naturally valenced association schemes are also studied

fixed smoothing asymptotics in the generalized empirical likelihood estimation framework this paper concerns the fixed smoothing asymptotics for two commonly used estimators in the generalized empirical likelihood estimation framework for time series data namely the continuous updating estimator and the maximum blockwise empirical likelihood estimator for continuously updating generalized method of moments gmm estimator we show that the results for the two step gmm estimator in sun 2014a continue to hold under suitable assumptions for continuous updating estimator obtained through solving a saddle point problem newey and smith 2004 and the maximum blockwise empirical likelihood estimator kitamura 1997 we show that their fixed smoothing asymptotic distributions up to an unknown linear transformation are mixed normal based on these results we derive the asymptotic distributions of the specification tests including the over identification testing and testing on parameters under the fixed smoothing asymptotics where the corresponding limiting distributions are nonstandard yet pivotal simulation studies show that i the fixed smoothing asymptotics provides better approximation to the sampling distributions of the continuous updating estimator and the maximum blockwise empirical likelihood estimator as compared to the standard normal approximation the testing procedures based on the fixed smoothing critical values are more accurate in size than the conventional chi square based tests ii the continuously updating gmm estimator is asymptotically more efficient and the corresponding specification tests are generally more powerful than the other two competitors finite sample results from an empirical data analysis are also reported

nonparametric rank tests for non stationary panels we develop a set of nonparametric rank tests for non stationary panels based on multivariate variance ratios which use untruncated kernels as such the tests do not require the choice of tuning parameters associated with bandwidth or lag length and also do not require choices with respect to numbers of common factors the tests allow for unrestricted cross sectional dependence and dynamic heterogeneity among the units of the panel provided simply that a joint functional central limit theorem holds for the panel of differenced series we provide a discussion of the relationships between our setting and the settings for which first and second generation panel unit root tests are designed in monte carlo simulations we illustrate the small sample performance of our tests when they are used as panel unit root tests under the more restrictive dgps for which panel unit root tests are typically designed and for more general dgps we also compare the small sample performance of our nonparametric tests to parametric rank tests finally we provide an empirical illustration by testing for income convergence among countries

improved quantile inference via fixed smoothing asymptotics and edgeworth expansion to estimate a sample quantile s variance the quantile spacing method involves smoothing parameter m when m n the corresponding studentized test statistic is asymptotically n 0 1 holding m fixed instead the asymptotic distribution contains the edgeworth expansion term capturing the variance of the quantile spacing consequently the fixed m distribution is more accurate than the standard normal under both asymptotic frameworks a testing optimal m is proposed to maximize power subject to size control in simulations the new method controls size better than similar methods while maintaining good power throughout are results for two sample quantile treatment effect inference code is available online

fixed b subsampling and the block bootstrap improved confidence sets based on p value calibration summary subsampling and block based bootstrap methods have been used in a wide range of inference problems for time series to accommodate the dependence these resampling methods involve a bandwidth parameter such as the subsampling window width and block size in the block based bootstrap in empirical work using different bandwidth parameters could lead to different inference results but traditional first order asymptotic theory does not capture the choice of the bandwidth we propose to adopt the fixed b approach as advocated by kiefer and vogelsang in the heteroscedasticity auto correlation robust testing context to account for the influence of the bandwidth on inference under the fixed b asymptotic framework we derive the asymptotic null distribution of the p values for subsampling and the moving block bootstrap and further propose a calibration of the traditional small b based confidence intervals regions or bands and tests our treatment is fairly general as it includes both finite dimensional parameters and infinite dimensional parameters such as the marginal distribution function simulation results show that the fixed b approach is more accurate than the traditional small b approach in terms of approximating the finite sample distribution and that the calibrated confidence sets tend to have smaller coverage errors than the uncalibrated counterparts

spectral density and spectral distribution inference for long memory time series via fixed b asymptotics this paper studies taper based estimates of the spectral density utilizing a fixed bandwidth ratio asymptotic framework and makes several theoretical contributions i we treat multiple frequencies jointly ii we allow for long range dependence or anti persistence at differing frequencies iii we allow for tapers that are only piecewise smooth or discontinuous including flat top and truncation tapers iv we study higher order accuracy through the limit distribution s laplace transform v we develop a taper based estimation theory for the spectral distribution and show how confidence bands can be constructed simulation results produce quantiles and document the finite sample size properties of the estimators and a few empirical applications demonstrate the utility of the new methods

territorial design optimization for business sales plan abstract a well designed territory enhances customer coverage increases sales fosters fair performance and rewards systems and lower travel cost this paper considers a real life case study to design the sales territory for a business sales plan the business plan consist of assigning the optimal quantity of sellers to a territory including the scheduling and routing plans for each seller the problem is formulated as a combination of assignment scheduling and routing optimization models the solution approach considers a meta heuristic using stochastic iterative projection method for large systems several real life instances of different sizes were tested with stochastic data to represent raise fall in the customers demand as well as the appearance loss of customers

the p maximal cover p partial center problem on networks abstract the p maximal cover problem is to find a set of locations for p facilities so as to maximize the total demand covered that is at most t units away from a closest facility the p partial center problem is to find a set of locations for the p facilities that minimizes the maximum distance between a closest facility and the demand covered in this paper we show the relationship between the two problems on networks for a tree network with one facility we present an algorithm to obtain all pareto locations with respect to the two objectives maximum cover and minimax distance for general networks we discuss the p maximal cover problem requiring that the optimal solution is a pareto location

inference with dependent data using cluster covariance estimators this paper presents a novel way to conduct inference using dependent data in time series spatial and panel data applications our method involves constructing t and wald statistics utilizing a cluster covariance matrix estimator cce we then use an approximation that takes the number of clusters groups as xed and the number of observations per group to be large and calcu late limiting distributions of the t and wald statistics this approximation is analogous to xed b asymptotics of kiefer and vogelsang 2002 2005 kv for heteroskedasticity and autocorrelation consistent inference but in our case yields standard t and f distributions where the number of groups essentially plays the role of sample size we provide simulation evidence that demonstrates our procedure outperforms conventional inference procedures and performs comparably to kv

trend function hypothesis testing in the presence of serial correlation in this paper test statistics are proposed that can be used to test hypotheses about the parameters of the deterministic trend function of a univariate time series the tests are valid in the presence of general forms of serial correlation in the errors and can be used without having to estimate the serial correlation parameters either parametrically or nonparametrically the tests are valid for i 0 and i 1 errors trend functions that are permitted include general linear polynomial trend functions that may have breaks at either known or unknown locations asymptotic distributions are derived and consistency of the tests is established the general results are applied to a model with a simple linear trend a local asymptotic analysis is used to compute asymptotic size and power of the tests for this example size is well controlled and is relatively unaffected by the variance of the initial condition asymptotic power curves are computed for the simple linear trend model and are compared to existing tests it is shown that the new tests have nontrivial asymptotic power a simulation study shows that the asymptotic approximations are adequate for sample sizes typically used in economics the tests are used to construct confidence intervals for average gnp growth rates for eight industrialized countries using post war data

a schur zassenhaus theorem for association schemes abstract conditions are given under which a normal closed subset of an association scheme of finite order possesses a complement our attempts are in the spirit of the schur zassenhaus theorem on finite groups and partially generalize that theorem

decomposition of products in nilpotent table algebras abstract two theorems on the decomposition of products in nilpotent commutative table algebras are established this generalizes several results of adan bante on the decomposition of products of irreducible characters and of conjugacy classes of finite p groups and extends these results to fusion rule algebras and association schemes

should we go one step further an accurate comparison of one step and two step procedures in a generalized method of moments framework abstract according to conventional asymptotic theory the two step generalized method of moments gmm estimator and test perform at least as well as the one step estimator and test in large samples the conventional asymptotic theory completely ignores the estimation uncertainty in the weighting matrix and as a result it may not reflect finite sample situations well in this paper we employ the more accurate fixed smoothing asymptotic framework to compare the performances of the one step and two step procedures we show that the two step procedures outperform the one step procedures only when the squared long run canonical correlation coefficients between two blocks of transformed moment conditions are larger than the thresholds established in this paper the thresholds depend on the criteria of interest a monte carlo study lends support to our asymptotic results

bootstrap confidence regions computed from autoregressions of arbitrary order summary given a linear time series e g an autoregression of infinite order we may construct a finite order approximation and use that as the basis for bootstrap confidence regions the sieve or autoregressive bootstrap as this method is often called is generally seen as a competitor with the better understood block bootstrap approach however in the present paper we argue that for linear time series the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities in particular since it does not corrupt second order properties then it may be used in a double bootstrap form with the second bootstrap application being employed to calibrate a basic percentile method confidence interval this approach confers secondorder accuracy without the need to estimate variance that offers substantial benefits since variances of statistics based on time series can be difficult to estimate reliably and partly because of the relatively small amount of information contained in a dependent process are notorious for causing problems when used to studentize other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter here equal to the autoregressive order and the fact that in contradistinction to the case of the block bootstrap the percentile t version of the sieve bootstrap may be based on the raw estimator of standard error in the process of establishing these properties we show that the sieve bootstrap is second order correct

randomization tests under an approximate symmetry assumption this paper develops a theory of randomization tests under an approximate symmetry assumption randomization tests provide a general means of constructing tests that control size in nite samples whenever the distribution of the observed data exhibits symmetry under the null hypothesis here by exhibits symmetry we mean that the distribution remains invariant under a group of transformations in this paper we provide conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis an important application of this idea is in settings where the data may be grouped into a xed number of clusters with a large number of observations within each cluster in such settings we show that the distribution of the observed data satises our approximate symmetry requirement under weak assumptions in particular our results allow for the clusters to be heterogeneous and also have dependence not only within each cluster but also across clusters this approach enjoys several advantages over other approaches in these settings among other things it leads to a test that is asymptotically similar which as shown in a simulation study translates into improved power at many alternatives finally we use our results to revisit the analysis of angrist and lavy 2009 who examine the impact of a cash award on exam performance for low achievement students in israel

simple robust testing of regression hypotheses in this paper we consider the problem of hypothesis testing in models with errors that have serial correlation or heteroskedasticity of unknown form this situation is often encountered in regression models applied to economic time series data it is a classic textbook result that while ordinary least squares ols estimates of regression parameters remain consistent and asymptotically normal when errors are heteroskedastic or autocorrelated provided usual regularity conditions hold and no lagged dependent variables are in the model standard tests are no longer valid if the true form of serial correlation heteroskedasticity were known then generalized least squares gls provides efficient estimates and standard inference can be conducted on the gls transformed model but in practice the form of serial correlation heteroskedasticity is often unknown and this has led to the development of techniques that permit valid asymptotic inference without having to specify a model of the serial correlation or heteroskedasticity the most common approach is to estimate the variance covariance matrix of the ols estimates nonparametrically using spectral methods heteroskedasticity and autocorrelation consistent hac estimators and construct standard tests using the asymptotic normality of the ols estimates hac estimators have been extensively analyzed in the econometrics literature and important contributions are given by andrews 1991 andrews and monahan 1992 gallant 1987 hansen 1992 newey and west 1987 robinson 1991 1998 and white 1984 among others the benefit of hac estimator tests is asymptotically valid inference that is robust to general forms of serial correlation heteroskedasticity in the errors we propose an alternative method of constructing robust test statistics we apply a nonsingular data dependent stochastic transformation to the ols estimates the asymptotic distribution of the transformed estimates does not depend on nuisance parameters then test statistics that are asymptotically invariant to nuisance parameters asymptotic pivotal statistics are constructed the resulting test statistics have nonstandard asymptotic distributions that only depend on the number of restrictions being tested and critical values are easy to simulate using standard techniques the main advantage of our approach compared to standard approaches is that estimates of the variance covariance matrix are not explicitly required to construct the tests this is potentially important for two reasons first with the exception of the estimator proposed by robinson 1998 2 consistent nonparametric estimates of variance covariance matrices in models with serial

bootstrapping gmm estimators for time series abstract this paper considers the bootstrap for the gmm estimator of overidentified linear models when autocorrelation structures of moment functions are unknown when moment functions are uncorrelated after finite lags hall and horowitz 1996 bootstrap critical values for tests based on generalized method of moments estimators econometrica 64 891 916 showed that errors in the rejection probabilities of the bootstrap tests are o t 1 however this rate cannot be obtained with the hac covariance matrix estimator since it converges at a nonparametric rate by incorporating the hac covariance matrix estimator in the edgeworth expansion of the distribution we show that the bootstrap provides asymptotic refinements when the characteristic exponent of the kernel function is greater than two

fusion algebras with negative structure constants abstract we introduce fusion algebras with not necessarily positive structure constants and without identity element we prove that they are semisimple when tensored with c and that their characters satisfy orthogonality relations then we define the proper notion of subrings and factor rings for such algebras for certain algebras r we prove the existence of a ring r with nonnegative structure constants such that r is a factor ring of r we give some examples of interesting factor rings of the representation ring of the quantum double of a finite group then we investigate the algebras associated to hadamard matrices for an n n matrix the corresponding algebra is a factor ring of a subalgebra of z z 2 z n 2

asymptotic f tests under possibly weak identification abstract this paper develops asymptotic f tests robust to weak identification and temporal dependence the test statistics we focus on are modified versions of the s statistic of stock and wright 2000 and the k statistic of kleibergen 2005 in the former case the modification involves only a multiplicative degree of freedom adjustment and the modified s statistic is asymptotically f distributed under fixed smoothing asymptotics regardless of the strength of the model identification in the latter case the modification involves an additional multiplicative adjustment that uses a j statistic for testing overidentification we show that the modified k statistic is asymptotically f distributed when the model parameters are completely unidentified or nearly weakly identified when the model parameters are weakly identified the f approximation for the k statistic can be justified under the conventional asymptotics the f approximations account for the estimation errors in the underlying heteroskedasticity and autocorrelation robust variance estimators which the chi squared approximations ignore monte carlo simulations show that the f approximations are much more accurate than the corresponding chi squared approximations in finite samples

efficient estimation of heterogeneous coefficients in panel data models with common shocks this paper investigates efficient estimation of heterogeneous coefficients in panel data models with common shocks which have been a particular focus of recent theoretical and empirical literature we propose a new two step method to estimate the heterogeneous coefficients in the first step the maximum likelihood ml method is first conducted to estimate the loadings and idiosyncratic variances the second step estimates the heterogeneous coefficients by using the structural relations implied by the model and replacing the unknown parameters with their ml estimates we establish the asymptotic theory of our estimator including consistency asymptotic representation and limiting distribution the two step estimator is asymptotically efficient in the sense that it has the same limiting distribution as the infeasible generalized least squares gls estimator intensive monte carlo simulations show that the proposed estimator performs robustly in a variety of data setups

some structure theory of table algebras and applications to association schemes abstract in this paper we prove some basic structure theorems for arbitrary table algebras in particular we prove a krull schmidt theorem for arbitrary table algebras and give applications to association schemes

optimal bandwidth selection in heteroskedasticity autocorrelation robust testing the paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors the studentization is based on robust standard errors with truncation lag m bt for some constant b 2 0 1 and sample size t it is shown that the nonstandard xed b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the nite sample distributions than the standard small b limit distribution we further show that for typical economic time series the optimal bandwidth that minimizes a weighted average of type i and type ii errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long run variance estimator a plug in procedure for implementing this optimal bandwidth is suggested and simulations not reported here con rm that the new plug in procedure works well in nite samples

heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects abstract this paper studies robust inference for linear panel models with fixed effects in the presence of heteroskedasticity and spatiotemporal dependence of unknown forms we propose a bivariate kernel covariance estimator that nests existing estimators as special cases our estimator improves upon existing estimators in terms of robustness efficiency and adaptiveness for distributional approximations we considered two types of asymptotics the increasing smoothing asymptotics and the fixed smoothing asymptotics under the former asymptotics the wald statistic based on our covariance estimator converges to a chi square distribution under the latter asymptotics the wald statistic is asymptotically equivalent to a distribution that can be well approximated by an f distribution simulation results show that our proposed testing procedure works well in finite samples

estimating deterministic trends with an integrated or stationary noise component abstract we propose a test for the slope of a trend function when it is a priori unknown whether the series is trend stationary or contains an autoregressive unit root the procedure is based on a feasible quasi generalized least squares method from an ar 1 specification with parameter the sum of the autoregressive coefficients the estimate of is the ols estimate obtained from an autoregression applied to detrended data and is truncated to take a value 1 whenever the estimate is in a t neighborhood of 1 this makes the estimate super efficient when 1 and implies that inference on the slope parameter can be performed using the standard normal distribution whether 1 or 1 theoretical arguments and simulation evidence show that 1 2 is the appropriate choice simulations show that our procedure has better size and power properties than the tests proposed by bunzel h vogelsang t j 2005 powerful trend function tests that are robust to strong serial correlation with an application to the prebish singer hypothesis journal of business and economic statistics 23 381 394 and harvey d i leybourne s j taylor a m r 2007 a simple robust and powerful test of the trend hypothesis journal of econometrics 141 1302 1330

a new semidirect product for association schemes abstract we propose a new definition for the semidirect product of association schemes generalizing work of bang hirasaka and song we define an action of one scheme on another and show how one can use such an action to construct all semidirect products satisfying a certain technical condition

inference for linear models with dependent errors summary the paper is concerned with inference for linear models with fixed regressors and weakly dependent stationary time series errors theoretically we obtain asymptotic normality for the m estimator of the regression parameter under mild conditions and establish a uniform bahadur representation for recursive m estimators methodologically we extend the recently proposed self normalized approach of shao from stationary time series to the regression set up where the sequence of response variables is typically non stationary in mean since the limiting distribution of the self normalized statistic depends on the design matrix and its corresponding critical values are case dependent we develop a simulation based approach to approximate the critical values consistently through a simulation study we demonstrate favourable finite sample performance of our method in comparison with a block bootstrap based approach empirical illustrations using two real data sets are also provided

fusion rings with few degrees abstract the main result characterizes fusion rings whose degree set consists of 1 and a fixed prime p a well known theorem of isaacs and passman on finite groups whose irreducible character degrees are 1 and p follows as a corollary numerically compatible nc fusion rings are defined as a potential generalization of the grothendieck rings of fusion categories and the nc fusion rings of order p p 2 p 3 pq and p q 2 where p q are primes are classified in terms of certain standard table algebras as another application of the main theorem

augmented quasigroups and character algebras abstract the conjugacy classes of groups and quasigroups form association schemes in which the relation products are defined by collapsing group or quasigroup multiplications in previous work sharp transitivity was used to identify association schemes such as certain johnson schemes which cannot appear as quasigroup schemes thus quasigroup schemes only constitute a fragment of the full set of all association schemes nevertheless the current paper shows that every association scheme is in fact obtained by collapsing a quasigroup multiplication in a second application of a similar technique character quasigroups are constructed for each finite group as analogues of the character groups of abelian groups to encode the multiplicative structure of group characters as infrastructure for these and related results three key unifying concepts in compact closed categories are established augmented comagmas augmented magmas and augmented quasigroups the latter serving to capture such diverse structures as groups and heyting algebras

on semisimple varietal terwilliger algebras whose non primary ideals are 1 dimensional abstract as an abstraction of the terwilliger algebra of a commutative association scheme the notion of a varietal terwilliger algebra was introduced in 11 in this paper we first prove that there exists a varietal terwilliger algebra defined by any given standard c algebra and a generalized terwilliger algebra 6 is also a varietal terwilliger algebra then we present a necessary and sufficient condition under which a quotient algebra of a varietal terwilliger algebra is also a varietal terwilliger algebra we will also give a characterization of a semisimple varietal terwilliger algebra whose non primary ideals are all 1 dimensional and prove that a semisimple regular varietal terwilliger algebra with 1 dimensional non primary ideals is characterized by the structure of its base c subalgebra as direct consequences we obtain some results in 18 for finite association schemes and a conceptual explanation of the results in 9

a fixed bandwidth view of the pre asymptotic inference for kernel smoothing with time series data this paper develops robust testing procedures for nonparametric kernel methods in the presence of temporal dependence of unknown forms based on the xed bandwidth asymptotic variance and the pre asymptotic variance we propose a heteroskedasticity and autocorrelation robust har variance estimator that achieves double robustness it is asymptotically valid regardless of whether the temporal dependence is present or not and whether the kernel smoothing bandwidth is held constant or allowed to decay with the sample size using the har variance estimator we construct the studentized test statistic and examine its asymptotic properties under both the xed smoothing and increasing smoothing asymptotics the xed smoothing approximation and the associated convenient t approximation achieve extra robustness it is asymptotically valid regardless of whether the truncation lag parameter governing the covariance weighting grows at the same rate as or a slower rate than the sample size finally we suggest a simulation based calibration approach to choose smoothing parameters that optimize testing oriented criteria simulation shows that the proposed procedures work very well in nite samples

empirical likelihood methods with weakly dependent processes this paper studies the method of empirical likelihood in models with weakly dependent processes in such cases if the likelihood function is formulated as if the data process were independent obviously empirical likelihood fails we propose to use empirical likelihood of blocks of observations to solve this problem in a nonparametric manner this method of blockwise empirical likelihood preserves the dependence of data and the resulting likelihood ratios can be used to construct asymptotically valid confidence intervals we consider general estimating equations for which an efficient estimator is derived by maximizing blockwise empirical likelihood we also introduce blocks of blocks empirical likelihood to conduct inference for parameters of the infinite dimensional joint distribution of data the smooth function model is used for such cases we show that blockwise empirical likelihood of the smooth function model with weakly dependent processes is bartlett correctable a wide variety of problems such as time series regressions and spectral densities can be treated using our methodology

robust trend inference with series variance estimator and testing optimal smoothing parameter abstract the paper develops a novel testing procedure for hypotheses on deterministic trends in a multivariate trend stationary model the trends are estimated by the ols estimator and the long run variance lrv matrix is estimated by a series type estimator with carefully selected basis functions regardless of whether the number of basis functions k is fixed or grows with the sample size the wald statistic converges to a standard distribution it is shown that critical values from the fixed k asymptotics are second order correct under the large k asymptotics a new practical approach is proposed to select k that addresses the central concern of hypothesis testing the selected smoothing parameter is testing optimal in that it minimizes the type ii error while controlling for the type i error simulations indicate that the new test is as accurate in size as the nonstandard test of vogelsang and franses 2005 and as powerful as the corresponding wald test based on the large k asymptotics the new test therefore combines the advantages of the nonstandard test and the standard wald test while avoiding their main disadvantages power loss and size distortion respectively

heteroskedasticity autocorrelation robust standard errors using the bartlett kernel without truncation in this paper we analyze heteroskedasticity autocorrelation hac robust tests constructed using the bartlett kernel without truncation we show that while such an hac estimator is not consistent asymptotically valid testing is still possible we show that tests using the bartlett kernel without truncation are exactly equivalent to recent hac robust tests proposed by kiefer vogelsang and bunzel 2000 econometrica 68 pp 695 714

a unifying theory of tests of rank the general principles underlying tests of matrix rank are investigated it is demonstrated that statistics for such tests can be seen as implicit functions of null space estimators in turn the asymptotic behaviour of the null space estimators is shown to determine the asymptotic behaviour of the statistics through a plug in principle the theory simplifies the asymptotics under a variety of alternatives of empirical relevance as well as misspecification clarifies the relationships between the various existing tests makes use of important results in the numerical analysis literature and motivates numerous new tests a brief monte carlo study illustrates the results

the gradual covering decay location problem on a network abstract in covering problems it is assumed that there is a critical distance within which the demand point is fully covered while beyond this distance it is not covered at all in this paper we define two distances within the lower distance a demand point is fully covered and beyond the larger distance it is not covered at all for a distance between these two values we assume a gradual coverage decreasing from full coverage at the lower distance to no coverage at the larger distance

robustifying multivariate trend tests to nonstationary volatility abstract this article studies inference of multivariate trend model when the volatility process is nonstationary within a quite general framework we analyze four classes of tests based on least squares estimation one of which is robust to both weak serial correlation and nonstationary volatility the existing multivariate trend tests which either use non robust standard errors or rely on non standard distribution theory are generally non pivotal involving the unknown time varying volatility function in the limit two step residual based i i d bootstrap and wild bootstrap procedures are proposed for the robust tests and are shown to be asymptotically valid simulations demonstrate the effects of nonstationary volatility on the trend tests and the good behavior of the robust tests in finite samples

the variable radius covering problem in this paper we propose a covering problem where the covering radius of a facility is controlled by the decision maker the cost of achieving a certain covering distance is assumed to be a monotonically increasing function of the distance i e it costs more to establish a facility with a greater covering radius the problem is to cover all demand points at a minimum cost by finding optimal number locations and coverage radii for the facilities both the planar and discrete versions of the model are considered heuristic approaches are suggested for solving large problems in the plane these methods were tested on a set of planar problems mathematical programming formulations are proposed for the discrete problem and a solution approach is suggested and tested

sieve inference on possibly misspecified semi nonparametric time series models this paper establishes the asymptotic normality of plug in sieve m estimators of possibly irregular functionals of semi nonparametric time series models we show that even when the sieve score process is not a martingale difference sequence the asymptotic variance in the case of irregular functionals is the same as those for independent data using an orthonormal series long run variance estimator we construct a pre asymptotic wald statistic and show that it is asymptotically f distributed simulations indicate that our pre asymptotic wald test with f critical values has more accurate size in finite samples than the conventional wald test with chi square critical values

let s fix it fixed b asymptotics versus small b asymptotics in heteroskedasticity and autocorrelation robust inference in the presence of heteroscedasticity and autocorrelation of unknown forms the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter depending on whether this lag truncation parameter is speci ed to grow at a slower rate than or the same rate as the sample size we obtain two types of asymptotic approximations the small b asymptotics and the xed b asymptotics using techniques for probability distribution approximation and high order expansions this paper shows that the xed b asymptotic approximation provides a higher order re nement to the rst order small b asymptotics this result provides a theoretical justi cation on the use of the xed b asymptotics in empirical applications on the basis of the xed b asymptotics and higher order small b asymptotics the paper introduces a new and easy to use asymptotic f test that employs a nite sample corrected wald statistic and uses an f distribution as the reference distribution finally the paper develops a bandwidth selection rule that is testing optimal in that the bandwidth minimizes the type ii error of the asymptotic f test while controlling for its type i error monte carlo simulations show that the asymptoticf test with the testing optimal bandwidth works very well in nite samples