strong consistency of the variance estimator in steady state simulation output analysis in this paper we study the problem of variance estimation in steady state simulation output analysis a confidence interval for the mean of an output sequence may be constructed using a weakly consistent estimator of the time average variance constant of the process moreover a strongly consistent estimator of the variance constant is required for fixed width confidence interval estimation procedures to be asymptotically valid here we establish sufficient conditions to ensure strong consistency of the estimator of the variance constant obtained by several widely used methods of steady state simulation output analysis namely batch means overlapping batch means spaced batch means and standardized time series area estimator we also introduce the overlapping area estimator of the variance constant the established sufficient conditions provide qualitative insight into the relation between the correlation of the process and certain parameters e g batch size of the output method used

a single pass algorithm for spectrum estimation with fast convergence we propose a single pass algorithm for estimating spectral densities of stationary processes our algorithm is computationally fast in the sense that when a new observation arrives it can provide a real time update within o 1 computation the proposed algorithm is probabilistically fast in that for stationary processes whose auto covariances decay geometrically the estimates from the algorithm converge at a rate which is optimal up to a multiplicative logarithmic factor we also establish asymptotic normality for the recursive estimate a simulation study is carried out and it confirms the superiority over the classical batched mean estimates

quantum thetas on noncommutative bb t d with general embeddings in this paper we construct quantum theta functions over noncommutative t a with general embeddings manin has constructed quantum theta functions from the lattice embedding into vector space x finite group we extend manin s construction of quantum thetas to the case of general embedding of vector space x lattice x torus it turns out that only for the vector space part of the embedding there exists the holomorphic theta vector while for the lattice part there does not furthermore the so called quantum translations from embedding into the lattice part become non additive while those from the vector space part are additive

mean square consistency of the variance estimator in steady state simulation output analysis in steady state simulation output analysis mean square consistency of the process variance estimator is important for a number of reasons one way to construct an asymptotically valid confidence interval around a sample mean is via construction of a consistent estimator of the process variance and a central limit theorem also if an estimator is consistent in the mean square sense a mean square error analysis is theoretically justified finally batch size selection is an open research problem in steady state output analysis and a mean square error analysis approach has been proposed in the literature to be valid the process variance estimators constructed must be consistent in the mean square sense in this paper we prove mean square consistency of the process variance estimator for the methods of batch means overlapping batch means standardized time series area and spaced batch means by rigorously computing the rate of decay of the variance of the process variance estimators asymptotic results for third and higher centered moments of the batch means and area variance estimators are also given along with central limit theorems

theta vectors and quantum theta functions in this paper we clarify the relation between manin s quantum theta function and schwarz s theta vector we do this in comparison with the relation between the kq representation which is equivalent to the classical theta function and the corresponding coordinate space wavefunction we first explain the equivalence relation between the classical theta function and the kq representation in which the translation operators of the phase space are commuting when the translation operators of the phase space are not commuting then the kq representation is no longer meaningful we explain why manin s quantum theta function obtained via algebra quantum torus valued inner product of the theta vector is a natural choice for the quantum version of the classical theta function we then show that this approach holds for a more general theta vector containing an extra linear term in the exponent obtained from a holomorphic connection of constant curvature than the simple gaussian one used in manin s construction

t test in a structural equation properties of t ratios associated with the liml tsls and ols estimators in a structural form estimation are studied the existence of moments of these t ratios including the liml form is proved first second monte carlo simulations are performed to find out real sizes of the t test and the likelihood ratio test third asymptotic expansions of the distributions of t ratios are derived under the null hypothesis to find out deviations of real sizes from nominal sizes theoretically the asymptotic power functions are also derived

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

bootstrap prediction intervals for autoregression abstract the nonparametric bootstrap is applied to the problem of prediction in autoregression let y t t 0 1 2 be a stationary autoregressive process of known order p ar p given a realization of the series up to time t y 1 y 2 y t a 100 prediction interval for y t k is desired standard forecasting techniques which assume that the error sequence of the process y t is gaussian rely on the fact that the conditional distribution of y t k given the data is gaussian as well as a nonparametric alternative the bootstrap provides an estimate of the conditional distribution of y t k the method is similar to other applications of the bootstrap for linear models because the residuals are resampled the proposed methodology represents a different approach since an alternative representation for ar p series is used allowing for bootstrap replicates generated backward in time it follows that the resulting replicates all have the same conditionally fixed values at the end

fuzzy modeling of high dimensional systems complexity reduction and interpretability improvement fuzzy modeling of high dimensional systems is a challenging topic this paper proposes an effective approach to data based fuzzy modeling of high dimensional systems an initial fuzzy rule system is generated based on the conclusion that optimal fuzzy rules cover extrema redundant rules are removed based on a fuzzy similarity measure then the structure and parameters of the fuzzy system are optimized using a genetic algorithm and the gradient method during optimization rules that have a very low firing strength are deleted finally interpretability of the fuzzy system is improved by fine training the fuzzy rules with regularization the resulting fuzzy system generated by this method has the following distinct features 1 the fuzzy system is quite simplified 2 the fuzzy system is interpretable and 3 the dependencies between the inputs and the output are clearly shown this method has successfully been applied to a system that has 11 inputs and one output with 20 000 training data and 80 000 test data

completeness and consistency conditions for learning fuzzy rules the completeness and consistency conditions were introduced in order to achieve acceptable concept recognition rules in real problems we can handle noise affected examples and it is not always possible to maintain both conditions moreover when we use fuzzy information there is a partial matching between examples and rules therefore the consistency condition becomes a matter of degree in this paper a learning algorithm based on soft consistency and completeness conditions is proposed this learning algorithm combines in a single process rule and feature selection and it is tested on different databases

the use of subseries values for estimating the variance of a general statistic from a stationary sequence let z i infty i infty be a strictly stationary infty mixing sequence without specifying the dependence model giving rise to z i and without specifying the marginal distribution of z i we address the question of variance estimation for a general statistic t n t n z 1 z n for estimating var t n from just the available data z 1 z n we propose computing subseries values t m z i 1 z i 2 z i m 0 leq i i m leq n these subseries values are used as replicates to model the sampling variability of t n in particular we use adjacent nonoverlapping subseries of length m m n with m rightarrow infty and m n n rigtharrow 0 our variance estimator is just the usual sample variance computed amongst these subseries values after appropriate standardization this estimator is shown to be consistent under mild integrability conditions we present optimal i e minimum m s e choices of m n for the special case where t n overset z n and z i is a normal ar 1 sequence a simulation study is conducted showing that those same choices of m n are effective when t n is a robust estimator of location and z i is subject to contamination

consistency of the jackknife after bootstrap variance estimator for the bootstrap quantiles of a studentized statistic efron j roy statist soc ser b 54 1992 83 1111 proposed a computationally efficient method called the jackknife after bootstrap for estimating the variance of a bootstrap estimator for independent data for dependent data a version of the jackknife after bootstrap method has been recently proposed by lahiri econometric theory 18 2002 79 98 in this paper it is shown that the jackknife after bootstrap estimators of the variance of a bootstrap quantile are consistent for both dependent and independent data results from a simulation study are also presented

nonparametric estimation of the moments of a general statistic computed from spatial data abstract a statistic s is computed on spatially indexed data x i i d where d is a finite subset of the integer lattice z2 we propose a simple nonparametric method for estimating the moments e g variance skewness of s d using only the observed data at hand the method uses replicates of s computed on smaller subsets of d no explicit knowledge of the underlying spatial dependence mechanism is needed and the marginal distribution of x i may also be unknown the shape of d can be quite irregular and s is allowed to be a general statistic the proposed estimator is shown to be consistent and asymptotically normal under mild conditions on s d and mixing conditions on the strength of spatial dependence as a numerical example the estimator is used in assessing the geographic clumping of cancer deaths in the united states

empirical likelihood based inference in conditional moment restriction models this paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions our estimator generalizes the maximum empirical likelihood estimator mele of qin and lawless 1994 using a kernel smoothing method we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood based procedure this yields a one step estimator which avoids estimating optimal instruments our likelihood ratio type statistic for parametric restrictions does not require the estimation of variance and achieves asymptotic pivotalness implicitly the estimation and testing procedures we propose are normalization invariant simulation results suggest that our new estimator works remarkably well in finite samples

a robust method for shift detection in time series we present a robust test for change points in time series which is based on the two sample hodges lehmann estimator we develop new limit theory for a class of statistics based on the two sample u quantile processes in the case of short range dependent observations using this theory we can derive the asymptotic distribution of our test statistic under the null hypothesis we study the finite sample properties of our test via a simulation study and compare the test with the classical cusum test and a test based on the wilcoxon mann whitney statistic

automatic optimal batch size selection for recursive estimators of time average covariance matrix abstractthe time average covariance matrix tacm k z k where k is the auto covariance function is an important quantity for the inference of the mean of an rd valued stationary process d 1 this article proposes two recursive estimators for with optimal asymptotic mean square error amse under different strengths of serial dependence the optimal estimator involves a batch size selection which requires knowledge of a smoothness parameter k z k k for some this article also develops recursive estimators for combining these two estimators we obtain a fully automatic procedure for optimal online estimation for consistency and convergence rates of the proposed estimators are derived applications to confidence region construction and markov chain monte carlo convergence diagnosis are discussed supplementary materials for this article are available online

the exact moments of ols in dynamic regression models with non normal errors abstract this paper studies the finite sample sensitivity of ols estimators of the autoregressive coefficient in a first order stochastic difference equation with i i d errors drawn from an edgeworth gram charlier population analytic formula for the first and second moments of the estimator are derived using the results of davis 1976 and sawa 1972 also numerical evaluation of these general formulae is undertaken and the results are presented under selected alternative parameter scenarios the results suggest that the exact bias is relatively insensitive to skewness and kurtosis in the underlying error distribution but that the exact mse is relatively sensitive to both skewness and kurtosis and this sensitivity increases as the signal to noise ratio increases

ten years of genetic fuzzy systems current framework and new trends fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains currently there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities two of the most successful approaches to hybridise fuzzy systems with learning and adaptation methods have been made in the realm of soft computing neural fuzzy systems and genetic fuzzy systems hybridise the approximate reasoning method of fuzzy systems with the learning capabilities of neural networks and evolutionary algorithms the objective of this paper is to provide an account of genetic fuzzy systems with special attention to genetic fuzzy rule based systems after a brief introduction to models and applications of genetic fuzzy systems the field is overviewed new trends are identified a critical evaluation of genetic fuzzy systems for fuzzy knowledge extraction is elaborated and open questions that remain to be addressed in the future are raised the paper also includes some of the key references required to quickly access implementation details of genetic fuzzy systems

subsampling for heteroskedastic time series abstract in this article a general theory for the construction of confidence intervals or regions in the context of heteroskedastic dependent data is presented the basic idea is to approximate the sampling distribution of a statistic based on the values of the statistic computed over smaller subsets of the data this method was first proposed by politis and romano 1994b for stationary observations we extend their results to heteroskedastic observations and prove a general asymptotic validity result under minimal conditions in contrast the usual bootstrap and moving blocks bootstrap are typically valid only for asymptotically linear statistics and their justification requires a case by case analysis our general asymptotic results are applied to a regression setting with dependent heteroskedastic errors

the second order bias and mean squared error of estimators in time series models we develop analytical results on the second order bias and mean squared error of estimators in time series models these results provide a unified approach to developing the properties of a large class of estimators in linear and nonlinear time series models and they are valid for both normal and nonnormal samples of observations and where the regressors are stochastic the estimators included are the generalized method of moments maximum likelihood least squares and other extremum estimators our general results are applied to four time series models we investigate the effects of nonnormality on the second order bias results for two of these models while for all four models the second order bias and mean squared error results are given under normality numerical results for some of these models are also presented

constructing fuzzy models with linguistic integrity from numerical data afreli algorithm this paper presents an algorithm to extract rules re lating input output data and including prior knowledge the rules are created in the environment of fuzzy systems the fuzzy sets describing the system are constructed within a framework of lin guistic integrity to guarantee its interpretability in the linguistic context two algorithms are presented in this paper the main al gorithm is the autonomous fuzzy rule extractor with linguistic in tegrity afreli this algorithm is complemented with the use of the fuzion algorithm created to merge consecutive member ship functions while guaranteeing the distinguish ability between fuzzy sets comparisons with other proposed methods show a good tradeoff between accuracy and interpretability

the student s t approximation in a stationary first order autoregressive model the basic model is a gaussian ar 1 model with an intercept but no additional exogenous variables the paper studies the distribution of the t statistic for testing the value of the autoregressive parameter when the model is estimated by least squares the monte carlo estimates of the quantiles of the t statistic show that student s t is not a satisfactory approximation for sample sizes typical in economic applications the main problem is not the shape of the distribution of the t statistic but its location adjusting the t statistic so that it has the same mean and standard deviation as student s t the distribution of this adjusted t statistic is accurately approximated by student s t techniques are presented for accurately approximating the mean and standard deviation of the t statistic such that the adjusted t statistic can be readily calculated in practice the analysis is extended in two directions the first is to examine the effect of introducing an exogenous variable into the basic model in the expanded model student s t also accurately approximates the distribution of the t statistic for testing the autoregressive parameter and for testing the coefficient of the exogenous variable after these t statistics are adjusted for mean and standard deviation the problem of obtaining a feasible adjustment procedure is that the moments of these t statistics now depend on nuisance parameters the second is to examine the robustness of the results in the basic model to several nonnormal error distributions for each nonnormal distribution the t statistic is adjusted using the mean and standard deviation appropriate for the case of normal errors and then the distribution of the modified t statistic is compared with that of student s t

semiparametric normal transformation models for spatially correlated survival data there is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiologic studies in this article we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data this class of models assumes that survival outcomes marginally follow a cox proportional hazard model with unspecified baseline hazard and their joint distribution is obtained by transforming survival outcomes to normal random variables whose joint distribution is assumed to be multivariate normal with a spatial correlation structure a key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields we study the relationship of the spatial correlation structure of the transformed no

quantum thetas on noncommutative bb t 4 from embeddings into lattice in this paper we investigate the theta vector and quantum theta function over noncommutative from the embedding of manin has constructed the quantum theta functions from the lattice embedding into vector space finite group we extend manin s construction of the quantum theta function to the embedding of vector space lattice case we find that the holomorphic theta vector exists only over the vector space part of the embedding and over the lattice part we can only impose the condition for the schwartz function the quantum theta function built on this partial theta vector satisfies the requirement of the quantum theta function however two subsequent quantum translations from the embedding into the lattice part are nonadditive contrary to the additivity of those from the vector space part

a theorem of validity for edgeworth expansisons on considere des equations autoregressives a variables exogenes et un terme de bruit blanc normal ce qui generalise les modeles dynamiques etudies precedemment

inference of trends in time series summary we consider statistical inference of trends in mean non stationary models a test statistic is proposed for the existence of structural breaks in trends on the basis of a strong invariance principle of stationary processes we construct simultaneous confidence bands with asymptotically correct nominal coverage probabilities the results are applied to global warming temperature data and nile river flow data our confidence band of the trend of the global warming temperature series supports the claim that the trend is increasing over the last 150 years

inference for non stationary time series regression with or without inequality constraints summary we consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non stationary behaviours over time meanwhile the regression parameters may be subject to linear inequality constraints a simple and unified procedure for structural stability checks and parameter inference is proposed in the case where the regression parameters are constrained the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones

coevolutionary genetic fuzzy systems a hierarchical collaborative approach abstract in this paper a coevolutionary genetic approach is devised to support hierarchical collaborative relations between individuals representing different parameters of takagi sugeno fuzzy models the coevolutionary approach assumes species to mean partial solutions of fuzzy modeling problems organized into four hierarchical levels individuals at each hierarchical level encode membership functions individual rules rule bases and fuzzy systems respectively a shared fitness evaluation scheme is used to measure the performance of each individual constraints are observed and particular targets are defined throughout the hierarchical levels with the purpose of promoting the occurrence of valid individuals and inducing rule compactness rule base consistency and partition set visibility the performance of the approach is evaluated via an example of function approximation with noisy data and a nonlinearly separable classification problem

the exact multi period mean square forecast error for the first order autoregressive model the finite sample behaviour of the multi period least squares forecast is considered in the simple normal autoregressive model yt yt 1 ut where 1 necessary and sufficient conditions are established for the existence of the forecast bias and the mean square forecast error msfe and an exact expression for the msfe is given exact numerical results are obtained for both the stationary and the fixed start up case our main conclusions are that for small values of the msfe is a decreasing function of the number of forecast periods and that the behaviour of the msfe in the stationary and the fixed start up case is very similar except for values of close to 1

symmetry of quantum torus with crossed product algebra in this paper we study the symmetry of quantum torus with the concept of crossed product algebra as a classical counterpart we consider the orbifold of classical torus with complex structure and investigate the transformation property of classical theta function an invariant function under the group action is constructed as a variant of the classical theta function then our main issue the crossed product algebra representation of a quantum torus with complex structure under the symplectic group is analyzed as a quantum version of orbifolding we perform this analysis with manin s so called model ii quantum theta function approach the symplectic group sp 2n z satisfies the consistency condition of a crossed product algebra representation of quantum torus times the algebra of functions on the siegel space however only a subgroup of sp 2n z satisfies the consistency condition for orbifolding of the quantum torus

some robust exact results on sample autocorrelations and tests of randomness abstract several exact results on the second moments of sample autocorrelations for both gaussian and non gaussian series are presented general formulae for the means variances and covariances of sample autocorrelations are given for the case where the variables in a sequence are exchangeable bounds for the variances and covariances of sample autocorrelations from an arbitrary random sequence are derived exact and explicit formulae for the variances and covariances of sample autocorrelations from a gaussian white noise are given it is observed that the latter results hold for all spherically symmetric distributions a simulation experiment with gaussian series indicates that normalizing each sample autocorrelation with its exact mean and variance instead of the usual approximate moments can improve considerably the accuracy of the asymptotic n 0 1 distribution to obtain critical values for tests of randomness the exact second moments of rank autocorrelations are also studied

efficient information theoretic inference for conditional moment restrictions abstract the generalised method of moments estimator may be substantially biased in finite samples especially so when there are large numbers of unconditional moment conditions this paper develops a class of first order equivalent semi parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel weighted version of the cressie read power divergence family of discrepancies this approach is similar in spirit to the empirical likelihood methods of kitamura et al 2004 empirical likelihood based inference in conditional moment restrictions models econometrica 72 1667 1714 and tripathi and kitamura 2003 testing conditional moment restrictions annals of statistics 31 2059 2095 these efficient local methods avoid the necessity of explicit estimation of the conditional jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations

markov chain monte carlo in stastical mechanics the appearance of the article by n metropolis a w rosenbluth m n rosenbluth a h teller and e teller marked the birth of the monte carlo method for the study of statistical mechanical systems and of a specific form of importance sampling namely markov chain monte carlo after nearly 40 years of statistical usage this technique has had a profound impact on statistical theory on both bayesian and classical statistics markov chain monte carlo is used essentially to estimate integrals in high dimensions this article addresses the accuracy of such estimation through computer experiments performed on the two dimensional ising model we compare the most common method for error estimates in statistical mechanics it appears that the moving block bootstrap outperforms other methods based on subseries values when the number of observations is relatively small and the time correlation between successive configurations decays slowly moreover the moving block bootstrap enables estimates of the sta

sieve bootstrap with variable length markov chains for stationary categorical time series a bootstrap for stationary categorical time series based on the method of sieves is studied here the data generating process is approximated by the so called variable length markov chain vlmc a flexible class of markov models that allows for parsimonious structure then the resampling is given by simulating from the fitted model it is shown that for a whole class of stationary categorical time series that is more general than vlmc the vlmc sieve has faster rate of convergence for variance estimation than the more general block bootstrap results are illustrated from a theoretical and empirical perspective for the latter a real data application about in homogeneity classification of a dna strand is also presented finally the vlmc sieve scheme enjoys an implementational advantage of using the plug in rule for bootstrapping a statistical procedure which generally is not the case for the block method

jackknife and analytical bias reduction for nonlinear panel models fixed effects estimators of panel models can be severely biased because of the well known incidental parameters problem we show that this bias can be reduced by using a panel jackknife or an analytical bias correction motivated by large t we give bias corrections for averages over the fixed effects as well as model parameters we find large bias reductions from using these approaches in examples we consider asymptotics where t grows with n as an approximation to the properties of the estimators in econometric applications we show that if t grows at the same rate as n the fixed effects estimator is asymptotically biased so that asymptotic confidence intervals are incorrect but that they are correct for the panel jackknife we show t growing faster than n 1 3 suffices for correctness of the analytic correction a property we also conjecture for the jackknife

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

bias in dynamic panel estimation with fixed effects incidental trends and cross section dependence abstract explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size n the results extend earlier work by nickell 1981 biases in dynamic models with fixed effects econometrica 49 1417 1426 and later authors in several directions that are relevant for practical work including models with unit roots deterministic trends predetermined and exogenous regressors and errors that may be cross sectionally dependent the asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient another finding of interest is that when there is cross section error dependence the probability limit of the dynamic panel regression estimator is a random variable rather than a constant which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where n is very large some proposals for bias correction are suggested and finite sample performance is analyzed in simulations

estimating space and space time covariance functions for large data sets a weighted composite likelihood approach in this article we propose two methods for estimating space and space time covariance functions from a gaussian random field based on the composite likelihood idea the first method relies on the maximization of a weighted version of the composite likelihood function while the second one is based on the solution of a weighted composite score equation this last scheme is quite general and could be applied to any kind of composite likelihood an information criterion for model selection based on the first estimation method is also introduced the methods are useful for practitioners looking for a good balance between computational complexity and statistical efficiency the effectiveness of the methods is illustrated through examples simulation experiments and by analyzing a dataset on ozone measurements

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

hierarchical genetic fuzzy systems abstract this paper introduces a hierarchical evolutionary approach to optimize the parameters of takagi sugeno ts fuzzy systems the approach includes a least squares method to determine the parameters of nonlinear consequents a pruning procedure is developed to avoid redundancy in each rule consequent and to achieve proper representation flexibility the performance of the hierarchical evolutionary approach is evaluated using function approximation and classification problems they demonstrate that the evolutionary algorithm working together with optimization and pruning procedures provides structurally simple fuzzy systems whose performance seems to be better than the ones produced by alternative approaches

a three step method for choosing the number of bootstrap repetitions this paper considers the problem of choosing the number of bootstrap repetitions b for bootstrap standard errors confidence intervals confidence regions hypothesis tests p values and bias correction for each of these problems the paper provides a three step method for choosing b to achieve a desired level of accuracy accuracy is measured by the percentage deviation of the bootstrap standard error estimate confidence interval length test s critical value test s p value or bias corrected estimate based on b bootstrap simulations from the corresponding ideal bootstrap quantities for which b the results apply quite generally to parametric semiparametric and nonparametric models with independent and dependent data the results apply to the standard nonparametric iid bootstrap moving block bootstraps for time series data parametric and semiparametric bootstraps and bootstraps for regression models based on bootstrapping residuals monte carlo simulations show that the proposed methods work very well

the dependent wild bootstrap we propose a new resampling procedure the dependent wild bootstrap for stationary time series as a natural extension of the traditional wild bootstrap to time series setting the dependent wild bootstrap offers a viable alternative to the existing block based bootstrap methods whose properties have been extensively studied over the last two decades unlike all of the block based bootstrap methods the dependent wild bootstrap can be easily extended to irregularly spaced time series with no implementational difficulty furthermore it preserves the favorable bias and mean squared error property of the tapered block bootstrap which is the state of the art block based method in terms of asymptotic accuracy of variance estimation and distribution approximation the consistency of the dependent wild bootstrap in distribution approximation is established under the framework of the smooth function model in addition we obtain the bias and variance expansions of the dependent wild bootstrap variance estimat

how to implement the bootstrap in static or stable dynamic regression models test statistic versus confidence region approach by combining two alternative formulations of a test statistic with two alternative resampling schemes we obtain four different bootstrap tests in the context of static linear regression models two of these are shown to have serious size and power problems whereas the remaining two are adequate and in fact equivalent the equivalence between the two valid implementations is shown to break down in dynamic regression models then the procedure based on the test statistic approach performs best at least in the ar 1 model similar finite sample phenomena are illustrated in the arma 1 1 model through a small scale monte carlo study and an empirical example

data tilting for time series summary we develop a general methodology for tilting time series data attention is focused on a large class of regression problems where errors are expressed through autoregressive processes the class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression robust statistical inference and estimation subject to constraints the method can be viewed as empirical likelihood with nuisance parameters

theta functions on noncommutative t4 we construct the so called theta vectors on noncommutative t4 which correspond to the theta functions on commutative tori with complex structures following the method of dieng and schwarz we first construct holomorphic connections and then find the functions satisfying the holomorphic conditions the theta vectors the holomorphic structure in the noncommutative t4 case is given by a 2 2 complex matrix and the consistency requires its off diagonal elements to be the same we also construct the tensor product of these functions satisfying the consistency requirement

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

a genetic algorithm for optimizing takagi sugeno fuzzy rule bases we show that a genetic algorithm can tune the parameters of the membership functions and outputs of a takagi sugeno fuzzy rule base the method is systematically tested for the approximation of one input analytical function

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

implementation of evolutionary fuzzy systems evolutionary fuzzy systems are discussed in which the membership function shapes and types and the fuzzy rule set including the number of rules inside it are evolved using a genetic evolutionary algorithm in addition the genetic parameters operators of the evolutionary algorithm are adapted via a fuzzy system benefits of the methodology are illustrated in the process of classifying the iris data set possible extensions of the methods are summarized

large sample results for batch means in analyzing the output process generated by a steady state simulation we often seek to estimate the expected value of the output the sample mean based on a finite sample of size n is usually the estimator of choice for the steady state mean and a measure of the sample mean s precision is the variance parameter i e the limiting value of the sample size multiplied by the variance of the sample mean as n becomes large this paper establishes asymptotic properties of the conventional batch means bm estimator of the variance parameter as both the batch size and the number of batches become large in particular we show that the bm variance estimator is asymptotically unbiased and convergent in mean square we also provide asymptotic expressions for the variance of the bm variance estimator exact and empirical examples illustrate our findings

empirical likelihood block bootstrapping monte carlo evidence has made it clear that asymptotic tests based on generalized method of moments gmm estimation have disappointing size the problem is exacerbated when the moment conditions are serially correlated several block bootstrap techniques have been proposed to correct the problem including hall and horowitz 1996 and inoue and shintani 2006 we propose an empirical likelihood block bootstrap procedure to improve inference where models are characterized by nonlinear moment conditions that are serially correlated of possibly infinite order combining the ideas of kitamura 1997 and brown and newey 2002 the parameters of a model are initially estimated by gmm which are then used to compute the empirical likelihood probability weights of the blocks of moment conditions the probability weights serve as the multinomial distribution used in resampling the first order asymptotic validity of the proposed procedure is proven and a series of monte carlo experiments show it may improve test sizes over conventional block bootstrapping

the bias of autoregressive coefficient estimators abstract this article presents simple expressions for the bias of estimators of the coefficients of an autoregressive model of arbitrary but known finite order the results include models both with and without a constant term the effects of overspecification of the model order on the bias are described the emphasis is on least squares and yule walker estimators but the methods extend to other estimators of similar design although only the order t 1 component of the bias is captured where t is the series length this asymptotic approximation is shown to be very accurate for least squares estimators through some numerical simulations the simulations examine fourth order autoregressions chosen to resemble some data series from the literature the order t 1 bias approximations for yule walker estimators need not be accurate especially if the zeros of the associated polynomial have moduli near 1 examples are given where the approximation is accurate and where it is useless the bias expressions are

on blocking rules for the bootstrap with dependent data summary we address the issue of optimal block choice in applications of the block bootstrap to dependent data it is shown that optimal block size depends significantly on context being equal to n 3 n 4 and nll5 in the cases of variance or bias estimation estimation of a onesided distribution function and estimation of a two sided distribution function respectively a clear intuitive explanation of this phenomenon is given together with outlines of theoretical arguments in specific cases it is shown that these orders of magnitude of block sizes can be used to produce a simple practical rule for selecting block size empirically that technique is explored numerically

efficient probabilistic forecasts for counts summary efficient probabilistic forecasts of integer valued random variables are derived the optimality is achieved by estimating the forecast distribution non parametrically over a given broad model class and proving asymptotic non parametric efficiency in that setting the method is developed within the context of the integer auto regressive class of models which is a suitable class for any count data that can be interpreted as a queue stock birth and death process or branching process the theoretical proofs of asymptotic efficiency are supplemented by simulation results that demonstrate the overall superiority of the non parametric estimator relative to a misspecified parametric alternative in large but finite samples the method is applied to counts of stock market iceberg orders a subsampling method is used to assess sampling variation in the full estimated forecast distribution and a proof of its validity is given

testing for structural change in conditional models in the past decade we have seen the development of a new set of tests for structural change of unknown timing in regression models most notably the supf statistic of andrews 1993 econometrica 61 825 856 the expf and avef statistics of andrewsploberger 1994 econometrica 62 1383 1414 and the statistic of nyblom 1989 journal of american statistical association 84 223 230 the distribution theory used for these tests is primarily asymptotic and has been derived under the maintained assumption that the regressors are stationary this excludes structural change in the marginal distribution of the regressors as a result these tests technically cannot discriminate between structural change in the conditional and marginal distributions this paper attempts to remedy this de ciency by deriving the large sample distributions of the test statistics allowing for structural change in the marginal distribution of the regressors we nd that the asymptotic distributions of the supf expf avef and statistics are not invariant to structural change in the regressors to solve the size problem we introduce a xed regressor bootstrap which achieves the rst order asymptotic distribution and appears to possess reasonable size properties in small samples our bootstrap theory allows for arbitrary structural change in the regressors including structural shifts polynomial trends and exogenous stochastic trends it allows for lagged dependent variables and heteroskedastic error processes 2000 elsevier science s a all rights reserved

an asymptotic expansion associated with the maximum likelihood estimators in arma models summary a technique is given for the edgeworth type asymptotic expansion for the joint as well as marginal and conditional distributions of the maximum likelihood estimators in autoregressive moving average arma models our methodology is illustrated and results on the expansions for some simple arma models are presented the present paper suggests a technique for obtaining the edgeworth type asymptotic expansion associated with the maximum likelihood estimator mle in arma models the expansion relates to joint as well as marginal and conditional distributions the approach developed here is simple and divided into two steps the first is to obtain the taylor expansion for the mle itself from the implicit function determining the mle on the basis of the explicit expression for the mle an asymptotic expansion for the distribution of the mle is derived at the second step these procedures are described in section 2 in section 3 our methodology is illustrated using a simple model and results on the expansions for some simple arma models are shown this paper ends with some discussion in section 4

a progressive block empirical likelihood method for time series this article develops a new blockwise empirical likelihood bel method for stationary weakly dependent time processes called the progressive block empirical likelihood pbel in contrast to the standard version of bel which uses data blocks of constant length for a given sample size and whose performance can depend crucially on the block length selection this new approach involves a data blocking scheme where blocks increase in length by an arithmetic progression consequently no block length selections are required for the pbel method which implies a certain type of robustness for this version of bel for inference of smooth functions of the process mean theoretical results establish the chi squared limit of the log likelihood ratio based on pbel which can be used to calibrate confidence regions using the same progressive block scheme distributional extensions are also provided for other nonparametric likelihoods with time series in the family of cressie read discrepancies simulation evidenc

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

subseries methods in regression abstract we extend subseries methods for stationary sequences to the regression setting to estimate sampling distributions the subseries approach computes the statistic of interest on all possible subseries of a shorter length than the original series and uses the distribution of these replicates to mimic the distribution of the original statistic for proper choice of subseries length the regression parameters can be estimated to order o n 2 3 thus improving on the normal approximation the replicates can also be used to reduce the bias of robust estimators simulation results demonstrate the finite sample effectiveness of the approach for both distribution function estimation and bias reduction applications to spatial data are also discussed

neuro fuzzy systems for function approximation abstract we present a neuro fuzzy architecture for function approximation based on supervised learning the learning algorithm is able to determine the structure and the parameters of a fuzzy system the approach is an extension to our already published nefcon and nefclass models which are used for control or classification purposes the proposed extended model which we call nefprox is more general and can be used for any application based on function approximation

the sampling distributions of the predictor for an autoregressive model under misspecifications abstract approximations to the sampling distributions of the predictor are given misspecifying the autoregressive moving average model as an autoregressive model we deal with both conditional and unconditional distributions for the dependent and independent cases according to whether the sample data used in estimation and in prediction are dependent or not the bias and mean squared error are easily obtained from these approximations

the moving blocks bootstrap and robust inference for linear least squares and quantile regressions abstract this paper presents the moving blocks bootstrap mbb as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms the mbb covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent hac standard errors for least squares ls and quantile regression qr coefficient estimators the mbb covariance estimator is shown to be asymptotically equivalent to the bartlett kernel estimator suggested by newey and west 1987 and the asymptotically optimal choice of the blocksize is discussed a monte carlo study is included showing that the mbb fares well in comparison to standard hac inference procedures considering strong mixing data generating processes the paper extends existing asymptotic results for the qr estimator the analogy to the ls case is stressed the paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new grenander like conditions for the latter case the use of the mbb approach is illustrated for a practical example using a standard econometric package

on noncommutative multi solitons solitons in noncommutative scalar field theories possess many stringy features in particular multi solitons in these theories behave like multiple d branes a useful moduli space description for multi solitons exists which reproduces stringy features of d brane moduli spaces in a simple way via properties of special projection operators in particular they are equivalent to a hilbert scheme resolution of symmetric product spaces