edgeworth correction by bootstrap in autoregressions we prove that the distribution of least squares estimates in autoregressions can be bootstrapped with accuracy o n 1 2 a s thereby improving the normal approximation error of o n

double block bootstrap confidence intervals for dependent data the block bootstrap confidence interval for dependent data can outperform the conventional normal approximation only with nontrivial studentization which in the case of complicated statistics calls for specialist treatment and often results in unstable endpoints we propose two double block bootstrap approaches for improving the accuracy of the block bootstrap confidence interval under very general conditions the first approach calibrates the nominal coverage level and the second calculates studentizing factors directly from a block bootstrap series without the need for nontrivial analytical treatment we prove that the two approaches reduce the coverage error of the block bootstrap interval by an order of magnitude with simple tuning of block lengths at the two block bootstrapping levels empirical properties of the procedures are investigated by simulations and application to an econometric time series

kernel weighted gmm estimators for linear time series models abstract this paper analyzes the higher order asymptotic properties of generalized method of moments gmm estimators for linear time series models using many lags as instruments a data dependent moment selection method based on minimizing the approximate mean squared error is developed in addition a new version of the gmm estimator based on kernel weighted moment conditions is proposed it is shown that kernel weighted gmm estimators can reduce the asymptotic bias compared to standard gmm estimators kernel weighting also helps to simplify the problem of selecting the optimal number of instruments a feasible procedure similar to optimal bandwidth selection is proposed for the kernel weighted gmm estimator

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

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

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

gel estimation for heavy tailed garch models with robust empirical likelihood inference abstract we construct a generalized empirical likelihood estimator for a garch 1 1 model with a possibly heavy tailed error the estimator imbeds tail trimmed estimating equations allowing for over identifying conditions asymptotic normality efficiency and empirical likelihood based confidence regions for very heavy tailed random volatility data we show the implied probabilities from the tail trimmed continuously updated estimator elevate weight for usable large values assign large but not maximum weight to extreme observations and give the lowest weight to non leverage points we derive a higher order expansion for gel with imbedded tail trimming gelitt which reveals higher order bias and efficiency properties available when the garch error has a finite second moment higher order asymptotics for gel without tail trimming requires the error to have moments of substantially higher order we use first order asymptotics and higher order bias to justify the choice of the number of trimmed observations in any given sample we also present robust versions of generalized empirical likelihood ratio wald and lagrange multiplier tests and an efficient and heavy tail robust moment estimator with an application to expected shortfall estimation finally we present a broad simulation study for gel and gelitt and demonstrate profile weighted expected shortfall for the russian ruble us dollar exchange rate we show that tail trimmed cue gmm dominates other estimators in terms of bias mse and approximate normality

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

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

graphical procedures for multiple comparisons under general dependence abstractit has been more than half a century since tukey first introduced graphical displays that relate nonoverlap of confidence intervals to statistically significant differences between parameter estimates in this article we show how tukey s graphical overlap procedure can be modified to accommodate general forms of dependence within and across samples we also develop a procedure that can be used to more effectively resolve rankings within the tails of the distributions of parameter values thereby generalizing existing methods for multiple comparisons with the best we show that these new procedures retain the simplicity of tukey s original procedure while maintaining asymptotic control of the familywise error rate under very general conditions simple examples are used throughout to illustrate the procedures supplementary materials for this article are available online

convergence analysis of a halpern type algorithm for accretive operators abstract in this paper we study the convergence of a halpern type proximal point algorithm for accretive operators in banach spaces our results fill the gap in the work of zhang and song 2012 1 and consequently all the results there can be corrected accordingly

istmo an interval reference point based method for stochastic multiobjective programming problems in this paper we present an interactive algorithm istmo for stochastic multiobjective problems with continuous random variables this method combines the concept of probability efficiency for stochastic problems with the reference point philosophy for deterministic multiobjective problems the decision maker expresses her his references by dividing the variation range of each objective into intervals and by setting the desired probability for each objective to achieve values belonging to each interval these intervals may also be redefined during the process this interactive procedure helps the decision maker to understand the stochastic nature of the problem to discover the risk level s he is willing to assume for each objective and to learn about the trade offs among the objectives

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

asymptotic expansions for sums of weakly dependent random vectors it is shown that formal edgeworth expansions are valid for sums of weakly dependent random vectors the error of approximation has ordero n s 2 2 if the strong mixing coefficients in iii are decreasing at an exponential rate the above conditions can easily be checked and are often satisfied when the sequence of random vectors is a gaussian or a markov or an autoregressive process explicit formulas are given for the distribution of finite fourier transforms of a strictly stationary time series

asymptotic distribution of statistics in time series veritable conditions are given for the validity of formal edgeworth expansions for the distribution of sums x 1 x n where x i f z i z i p 1 and z 1 z 2 is a strict sense stationary sequence that can be written as z j g e j k k 0 with an iid sequence e i of innovations these models include nonlinear functions of arma processes z i as well as certain nonlinear ar processes the results apply to many statistics in nonlinear time series models

the second order bias and mean squared error of nonlinear estimators abstract despite the now widespread use of nonlinear estimators their finite sample properties have received very little attention in either the statistics or econometrics literature we partially redress this problem by deriving and examining the second order bias and mean squared error of a fairly wide class of nonlinear estimators which includes nonlinear least squares maximum likelihood and many generalized method of moments estimators as special cases a number of examples are provided the results from a monte carlo exercise demonstrate how the results can be applied for improved inferences

edgeworth expansions of suitably normalized sample mean statistics for atomic markov chains this paper is devoted to the problem of estimating functionals of type f fd from observations drawn from a positive recurrent atomic markov chain open image in new window with stationary distribution the properties of different estimators are studied beyond an accurate estimation of their bias the estimation of their asymptotic variance is considered we also show that the results of malinovskii 1987 on the validity of the formal edgeworth expansion for sample mean statistics of type t n n 1 n i 1 f x i extend to their studentized versions normalized by the asymptotic variance estimates we consider

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

estimated wold representation and spectral density driven bootstrap for time series the second order dependence structure of purely non deterministic stationary processes is described by the coefficients of the famous wold representation these coefficients can be obtained by factorizing the spectral density of the process this relationship together with some spectral density estimator is used to obtain consistent estimators of these coefficients a spectral density driven bootstrap for time series is then developed which uses the entire sequence of estimated moving average coefficients together with appropriately generated pseudoinnovations to obtain a bootstrap pseudo time series it is shown that if the underlying process is linear and if the pseudoinnovations are generated by means of an independent and identically distributed wild bootstrap which mimics to the extent necessary the moment structure of the true innovations this bootstrap proposal asymptotically works for a wide range of statistics the relationships of the proposed bootstrap procedure to some other bootstrap procedures including the auto regressive sieve bootstrap are discussed it is shown that the latter is a special case of the spectral density driven bootstrap if a parametric auto regressive spectral density estimator is used simulations investigate the performance of the new bootstrap procedure in finite sample situations furthermore a real life data example is presented

on iterations methods for zeros of accretive operators in banach spaces in this paper three iterations are designed to approach zeros of set valued accretive operators in banach spaces the first one is the continuous picard type iteration involving the resolvent the second one is the approximate picard type iteration involving the resolvent and the third one is the halpern type iteration involving the resolvent some strong convergence theorems for three iterations are proved

satisfactory solution concepts and their relations for stochastic multiobjective programming problems abstract this work deals with the concept of satisfactory solution for stochastic multiobjective programming smp problems based on previous literature we will introduce different concepts of satisfactory solutions for smp problems define a new concept of solution where the decision maker dm sets his her preferences in terms of two aspiration levels for the stochastic objective and two probabilities to reach those levels and establish some relationship between these concepts the results will aim at featuring these concepts and determine the differences between them moreover the paper proposes a new step by step procedure to exchange information between the analyst and dm prior to solving the problem thus the dm will be able to choose the transformation criterion for each stochastic objective and the aspiration level

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

heteroskedasticity autocorrelation and spatial correlation robust inference in linear panel models with fixed effects abstract this paper develops an asymptotic theory for test statistics in linear panel models that are robust to heteroskedasticity autocorrelation and or spatial correlation two classes of standard errors are analyzed both are based on nonparametric heteroskedasticity autocorrelation hac covariance matrix estimators the first class is based on averages of hac estimators across individuals in the cross section i e averages of hacs this class includes the well known cluster standard errors analyzed by arellano 1987 as a special case the second class is based on the hac of cross section averages and was proposed by driscoll and kraay 1998 the hac of averages standard errors are robust to heteroskedasticity serial correlation and spatial correlation but weak dependence in the time dimension is required the averages of hacs standard errors are robust to heteroskedasticity and serial correlation including the nonstationary case but they are not valid in the presence of spatial correlation the main contribution of the paper is to develop a fixed b asymptotic theory for statistics based on both classes of standard errors in models with individual and possibly time fixed effects dummy variables the asymptotics is carried out for large time sample sizes for both fixed and large cross section sample sizes extensive simulations show that the fixed b approximation is usually much better than the traditional normal or chi square approximation especially for the driscoll kraay standard errors the use of fixed b critical values will lead to more reliable inference in practice especially for tests of joint hypotheses

asymptotic refinements of a misspecification robust bootstrap for gel estimators abstract i propose a nonparametric iid bootstrap procedure for the empirical likelihood the exponential tilting and the exponentially tilted empirical likelihood estimators that achieves asymptotic refinements for t tests and confidence intervals and wald tests and confidence regions based on such estimators furthermore the proposed bootstrap is robust to model misspecification i e it achieves asymptotic refinements regardless of whether the assumed moment condition model is correctly specified or not this result is new because asymptotic refinements of the bootstrap based on these estimators have not been established in the literature even under correct model specification monte carlo experiments are conducted in dynamic panel data setting to support the theoretical finding as an application bootstrap confidence intervals for the returns to schooling of hellerstein and imbens 1999 are calculated the result suggests that the returns to schooling may be higher

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

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

halpern type proximal point algorithm of accretive operators abstract the main objectives of this paper are to employ a new proof technique to prove the strong convergence of x n and y n defined respectively by x n 1 n u n x n 1 n n j r n a x n and y n 1 n y n 1 n j r n a n u 1 n y n to some zero of accretive operator a in a uniformly convex banach space e with a uniformly g teaux differentiable norm or with a weakly continuous duality mapping j whenever n and n are sequences in 0 1 and r n 0 satisfying the conditions lim n n 0 n 1 n lim sup n n 1 lim inf n r n 0

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

gel statistics under weak identification abstract the central concern of this paper is the provision in a time series moment condition framework of practical recommendations of confidence regions for parameters whose coverage probabilities are robust to the strength or weakness of identification to this end we develop pearson type test statistics based on gel implied probabilities formed from general kernel smoothed versions of the moment indicators we also modify the statistics suggested in guggenberger and smith 2008 for a general kernel smoothing function importantly for our conclusions we provide gel time series counterparts to gmm and gel conditional likelihood ratio statistics given in kleibergen 2005 and smith 2007 our analysis not only demonstrates that these statistics are asymptotically conditionally pivotal under both classical asymptotic theory and weak instrument asymptotics of stock and wright 2000 but also provides asymptotic power results in the weakly identified time series context consequently the empirical null rejection probabilities of the associated tests and thereby the coverage probabilities of the corresponding confidence regions should not be affected greatly by the strength or otherwise of identification a comprehensive monte carlo study indicates that a number of the tests proposed here represent very competitive choices in comparison with those suggested elsewhere in the literature

a generalized stochastic goal programming model in this paper we show how one can get stochastic solutions of stochastic multi objective problem smop using goal programming models in literature it is well known that one can reduce a smop to deterministic equivalent problems and reduce the analysis of a stochastic problem to a collection of deterministic problems the first sections of this paper will be devoted to the introduction of deterministic equivalent problems when the feasible set is a random set and we show how to solve them using goal programming technique in the second part we try to go more in depth on notion of smop solution and we suppose that it has to be a random variable we will present stochastic goal programming model for finding stochastic solutions of smop our approach requires more computational time than the one based on deterministic equivalent problems due to the fact that several optimization programs which depend on the number of experiments to be run needed to be solved on the other hand since in our approach we suppose that a smop solution is a random variable according to the central limit theorem the larger will be the sample size and the more precise will be the estimation of the statistical moments of a smop solution the developed model will be illustrated through numerical examples

bootstrap standard error estimates for linear regression standard errors of parameter estimates are widely used in empirical work the bootstrap often can provide a convenient means of estimating standard errors the conditions under which bootstrap standard error estimates are theoretically justified have not received much attention however this article establishes conditions for the consistency of the moving blocks bootstrap estimators of the variance of the least squares estimator in linear dynamic models with dependent data we discuss several applications of this result in particular the use of bootstrap standard error estimates for bootstrapping studentized statistics a simulation study shows that inference based on bootstrap standard error estimates may be considerably more accurate in small samples than inference based on closed form asymptotic estimates

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

local gmm estimation of time series models with conditional moment restrictions this paper investigates statistical properties of the local generalized method of moments lgmm estimator for some time series models defined by conditional moment restrictions first we consider markov processes with possible conditional heteroskedasticity of unknown forms and establish the consistency asymptotic normality and semi parametric efficiency of the lgmm estimator second we undertake a higher order asymptotic expansion and demonstrate that the lgmm estimator possesses some appealing bias reduction properties for positively autocorrelated processes our analysis of the asymptotic expansion of the lgmm estimator reveals an interesting contrast with the ols estimator that helps to shed light on the nature of the bias correction performed by the lgmm estimator the practical importance of these findings is evaluated in terms of a bond and option pricing exercise based on a diffusion model for spot interest rate

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

bootstrap methods for markov processes the block bootstrap is the best known bootstrap method for time series data when the analyst does not have a parametric model that reduces the data generation process to simple random sampling however the errors made by the block bootstrap converge to zero only slightly faster than those made by first order asymptotic approximations this paper describes a bootstrap procedure for data that are generated by a markov process or a process that can be approximated by a markov process with sufficient accuracy the procedure is based on estimating the markov transition density nonparametrically bootstrap samples are obtained by sampling the process implied by the estimated transition density conditions are given under which the errors made by the markov bootstrap converge to zero more rapidly than those made by the block bootstrap

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

gel estimation and tests of spatial autoregressive models abstract this paper considers the generalized empirical likelihood gel estimation and tests of high order spatial autoregressive sar models by exploring an inherent martingale structure the gel estimator has the same asymptotic distribution as the generalized method of moments estimator explored with same moment conditions for estimation but circumvents a first step estimation of the optimal weighting matrix with a preliminary estimator and thus can be robust to unknown heteroskedasticity and non normality while the gel removes the asymptotic bias from the preliminary estimator and partially removes the bias due to the correlation between the moment conditions and their jacobian the empirical likelihood as a special member of gels further partially removes the bias from estimating the second moment matrix we also formulate the gel overidentification test moran s i test and gel ratio tests for parameter restrictions and non nested hypotheses while some of the conventional tests might not be robust to non normality and or unknown heteroskedasticity the corresponding gel tests can be robust

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

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

halpern iteration for firmly type nonexpansive mappings abstract the main aim of this paper is to study the strong convergence of halpern iteration for firmly type nonexpansive mappings defined on a banach space with a uniformly g teaux differentiable norm and the proof techniques are simpler and different from much existing literature also which gives the affirmative answer of the halpern open problem for this class of mapping

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

gmm gel serial correlation and asymptotic bias for stationary time series models with serial correlation we consider generalized method of moments gmm estimators that use heteroskedasticity and autocorrelation consistent hac positive definite weight matrices and generalized empirical likelihood gel estimators based on smoothed moment conditions following the analysis of newey and smith 2004 for independent observations we derive second order asymptotic biases of these estimators the inspection of bias expressions reveals that the use of smoothed gel in contrast to gmm removes the bias component associated with the correlation between the moment function and its derivative while the bias component associated with third moments depends on the employed kernel function we also analyze the case of no serial correlation and find that the seemingly unnecessary smoothing and hac estimation can reduce the bias for some of the estimators