an implicit bidiagonal numerical method for solving the navier stokes equations in recent years much progress has been made in solving fluid dynamical problems using finite difference methods solving inviscid compressible problems in two and three dimensions has become almost routine with many suitable methods explicit or implicit available the problem of compressible viscous flows in complicated geometries remains however a major challenge here fine mesh spacing in the viscous flow regions makes the explicit methods with their simple boundary conditions extremely costly existing implicit methods can make use of large time steps but require inversions of large block tridiagonal matrices a method recently developed by maccormack eliminates this disadvantage by introducing a predictor corrector scheme requiring the inversion of only block bidiagonal matrices it is the aim of present work to extend this method to allow solution of viscous compressible problems in general coordinates for arbitrary two dimensional geometries

time domain procedures for testing that a stationary time series is gaussian a class of time domain procedures for testing that a stationary time series is gaussian is presented and analyzed these tests are based on the deviations of the sample value of finite memory nonlinear transformations of the process from their ensemble averaged counterparts asymptotic distributions of these tests are derived under the null hypothesis of gaussianity and under a class of local and fixed alternatives specific tests are then developed based respectively on higher order moments and on the characteristic functions practical construction of the test statistics is discussed with a special emphasis on the estimation of the covariance of the sample statistics which appears to play a key role in the performance of the tests when dealing with small samples

texture synthesis and nonparametric resampling of random fields this paper introduces a nonparametric algorithm for bootstrapping a stationary random field and proves certain consistency properties of the algorithm for the case of mixing random fields the motivation for this paper comes from relating a heuristic texture synthesis algorithm popular in computer vision to general nonparametric bootstrapping of stationary random fields we give a formal resampling scheme for the heuristic texture algorithm and prove that it produces a consistent estimate of the joint distribution of pixels in a window of certain size under mixing and regularity conditions on the random field the joint distribution of pixels is the quantity of interest here because theories of human perception of texture suggest that two textures with the same joint distribution of pixel values in a suitably chosen window will appear similar to a human thus we provide theoretical justification for an algorithm that has already been very successful in practice and suggest an explanation for its perceptually good results

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

a smooth block bootstrap for quantile regression with time series quantile regression allows for broad conditional characterizations of a response distribution beyond conditional means and is of increasing interest in economic and financial applications because quantile regression estimators have complex limiting distributions several bootstrap methods for the independent data setting have been proposed many of which involve smoothing steps to improve bootstrap approximations currently no similar advances in smoothed bootstraps exist for quantile regression with dependent data to this end we establish a smooth tapered block bootstrap procedure for approximating the distribution of quantile regression estimators for time series this bootstrap involves two rounds of smoothing in resampling individual observations are resampled via kernel smoothing techniques and resampled data blocks are smoothed by tapering the smooth bootstrap results in performance improvements over previous unsmoothed versions of the block bootstrap as well as normal approximations based on powell s kernel variance estimator which are common in application our theoretical results correct errors in proofs for earlier and simpler versions of the unsmoothed moving blocks bootstrap for quantile regression and broaden the validity of block bootstraps for this problem under weak conditions we illustrate the smooth bootstrap through numerical studies and examples

testing that a dependent process is uncorrelated an analysis is presented of a new testing procedure for the null hypothesis that a stochastic process is uncorrelated when the process is possibly dependent unlike with existing procedures the user does not need to choose any arbitrary number to implement the proposed test the asymptotic null distribution of the proposed test statistic is not standard but it is tabulated by means of simulations the test is compared with two alternative test procedures that require selection of user chosen numbers on the basis of asymptotic local power and finite sample behavior although the asymptotic local power of the proposed test is lower than those corresponding to the alternative tests in a monte carlo study i show that in small samples the test typically better controls the type i error and that the loss of power is not substantial

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

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

parameter estimation for a stationary process on a d dimensional lattice summary we study asymptotic properties of various estimation procedures for a general stationary regular process on a d dimensional lattice differences between d 1 time series and d 2 spatial processes are pointed out we suppose that the process is observed on a set pn with cn points which tends to infinity with the same speed in all directions the relative edge effect is of order cn lid increasing with d this effect is without statistical importance if d 1 but is important if d 2 we give a lcn consistent asymptotically normal estimator of the underlying parameter the procedure being constructed by a modification of whittle s approximation to the log likelihood in the gaussian case this procedure is asymptotically efficient

bootstrap resampling for image registration uncertainty estimation without ground truth we address the problem of estimating the uncertainty of pixel based image registration algorithms given just the two images to be registered for cases when no ground truth data is available our novel method uses bootstrap resampling it is very general applicable to almost any registration method based on minimizing a pixel based similarity criterion we demonstrate it using the ssd sad correlation and mutual information criteria we show experimentally that the bootstrap method provides better estimates of the registration accuracy than the state of the art cramer rao bound method additionally we evaluate also a fast registration accuracy estimation frae method which is based on quadratic sensitivity analysis ideas and has a negligible computational overhead frae mostly works better than the cramer rao bound method but is outperformed by the bootstrap method

application of the implicit maccormack scheme to the parabolized navier stokes equations application de la methode de differences finies implicite de maccormack a la resolution des equations bidimensionnelles parabolisees de navier stokes discussion des avantages et inconvenients de la methode comparaison avec le schema de beam warming en ce qui concerne la precision la stabilite le temps de calcul la place en memoire et la facilite d implementation application a un ecoulement laminaire hypersonique sur un coin de compression

on optimal spatial subsample size for variance estimation we consider the problem of determining the optimal block or subsample size for a spatial subsampling method for spatial processes observed on regular grids we derive expansions for the mean square error of the subsampling variance estimator which yields an expression for the theoretically optimal block size the optimal block size is shown to depend in an intricate way on the geometry of the spatial sampling region as well as characteristics of the underlying random field final expressions for the optimal block size make use of some nontrivial estimates of lattice point counts in shifts of convex sets optimal block sizes are computed for sampling regions of a number of commonly encountered shapes numerical studies are performed to compare subsampling methods as well as procedures for estimating the theoretically best block size

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

infinitesimal robustness for autoregressive processes we define the influence function and construct optimal robust estimators for autoregressive processes we show that the asymptotic bias caused by small contaminations of the marginals can be written as the integral of a certain function with respect to the contamination this function is called the influence function it is unique only up to an equivalence relation but there is a natural unique version which describes the limiting influence of an additional observation given the previous observations moreover with this version the asymptotic variance at the true model can be expressed in a simple form optimal robust estimators minimize this asymptotic variance under a constraint on the influence function as in the i i d case they are found by truncating a multiple of the influence function of the maximum likelihood estimator

theoretical comparisons of block bootstrap methods in this paper we compare the asymptotic behavior of some common block bootstrap methods based on nonrandom as well as random block lengths it is shown that asymptotically bootstrap estimators derived using any of the methods considered in the paper have the same amount of bias to the first order however the variances of these bootstrap estimators may be different even in the first order expansions for the bias the variance and the mean squared error of different block bootstrap variance estimators are obtained it follows from these expansions that using overlapping blocks is to be preferred over nonoverlapping blocks and that using random block lengths typically leads to mean squared errors larger than those for nonrandom block lengths

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

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

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

a bootstrap evaluation of the effect of data splitting on financial time series exposes problems of the commonly used technique of splitting the available data into training validation and test sets that are held fixed warns about drawing too strong conclusions from such static splits and shows potential pitfalls of ignoring variability across splits using a bootstrap or resampling method we compare the uncertainty in the solution stemming from the data splitting with neural network specific uncertainties parameter initialization choice of number of hidden units etc we present two results on data from the new york stock exchange first the variation due to different resamplings is significantly larger than the variation due to different network conditions this result implies that it is important to not over interpret a model or an ensemble of models estimated on one specific split of the data second on each split the neural network solution with early stopping is very close to a linear model no significant nonlinearities are extracted

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

a nearest neighbor bootstrap for resampling hydrologic time series a nonparametric method for resampling scalar or vector valued time series is introduced multivariate nearest neighbor probability density estimation provides the basis for the resampling scheme developed the motivation for this work comes from a desire to preserve the dependence structure of the time series while bootstrapping resampling it with replacement the method is data driven and is preferred where the investigator is uncomfortable with prior assumptions as to the form e g linear or nonlinear of dependence and the form of the probability density function e g gaussian such prior assumptions are often made in an ad hoc manner for analyzing hydrologic data connections of the nearest neighbor bootstrap to markov processes as well as its utility in a general monte carlo setting are discussed applications to resampling monthly streamflow and some synthetic data are presented the method is shown to be effective with time series generated by linear and nonlinear autoregressive models the utility of the method for resampling monthly streamflow sequences with asymmetric and bimodal marginal probability densities is also demonstrated

computing of separated flow using the space marching conservative supra characteristics method steady hypersonic viscous flows over compression corners with streamwise separation have been computed using the space marching conservative supra characteristics method of lombard this method permits stable space marching of the parabolized navier stokes equations through large separated flow regions the present method has been used to compute surface pressure heat transfer and skin friction coefficients for two compression corner cases studied experimentally by holden and moselle the computed results compare favorably with previous navier stokes results and experimental data the present method has also been compared with the conventional beam warming scheme for solving the parabolized navier stokes equations comparisons are made for accuracy computer time and computer storage

a numerical method for solving the equations of compressible viscous flow although much progress has already been made in solving problems in aerodynamic design many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely this paper describes one such development a new method for solving these equations has been devised that 1 is second order accurate in space and time 2 is unconditionally stable 3 preserves conservation form 4 requires no block or scalar tridiagonal inversions 5 is simple and straightforward to program estimated 10 modification for the update of many existing programs 6 is more efficient than present methods and 7 should easily adapt to current and future computer architectures computational results for laminar and turbulent flows at reynolds numbers from 3 x 10 exp 5 to 3 x 10 exp 7 and at cfl numbers as high as 10 exp 3 are compared with theory and experiment

a statistical framework for testing chaotic dynamics via lyapunov exponents abstract one common criticism of the existing lyapunov exponents algorithms is the absence of a distributional theory which provides a framework for the statistical hypothesis testing for the calculated lyapunov exponents this paper presents a methodology to calculate the empirical distributions of lyapunov exponents by using a bootstrapping technique the methodology of the paper provides a formal test of chaos under the null hypothesis the numerical examples show that the method works well with small data sets

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

space marching calculations about hypersonic configurations using a solution adaptive mesh algorithm a solution adaptive marching algorithm is developed and applied to a three dimensional parabolized navierstokes equation solver the resulting algorithm obtains accurate solutions by using a spatial marching adaptivegrid procedure the adaptation step redistributes grid points line by line in both crossflow directions with grid point motion controlled by forces analogous to tensional and torsional spring forces with the tensional force proportional to the error measure or weighting functions the solution adaptive marching procedure is applied to the hypersonic flow about two generic aircraft configurations the first of these is an all body type geometry with elliptical cross sections and is studied at angles of attack of 0 5 and 15 deg the second geometry is a generic blended vv ing body design results are presented that demonstrate the improvements in flow field resolution obtainable with the solution adaptive marching procedure over conventional fixed grid techniques computed pitot pressure profiles obtained using the solution adaptive algorithm show improved agreement with experimental data compared to predictions obtained using a fixed grid

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

bootstrap refinements for qml estimators of the garch 1 1 parameters a b s t r a c t this paper reconsiders a block bootstrap procedure for quasi maximum likelihood estimation of garch models based on the resampling of the likelihood function as proposed by goncalves and white 2004 maximum likelihood and the bootstrap for nonlinear dynamic models journal of econometrics 119 199 219 first we provide necessary conditions and sufficient conditions in terms of moments of the innovation process for the existence of the edgeworth expansion of the garch 1 1 estimator up to the k th term second we provide sufficient conditions for higher order refinements for equally tailed and symmetric test statistics in particular the bootstrap estimator based on resampling the likelihood has the same higher order improvements in terms of error in the rejection probabilities as those in andrews 2002 higher order improvements of a computationally attractive k step bootstrap for extremum estimators econometrica 70 119 162

simple estimation of hidden correlation in repeated measures in medical and social studies it is often desirable to assess the correlation between characteristics of interest that are not directly observable in such cases repeated measures are often available but the correlation between the repeated measures is not the same as that between the true characteristics that are confounded with the measurement errors the latter is called the hidden correlation previously the problem has been treated by assuming prior knowledge about the measurement errors or by using relatively complex statistical models such as the mixed effects models with no closed form expression for the estimated hidden correlation we propose a simple estimator of the hidden correlation that is very much like the pearson correlation coefficient with a closed form expression under assumptions much weaker than the mixed effects model simulation results show that the proposed simple estimator performs similarly as the restricted maximum likelihood reml estimator in mixed models but is computationally much more efficient than reml simulation comparison with the pearson correlation is also made a real data example is considered

point and interval estimation of variogram models using spatial empirical likelihood we present a spatial blockwise empirical likelihood method for estimating variogram model parameters in the analysis of spatial data on a grid the method produces point estimators that require no spatial variance estimates to compute unlike least squares methods for variogram fitting but are as efficient as the best least squares estimator in large samples our approach also produces confidence regions for the variogram without requiring knowledge of the full joint distribution of the spatial data in addition the empirical likelihood formulation extends to spatial regression problems and allows simultaneous inference on both spatial trend and variogram parameters we examine the asymptotic behavior of the estimator analytically and investigate its behavior in finite samples through simulation studies

general m estimates for contaminated p th order autoregressive processes consistency and asymptotic normality this work is concerned with simultaneous estimation of coefficients and a scale parameter of a p th order autoregressive process x t the observations are y t v t z t 1 v t x t where z t is a contaminating process and v t represents the proportion of contamination if x t or z t have heavy tails both least squares estimates and ordinary m estimates are seriously affected under general conditions we prove consistency and asymptotic normality of a general class of m estimates which contains some m estimates studied by denby and martin 6

leave k out diagnostics for time series abstract the authors propose diagnostics for arima model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters the use of leave one out diagnostics is a well established tool in regression analysis this document demonstrates the efficacy of observation deletion based diagnostics for arima models addressing issues special to the time diagnostics based on the innovations variance it is shown that the dependency aspect of time series data gives rise to a smearing effect which confounds the diagnostics for the coefficients it is also shown that the diagnostics based on the innovations variance are much clearer and more sensitive than those for the coefficients a leave k out diagnostics approach is proposed to deal with patches of outliers and problems caused by masking are handled by use of iterative deletion an overall strategy for arima model fitting is given and applied to two data sets

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

a theory of proximity based clustering structure detection by optimization abstract in this paper a systematic optimization approach for clustering proximity or similarity data is developed starting from fundamental invariance and robustness properties a set of axioms is proposed and discussed to distinguish different cluster compactness and separation criteria the approach covers the case of sparse proximity matrices and is extended to nested partitionings for hierarchical data clustering to solve the associated optimization problems a rigorous mathematical framework for deterministic annealing and mean field approximation is presented efficient optimization heuristics are derived in a canonical way which also clarifies the relation to stochastic optimization by gibbs sampling similarity based clustering techniques have a broad range of possible applications in computer vision pattern recognition and data analysis as a major practical application we present a novel approach to the problem of unsupervised texture segmentation which relies on statistical tests as a measure of homogeneity the quality of the algorithms is empirically evaluated on a large collection of brodatz like micro texture mondrians and on a set of real word images to demonstrate the broad usefulness of the theory of proximity based clustering the performances of different criteria and algorithms are compared on an information retrieval task for a document database the superiority of optimization algorithms for clustering is supported by extensive experiments

diagnostics for dependence within time series extremes summary the analysis of extreme values within a stationary time series entails various assumptions concerning its long and short range dependence we present a range of new diagnostic tools for assessing whether these assumptions are appropriate and for identifying structure within extreme events these tools are based on tail characteristics of joint survivor functions but can be implemented by using existing estimation methods for extremes of univariate independent and identically distributed variables our diagnostic aids are illustrated through theoretical examples simulation studies and by application to rainfall and exchange rate data on the basis of these diagnostics we can explain characteristics that are found in the observed extreme events of these series and also gain insight into the properties of events that are more extreme than those observed

monte carlo state space likelihoods by weighted posterior kernel density estimation maximum likelihood estimation and likelihood ratio tests for nonlinear non gaussian state space models require numerical integration for likelihood calculations several methods including monte carlo mc expectation maximization mc likelihood ratios direct mc integration and particle filter likelihoods are inefficient for the motivating problem of stage structured population dynamics models in experimental settings an mc kernel likelihood mckl method is presented that estimates classical likelihoods up to a constant by weighted kernel density estimates of bayesian posteriors mckl is derived by using bayesian posteriors as importance sampling densities for unnormalized kernel smoothing integrals mc error and mode bias due to kernel smoothing are discussed and two methods for reducing mode bias are proposed zooming in on the maximum likelihood parameters using a focused prior based on an initial estimate and using a posterior cumulant based approximation of mode bias a simulated example show

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

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

solution adaptive grid procedure for high speed parabolic flow solvers a solution adaptive grid procedure based bn an error equidistribution scheme is developed and applied to a parabolized navier stokes solver an improved method of selecting weighting functions is introduced that involves normalizing a combination of flowfield gradients and curvature of a number of dependent variables and then selecting the largest at each point the scheme redistributes grid points line by line with grid point motion controlled by forces analogous to tensional and torsional spring forces with the spring constants set equal to the weighting functions torsional terms are functions of the grid point positions along neighboring grid lines and provide grid smoothness and stability a grid fitting scheme is introduced for external flows in which the number of grid points in the freestream are reduced to a minimum results for several problems are presented to demonstrate the improvements obtainable with the solution adaptive grid procedure

blockwise bootstrapped empirical process for stationary sequences we apply the bootstrap for general stationary observations proposed by kunsch to the empirical process for p dimensional random vectors it is known that the empirical process in the multivariate case converges weakly to a certain gaussian process we show that the bootstrapped empirical process converges weakly to the same gaussian process almost surely assuming that the block length l for constructing bootstrap replicates satisfies l n o n 1 2 varepsilon 0 varepsilon frac 1 2 and l n rightarrow infty an example where the multivariate setup arises are the robust gm estimates in an autoregressive model we prove the asymptotic validity of the bootstrap approximation by showing that the functional associated with the gm estimates is frechet differentiable

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