existence results for operator equations in partially ordered sets and applications in this paper we prove existence results for operator equations in partially ordered sets and apply the obtained results to operator equations in ordered banach spaces and to semilinear functional parabolic and elliptic problems involving discontinuous nonlinearities

on matching cover of graphs a k matching cover of a graph g g is a union of k k matchings of g g which covers v g v g the matching cover number of g g denoted by mc g m c g is the minimum number k k such that g g has a k k matching cover a matching cover of g g is optimal if it consists of mc g m c g matchings of g g in this paper we present an algorithm for finding an optimal matching cover of a graph on n n vertices in o n 3 o n 3 time if use a faster maximum matching algorithm the time complexity can be reduced to o nm o n m where m e g m e g and give an upper bound on matching cover number of graphs in particular for trees a linear time algorithm is given and as a by product the matching cover number of trees is determined

bootstrap determination of the co integration rank in vector autoregressive models this paper discusses a consistent bootstrap implementation of the likelihood ratio lr co integration rank test and associated sequential rank determination procedure of johansen 1996 the bootstrap samples are constructed using the restricted parameter estimates of the underlying vector autoregressive var model that obtain under the reduced rank null hypothesis a full asymptotic theory is provided that shows that unlike the bootstrap procedure in swensen 2006 where a combination of unrestricted and restricted estimates from the var model is used the resulting bootstrap data are i 1 and satisfy the null co integration rank regardless of the true rank this ensures that the bootstrap lr test is asymptotically correctly sized and that the probability that the bootstrap sequential procedure selects a rank smaller than the true rank converges to zero monte carlo evidence suggests that our bootstrap procedures work very well in practice

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

testing for co integration in vector autoregressions with non stationary volatility abstract many key macroeconomic and financial variables are characterized by permanent changes in unconditional volatility in this paper we analyse vector autoregressions with non stationary unconditional volatility of a very general form which includes single and multiple volatility breaks as special cases we show that the conventional rank statistics computed as in johansen 1988 johansen 1991 are potentially unreliable in particular their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co integration tests as we demonstrate numerically a solution to the identified inference problem is provided by considering wild bootstrap based implementations of the rank tests these do not require the practitioner to specify a parametric model for volatility or to assume that the pattern of volatility is common to or independent across the vector of series under analysis the bootstrap is shown to perform very well in practice

forecasting the term structure of government bond yields despite powerful advances in yield curve modeling in the last 20 years comparatively little attention has been paid to the key practical problem of forecasting the yield curve in this paper we do so we use neither the no arbitrage approach nor the equilibrium approach instead we use variations on the nelson siegel exponential components framework to model the entire yield curve period by period as a three dimensional parameter evolving dynamically we show that the three time varying parameters may be interpreted as factors corresponding to level slope and curvature and that they may be estimated with high efficiency we propose and estimate autoregressive models for the factors and we show that our models are consistent with a variety of stylized facts regarding the yield curve we use our models to produce term structure forecasts at both short and long horizons with encouraging results in particular our forecasts appear much more accurate at long horizons than various standard benchmark forecasts r 2005 published by elsevier b v

bootstrap testing of hypotheses on co integration relations in vector autoregressive models it is well known that the finite sample properties of tests of hypotheses on the co integrating vectors in vector autoregressive models can be quite poor and that current solutions based on bartlett type corrections or bootstrap based on unrestricted parameter estimators are unsatisfactory in particular in those cases where also asymptotic 2 tests fail most severely in this paper we solve this inference problem by showing the novel result that a bootstrap test where the null hypothesis is imposed on the bootstrap sample is asymptotically valid that is not only does it have asymptotically correct size but in contrast to what is claimed in existing literature it is consistent under the alternative compared to the theory for bootstrap tests on the co integration rank cavaliere rahbek and taylor 2012 establishing the validity of the bootstrap in the framework of hypotheses on the co integrating vectors requires new theoretical developments including the introduction of multivariate ornstein uhlenbeck processes with random reduced rank drift parameters finally as documented by monte carlo simulations the bootstrap test outperforms existing methods

inference on co integration parameters in heteroskedastic vector autoregressions we consider estimation and hypothesis testing on the coefficients of the co integrating relations and the adjustment coefficients in vector autoregressions driven by shocks which display both conditional and unconditional heteroskedasticity of a quite general and unknown form we show that the conventional results in johansen 1996 for the maximum likelihood estimators and associated likelihood ratio tests derived under homoskedasticity do not in general hold under heteroskedasticity as a result standard confidence intervals and hypothesis tests on these coefficients are potentially unreliable solutions based on wald tests using a sandwich estimator of the variance matrix and on the use of the wild bootstrap are discussed these do not require the practitioner to specify a parametric model for volatility we establish the conditions under which these methods are asymptotically valid a monte carlo simulation study demonstrates that significant improvements in finite sample size can be obtained by the bootstrap over the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments an application to the term structure of interest rates in the us illustrates the difference between standard and bootstrap inferences regarding hypotheses on the co integrating vectors and adjustment coefficients

improved bounds for matroid partition and intersection algorithms we give bounds on total lengths of augmenting paths in standard implementations of the matroid partition and intersection algorithms and indicate how these observations can be used to improve the running times in certain applications for example for the matroid intersection algorithm on two r by n matrices the running time is shown to be o nr 2 log r we also give improved versions of the two algorithms when running times are measured in terms of calls to an independence oracle for example there is a matroid partition algorithm on o n n element matroids using o n 2 5 independence tests

inference when a nuisance parameter is not identified under the null hypothesis many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses this paper studies the asymptotic distribution theory for such tests the asymptotic distributions of standard test statistics are described as functionals of chi square processes in general the distributions depend upon a large number of unknown parameters we show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters and we show that this transformation can be easily approximated via simulation the theory is applied to threshold models with special attention given to the so called self exciting threshold autoregressive model monte carlo methods are used to assess the finite sample distributions the tests are applied to u s gnp growth rates and we find that potter s 1995 threshold effect in this series can be possibly explained by sampling variation

differential and integral equations with henstock kurzweil integrable functions abstract in this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing henstock kurzweil integrable functions

bootstrapping general empirical measures it is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions mathscr f and based on a probability measure p holds a s if and only if mathscr f in mathrm clt p and int f 2 dp infty where f sup f in mathscr f f and it holds in probability if and only if mathscr f in mathrm clt p thus for a large class of statistics no local uniformity of the clt about p is needed for the bootstrap to work consistency of the bootstrap the bootstrapped law of large numbers is also characterized these results are proved under certain weak measurability assumptions on mathscr f

bootstrap algorithms for testing and determining the cointegration rank in var models in this paper a bootstrap algorithm for a reduced rank vector autoregressive model with a restricted linear trend and independent identically distributed errors is analyzed for testing the cointegration rank the asymptotic distribution under the hypothesis is the same as for the usual likelihood ratio test so that the bootstrap is consistent it is furthermore shown that a bootstrap procedure for determining the rank is asymptotically consistent in the sense that the probability of choosing the rank smaller than the true one converges to zero

a monotone iterative technique for stationary and time dependent problems in banach spaces an abstract monotone iterative method is developed for operators between partially ordered banach spaces for the nonlinear problem lu nu and the nonlinear time dependent problem u l n u under appropriate assumptions on l and n we obtain maximal and minimal solutions as limits of monotone sequences of solutions of linear problems the results are illustrated by means of concrete examples

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

bootstrap and wild bootstrap for high dimensional linear models in this paper two bootstrap procedures are considered for the estimation of the distribution of linear contrasts and of f test statistics in high dimensional linear models an asymptotic approach will be chosen where the dimension p of the model may increase for sample size n rightarrow infty the range of validity will be compared for the normal approximation and for the bootstrap procedures furthermore it will be argued that the rates of convergence are different for the bootstrap procedures in this asymptotic framework this is in contrast to the usual asymptotic approach where p is fixed

sample splitting and threshold estimation threshold models have a wide variety of applications in economics direct applications include models of separating and multiple equilibria other applications include empirical sample splitting when the sample split is based on a continuously distributed variable such as firm size in addition threshold models may be used as a parsimonious strategy for nonparametric function estimation for example the threshold autoregressive model tar is popular in the nonlinear time series literature threshold models also emerge as special cases of more complex statistical frameworks such as mixture models switching models markov switching models and smooth transition threshold models it may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures despite the large number of potential applications the statistical theory of threshold estimation is undeveloped it is known that threshold estimates are super consistent but a distribution theory useful for testing and inference has yet to be provided this paper develops a statistical theory for threshold estimation in the regression context we allow for either cross section or time series observations least squares estimation of the regression parameters is considered an asymptotic distribution theory for the regression estimates the threshold and the regression slopes is developed it is found that the distribution of the threshold estimate is nonstandard a method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic it is shown that this yields asymptotically conservative confidence regions monte carlo simulations are presented to assess the accuracy of the asymptotic approximations the empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of durlauf and johnson 1995

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

properties of moments of a family of garch processes this paper considers the moments of a family of first order garch processes first a general condition for the existence of any integer moment of the absolute values of the observations is given second a general expression for this moment as a function of lower order moments is derived third the kurtosis and the autocorrelation function of the squared and absolute valued observations are derived the results apply to a number of different garch parameterizations finally the existence or lack thereof of the theoretical counterpart to the so called taylor effect in some members of this garch family is discussed possibilities of extending the results to higher order garch processes are indicated and potential applications of the statistical theory proposed

existence and comparison results for operator and differential equations in abstract spaces in this paper we apply the chain methods developed in heikkila and lakshmikantham 1994 to obtain new fixed point theorems and new existence and comparison results for operator equations in partially ordered sets these results are then applied to discontinuous implicit functional differential equations in ordered banach spaces

existence results for operator and differential equations and inclusions abstract this paper contains a brief summary of existence results for operator and differential equations and inclusions derived recently via a recursion method and generalized iteration methods introduced in 11 12 23

bootstrapping structural change tests this paper demonstrates the asymptotic validity of methods based on the wild recursive and wild fixed bootstraps for testing hypotheses about discrete parameter change in linear models estimated via two stage least squares the framework allows for the errors to exhibit conditional and or unconditional heteroscedasticity and for the reduced form to be unstable simulation evidence indicates the bootstrap tests yield reliable inferences in the sample sizes often encountered in macroeconomics if the errors exhibit unconditional heteroscedasticity and or the reduced form is unstable then the bootstrap methods are particularly attractive because the limiting distributions of the test statistics are not pivotal

fast matrix rank algorithms and applications we consider the problem of computing the rank of an m n matrix a over a field we present a randomized algorithm to find a set of r rank a linearly independent columns in o vav p r field operations where vav denotes the number of nonzero entries in a and

the wild bootstrap tamed at last the wild bootstrap is studied in the context of regression models with heteroskedastic disturbances we show that in one very specific case perfect bootstrap inference is possible and a substantial reduction in the error in the rejection probability of a bootstrap test is available much more generally however the version of the wild bootstrap with this desirable property is without the skewness correction afforded by the currently most popular version of the wild bootstrap simulation experiments show that this does not prevent the preferred version from having the smallest error in rejection probability in small and medium sized samples

existence results for operator equations in abstract spaces and an application in this paper we apply the recursion method presented in heikkila and lakshmikantham 1994 to derive fixed point theorems and existence results for operator equations in partially ordered sets the obtained results combined with related results of heikkila 2002 are then applied to operator equations in ordered hilbert spaces and to a functional elliptic boundary value problem

bootstrap procedures under some non i i d models it is shown in this article that the classical i i d bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location as long as the random observations are independently drawn from distributions with essentially a common location this may be viewed as a robust property of the classical i i d bootstrap also included is a study of the second order properties of a different bootstrap procedure proposed by wu in the context of heteroscedasticity in regression