time varying coefficients models for recurrent event data when different varying coefficients admit different degrees of smoothness application to heart disease modeling we consider a class of semiparametric marginal rate models for analyzing recurrent event data in these models both time varying and time free effects are present and the estimation of time varying effects may result in non smooth regression functions a typical approach for avoiding this problem and producing smooth functions is based on kernel methods the traditional kernel based approach however assumes a common degree of smoothness for all time varying regression functions which may result in suboptimal estimators if the functions have different levels of smoothness in this paper we extend the traditional approach by introducing different bandwidths for different regression functions first we establish the asymptotic properties of the suggested estimators next we demonstrate the superiority of our proposed method using two finite sample simulation studies finally we illustrate our methodology by analyzing a real world heart disease dataset copyright 2016 john wiley sons ltd

bootstrap validity for the score test when instruments may be weak it is well known that size adjustments based on bootstrapping the t statistic perform poorly when instruments are weakly correlated with the endogenous explanatory variable in this paper we provide a theoretical proof that guarantees the validity of the bootstrap for the score statistic this theory does not follow from standard results since the score statistic is not a smooth function of sample means and some parameters are not consistently estimable when the instruments are uncorrelated with the explanatory variable

a dual element based geometric element transformation method for all hexahedral mesh smoothing abstract due to their increased complexity hexahedral elements are more challenging with respect to mesh generation and mesh improvement techniques than tetrahedral elements in particular there is a lack of geometry based all hexahedral smoothing methods for mesh quality improvement being easy to implement practicable and efficient the recently introduced geometric element transformation method represents a new promising element oriented smoothing concept to resolve this deficiency by giving a dual octahedron based regularizing transformation this new approach is adapted in order to smooth all hexahedral meshes first numerical tests indicate that the resulting smoothing method yields high quality results at least comparable to those of a state of the art global optimization based approach while being significantly faster

automatic mesh generation over intersecting surfaces a fully automatic general scheme is proposed to determine and analyse the intersections between two groups of surfaces composed of triangular facets by carefully maintaining the spatial position of the lines of intersection in regenerating mesh locally around surface intersections pieces of surfaces can be arbitrarily combined and merged a great variety of objects can be easily created by selectively putting together different surface parts derived from surface intersections the new algorithm is best applied in conjunction with an existing surface mesh generator to enhance its general capability in dealing with objects built from intersecting surfaces in fact it is a powerful surface mesh manipulator and through the repeated use of the process complex structures can be rapidly and accurately constructed

testing and estimating shape constrained nonparametric density and regression in the presence of measurement error in many applications we can expect that or are interested to know if a density function or a regression curve satisfies some specific shape constraints for example when the explanatory variable x represents the value taken by a treatment or dosage the conditional mean of the response y is often anticipated to be a monotone function of x indeed if this regression mean is not monotone in the appropriate direction then the medical or commercial value of the treatment is likely to be significantly curtailed at least for values of x that lie beyond the point at which monotonicity fails in the case of a density common shape constraints include log concavity and unimodality if we can correctly guess the shape of a curve then nonparametric estimators can be improved by taking this information into account addressing such problems requires a method for testing the hypothesis that the curve of interest satisfies a shape constraint and if the conclusion of the test is positive a technique for e

on the conservativity of the functor assigning to a motivic spectrum its motive given a 0 connective motivic spectrum e is an element of sh k over a perfect field k we determine h under bar 0 of the associated motive me is an element of dm k in terms of pi under bar 0 e using this we show that if k has finite 2 etale cohomological dimension then the functor m w sh k dm k is conservative when restricted to the subcategory of compact spectra and induces an injection on picard groups we extend the conservativity result to fields of finite virtual 2 etale cohomological dimension by considering what we call real motives

testing additivity in generalized nonparametric regression models with estimated parameters we develop several kernel based consistent tests of an hypothesis of additivity in nonparametric regression we allow for discrete covariates and parameters estimated from a semiparametric gmm criterion function the additivity hypothesis is of interest because it delivers interpretability and reasonably fast convergence rates for nonparametric estimators the asymptotic distribution of the parameter estimators are found we also derive the asymptotic distribution of the additivity test statistics under a sequence of local alternatives we give a ranking of the different tests based on local asymptotic power the practical performance is investigated through simulations based on the data set used in linton and hardle 1996

nonparametric bootstrap confidence intervals for discrete regression functions abstract this is a study of a binary response bootstrap for constructing confidence intervals in a nonparametric setup some first order asymptotic results are proved for this method which hold true when generalizing to the multinomial case this method is illustrated by means of an application to real medical data

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

a fast resample method for parametric and semiparametric models abstract we propose a fast resample method for two step nonlinear parametric and semiparametric models which does not require recomputation of the second stage estimator during each resample iteration the fast resample method directly exploits the score function representations computed on each bootstrap sample thereby reducing computational time considerably this method is used to approximate the limit distribution of parametric and semiparametric estimators possibly simulation based that admit an asymptotic linear representation monte carlo experiments demonstrate the desirable performance and vast improvement in the numerical speed of the fast bootstrap method

wild bootstrap for quantile regression the existing theory of the wild bootstrap has focused on linear estimators in this note we broaden its validity by providing a class of weight distributions that is asymptotically valid for quantile regression estimators as most weight distributions in the literature lead to biased variance estimates for nonlinear estimators of linear regression we propose a modification of the wild bootstrap that admits a broader class of weight distributions for quantile regression a simulation study on median regression is carried out to compare various bootstrap methods with a simple finite sample correction the wild bootstrap is shown to account for general forms of heteroscedasticity in a regression model with fixed design points

bootstrap confidence regions for the intensity of a poisson point process abstract bootstrap methods are developed for constructing confidence regions for the intensity function of a nonstationary poisson process several different resampling algorithms are suggested ranging from resampling a poisson process with intensity equal to that estimated nonparametrically from the data to resampling the data points themselves in the same manner that the bootstrap is used in problems involving independent and identically distributed observations for each different bootstrap method various percentile t ways of constructing confidence bands are described the effectiveness of these different approaches is demonstrated both theoretically and numerically for real and simulated data issues such as bias correction are addressed

rate of convergence for the wild bootstrap in nonparametric regression this paper concerns the distributions used to construct confidence intervals for the regression function in a nonparametric setup some rates of convergence for the normal limit its plug in approach and the wild bootstrap are obtained conditionally on the explanatory variable x and also unconditionally the bound found for the wild bootstrap approximation is slightly better by a factor n 1 45 than the bounds given by the plug in approach or the clt for the conditional probability on the contrary the unconditional bounds present a different feature the rate obtained when approximating by the clt improves the one given by the plug in approach by a factor of n8 45 while this last one performs better than the wild bootstrap approximation and the corresponding ratio is n1 45 it should be mentioned that these two sequences especially the last one tend to zero at an extremely slow rate

bootstrapping regression models the regression and correlation models are considered it is shown that the bootstrap approximation to the distribution of the least squares estimates is valid and some error bounds are given

ultimate robustness in meshing an arbitrary polyhedron given a boundary surface mesh a set of triangular facets of a polyhedron the problem of deciding whether or not a triangulation exists is reported to be np hard in this paper an algorithm to triangulate a general polyhedron is presented which makes use of a classical delaunay triangulation algorithm a phase for recovering the missing boundary facets by means of facet partitioning and a final phase that makes it possible to remove the additional points defined in the previous step following this phase the resulting mesh conforms to the given boundary surface mesh the proposed method results in a discussion of theoretical interest about existence and complexity issues in practice however the method should provide what we call ultimate robustness in mesh generation methods copyright 2003 john wiley sons ltd

autoregressive wild bootstrap inference for nonparametric trends in this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend the bootstrap method is easy to implement and does not require any adjustments in the presence of missing data which makes it particularly suitable for climatological applications we establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions allowing for general patterns of missing data serial dependence and heteroskedasticity the finite sample properties of the method are studied in a simulation study we use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the swiss alps where the method can easily deal with the many missing observations due to adverse weather conditions

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

simultaneous confidence bands for linear regression and smoothing suppose we observe y i f x i varepsilon i i 1 ldots n we wish to find approximate 1 alpha simultaneous confidence regions for f x x in mathscr x our regions will be centered around linear estimates hat f x of nonparametric or nonparametric f x there is a large amount of previous work on this subject substantial restrictions have been usually placed on some or all of the dimensionality of x the class of functions f that can be considered the class of linear estimates hat f and the region mathscr x the method we present is an approximation to the tube formula dn can be used for multidimensional x and a wide class of linear estimates by considering the effect of bias we are able to relax assumptions on the class of functions f which are considered simultaneous and numerical computations are used to illustrate the performance

free knot polynomial splines with confidence intervals the estimates of knot locations and coefficients are obtained through a non linear least squares solution that corresponds to the maximum likelihood estimate confidence intervals are then constructed based on the asymptotic distribution of the maximum likelihood estimator average coverage probabilities and the accuracy of the estimate are examined via simulation this includes comparisons between our method and some existing methods such as smoothing spline and variable knots selection as well as a bayesian version of the variable knots method simulation results indicate that our method works well for smooth underlying functions and also reasonably well for discontinuous functions it also performs well for fairly small sample sizes

a bootstrap based on the estimating equations of the linear model summary this paper presents a method of bootstrap estimation for the linear model rather than resampling from the original sample as is conventional the proposed method resamples summands in an estimating function used to produce the original estimate the method is computationally simpler then existing competitors however its main advantage lies in the robustness to heteroscedasticity of the estimators it produces these estimators are shown to have desirable asymptotic properties under fairly general conditions a simulation study provides small sample support for the new method

markov chain marginal bootstrap markov chain marginal bootstrap mcmb is a new method for constructing confidence intervals or regions for maximum likelihood estimators of certain parametric models and for a wide class of m estimators of linear regression the mcmb method distinguishes itself from the usual bootstrap methods in two important aspects it involves solving only one dimensional equations for parameters of any dimension and produces a markov chain rather than a conditionally independent sequence it is designed to alleviate computational burdens often associated with bootstrap in high dimensional problems the validity of mcmb is established through asymptotic analyses and illustrated with empirical and simulation studies for linear regression and generalized linear models

mixture of regression models with varying mixing proportions a semiparametric approach in this article we study a class of semiparametric mixtures of regression models in which the regression functions are linear functions of the predictors but the mixing proportions are smoothing functions of a covariate we propose a one step backfitting estimation procedure to achieve the optimal convergence rates for both regression parameters and the nonparametric functions of mixing proportions we derive the asymptotic bias and variance of the one step estimate and further establish its asymptotic normality a modified expectation maximization type em type estimation procedure is investigated we show that the modified em algorithms preserve the asymptotic ascent property numerical simulations are conducted to examine the finite sample performance of the estimation procedures the proposed methodology is further illustrated via an analysis of a real dataset

confidence bands in nonparametric regression abstract new bias corrected confidence bands are proposed for nonparametric kernal regression these bands are constructed using only a kernel estimator of the regression curve and its data selected bandwidth they are shown to have asymptotically correct coverage properties and to behave well in a small sample study one consequence of the large sample developments is that bonferroni type bands for the regression curve at the design points also have conservative asymptotic coverage behavior with no bias correction

sizer for exploration of structures in curves abstract in the use of smoothing methods in data analysis an important question is which observed features are really there as opposed to being spurious sampling artifacts an approach is described based on scale space ideas originally developed in the computer vision literature assessment of significant zero crossings of derivatives results in the sizer map a graphical device for display of significance of features with respect to both location and scale here scale means level of resolution that is bandwidth

confidence bands in generalized linear models generalized linear models glm include many useful models this paper studies simultaneous confidence regions for the mean response function in these models the coverage probabilities of these regions are related to tail probabilities of maxima of gaussian random fields asymptotically and hence the so called tube formula is applicable without any modification however in the generalized linear models the errors are often non additive and non gaussian and may be discrete this poses a challenge to the accuracy of the approximation by the tube formula in the moderate sample situation here two alternative approaches are considered these approaches are based on an edgeworth expansion for the distribution of a maximum likelihood estimator and a version of skorohod s representation theorem which are used to convert an error term which is of order n 1 2 in one sided confidence regions and of n 1 in two sided confidence regions from the edgeworth expansion to a bias term the bias is then estimated and corrected in two ways to adjust the approximation formula examples and simulations show that our methods are viable and complementary to existing methods an application to insect data is provided code for implementing our procedures is available via the software parfit

an adaptation theory for nonparametric confidence intervals a nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals a between class modulus of continuity captures the expected length of adaptive confidence intervals sharp lower bounds are given for the expected length and an ordered modulus of continuity is used to construct adaptive confidence procedures which are within a constant factor of the lower bounds in addition minimax theory over nonconvex parameter spaces is developed

boundary recovery after 3d delaunay tetrahedralization without adding extra nodes in this paper we investigate boundary recovery the problem that has troubled researchers ever since delaunay based methods were applied to generate mesh there are a number of algorithms for boundary recovery already and most of them depend heavily on adding extra nodes in this paper we make an effort to seek a method to recover boundaries without using extra nodes it was noted that some previous algorithms imposed artificial boundary constraints on a meshing problem at the recovering stage we first try to discard these artificial constraints and thus make things easier then a new method is proposed by which the boundaries can be recovered by means of two operations 1 creating a segment in the mesh and 2 removing a segment from the mesh both operations are special cases of a general local transformation called small polyhedron reconnection operation the method works well when coupled with the sphere packing method proposed by the first author if the mesh sizing function is suitable a good configuration of nodes will be created accordingly by the sphere packing method and the boundary can be recovered by the local transformation presented here without inserting extra nodes

effect of bias estimation on coverage accuracy of bootstrap confidence intervals for a probability density tion and so bias must be corrected by other means when the bootstrap is used to construct confidence intervals for a probability density bias may either be estimated explicitly or allowed for by undersmoothing the curve estimator which of these two approaches is to be preferred in the present paper we address this question from the viewpoint of coverage accuracy assuming a given number of derivatives of the unknown density we conclude that the simpler undersmoothing method is more efficacious undersmoothing also has advantages from the standpoint of minimizing interval width we derive formulae for bandwidths which are optimal in terms of coverage accuracy and also give formulae for the coverage error which results from using those bandwidths 1 introduction the bootstrap can be a notoriously poor estimator of bias in problems of nonparametric curve estimation e g 5 and this fact should be taken into account when using bootstrap methods to construct confidence intervals bias is usually significant when a curve estimator is constructed so as to minimize mean squared error but decreases as the amount of statistical smoothing is reduced therefore one way of alleviating bias is to smooth the curve estimator less than would be appropriate for point estimation as opposed to interval estimation a statistician must either estimate bias explicitly or allow for bias by undersmoothing the curve estimator which of these two methods is to be preferred in this paper we address this problem in the case of nonparametric density estimation and from the viewpoint of coverage error we use the percentile t approach to confidence interval construction and show that in a sense which we shall make precise two paragraphs below the undersmoothing method produces confidence intervals with greater coverage accuracy than those obtained by explicit bias correction l l f x nh h for the density estimator based on kernel k and bandwidth h let b and o2

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

regression smoothing parameters that are not far from their optimum abstract it is well known that data driven regression smoothing parameters based on cross validation and related methods exhibit a slow rate of convergence to their optimum in an earlier article we showed that this rate can be as slow as n 1 10 that is for a bandwidth 0 optimizing the averaged squared error n 1 10 0 0 tends to an asymptotic normal distribution in this article we consider mean averaged squared error optimal bandwidths h 0 this nonrandom smoothing parameter can be approximated much faster we use the technique of double smoothing to show that there is an such that under certain conditions n 1 2 h 0 h 0 tends to an asymptotic normal distribution

bootstrap of residual processes in regression to smooth or not to smooth summaryin this paper we consider regression models with centred errors independent of the covariates given independent and identically distributed data and given an estimator of the regression function which can be parametric or nonparametric in nature we estimate the distribution of the error term by the empirical distribution of estimated residuals to approximate the distribution of this estimator koul lahiri 1994 and neumeyer 2009 proposed bootstrap procedures based on smoothing the residuals before drawing bootstrap samples so far it has been an open question as to whether a classical nonsmooth residual bootstrap is asymptotically valid in this context here we solve this open problem and show that the nonsmooth residual bootstrap is consistent we illustrate the theoretical result by means of simulations which demonstrate the accuracy of this bootstrap procedure for various models testing procedures and sample sizes

nonparametric bootstrap analysis with applications to demographic effects in demand functions abstract a new bootstrap proposal labeled smooth conditional moment scm bootstrap is introduced for independent but not necessarily identically distributed data where the classical bootstrap procedure fails the procedure is shown to encompass the iid and wild bootstrap procedures as special cases the scm bootstrap is applied to the construction of confidence intervals for nonparametric equivalence scales estimates and of critical values for consistent nonparametric test statistics in both cases the bootstrap approximations to the small sample properties are usually far superior to those provided by the first order asymptotic approximations

asymptotic confidence regions for kernel smoothing of a varying coefficient model with longitudinal data abstract we consider the estimation of the k 1 dimensional nonparametric component t of the varying coefficient model y t x t t t e t based on longitudinal observations yij x i tij tij i 1 n j 1 ni where tij is the jth observed design time point t of the ith subject and yij and x i tij are the real valued outcome and r k 1 valued covariate vectors of the ith subject at tij the subjects are independently selected but the repeated measurements within subject are possibly correlated asymptotic distributions are established for a kernel estimate of t that minimizes a local least squares criterion these asymptotic distributions are used to construct a class of approximate pointwise and simultaneous confidence regions for t applying these methods to an epidemiological study we show that our procedures are useful for predicting cd4 t helper lymphocytes cell changes among hiv human immunodeficiency virus infected persons the finite sample properties of o

fast delaunay triangulation in three dimensions abstract an efficient algorithm for delaunay triangulation of a given set of points in three dimensions based on the point insertion technique is presented various steps of the triangulation algorithm are reviewed and many acceleration procedures are devised to speed up the triangulation process new features include the search of a neighbouring point by the layering scheme locating the containing tetrahedron by random walk formulas of important geometrical quantities of a new tetrahedron based on those of an existing one a novel approach in establishing the adjacency relationship the use of adjacency table and the management of memory the resulting scheme is one of the fastest triangulation algorithms known to the authors which is able to generate tetrahedra generation rate of 15 000 tetrahedra per second for randomly generated points on a hp 735 machine

delaunay triangulation of non convex planar domains this paper investigates the possibility of integrating the two currently most popular mesh generation techniques namely the method of advancing front and the delaunay triangulation algorithm the merits of the resulting scheme are its simplicity efficiency and versatility with the introduction of non delaunay line segments the concept of using delaunay triangulation as a means of mesh generation is clarified an efficient algorithm is proposed for the construction of delaunay triangulations over non convex planar domains interior nodes are first generated within the planar domain these interior nodes and the boundary nodes are then linked up together to produce a valid triangulation in the mesh generation process the delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle in contrast to convex domains intersection between the proposed triangle and the domain boundary has to be checked this can be simply done by considering only the non delaunay segments on the generation front through the study of numerous examples of various characteristics it is found that high quality triangular element meshes are obtained by the proposed algorithm and the mesh generation time bears a linear relationship with the number of elements nodes of the triangulation

bootstrapping neural networks knowledge about the distribution of a statistical estimator is important for various purposes such as the construction of confidence intervals for model parameters or the determination of critical values of tests a widely used method to estimate this distribution is the so called boot strap which is based on an imitation of the probabilistic structure of the data generating process on the basis of the information provided by a given set of random observations in this article we investigate this classical method in the context of artificial neural networks used for estimating a mapping from input to output space we establish consistency results for bootstrap estimates of the distribution of parameter estimates

bootstrapping robust estimates of regression we introduce a new computer intensive method to estimate the distribution of robust regression estimates the basic idea behind our method is to bootstrap a reweighted representation of the estimates to obtain a bootstrap method that is asymptotically correct we include the auxiliary scale estimate in our reweighted representation of the estimates our method is computationally simple because for each bootstrap sample we only have to solve a linear system of equations the weights we use are decreasing functions of the absolute value of the residuals and hence outlying observations receive small weights this results in a bootstrap method that is resistant to the presence of outliers in the data the breakdown points of the quantile estimates derived with this method are higher than those obtained with the bootstrap we illustrate our method on two datasets and we report the results of a monte carlo experiment on confidence intervals for the parameters of the linear model

edgeworth expansions for bootstrapping regression models on etudie la performance asymptotique de la methode bootstrap dans des modeles de regression lineaire des expansions d edgeworth montrent que la methode bootstrap est asymptotiquement toujours au moins aussi bonne et dans certains cas meilleure que l approximation normale classique les performances de l approximation normale et du bootstrap dependent du taux de croissance dans les elements de la matrice plan

an assumption free exact test for fixed design linear models with exchangeable errors we propose the cyclic permutation test cpt to test general linear hypotheses for linear models this test is non randomized and valid in finite samples with exact type i error alpha for an arbitrary fixed design matrix and arbitrary exchangeable errors whenever 1 alpha is an integer and n p ge 1 alpha 1 the test involves applying the marginal rank test to 1 alpha linear statistics of the outcome vector where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a non standard cyclic permutation group under the null hypothesis the power can be further enhanced by solving a secondary non linear travelling salesman problem for which the genetic algorithm can find a reasonably good solution extensive simulation studies show that the cpt has comparable power to existing tests when testing for a single contrast of coefficients an exact confidence interval can be obtained by inverting the test furthermore we provide a selective yet extensive literature review of the century long efforts on this problem highlighting the novelty of our test

an algorithm for the intersection of quadrilateral surfaces by tracing of neighbours the use of discrete data to represent engineering structures as derivatives from intersecting components requires algorithms to perform boolean operations between groups of quadrilateral and triangular surfaces in the intersection process an accurate and efficient method for the determination of intersection lines is a crucial step for large scale and complex surface intersections an algorithm based on tracing the neighbours of intersecting quadrilaterals is proposed to determine the intersection lines a background grid is employed to limit the scope of searching for candidate quadrilaterals that may intersect this will drastically cut down the time of geometrical check for intersections between quadrilaterals making the surface intersection and mesh generation a quasi linear process with respect to the number of elements involved given the node numbers at the vertices of the candidate quadrilaterals the neighbour relationship is then established in the determination of intersection each quadrilateral is divided into two triangles and four fundamental cases are identified and treated systematically to enhance robustness and reliability tracing the neighbours for the determination of intersection lines not only greatly increases the efficiency of the process it also improves the reliability as branching and degenerated cases can all be dealt with in a consistent manner on the intersecting surfaces concerned examples on a great variety of surface and mesh characteristics are given to demonstrate the effectiveness and robustness of the algorithm

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

the geometric element transformation method for tetrahedral mesh smoothing the geometric element transformation method getme has been introduced as a new element driven approach to mesh smoothing it is based on simple geometric transformations which if applied iteratively lead to the regularization of mesh elements global mesh smoothing can be accomplished by successively improving the worst elements or by averaging node positions obtained by the simultaneous transformation of all elements getme smoothing has been successfully applied in the case of surface meshes as shown in this paper this approach also naturally extends to tetrahedral mesh smoothing without major conceptual modifications a regularizing transformation for tetrahedra is presented and a combined approach of simultaneous and sequential getme smoothing is described first numerical examples yield high quality meshes superior to those obtained by other geometry based methods in fact the presented results are in a majority of cases at least comparable to those obtained by a state of the art global optimization based method

edgeworth approximations for semiparametric instrumental variable estimators and test statistics abstract we establish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable estimator considered in newey econometrica 58 1990 809 as well as to the distribution of a wald statistic derived from it we employ local polynomial smoothing with variable bandwidth which includes local linear kernel and a version of nearest neighbor estimates as special cases our expansions are valid to order n 2e for some 0

constructing a bootstrap confidence interval for the unknown concentration in radioimmunoassay the statistical problem associated with radioimmunoassay is known as calibration or inverse regression in the current study we propose a bootstrap procedure aimed at constructing an inverse confidence interval for the univariate calibration problem the calibration curve is estimated either parametrically or by non parametric regression the methods are illustrated by an example

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

a simple bootstrap method for constructing nonparametric confidence bands for functions standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators to overcome this problem it is common practice to either undersmooth so as to reduce the impact of bias or oversmooth and thereby introduce an explicit or implicit bias estimator however these approaches and others based on nonstandard smoothing methods complicate the process of inference for example by requiring the choice of new unconventional smoothing parameters and in the case of undersmoothing producing relatively wide bands in this paper we suggest a new approach which exploits to our advantage one of the difficulties that in the past has prevented an attractive solution to the problem the fact that the standard bootstrap bias estimator suffers from relatively high frequency stochastic error the high frequency together with a technique based on quantiles can be exploited to dampen down the stochastic error term leading to relatively narrow simple to construct confidence bands

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

a feature preserving volumetric technique to merge surface triangulations several extensions and improvements to surface merging procedures based on the extraction of iso surfaces from a distance map defined on an adaptive background grid are presented the main objective is to extend the application of these algorithms to surfaces with sharp edges and corners in order to deal with objects of different length scales the initial background grids are created using a delaunay triangulation method and local voxelizations a point enrichment technique that introduces points into the background grid along detected surface features such as ridges is used to ensure that these features are preserved in the final merged surface the surface merging methodology is extended to include other boolean operations between surface triangulations the iso surface extraction algorithms are modified to obtain the correct iso surface for multi component objects the procedures are demonstrated with various examples ranging from simple geometrical entities to complex engineering applications the present algorithms allow realistic modelling of a large number of complex engineering geometries using overlapping components defined discretely i e via surface triangulations this capability is very useful for grid generation starting from data originated in measurements or images copyright 2002 john wiley sons ltd

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

automatic merging of tetrahedral meshes summary a generic algorithm is proposed to merge arbitrary solid tetrahedral meshes automatically into one single valid finite element mesh the intersection segments in the form of distinct nonoverlapping loops between the boundary surfaces of the given solid objects are determined by the robust neighbor tracing technique each intersected triangle on the boundary surface will be triangulated to incorporate the intersection segments onto the boundary surface of the objects the tetrahedra on the boundary surface associated with the intersected triangular facets are each divided into as many tetrahedra as the number of subtriangles on the triangulated facet there is a natural partition of the boundary surfaces of the solid objects by the intersection loops into a number of zones volumes of intersection can now be identified by collected bounding surfaces from the surface patches of the partition whereas mesh compatibility has already been established on the boundary of the solid objects mesh compatibility has yet to be restored on the bounding surfaces of the regions of intersection tetrahedra intersected by the cut surfaces are removed and new tetrahedra can be generated to fill the volumes bounded by the cut surfaces and the portion of cavity boundary connected to the cut surfaces to restore mesh compatibility at the cut surfaces upon restoring compatibility on the bounding surfaces of the regions of intersection the objects are ready to be merged together as all regions of intersection can be detached freely from the objects all operations besides the determination of intersections structurally in the form of loops are virtually topological and no parameter and tolerance is needed in the entire merging process examples are presented to show the steps and the details of the mesh merging procedure copyright 2012 john wiley sons ltd

prepivoting by weighted bootstrap iteration summary prepivoting by conventional bootstrap iteration is known to yield a progressively more accurate pivot in certain problems and has important application in the construction of confidence limits and estimation of null distributions we investigate the theoretical effects of weighted bootstrap iteration on prepivoting and show that each weighted bootstrap iteration with weights chosen carefully but empirically is asymptotically equivalent to two consecutive conventional bootstrap iterations in terms of reducing the order of error prepivoting can therefore be carried out much more efficiently if based on weighted boot

adaptive confidence bands we show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions we propose instead to construct adaptive bands that cover a surrogate function f which is close to but simpler than f the surrogate captures the significant features in f we establish lower bounds on the width for any confidence band for f and construct a procedure that comes within a small constant factor of attaining the lower bound for finite samples

estimation and inference in generalized additive coefficient models for nonlinear interactions with high dimensional covariates in the low dimensional case the generalized additive coefficient model gacm proposed by xue and yang statist sinica16 2006 1423 1446 has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables in this paper we propose estimation and inference procedures for the gacm when the dimension of the variables is high specifically we propose a groupwise penalization based procedure to distinguish significant covariates for the large p small n setting the procedure is shown to be consistent for model structure identification further we construct simultaneous confidence bands for the coefficient functions in the selected model based on a refined two step spline estimator we also discuss how to choose the tuning parameters to estimate the standard deviation of the functional estimator we adopt the smoothed bootstrap method we conduct simulation experiments to evaluate the numerical performance of the proposed methods and analyze an obesity data set from a genome wide association study as an illustration

bootstrap simultaneous error bars for nonparametric regression simultaneous error bars are constructed for nonparametric kernel estimates of regression functions the method is based on the bootstrap where resampling is done from a suitably estimated residual distribution the error bars are seen to give asymptotically correct coverage probabilities uniformly over any number of gridpoints applications to an economic problem are given and comparison to both pointwise and bonferroni type bars is presented through a simulation study

on bootstrap confidence intervals in nonparametric regression priate in this paper we point out some of the theoretical advantages of pivoting they include a reduction in the error of the bootstrap distribution function estimate from n 1 2 to n lh 1 2 where h denotes bandwidth and a reduction in coverage error of confidence intervals from either n l 1 2h 1 2 or n 1 2h1 2 depending on which nonpivotal method is used to n 1 several comparisons are drawn with the case of nonparametric density estimation where a pivotal approach also reduces errors associated with confidence intervals but where the orders of magnitude of the respective errors are quite different from their counterparts for nonparametric regression

robust analysis of semiparametric renewal process models a rate model is proposed for a modulated renewal process comprising a single long sequence where the covariate process may not capture the dependencies in the sequence as in standard intensity models we consider partial likelihood based inferences under a semiparametric multiplicative rate model which has been widely studied in the context of independent and identical data under an intensity model gap times in a single long sequence may be used naively in the partial likelihood with variance estimation utilizing the observed information matrix under a rate model the gap times cannot be treated as independent and studying the partial likelihood is much more challenging we employ a mixing condition in the application of limit theory for stationary sequences to obtain consistency and asymptotic normality the estimator s variance is quite complicated owing to the unknown gap times dependence structure we adapt block bootstrapping and cluster variance estimators to the partial likelihood simulation studies and an analysis of a semiparametric extension of a popular model for neural spike train data demonstrate the practical utility of the rate approach in comparison with the intensity approach

confidence bands in nonparametric time series regression we consider nonparametric estimation of mean regression and conditional variance or volatility functions in nonlinear stochastic regression models simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct the imposed dependence structure allows applications in many linear and nonlinear auto regressive processes the results are applied to the s p 500 index data

significance testing in nonparametric regression based on the bootstrap this paper proposes a test for selecting explanatory variables in nonparametric regression the test does not need to estimate the conditional expectation function given all the variables but only those which are significant under the null hypothesis this feature is computationally convenient and solves in part the problem of the curse of dimensionality when selecting regressors in a nonparametric context the proposed test statistic is based on functionals of a u process contiguous alternatives converging to the null at a rate n 1 2 can be detected the asymptotic null distribution of the statistic depends on certain features of the data generating process and asymptotic tests are difficult to implement except in rare circumstances we justify the consistency of two easy to implement bootstrap tests which exhibit good level accuracy for fairly small samples according to the reported monte carlo simulations these results are also applicable to test other interesting restrictions on nonparametric curves like partial linearity and conditional independence

confidence bands in non parametric errors in variables regression summary errors in variables regression is important in many areas of science and social science e g in economics where it is often a feature of hedonic models in environmental science where air quality indices are measured with error in biology where the vegetative mass of plants is frequently obscured by mismeasurement and in nutrition where reported fat intake is typically subject to substantial error to date in non parametric contexts the great majority of work has focused on methods for estimating the mean as a function with relatively little attention being paid to techniques for empirical assessment of the accuracy of the estimator we develop methodologies for constructing confidence bands our contributions include techniques for tuning parameter choice aimed at minimizing the coverage error of confidence bands

convergence analysis of generalized iteratively reweighted least squares algorithms on convex function spaces the computation of robust regression estimates often relies on minimization of a convex functional on a convex set in this paper we discuss a general technique for a large class of convex functionals to compute the minimizers iteratively which is closely related to majorization minimization algorithms our approach is based on a quadratic approximation of the functional to be minimized and includes the iteratively reweighted least squares algorithm as a special case we prove convergence on convex function spaces for general coercive and convex functionals f and derive geometric convergence in certain unconstrained settings the algorithm is applied to total variation tv penalized quantile regression and is compared with a step size corrected newton raphson algorithm it is found that typically in the first steps the iteratively reweighted least squares algorithm performs significantly better whereas the newton type method outpaces the former only after many iterations finally in the setting of bivariate regression with unimodality constraints we illustrate how this algorithm allows one to utilize highly efficient algorithms for special quadratic programs in more complex settings

simultaneous inference of linear models with time varying coefficients summary the paper considers construction of simultaneous confidence tubes for time varying regression coefficients in functional linear models using a gaussian approximation result for non stationary multiple time series we show that the constructed simultaneous confidence tubes have asymptotically correct nominal coverage probabilities our results are applied to the problem of testing whether the regression coefficients are of certain parametric forms which is a fundamental problem in the inference of functional linear models as an application we analyse an environmental data set and study the association between levels of pollutants and hospital admissions