goodness of fit tests for kernel regression with an application to option implied volatilities this paper proposes a test of a restrictedspeci cation of regression basedon comparing residual sum of squares from kernel regression our main case is where both the restrictedspeci cation andthe general mod el are nonparametric with our test equivalently viewed as a test of dimension reduction we discuss practical features of implementing the test andvariations applicable to testing parametric mod els as the null hypothesis or semiparametric models that depend on a nite parameter vector as well as unknown functions we apply our testing procedure to option prices we reject a parametric version of the black scholes formula but fail to reject a semiparametric version against a general nonparametric regression 2001 elsevier science s a all rights reserved jel classi cation c12 c14

testing single index restrictions with a focus on average derivatives abstract this paper considers a situation where the violation of a single index restriction is a concern only to the extent that it causes bias to the estimates of the average derivatives we propose a method to construct tests that concentrate their asymptotic powers upon only such interesting alternatives the test has a 1 2 limiting distribution under the null hypothesis and even accommodates the case where the parameter estimates have a convergence rate slower than n as in the case of maximum score estimation the testing procedure can be easily modified when the main interest lies in average increment effects of binary covariates multivariate average derivatives or linear restrictions other than those of average derivatives results from monte carlo experiments show that the asymptotic theory is a reasonable approximation of the finite sample distributions and an application of our methods to female labor market participation illustrates the importance of this non omnibus approach

bootstrap approximations in model checks for regression abstract let m m be a parametric model for an unknown regression function m for example m may consist of all polynomials or trigonometric polynomials with a given bound on the degree to check the full model m i e to test for h 0 m e m it is known that optimal tests should be based on the empirical process of the regressors marked by the residuals in this article we show that the distribution of this process may be approximated by the wild bootstrap the method is applied to simulated datasets as well as to real data

estimation for a partial linear single index model in this paper we study the estimation for a partial linear single index model a two stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index as well as the parameters in the linear component of the model asymptotic normality is established for both parametric components for the index a constrained estimating equation leads to an asymptotically more efficient estimator than existing estimators in the sense that it is of a smaller limiting variance the estimator of the nonparametric link function achieves optimal convergence rates and the structural error variance is obtained in addition the results facilitate the construction of confidence regions and hypothesis testing for the unknown parameters a simulation study is performed and an application to a real dataset is illustrated the extension to multiple indices is briefly sketched

a domain decomposition message passing approach to transient viscous incompressible flow using explicit time integration this paper discusses the design and implementation of solution algorithms suitable for performing transient incompressible viscous flow simulations on massively parallel computers the finite element formulation for incompressible flow along with the ad hoc modifications for explicit time integration are discussed with an emphasis on implementation aspects for achieving scalable parallel computations the issues associated with a domain decomposition message passing paradigm are presented in the context of explicit time integration and the solution of a pressure poisson equation using a staggered grid an element by element conjugate gradient algorithm for the pressure equation is outlined with a parallel sub domain preconditioner sample calculations are presented with scaled speedup and efficiency results to demonstrate the scalability of the domain decomposition message passing approach

identifiability of single index models and additive index models summary we provide a proof for the identifiability for both single index models and partially linear single index models assuming only the continuity of the regression function a condition much weaker than the differentiability conditions assumed in the existing literature our discussion is then extended to the identifiability of the additive index models

on the sphere decoding algorithm i expected complexity the problem of finding the least squares solution to a system of linear equations where the unknown vector is comprised of integers but the matrix coefficient and given vector are comprised of real numbers arises in many applications communications cryptography gps to name a few the problem is equivalent to finding the closest lattice point to a given point and is known to be np hard in communications applications however the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known therefore in this paper rather than dwell on the worst case complexity of the integer least squares problem we study its expected complexity averaged over the noise and over the lattice for the sphere decoding algorithm of fincke and pohst we find a closed form expression for the expected complexity both for the infinite and finite lattice it is demonstrated in the second part of this paper that for a wide range of signal to noise ratios snrs and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications

multi domain parallel computation of wake flows abstract we present a new multi domain parallel computational method for simulation of unsteady flows involving a primary object a long wake region and possibly a secondary object affected by the wake flow the method is based on the stabilized finite element formulation of the time dependent navier stokes equations of incompressible flows in the multi domain computational method the entire simulation domain is divided into an ordered sequence of overlapping subdomains the flow data computed over the leading subdomain is used for specifying the inflow boundary conditions for the next subdomain the subdomain corresponding to the wake would not involve any objects hence the mesh constructed over this domain would be structured a special purpose finite element implementation for structured meshes is used for the wake domain to achieve much higher computational speeds compared to a general purpose implementation we present verification studies for the multi domain method and special purpose implementation followed by two numerical examples the first example is the wake behavior behind a circular cylinder the second one is the aerodynamic effect of tip vortices released from a leading wing on a trailing wing placed in the far wake

testing the parametric null model hypothesis in semiparametric partial and generalized spline models on etend les resultats de cox et koh 1986 aux modeles generalises de wahba 1985 et a divers autres modeles splines partiels on montre que la statistique de test a une relation etroite avec le comportement de la fonction de validation croisee generalisee

direct estimation of the index coefficient in a single index model single index modeling is widely applied in for example econometric studies as a compromise between too restrictive parametric models and flexible but hardly estimable purely nonparametric models by such modeling the statistical analysis usually focuses on estimating the index coefficients the average derivative estimator ade of the index vector is based on the fact that the average gradient of a single index function f x t is proportional to the index vector unfortunately a straightforward application of this idea meets the so called curse of dimensionality problem if the dimensionality d of the model is larger than 2 however prior information about the vector can be used for improving the quality of gradient estimation by extending the weighting kernel in a direction of small directional derivative the method proposed in this paper consists of such iterative improvements of the original ade the whole procedure requires at most 2 log n iterations and the resulting estimator is n consistent under relatively mild assumptions on the model independently of the dimensionality d

testing parametric versus semiparametric modeling in generalized linear models abstract we consider a generalized partially linear model e y x t g x t m t where g is a known function is an unknown parameter vector and m is an unknown function we introduce a test statistic that allows one to decide between a parametric and a semiparametric model a m is linear i e m t t t for a parameter vector and b m is a smooth nonlinear function under linearity a we show that the test statistic is asymptotically normal moreover we prove that the bootstrap works asymptotically simulations suggest that in small samples the bootstrap outperforms the calculation of critical values from the normal approximation the practical performance of the test is demonstrated in applications to data on east west german migration and credit scoring

finite element stabilization matrices a unification approach abstract in this paper we show that the stabilization vector can be obtained naturally by taking the partial derivatives with respect to the natural coordinates hence the components of the strains and stresses can be expressed in terms of a set of orthogonal coordinates with these definitions of stresses and strains a general form of the finite element stabilization matrices is then constructed for underintegrated irregular shape and anisotropic elements the explicit expressions of the stabilization matrices for the 4 9 and 8 node laplace and continuum elements and the 4 node plate element are then derived from the general form these are sufficiently general for the developments herein the generalization of the stabilization matrices concept to nonlinear problems which usually require the numerical integration of a fairly general class of nonlinear finite deformation constitutive equations is also presented the computer implementation aspects and numerical evaluation of these stabilized elements are also considered numerical tests confirm the stability and accuracy characteristics of the resulting elements in particular the numerical experiments reported here also show that the rates of convergence in the l2 norm and in the energy norm agree well with the expected convergence rates

diagnostics for nonparametric regression models with additive terms abstract recent developments of multivariate smoothing methods provide a rich collection of feasible models for nonparametric multivariate data analysis among the most interpretable are models with additive terms construction of various models and algorithms for computing the models have been the main concern of the existing literature in this area few results are available on the validation of computed fits and many applications of nonparametric methods unfortunately end up interpreting the noise this article proposes and illustrates some simple retrospective diagnostics to help data analysts in detecting possible aliasing effects in computed nonparametric fits and in building parsimonious models in an interactive fashion it also discusses the concepts and rationale behind the proposal including concurvity diagnostics versus tests and so forth for their ready availability interaction splines are used in the illustrations

lattice reduction based approximate map detection with bit wise combining and integer perturbed list generation for iterative detection and decoding idd in multiple input multiple output mimo systems the log likelihood ratio llr of each coded bit can be found by an optimal bit wise maximum a posteriori probability map detector however since this map detector requires a prohibitively high computational complexity low complexity suboptimal detectors are desirable in this paper lattice reduction lr based mimo detection is investigated to derive a low complexity detector that can achieve near map performance for idd in order to approximate llr values incorporating the extrinsic information provided by a soft input soft output siso decoder bit wise lr based minimum mean square error mmse filters are derived furthermore in order to minimize the performance degradation due to quantization or rounding errors in the lr based detection a low complexity integer perturbed list generation method is proposed where no tree search is used by taking advantage of a near orthogonal channel basis obtained by lr through a complexity analysis and simulations it is shown that the proposed approach achieves near optimal performance while the complexity is comparable with that of the mmse soft cancellation method which is known to be computationally efficient as a bit wise detector a parallel implementation of the proposed method would be straightforward which lowers the detection delay

lattice reduction aided gibbs algorithm for lattice gaussian sampling convergence enhancement and decoding optimization sampling from the lattice gaussian distribution has emerged as an important problem in coding decoding and cryptography in this paper lattice reduction technique is adopted to gibbs sampler for lattice gaussian sampling first with respect to lattice gaussian distribution we show the convergence rate of systematic scan gibbs sampling is characterized by the hirschfeld gebelein renyi maximal correlation among the multivariate of being sampled then lattice reduction aided gibbs algorithm is proposed to sample from an equivalent lattice gaussian distribution but with less correlated multivariate thus leading to a better markov mixing after that we extend the proposed lattice reduction aided gibbs sampling to lattice decoding where the choice of the standard deviation for the sampling is fully investigated a customized solution that suits for each specific decoding case by euclidean distance is given which results in a better tradeoff between markov mixing and sampler decoding based on it a startup mechanism is also proposed for gibbs sampler decoding where decoding complexity can be reduced without performance loss moreover the recycling gibbs sampling that exploits the potential of samples is also considered to improve the decoding performance in lattice decoding simulation results based on large scale uncoded multiple input multiple output detection are presented to confirm the performance gain and complexity reduction

efficient linear and nonlinear heat conduction with a quadrilateral element a method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one point quadrature the stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter it is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values in fact the values 3 2 and 1 for the normalized stabilization parameter lead to the 5 point finite difference 9 point finite difference and fully integrated finite element operators respectively for rectangular meshes numerical experiments reported here show that the three have identical rates of convergence in the l2 norm eigenvalues of the element matrices which are needed for stability limits are also given numerical applications are used to show that the method yields accurate solutions with large increases in efficiency particularly in nonlinear problems

on the use of nonparametric regression for model checking summary the use of nonparametric regression is explored to check the fit of a parametric regression model the principal aim is to check the validity of the regression curve rather than necessarily to detect outliers a pseudo likelihood ratio test is developed to provide a global assessment of fit and simulation bands are used to indicate the nature of departures from the model the types of data considered include discrete response variables where standard diagnostic techniques are often not appropriate and first order autoregressive series several numerical examples are given nonparametric regression can be used in an informal graphical way to assess the relationship between a response and an explanatory variable in this paper we aim to develop more formal methods of assessing the assumptions of a parametric model in particular when regression diagnostics of the type developed for normal linear models are not readily available the principal aim is to check the validity of the systematic part of the model by comparing a nonparametric estimate of the regression curve with a parametric one such a comparison may also identify outliers although the distinction between outliers and model inadequacy is not always easy two techniques are used to assess the fit of a parametric model in 2 confidence bands are constructed around the fitted regression curve by simulation a comparison of these with the nonparametric curve gives an indication of the nature of any departures from the model in 3 a pseudo likelihood ratio test is developed this provides a quantitative global assessment of fit in applying these ideas special emphasis is given to discrete data and notably logistic regression because of the difficulty in applying standard residual based model checking techniques to this type of response variable a poisson regression example is discussed in 4 however the underlying ideas have wider applications autoregressive time series of order 1 are discussed in 6 sections 5 and 7 discuss general issues we first discuss the context of binary regression with a single covariate and the difficulties caused by the discreteness of the response variable the observed data are assumed to be of the form xi yi ni where xi is a covariate value and yi has a binomial

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response models

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

asymptotics for sliced average variance estimation in this paper we systematically study the consistency of sliced average variance estimation save the findings reveal that when the response is continuous the asymptotic behavior of save is rather different from that of sliced inverse regression sir sir can achieve sqrt n consistency even when each slice contains only two data points however save cannot be sqrt n consistent and it even turns out to be not consistent when each slice contains a fixed number of data points that do not depend on n where n is the sample size these results theoretically confirm the notion that save is more sensitive to the number of slices than sir taking this into account a bias correction is recommended in order to allow save to be sqrt n consistent in contrast when the response is discrete and takes finite values sqrt n consistency can be achieved therefore an approximation through discretization which is commonly used in practice is studied a simulation study is carried out for the purposes of illustration

nonparametric checks for single index models in this paper we study goodness of fit testing of single index models the large sample behavior of certain score type test statistics is investigated as a by product we obtain asymptotically distribution free maximin tests for a large class of local alternatives furthermore characteristic function based goodness of fit tests are proposed which are omnibus and able to detect peak alternatives simulation results indicate that the approximation through the limit distribution is acceptable already for moderate sample sizes applications to two real data sets are illustrated

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

linear functions of concomitants of order statistics with application to nonparametric estimation of a regression function abstract let xi yi i 1 2 n be independent identically distributed as x y then the rth ordered x variate is denoted by xr n and the associated y variate the concomitant of the rth order statistic by y r n this paper considers statistics of the form and more generally of the form where j is a bounded smooth function and may depend on n under certain regularity conditions the asymptotic normality of these statistics is established these statistics are used to construct consistent estimators of various conditional quantities for example e y x x p y a x x and var y x x

testing the goodness of fit of a linear model via nonparametric regression techniques abstract this article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model the large sample properties of parametric goodness of fit tests for linearity are considered the inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression large sample theory is derived for two variants of this type of statistic the results demonstrate that such tests are consistent against all fixed smooth alternatives to linearity but are incapable of detecting local alternatives converging to a linear model at the parametric rate n 1 2 simulation experiments involving a test based on fitting cubic smoothing splines to residuals reveals that this test has good power properties against several reasonable alternatives

decoding by sampling part ii derandomization and soft output decoding in this paper a derandomized algorithm for sampling decoding is proposed to achieve near optimal performance in lattice decoding by setting a probability threshold to sample candidates the whole sampling procedure becomes deterministic which brings considerable performance improvement and complexity reduction over to the randomized sampling moreover the upper bound on the sample size k which corresponds to near maximum likelihood ml performance is derived we also find that the proposed algorithm can be used as an efficient tool to implement soft output decoding in multiple input multiple output mimo systems an upper bound of the sphere radius r in list sphere decoding lsd is derived based on it we demonstrate that the derandomized sampling algorithm is capable of achieving near maximum a posteriori map performance simulation results show that near optimum performance can be achieved by a moderate size k in both lattice decoding and soft output decoding

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

diagnostic studies in sufficient dimension reduction sufficient dimension reduction in regression aims to reduce the predictor dimension by replacing the original predictors with some set of linear combinations of them without loss of information numerous dimension reduction methods have been developed based on this paradigm however little effort has been devoted to diagnostic studies within the context of dimension reduction in this paper we introduce methods to check goodness of fit for a given dimension reduction subspace the key idea is to extend the so called distance correlation to measure the conditional dependence relationship between the covariates and the response given a reduction subspace our methods require minimal assumptions which are usually much less restrictive than the conditions needed to justify the original methods asymptotic properties of the test statistic are studied numerical examples demonstrate the effectiveness of the proposed approach

testing conditional independence via rosenblatt transforms this paper proposes new tests of conditional independence of two random variables given a single index involving an unknown finite dimensional parameter the tests employ rosenblatt transforms and are shown to be distribution free while retaining computational convenience some results from monte carlo simulations are presented and discussed

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

low complexity soft output decoding with lattice reduction aided detectors lattice reduction lr techniques have been introduced to enhance the performance of linear equalizers by collecting diversity with low complexity for many transmission systems although lr aided linear detectors may collect the same diversity as that collected by the maximum likelihood ml detector there still exists a performance gap between lr aided and ml equalizers one approach to fill this gap is to adopt soft output detectors soft output detectors enable iterative decoding when error control codes are employed for a system in this paper we propose three lr aided soft output detectors with different methods to generate the candidate lists we compare the performance and complexity of our algorithms with the existing alternatives and show that our methods achieve better performance with lower complexity the performance complexity tradeoffs of our proposed algorithms are also studied iterative decoders are performed based on these soft output detectors in the simulations to validate the effectiveness of our algorithms

a partitioned model for fluid structure interaction problems using hexahedral finite elements with one point quadrature a partitioned numerical model for fluid structure interaction analysis of incompressible flows and structures with geometrically non linear behavior is presented in this work the flow analysis is performed considering the well known navier stokes equations for newtonian fluids and the continuity equation obtained from the pseudo compressibility hypothesis an explicit two step taylor galerkin scheme is employed in the time discretization procedure of the system of governing equations which is expressed in terms of an arbitrary lagrangean eulerian description the structural subsystem is analyzed using a geometrically non linear elastic model and the respective equation of motion is discretized in the time domain employing the generalized scheme fluid structure coupling is taken into account regarding a new energy conserving partitioned scheme with non linear effects which is accomplished by enforcing equilibrium and kinematical compatibility conditions at the solid fluid interface non matching meshes and subcycling are also considered in the present model the finite element method is employed for spatial discretizations using eight node hexahedral elements with one point integration in both fields some numerical examples are simulated in order to demonstrate the applicability of the proposed formulation copyright 2009 john wiley sons ltd

on the use of nonparametric regression for checking linear relationships summary the problem of checking the linearity of a regression relationship is addressed through the idea of smoothing of a residual plot a pseudolikelihood ratio test statistic which measures the distance between the nonparametric and the parametric models is derived as a ratio of quadratic forms the distribution of this statistic under the null hypothesis of linearity is calculated numerically by using johnson curves a power study shows the new statistic to be more sensitive to non linearity than the durbin watson statistic

model checks for regression an innovation process approach in the context of regression analysis it is known that the residual cusum process may serve as a basis for the construction of various omnibus smooth and directional goodness of fit tests since a deeper analysis requires the decomposition of the cusums into their principal components and this is difficult to obtain we propose to replace this process by its innovation martingale it turns out that the resulting tests are asymptotically distribution free under composite null models and may be readily performed a simulation study is included which indicates that the distributional approximations already work for small to moderate sample sizes

nonparametric monte carlo tests for multivariate distributions summary in this paper nonparametric monte carlo test procedures are proposed for composite hypotheses in which the multivariate distribution belongs to a nonparametric family when a random variable is in distribution equal to a product of two independent variables monte carlo simulations can be performed conditionally on one of the variables they can be applied to testing several commonly used distributions including elliptically symmetric reflectively symmetric liouville dirichlet and symmetric scale mixture distributions the tests are exactly valid when the hypothetical distributions are without nuisance location parameters finite sample simulations show that the monte carlo tests outperform bootstrap tests the method is illustrated with analysis of a real dataset

reduced and fixed complexity variants of the lll algorithm for communications the lenstra lenstra lovasz lll algorithm is a popular lattice reduction algorithm in communications in this paper variants of the lll algorithm with either reduced or fixed complexity are proposed and analyzed specifically the use of effective lll reduction for lattice decoding is presented where size reduction is only performed for pairs of consecutive basis vectors its average complexity measured by the number of floating point operations and averaged over i i d standard normal lattice bases is shown to be o n 3 log n where n is the lattice dimension this average complexity is an order lower than previously thought to address the issue of variable complexity of the lll algorithm two fixed complexity approximations are proposed one is fixed complexity effective lll for which the first vector of the basis is proven to be bounded in length the other is fixed complexity lll with deep insertion which is shown to be closely related to the well known v blast algorithm such fixed complexity structures are much desirable in hardware implementation since they allow straightforward constant throughput implementation

transforming a response variable for linearity summary we consider the problem of choosing a transformation t y of a univariate response variable y so that the regression function e t y jx is linear in the predictor vector x let y be the fitted values from a linear regression of y on x given a few simple assumptions we show that the plot with y on the horizontal axis and 9 on the vertical axis can be used to visualise the needed transformation t y a smoother can then be used as an aid to assessing t y visually