martingale transforms goodness of fit tests in regression models this paper discusses two goodness of fit testing problems the first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model while the second pertains to fitting a parametric regression model when the error distribution is unknown for the first problem the paper contains tests based on a certain martingale type transform of residual empirical processes the advantage of this transform is that the corresponding tests are asymptotically distribution free for the second problem the proposed asymptotically distribution free tests are based on innovation martingale transforms a monte carlo study shows that the simulated level of the proposed tests is close to the asymptotic level for moderate sample sizes

contour regression a general approach to dimension reduction we propose a novel approach to sufficient dimension reduction in regression based on estimating contour directions of small variation in the response these directions span the orthogonal complement of the minimal space relevant for the regression and can be extracted according to two measures of variation in the response leading to simple and general contour regression scr and gcr methodology in comparison with existing sufficient dimension reduction techniques this contour based methodology guarantees exhaustive estimation of the central subspace under ellipticity of the predictor distribution and mild additional assumptions while maintaining sqrt n consistency and computational ease moreover it proves robust to departures from ellipticity we establish population properties for both scr and gcr and asymptotic properties for scr simulations to compare performance with that of standard techniques such as ordinary least squares sliced inverse regression principal hessian directions and sliced average variance estimation confirm the advantages anticipated by the theoretical analyses we demonstrate the use of contour based methods on a data set concerning soil evaporation

a consistent nonparametric test of parametric regression functional form in fixed effects panel data models abstract we propose a consistent test for a linear functional form against a nonparametric alternative in a fixed effects panel data model we show that the test has a limiting standard normal distribution under the null hypothesis and show that the test is a consistent test we also establish the asymptotic validity of a bootstrap procedure which is used to better approximate the finite sample null distribution of the test statistic simulation results show that the proposed test performs well for panel data with a large number of cross sectional units and a finite number of observations across time

a consistent test for the functional form of a regression based on a difference of variance estimators in this paper we study the problem of testing the functional form of a given regression model a consistent test is proposed which is based on the difference of the least squares variance estimator in the assumed regression model and a nonparametric variance estimator the corresponding test statistic can be shown to be asymptotically normal under the null hypothesis and under fixed alternatives with different rates of convergence corresponding to both cases this provides a simple asymptotic test where the asymptotic results can also be used for the calculation of the type ii error of the procedure at any particular point of the alternative and for the construction of tests for precise hypotheses finally the finite sample performance of the new test is investigated in a detailed simulation study which also contains a comparison with the commonly used tests

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

a mixed binary non linear programming approach for the numerical solution of a family of singular optimal control problems abstractthis paper presents a new approach for the efficient solution of singular optimal control problems socps a novel feature of the proposed method is that it does not require a priori knowledge of the structure of solution at first the socp is converted into a binary optimal control problem then by utilising the pseudospectral method the resulting problem is transcribed to a mixed binary non linear programming problem this mixed binary non linear programming problem which can be solved by well known solvers allows us to detect the structure of the optimal control and to compute the approximating solution the main advantages of the present method are that 1 without a priori information the structure of optimal control is detected 2 it produces good results even using a small number of collocation points 3 the switching times can be captured accurately these advantages are illustrated through a numerical implementation of the method on four examples

a constructive approach to the estimation of dimension reduction directions in this paper we propose two new methods to estimate the dimension reduction directions of the central subspace cs by constructing a regression model such that the directions are all captured in the regression mean compared with the inverse regression estimation methods e g j amer statist assoc 86 1991 328 332 j amer statist assoc 86 1991 316 342 j amer statist assoc 87 1992 1025 1039 the new methods require no strong assumptions on the design of covariates or the functional relation between regressors and the response variable and have better performance than the inverse regression estimation methods for finite samples compared with the direct regression estimation methods e g j amer statist assoc 84 1989 986 995 ann statist 29 2001 1537 1566 j r stat soc ser b stat methodol 64 2002 363 410 which can only estimate the directions of cs in the regression mean the new methods can detect the directions of cs exhaustively consistency of the estimators and the convergence of corresponding algorithms are proved

complex dynamics of the biological rhythms gallbladder and heart cases abstract a theoretical analysis of the mechanisms underlying the dynamics of gallbladder and heart pulsation could clarify the question regarding the classification as chaotic of the associated behaviour eventually related to a normal and healthy beat this analysis is particularly relevant in view of the control of dynamic bifurcations arising in situations of disease in this work a summary of the dfa method applied to gallbladder volume data for a modest number of healthy and ill patients is presented the presence of signal correlation is found in both cases but the fit shapes differ from some critical values

nonparametric stochastic frontiers a local maximum likelihood approach this paper proposes a new approach to handle nonparametric stochastic frontier sf models it is based on local maximum likelihood techniques the model is presented as encompassing some anchorage parametric model in a nonparametric way first we derive asymptotic properties of the estimator for the general case local linear approximations then the results are tailored to a sf model where the convoluted error term efficiency plus noise is the sum of a half normal and a normal random variable the parametric anchorage model is a linear production function with a homoscedastic error term the local approximation is linear for both the production function and the parameters of the error terms the performance of our estimator is then established in finite samples using simulated data sets as well as with a cross sectional data on us commercial banks the methods appear to be robust numerically stable and particularly useful for investigating a production process and the derived efficiency scores

a new test for the parametric form of the variance function in non parametric regression in the common non parametric regression model the problem of testing for the parametric form of the conditional variance is considered a stochastic process based on the difference between the empirical processes that are obtained from the standardized non parametric residuals under the null hypothesis of a specific parametric form of the variance function and the alternative is introduced and its weak convergence established this result is used for the construction of a kolmogorov smimov and a cramer von mises type of statistic for testing the parametric form of the conditional variance the consistency of a bootstrap approximation is established and the finite sample properties of this approximation are investigated by means of a simulation study in particular the new procedure is compared with some of the currently available methods for this problem

continuous time linear predictive control and flatness a module theoretic setting with examples a general flatness based framework for linear continuous time predictive control is presented the mathematical setting which is valid for multivariable systems is provided by the algebraic theory of modules where a controllable system corresponds to a finitely generated free module over a principal ideal ring any basis of this free module is a flat output which yields an easy calculation of the predicted trajectory this formalism permits one to handle non minimum phase systems system constraints and to deal with additive perturbations three concrete case studies namely a dc motor a flexible system and a cement mill are analysed and simulations are given these examples are written in such a way that any reader who is not familiar with module theory may nevertheless grasp the proposed control strategy

flatness based trajectory planning for diffusion reaction systems in a parallelepipedon a spectral approach spectral analysis is considered for the flatness based solution of the trajectory planning problem for a boundary controlled diffusion reaction system defined on a 1 r dimensional parallelepipedon by exploiting the riesz spectral properties of the system operator it is shown that a suitable reformulation of the resolvent operator allows a systematic introduction of a basic output which yields a parametrization of both the system state and the boundary input in terms of differential operators of infinite order their convergence is verified for both infinite dimensional and finite dimensional actuator configurations by restricting the basic output to certain gevrey classes involving non analytic functions with this a systematic approach is introduced for basic output trajectory assignment and feedforward tracking control towards the realization of finite time transitions between stationary profiles

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

brief paper a unified framework for the numerical solution of optimal control problems using pseudospectral methods a unified framework is presented for the numerical solution of optimal control problems using collocation at legendre gauss lg legendre gauss radau lgr and legendre gauss lobatto lgl points it is shown that the lg and lgr differentiation matrices are rectangular and full rank whereas the lgl differentiation matrix is square and singular consequently the lg and lgr schemes can be expressed equivalently in either differential or integral form while the lgl differential and integral forms are not equivalent transformations are developed that relate the lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem the lg and lgr discrete costate systems are full rank while the lgl discrete costate system is rank deficient the lgl costate approximation is found to have an error that oscillates about the true solution and this error is shown by example to be due to the null space in the lgl discrete costate system an example is considered to assess the accuracy and features of each collocation scheme

on specification testing of ordered discrete choice models we discuss how to test the specification of an ordered discrete choice model against a general alternative two main approaches can be followed tests based on moment conditions and tests based on comparisons between parametric and nonparametric estimations following these approaches various statistics are proposed and their asymptotic properties are discussed the performance of the statistics is compared by means of simulations an easy to compute variant of the standard moment based statistic yields the best results in models with a single explanatory variable in models with various explanatory variables the results are less conclusive since the relative performance of the statistics depends on both the fit of the model and the type of misspecification that is considered

nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation abstractthis paper presents a fast constrained optimization approach which is tailored for nonlinear model predictive control of wave energy converters wec the advantage of this approach relies on its exploitation of the differential flatness of the wec model this can reduce the dimension of the resulting nonlinear programming problem nlp derived from the continuous constrained optimal control of wec using pseudospectral method the alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for wec control problems the method is applicable to nonlinear wec models nonconvex objective functions and nonlinear constraints which are commonly encountered in wec control problems numerical simulations demonstrate the efficacy of this approach

dimension reduction in regressions through cumulative slicing estimation in this paper we offer a complete methodology of cumulative slicing estimation to sufficient dimension reduction in parallel to the classical slicing estimation we develop three methods that are termed respectively as cumulative mean estimation cumulative variance estimation and cumulative directional regression the strong consistency for p o n1 2 log n and the asymptotic normality for p o n1 2 are established where p is the dimension of the predictors and n is sample size such asymptotic results improve the rate p o n1 3 in many existing contexts of semiparametric modeling in addition we propose a modified bic type criterion to estimate the structural dimension of the central subspace its consistency is established when p o n1 2 extensive simulations are carried out for comparison with existing methods and a real data example is presented for illustration

model checking for parametric single index models a dimension reduction model adaptive approach summary local smoothing testing based on multivariate non parametric regression estimation is one of the main model checking methodologies in the literature however the relevant tests suffer from the typical curse of dimensionality resulting in slow rates of convergence to their limits under the null hypothesis and less deviation from the null hypothesis under alternative hypotheses this problem prevents tests from maintaining the level of significance well and makes tests less sensitive to alternative hypotheses in the paper a model adaptation concept in lack of fit testing is introduced and a dimension reduction model adaptive test procedure is proposed for parametric single index models the test behaves like a local smoothing test as if the model were univariate it is consistent against any global alternative hypothesis and can detect local alternative hypotheses distinct from the null hypothesis at a fast rate that existing local smoothing tests can achieve only when the model is univariate simulations are conducted to examine the performance of our methodology an analysis of real data is shown for illustration the method can be readily extended to global smoothing methodology and other testing problems

the pseudospectral legendre method for discretizing optimal control problems this paper presents a computational technique for optimal control problems including state and control inequality constraints the technique is based on spectral collocation methods used in the solution of differential equations the system dynamics are collocated at legendre gauss lobatto points the derivative x spl dot t of the state x t is approximated by the analytic derivative of the corresponding interpolating polynomial state and control inequality constraints are collocated at legendre gauss lobatto nodes the integral involved in the definition of the performance index is discretized based on the gauss lobatto quadrature rule the optimal control problem is thereby converted into a mathematical programming program thus existing well developed optimization algorithms may be used to solve the transformed problem the method is easy to implement capable of handling various types of constraints and yields very accurate results illustrative examples are included to demonstrate the capability of the proposed method and a comparison is made with existing methods in the literature

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