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

copositive relaxation beats lagrangian dual bounds in quadratically and linearly constrained quadratic optimization problems we study nonconvex quadratic minimization problems under possibly nonconvex quadratic and linear constraints characterizing both lagrangian and semi lagrangian dual bounds in terms of conic optimization while the lagrangian dual is equivalent to the sdp relaxation which has been known for quite a while although the presented form incorporating explicitly linear constraints seems to be novel we show that the semi lagrangian dual is equivalent to a natural copositive relaxation and this has apparently not been observed before this way we arrive at conic bounds tighter than the usual lagrangian dual and thus than the sdp bounds any of the known tractable inner approximations of the copositive cone can be used for this tightening but in particular the above mentioned characterization with explicit linear constraints is a natural much cheaper relaxation than the usual zero order approximation by doubly nonnegative dnn matrices and still improves upon the lagrangian dual bounds these app

the enskog boltzmann equation in the whole space r3 some global existence uniqueness and stability results abstract the enskog boltzmann equation a partial differential integral equation of the hyperbolic type is a model which generalizes the classical boltzmann equation to high gas densities and is here considered with an analysis of the well posedness of the initial value problem in unbounded domains some new global existence and uniqueness results for the solutions of the initial value problem and a discussion on the asymptotic stability are provided under suitable assumptions about the size of the norm of the initial data and about the rate of decay to zero at infinity in the phase space

on the inelastic enskog equation near vacuum the cauchy problem for the inelastic enskog equation is considered for near vacuum data the global existence of mild and classical solutions of the inelastic enskog equation is obtained then based on some new functionals we give the uniform l1 x v stability of solutions for the inelastic enskog equation

nonparametric comparison of several regression functions exact and asymptotic theory a new test is proposed for the comparison of two regression curves f and g we prove an asymptotic normal law under fixed alternatives which can be applied for power calculations for constructing confidence regions and for testing precise hypotheses of a weighted l 2 distance between f and g in particular the problem of nonequal sample sizes is treated which is related to a peculiar formula of the area between two step functions these results are extended in various directions such as the comparison of k regression functions or the optimal allocation of the sample sizes when the total sample size is fixed the proposed pivot statistic is not based on a nonparametric estimator of the regression curves and therefore does not require the specification of any smoothing parameter

testing for polynomial regression using nonparametric regression techniques abstract in regression analysis it is important to test the validity of the assumed model prior to making inferences regarding the population of interest in this investigation we utilize nonparametric regression techniques to test the validity of a kth order polynomial regression model the departures from the polynomial model are assumed to belong to a smooth class of functions a parametric form is not assumed a test based on nonparametric regression fits to the residuals from kth order polynomial regression is proposed it utilizes a smoothing spline fit of order 2k to the residuals from kth order polynomial regression a test statistic based on this estimator is formulated and its asymptotic distribution is derived under alternatives converging to the null at a rate of n k where is the smoothing parameter we note that this rate of convergence is slower than the parametric rate of n power investigations are conducted through a small scale simulation study

optimality condition and complexity analysis for linearly constrained optimization without differentiability on the boundary in this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region by exploiting an interior point technique we present first and second order optimality conditions for this problem that reduces to classical ones when the derivative on the boundary is available for this type of problems existing necessary conditions often rely on the notion of subdifferential or become non trivially weaker than the kkt condition in the twice differentiable counterpart problems in contrast this paper presents a new set of first and second order necessary conditions that are derived without the use of subdifferential and reduce to exactly the kkt condition when twice differentiability holds as a result these conditions are stronger than some existing ones considered for the discussed minimization problem when only non negativity constraints are present to solve for these optimality conditions in the special but important case of linearly constrained problems we present two novel interior point trust region algorithms and show that their worst case computational efficiency in achieving the potentially stronger optimality conditions match the best known complexity bounds since this work considers a more general problem than those in the literature our results also indicate that best known existing complexity bounds are actually held for a wider class of nonlinear programming problems this new development is significant since optimality conditions play a fundamental role in computational optimization and more and more nonlinear and nonconvex problems need to be solved in practice

on affine scaling algorithms for nonconvex quadratic programming we investigate the use of interior algorithms especially the affine scaling algorithm to solve nonconvex indefinite or negative definite quadratic programming qp problems although the nonconvex qp with a polytope constraint is a hard problem we show that the problem with an ellipsoidal constraint is easy when the hard qp is solved by successively solving the easy qp the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions

global existence inl1 for the generalized enskog equation various existence theorems are given for the generalized enskog equation inr3 and in a bounded spatial domain with periodic boundary conditions a very general form of the geometric factory is allowed including an explicit space velocity and time dependence the method is based on the existence of a liapunov functional an analog of theh function in the boltzmann equation and utilizes a weak compactness argument inl1

adaptive smoothing and density based tests of multivariate normality abstract methods of adaptive smoothing of density estimates where the amount of smoothing applied varies according to local features of the underlying density are investigated the difficulties of applying taylor series arguments in this context are explored simple properties of the estimates are investigated by numerical integration and compared with the fixed kernel approach optimal smoothing strategies based on the multivariate normal distribution are derived as an application of these techniques two tests of multivariate normality one based on integrated squared error and one on entropy are developed and some power calculations are carried out

stability of global solution for the relativistic enskog equation near vacuum the cauchy problem of the relativistic enskog equation with near vacuum data is considered in this paper under the same assumption as that in jiang j stat phys 127 805 812 2007 for the relativistic enskog equation we obtain the uniform l stability of the solution what s more important is that for two new types of the scattering cross section we give the global existence and l1 x v stability for mild solution when the initial data lies in the space l1 x v as a corollary we have a bv type estimate it is worth mentioning that the stability results in this paper can be applied to the case in jiang j stat phys 127 805 812 2007

automatic smoothing of regression functions in generalized linear models abstract we consider the penalized likelihood method for estimating nonparametric regression functions in generalized linear models nelder and wedderburn 1972 and present a generalized cross validation procedure for empirically assessing an appropriate amount of smoothing in these estimates asymptotic arguments and numerical simulations are used to show that the generalized cross validatory procedure preforms well from the point of view of a weighted mean squared error criterion the methodology adds to the battery of graphical tools for model building and checking within the generalized linear model framework included are two examples motivated by medical and horticultural applications

local and global asymptotic inference in smoothing spline models this article studies local and global inference for smoothing spline estimation in a unified asymptotic framework we first introduce a new technical tool called functional bahadur representation which significantly generalizes the traditional bahadur representation in parametric models that is bahadur ann inst statist math 37 1966 577 580 equipped with this tool we develop four interconnected procedures for inference i pointwise confidence interval ii local likelihood ratio testing iii simultaneous confidence band iv global likelihood ratio testing in particular our confidence intervals are proved to be asymptotically valid at any point in the support and they are shorter on average than the bayesian confidence intervals proposed by wahba j r stat soc ser b stat methodol 45 1983 133 150 and nychka j amer statist assoc 83 1988 1134 1143 we also discuss a version of the wilks phenomenon arising from local global likelihood ratio testing it is also worth noting that our simultaneous confidence bands are the first ones applicable to general quasi likelihood models furthermore issues relating to optimality and efficiency are carefully addressed as a by product we discover a surprising relationship between periodic and nonperiodic smoothing splines in terms of inference

penalized quasi likelihood estimation in partial linear models consider a partial linear model where the expectation of a random variable y depends on covariates x z through f theta 0 x m 0 z with theta 0 an unknown parameter and m 0 an unknown function we apply the theory of empirical processes to derive the asymptotic properties of the penalized quasi likelihood estimator

the complexity of approximating a nonlinear program we consider the problem of finding the maximum of a multivariate polynomial inside a convex polytope we show that there is no polynomial time approximation algorithm for this problem even one with a very poor guarantee unless p np we show that even when the polynomial is quadratic i e quadratic programming there is no polynomial time approximation unless np is contained in quasi polynomial time

a lack of fit test for quantile regression we propose an omnibus lack of fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector the test does not involve nonparametric smoothing but is consistent for all nonparametric alternatives without any moment conditions on the regression error in addition the test is suitable for detecting the local alternatives of any order arbitrarily close to n 1 2 from the null hypothesis the limiting distribution of the proposed test statistic is non gaussian but can be characterized by a gaussian process we propose a simple sequential resampling scheme to carry out the test whose nominal levels are well approximated in our empirical study for

a flexible model for human circadian rhythms many hormones and other physiological processes vary in a circadian pattern although a sine cosine function can be used to model these patterns this functional form is not appropriate when there is asymmetry between the peak and nadir phases in this paper we describe a semiparametric periodic spline function that can be fit to circadian rhythms the model includes both phase and amplitude so that the time and the magnitude of the peak or nadir can be estimated we also describe tests of fit for components in the model data from an experiment to study immunological responses in humans are used to demonstrate the methods

validation of linear regression models a new test is proposed in order to verify that a regression function say g has a prescribed linear parametric form this procedure is based on the large sample behavior of an empirical l 2 distance between g and the subspace u spanned by the regression functions to be verified the asymptotic distribution of the test statistic is shown to be normal with parameters depending only on the variance of the observations and the l 2 distance between the regression function g and the model space u based on this result a test is proposed for the hypothesis that g is not in a preassigned l 2 neighborhood of u whichallows the verification of the model u at a controlled type i error rate the suggested procedure is very easy to apply because of its asymptotic normal law and the simple form of the test statistic in particular it does not require nonparametric estimators of the regression function and hence the test does not depend on the subjective choice of smoothing parameters

new properties of a class of generalized kinetic equations we give some properties of a new class of hard sphere kinetic equations of great generality introduced earlier by polewczak the assumptions used to obtain the general class are very weak and the equations include not only the standard and revised enskog equations but also generalizations thereof that can be expected to yield essentially exact transport coefficients in particular there is a natural two particle realization that is obtained from maximizing the information entropy subject to prescribed two particle and one particle probability distribution functions k particle analogs fork 2 also naturally follow we obtain liapunov functionals for the whole class of equations under consideration and discuss the question of which of these functionals can be expected to play the role ofh functions we also obtain several more special results that include new lower bounds on the potential part of theh function for the revised enskog equation the bounds are instrumental in obtaining global existence theorems and also imply that the necessary condition for invertibility of the nonequilibrium extension of local activity as a functional of local density is satisfied

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

on the complexity of approximating a kkt point of quadratic programming we present a potential reduction algorithm to approximate a karush kuhn tucker kkt point of general quadratic programming qp we show that the algorithm is a fully polynomial time approximation scheme and its running time dependency on accuracy 0 1 is o l log l log log l compared to the previously best known result o l 2 furthermore the limit of the kkt point satisfies the second order necessary optimality condition of being a local minimizer 1998 the mathematical programming society inc published by elsevier science b v

testing against a linear regression model using ideas from shape restricted estimation summary a formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed using a large dimensional non parametric double cone alternative for example the test against a constant function uses the alternative of increasing or decreasing regression functions and the test against a linear function uses the convex or concave alternative the test proposed is exact and unbiased and the critical value is easily computed the power of the test increases to 1 as the sample size increases under very mild assumptions even when the alternative is misspecified i e the power of the test converges to 1 for any true regression function that deviates in a non degenerate way from the parametric null hypothesis we also formulate tests for the linear versus partial linear model and consider the special case of the additive model simulations show that our procedure behaves well consistently when compared with other methods although the alternative fit is non parametric no tuning parameters are involved supplementary materials with proofs and technical details are available on line

a continuous approach to inductive inference in this paper we describe an interior point mathematical programming approach to inductive inference we list several versions of this problem and study in detail the formulation based on hidden boolean logic we consider the problem of identifying a hidden boolean function 0 1 n 0 1 using outputs obtained by applying a limited number of random inputs to the hidden function given this input output sample we give a method to synthesize a boolean function that describes the sample we pose the boolean function synthesis problem as a particular type of satisfiability problem the satisfiability problem is translated into an integer programming feasibility problem that is solved with an interior point algorithm for integer programming a similar integer programming implementation has been used in a previous study to solve randomly generated instances of the satisfiability problem in this paper we introduce a new variant of this algorithm where the riemannian metric used for defining the search region is dynamically modified computational results on 8 16 and 32 input 1 output functions are presented our implementation successfully identified the majority of hidden functions in the experiment

diagnostics for assessing regression models abstract we concern ourselves with diagnostics for checking the overall and local goodness of fit of a model s x used in the regression of y on x u 0 1 d the model for s x is a functional form that depends on a finite number of unknown parameters two statistics and w are proposed that measure the level of agreement between the model fit to the data and the nonparametric kernel estimator on m preselected points in u conditions are given under which and w are asymptotically equivalent both of these statistics measure overall lack of fit and are related to the deviance their asymptotic distribution under the null model and under local alternatives is derived this work is motivated by the local mean deviance plot of landwehr pregibon and shoemaker for assessing overall lack of fit in logistic regression their plot is summarized by our test statistics and is extended to other likelihood based regressions of y on x

on the use of nonparametric regression techniques for fitting parametric regression models a new method for fitting parametric regression models is proposed it consists of applying the least squares ls principle on the pairs xi rh xi i 1 n where x denotes the explanatory variable and mn x is a location estimate of the conditional distribution of the response variable y given that x x consistency and asymptotic normality of the estimators are established under general conditions these conditions are shown to be satisfied when the data are incomplete due to random censoring or truncation usable expressions for the asymptotic variance covariance matrix of the parameters are provided in these incomplete data cases as an extra bonus this regression method allows the use of ordinary residual plots as a data analytic aide this is illustrated on two real data sets a simulation study examines the small sample behavior of the estimators and their estimated asymptotic variance extension of the method to more complicated models is discussed

smoothing spline models with correlated random errors abstract spline smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model their performances depend greatly on the choice of smoothing parameters many methods of selecting smoothing parameters such as generalized maximum likelihood gml generalized cross validation gcv and unbiased risk ubr have been developed under the assumption of independent observations they tend to underestimate smoothing parameters when data are correlated in this article i assume that observations are correlated and that the correlation matrix depends on a parsimonious set of parameters i extend the gml gcv and ubr methods to estimate the smoothing parameters and the correlation parameters simultaneously i also relate a smoothing spline model to three mixed effects models these relationships show that the smoothing spline estimates evaluated at design points are best linear unbiased prediction blup estimates and that the gml estimates of the smoothing parameters an

uniform stability of the solutions to the relativistic enskog equation abstract we present the uniform stability of classical solutions to the relativistic enskog equation under the locally lipschitz assumption of the collision factors given by polewczak this stability is an extension of the result given by ha and xiao for the relativistic boltzmann equation and it is very useful for the study of the cauchy problem for the relativistic enskog equation

semiparametric estimates of the relation between weather and electricity sales abstract a nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data this accommodates introduction of covariates timing adjustments due to the actual billing schedules and serial correlation the procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross validation criterion introduced by craven and wahba 1979 estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines

newton s method with a model trust region modification a modified newton method for unconstrained minimization is presented and analyzed the modification is based upon the model trust region approach this report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified newton iteration several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis very strong convergence results are presented concerning the minimization algorithm in particular the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization with the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives

covariate matched one sided tests for the difference between functional means abstract when testing hypotheses about the effects of different treatments variation among covariates can become confounded with that between treatments unless the treatments are applied using paired covariates in the context of unpaired covariates we propose implicit covariate matching methods for testing the hypothesis that one treatment effect is greater than another the methods are founded on the assumption that the mean treatment effect conditional on the covariate is a smooth function of the covariate they are implemented using new interpolation techniques for nonparametric curve estimation bootstrap arguments are used to construct critical points we show that even when the covariate distributions are identical for both treatments covariate matching of the type that we propose produces tests of greater power than methods that do not attempt matching our techniques have application to two sided hypothesis testing

testing for cubic smoothing splines under dependent data in most research on smoothing splines the focus has been on estimation while inference especially hypothesis testing has received less attention by defining design matrices for fixed and random effects and the structure of the covariance matrices of random errors in an appropriate way the cubic smoothing spline admits a mixed model formulation which places this nonparametric smoother firmly in a parametric setting thus nonlinear curves can be included with random effects and random coefficients the smoothing parameter is the ratio of the random coefficient and error variances and tests for linear regression reduce to tests for zero random coefficient variances we propose an exact f test for the situation and investigate its performance in a real pine stem data set and by simulation experiments under certain conditions the suggested methods can also be applied when the data are dependent

a lack of fit test for the mean function in a generalized linear model abstract a supremum type statistic based on partial sums of residuals is proposed to test the validity of the mean function of the response variable in a generalized linear model the proposed test does not need a partition of the space of covariates to handle the case of nonreplication the new test is consistent against the alternative under which the deterministic part of the model is not the one specified in the null hypothesis the asymptotic null distribution of the test statistic can be approximated through simulations this approximation is valid even if the variance of the response variable is misspecified in the model for practical sample sizes the adequacy of this large sample approximation to the null distribution of the test statistic is carefully examined power comparisons with other lack of fit tests are also performed to show the advantage of the test in particular we find that the new procedure is rather sensitive to detect a misspecified mean function if the assumed mean functio

spline smoothing in a partly linear model on donne des estimations qui minimisent la somme des sommes residuelles des carres et une penalite de difficulte

comparison of regression curves using quasi residuals abstract we consider testing the equality of two regression functions using two independent samples three tests are proposed that are free of the restriction of having the same covariate values or sample sizes for both samples asymptotic distributions are given and results from a simulation study are presented that show the superior power properties of these tests over a competing test in a variety of cases including the testing of hypotheses involving high frequency curves when the design points for the two samples differ it is also observed that the tests have good level properties when proper smoothing parameters are selected

testing for no effect when estimating a smooth function by nonparametric regression a randomization approach abstract when a linear regression function is estimated by ordinary least squares the null hypothesis of no relationship between the response and the design variable can be tested by the normal theory f test this article describes a new test for use in the case in which a smooth regression function is estimated by a nonparametric procedure such as kernel estimation or local regression the test is constructed as an approximation to an exact permutation test the test statistic is the ratio of sums of squares that are defined by analogy to the analysis of variance the null permutation distribution of the test statistic is approximated by matching its exact mean and variance to the moments of a gamma distribution a simulation study shows that the approximation is excellent for several regression procedures and for normal heavy tailed and skewed error distributions simulation results are also used to investigate the power of the test as a function of the smoothing parameter the test is applied to dat

model checking with nonparametric curves summary the use of local likelihood curve estimates in model checking is described test statistics are based on deviance differences and are interpreted using nonparametric bootstrap monte carlo some theoretical aspects are discussed methods are illustrated for regression with discrete data

an omnibus test for departures from constant mean observations y i are made at points x i according to the model y i f x i e i where the e i are independent normals with constant variance in order to decide whether or not f x is constant a likelihood ratio test is constructed comparing f x with f x z x where z x is a brownian motion the ratio of error variance to brownian motion variance is chosen to maximize the likelihood and the resulting maximum likelihood statistic b is used to test departures from constant mean its asymptotic distribution is derived and its finite sample size behavior is compared with five other tests

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

on the cauchy problem for the nonlinear boltzmann equation global existence uniqueness and asymptotic stability the analysis of the initial value problem for the nonlinear boltzmann equation is considered in this paper a theorem defining global existence and uniqueness for initial data which decay at infinity with an inverse power law is the main result of this work and is obtained by suitable application of fixed point theorems in banach spaces the theorem also defines the asymptotic stability of the solutions

a semidefinite framework for trust region subproblems with applications to large scale minimization primal dual pairs of semidefinite programs provide a general framework for the theory and algorithms for the trust region subproblem trs this latter problem consists in minimizing a general quadratic function subject to a convex quadratic constraint and therefore it is a generalization of the minimum eigenvalue problem the importance of trs is due to the fact that it provides the step in trust region minimization algorithms the semidefinite framework is studied as an interesting instance of semidefinite programming as well as a tool for viewing known algorithms and deriving new algorithms for trs in particular a dual simplex type method is studied that solves trs as a parametric eigenvalue problem this method uses the lanczos algorithm for the smallest eigenvalue as a black box therefore the essential cost of the algorithm is the matrix vector multiplication and thus sparsity can be exploited a primal simplex type method provides steps for the so called hard case extensive numerical tests for large sparse problems are discussed these tests show that the cost of the algorithm is 1 n times the cost of finding a minimum eigenvalue using the lanczos algorithm where 0 n 1 is a fraction which decreases as the dimension increases

nonparametric regression analysis of longitudinal data abstract nonparametric methods are developed for estimating the dose effect when a response consists of correlated observations over time measured in a dose response experiment the methods can also be applied to data collected from a completely randomized design experiment methods are developed for the detection and description of the effects of dose time and their interaction the methods allow for individual variation in the timing and number of observations a generalization allowing baseline covariates to be incorporated is addressed these results may be used in an exploratory fashion in the process of building a random effects model for longitudinal data

global existence and asymptotic behavior for the discrete velocity models of the boltzmann equation by using fixed point techniques some theorems which supply local and global existence uniqueness and asymptotic behavior of the solution of a general discrete velocity model of the boltzmann equation in three dimensions are given

some tools for functional data analysis multivariate data analysis permits the study of observations which are finite sets of numbers but modern data collection situations can involve data or the processes giving rise to them which are functions functional data analysis involves infinite dimensional processes and or data the paper shows how the theory of l splines can support generalizations of linear modelling and principal components analysis to samples drawn from random functions spline smoothing rests on a partition of a function space into two orthogonal subspaces one of which contains the obvious or structural components of variation among a set of observed functions and the other of which contains residual components this partitioning is achieved through the use of a linear differential operator and we show how the theory of polynomial splines can be applied more generally with an arbitrary operator and associated boundary constraints these data analysis tools are illustrated by a study of variation in temperature precipitation patterns among some canadian weather stations

smoothing spline based score tests for proportional hazards models we propose score type tests for the proportional hazards assumption and for covariate effects in the cox model using the natural smoothing spline representation of the corresponding nonparametric functions of time or covariate the tests are based on the penalized partial likelihood and are derived by viewing the inverse of the smoothing parameter as a variance component and testing an equivalent null hypothesis that the variance component is zero we show that the tests have a size close to the nominal level and good power against general alternatives and we apply them to data from a cancer clinical trial

testing independence and goodness of fit in linear models we consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and predictor variables and the goodness of fit of the parametric model our approach is based on testing for independence between the predictor and the residual obtained from the parametric fit by using the hilbert schmidt independence criterion gretton et al 2008 the proposed method requires no user defined regularization is simple to compute based on only pairwise distances between points in the sample and is consistent against all alternatives we develop distribution theory for the proposed test statistic under both the null and the alternative hypotheses and devise a bootstrap scheme to approximate its null distribution we prove the consistency of the bootstrap scheme a simulation study shows that our method has better power than its main competitors two real datasets are analysed to demonstrate the scope and usefulness of our method

exponential dispersion models on etudie les proprietes generales de la classe des modeles de dispersion exponentiels qui est la generalisation multivariable des modeles de distribution d erreur de nelder et wedderburn 1972

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

a comparison of gcv and gml for choosing the smoothing parameter in the generalized spline smoothing problem the partially improper prior behind the smoothing spline model is used to obtain a generalization of the maximum likelihood gml estimate for the smoothing parameter then this estimate is compared with the generalized cross validation gcv estimate both analytically and by monte carlo methods the comparison is based on a predictive mean square error criteria it is shown that if the true unknown function being estimated is smooth in a sense to be defined then the gml estimate undersmooths relative to the gcv estimate and the predictive mean square error using the gml estimate goes to zero at a slower rate than the mean square error using the gcv estimate if the true function is rough then the gcv and gml estimates have asymptotically similar behavior a monte carlo experiment was designed to see if the asymptotic results in the smooth case were evident in small sample sizes mixed results were obtained for n 32 gcv was somewhat better than gml for n 64 and gcv was decidedly superior for n 128 in the n 32 case gcv was better for smaller sigma 2 and the comparison close for larger sigma 2 the theoretical results are shown to extend to the generalized spline smoothing model which includes the estimate of functions given noisy values of various integrals of them

restricted likelihood ratio lack of fit tests using mixed spline models penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non linearity in the smooth function estimates this motivates the study of lack of fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values for this one sided testing problem a further complication is that the variance component belongs to the boundary of the parameter space under the null hypothesis conditions are obtained on the design of the regression spline models under which asymptotic distribution theory applies and finite sample approximations to the asymptotic distribution are provided test statistics are studied for simple as well as multiple regression models

bootstrap test for difference between means in nonparametric regression abstract a bootstrap test is proposed for detecting a difference between two mean functions in the setting of nonparametric regression error distributions in the regression model are permitted to be arbitrary and unequal the test enjoys power properties akin to those in a parametric setting in the sense that it can distinguish between regression functions distant only n 1 2 apart where n is the sample size it has exceptional level accuracy with level error of only n 2 and uses a very accurate estimate of the critical point of an exact test being in error by only n 3 2 under the null hypothesis the test admits several generalizations for example to the case of testing for differences between several regression means this is a nonparametric regression analog of analysis of variance a simulation study using n as small as 15 corroborates the asymptotic result on level accuracy of the bootstrap test applications are illustrated with an example involving acid rain data

some np complete problems in quadratic and nonlinear programming in continuous variable smooth nonconvex nonlinear programming we analyze the complexity of checking whether a a given feasible solution is not a local minimum and b the objective function is not bounded below on the set of feasible solutions we construct a special class of indefinite quadratic programs with simple constraints and integer data and show that checking a or b on this class is np complete as a corollary we show that checking whether a given integer square matrix is not copositive is np complete

line integral alternating minimization algorithm for dual energy x ray ct image reconstruction we propose a new algorithm called line integral alternating minimization liam for dual energy x ray ct image reconstruction instead of obtaining component images by minimizing the discrepancy between the data and the mean estimates liam allows for a tunable discrepancy between the basis material projections and the basis sinograms a parameter is introduced that controls the size of this discrepancy and with this parameter the new algorithm can continuously go from a two step approach to the joint estimation approach liam alternates between iteratively updating the line integrals of the component images and reconstruction of the component images using an image iterative deblurring algorithm an edge preserving penalty function can be incorporated in the iterative deblurring step to decrease the roughness in component images images from both simulated and experimentally acquired sinograms from a clinical scanner were reconstructed by liam while varying the regularization parameters to identify good choices the results from the dual energy alternating minimization algorithm applied to the same data were used for comparison using a small fraction of the computation time of dual energy alternating minimization liam achieves better accuracy of the component images in the presence of poisson noise for simulated data reconstruction and achieves the same level of accuracy for real data reconstruction

commonality of cusum von neumann and smoothing based goodness of fit tests summary recent papers by munson jernigan 1989 and buckley 1991 propose nonparametric tests for the hypothesis of no predictor effect in regression the munson jernigan test is similar to the von neumann 1941 test while that of buckley is based on a functional of cusums these tests are shown to be special cases of a wider class of tests based on nonparametric function estimation ideas fourier analysis is used to qualitatively compare the munson jernigan and buckley tests with two new tests constructed from nonparametric smoothers their relative powers are then studied by means of large sample analysis and simulation the cusum test is the most powerful for very smooth departures from the no effect hypothesis while the new tests based on smoothing ideas are clearly superior when the alternative is high frequency

a fully polynomial time approximation algorithm for computing a stationary point of the general linear complementarity problem we apply a potential reduction algorithm to solve the general linear complementarity problem glcp minimize xty subject to ax by cz q and x y z 0 we show that the algorithm is a fully polynomial time approximation scheme fptas for computing an e approximate stationary point of the glcp note that there are some glcps in which every stationary point is a solution xty 0 these include the lcps with row sufficient matrices we also show that the algorithm is a polynomial time algorithm for a special class of glcps

detecting a smooth signal optimality of cusum based procedures summary cox et al 1988 show that under a random smooth function model with signal covariance matrix v a locally most powerful test for the presence of a nonpolynomial signal is based on the statistic ytvy we show that if a well known difference based roughness measure is used to derive a natural choice for v then this statistic is the sum of squares of a residual cusum sequence thus we confirm theoretically the long held impression that the residual cusum sequence is powerful as a tool for the detection of smooth signal

joint power and admission control non convex l_ q approximation and an effective polynomial time deflation approach in an interference limited network joint power and admission control jpac aims at supporting a maximum number of links at their specified signal to interference plus noise ratio sinr targets while using minimum total transmission power various convex approximation deflation approaches have been developed for the jpac problem in this paper we propose an effective polynomial time non convex approximation deflation approach for solving the problem the approach is based on the non convex ell q 0 approximation of an equivalent sparse ell 0 reformulation of the jpac problem we show that for any instance of the jpac problem there exists a bar q in 0 1 such that it can be exactly solved by solving its ell q approximation problem with any q in 0 bar q we also show that finding the global solution of the ell q approximation problem is np hard then we propose a potential reduction interior point algorithm which can return an epsilon kkt solution of the np hard ell q approximation problem in polynomial time the returned solution can be used to check the simultaneous supportability of all links in the network and to guide an iterative link removal procedure resulting in the polynomial time non convex approximation deflation approach for the jpac problem numerical simulations show that the proposed approach outperforms the existing convex approximation approaches in terms of the number of supported links and the total transmission power particularly exhibiting a quite good performance in selecting which subset of links to support

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

global existence and asymptotic behavior for the nonlinear enskog equation the existence of a classical solution to the nonlinear enskog equation in all mathbb r 3 is proved the solution which is global in time exists if the initial data go to zero fast enough at infinity and the mean path is sufficiently large the solution is smooth in space variable if the initial value is smooth the asymptoticbehavior of solutions is also given it is shown that as t to infty the solution to the enskog equation can be approximated by the solution to the free motion problem key words partial differential equations nonlinear integral equation asymptotic behavior kinetic theory boltzmann equation

the boltzmann equation global existence for a rare gas in an infinite vacuum solutions of the boltzmann equation are proved to exist globally in time under conditions that include the case of a finite volume of gas in an infinite vacuum when the mean free path of the gas is large enough it is also proved as might be expected in this case that the density of the gas at each point in space goes to zero as time goes to infinity

global weak solutions and uniform lp stability of the boltzmann enskog equation abstract we present the regularity theory of renormalized solutions and uniform l p stability estimates of the boltzmann enskog model we use a multi dimensional bony type functional to control the time phase space integral of a truncated collision operator we employ cercignani s arguments and a bony type functional to show that the renormalized solutions to the boltzmann enskog model are weak solutions in usual distributional sense for the uniform l p stability estimate we use lu s trick together with the holder inequality

testing goodness of fit in regression a general approach for specified alternatives when fitting generalized linear models or the cox proportional hazards model it is important to have tools to test for lack of fit because lack of fit comes in all shapes and sizes distinguishing among different types of lack of fit is of practical importance we argue that an adequate diagnosis of lack of fit requires a specified alternative model such specification identifies the type of lack of fit the test is directed against so that if we reject the null hypothesis we know the direction of the departure from the model the goodness of fit approach of this paper allows to treat different types of lack of fit within a unified general framework and to consider many existing tests as special cases connections with penalized likelihood and random effects are discussed and the application of the proposed approach is illustrated with medical examples tailored functions for goodness of fit testing have been implemented in the r package globaltest copyright 2012 john wiley sons ltd

on p values for smooth components of an extended generalized additive model the problem of testing smooth components of an extended generalized additive model for equality to zero is considered confidence intervals for such components exhibit good across the function coverage probabilities if based on the approximate result hat f i n f i v f i i where f is the vector of evaluated values for the smooth component of interest and v f is the covariance matrix for f according to the bayesian view of the smoothing process based on this result a wald type test of f 0 is proposed it is shown that care must be taken in selecting the rank used in the test statistic the method complements previous work by extending applicability beyond the gaussian case while considering tests of zero effect rather than testing the parametric hypothesis given by the null space of the component s smoothing penalty the proposed p values are routine and efficient to compute from a fitted model without requiring extra model fits or null distribution simulation

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

a fptas for computing a symmetric leontief competitive economy equilibrium in this paper we consider a linear complementarity problem lcp arisen from the nash and arrow debreu competitive economy equilibria where the lcp coefficient matrix is symmetric we prove that the decision problem to decide whether or not there exists a complementary solution is np complete under certain conditions an lcp solution is guaranteed to exist and we present a fully polynomial time approximation scheme fptas for approximating a complementary solution although the lcp solution set can be non convex or non connected our method is based on approximating a quadratic social utility optimization problem qp and showing that a certain kkt point of the qp problem is an lcp solution then we further show that such a kkt point can be approximated with a new improved running time complexity o frac n 4 epsilon log log frac 1 epsilon arithmetic operation in accuracy epsilon in 0 1 we also report preliminary computational results which show that the method is highly effective applications in competitive market model problems with other utility functions are also presented including global trading and dynamic spectrum management problems

nonparametric residue analysis of dynamic pet data with application to cerebral fdg studies in normals kinetic analysis is used to extract metabolic information from dynamic positron emission tomography pet uptake data the theory of indicator dilutions developed in the seminal work of meier and zierler 1954 provides a probabilistic framework for representation of pet tracer uptake data in terms of a convolution between an arterial input function and a tissue residue the residue is a scaled survival function associated with tracer residence in the tissue nonparametric inference for the residue a deconvolution problem provides a novel approach to kinetic analysis critically one that is not reliant on specific compartmental modeling assumptions a practical computational technique based on regularized cubic b spline approximation of the residence time distribution is proposed nonparametric residue analysis allows formal statistical evaluation of specific parametric models to be considered this analysis needs to properly account for the increased flexibility of the nonparametric estimator the met

complexity analysis of interior point algorithms for non lipschitz and nonconvex minimization we propose a first order interior point algorithm for a class of non lipschitz and nonconvex minimization problems with box constraints which arise from applications in variable selection and regularized optimization the objective functions of these problems are continuously differentiable typically at interior points of the feasible set our first order algorithm is easy to implement and the objective function value is reduced monotonically along the iteration points we show that the worst case iteration complexity for finding an epsilon scaled first order stationary point is o epsilon 2 o 2 furthermore we develop a second order interior point algorithm using the hessian matrix and solve a quadratic program with a ball constraint at each iteration although the second order interior point algorithm costs more computational time than that of the first order algorithm in each iteration its worst case iteration complexity for finding an epsilon scaled second order stationary point is reduced to o epsilon 3 2 o 3 2 note that an epsilon scaled second order stationary point must also be an epsilon scaled first order stationary point

smoothing spline anova for exponential families with application to the wisconsin epidemiological study of diabetic retinopathy the 1994 neyman memorial lecture let y i i 1 n be independent observations with the density of y i of the form h y i f i exp y i f i b f i c y i where b and c are given functions and b is twice continuously differentiable and bounded away from 0 let i t f t i where t t 1 t d t 1 t d t the t are measurable spaces of rather general form and f is an unknown function on t with some assumed smoothness properties given y i t i i 1 n it is desired to estimate f t for t in some region of interest contained in t we develop the fitting of smoothing spline anova models to this data of the form f t c f t f t t the components of the decomposition satisfy side conditions which generalize the usual side conditions for parametric anova the estimate of f is obtained as the minimizer in an appropriate function space of l y f j f j f where l y f is the negative log likelihood of y y 1 y n given f the j j are quadratic penalty functionals and the anova decomposition is terminated in some manner there are five major parts required to turn this program into a practical data analysis tool 1 methods for deciding which terms in the anova decomposition to include model selection 2 methods for choosing good values of the smoothing parameters 3 methods for making confidence statements concerning the estimate 4 numerical algorithms for the calculations and finally 5 public software in this paper we carry out this program relying on earlier work and filling in important gaps the overall scheme is applied to bernoulli data from the wisconsin epidemiologic study of diabetic retinopathy to model the risk of progression of diabetic retinopathy as a function of glycosylated hemoglobin duration of diabetes and body mass index it is believed that the results have wide practical application to the analysis of data from large epidemiologic studies

semiparametric analysis of variance with tensor product thin plate splines we consider fitting multivariate models to response data based on analysis of variance anova like decompositions of functions of several variables f t 1 t d c f t f t t a theory for fitting some components of these models with polynomial smoothing splines exists when each t is in a subset of the real line in this case the various estimated components turn out to be certain tensor sums and products of polynomial splines this approach may not be natural when one or more of the variables are geographic in particular where nature does not know north from east

testing for linearity in a semiparametric regression model abstract we propose a new exact test for nonlinearity in a regression model with one possibly nonlinear component the test is based on the stochastic interpretation of spline smoothing given in wahba 1978 and is a point optimal invariant test as defined in king 1988 based on this stochastic model we show that the power of the exact test compares favourably with several other exact tests for nonlinearity proposed in the literature and that its level and power are robust to long and short tailed symmetric error distributions we also present an o n algorithm based on a state space approach to compute exact p values for the point optimal invariant test whereas previous implementations required o n3 operations an example is presented to illustrate the theory

smoothness priors and nonlinear regression abstract smoothness priors represent prior information that an unknown function does not change slope quickly and hence that the function describes a simple curve e g wahba 1978 in this article such priors for the multiple nonlinear regression model are developed in such a way that estimates and standard errors can be obtained as a natural and conceptually straightforward extension of linear multiple regression estimation with the addition of dummy variables and dummy observations relations to spline and polynomial interpolation are described an illustrative example of cost function estimation is provided

smoothing parameter selection for a class of semiparametric linear models summary spline based approaches to non parametric and semiparametric regression as well as to regression of scalar outcomes on functional predictors entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized we demonstrate that the equations determining two popular methods for smoothing parameter selection generalized cross validation and restricted maximum likelihood share a similar form that allows us to prove several results which are common to both and to derive a condition under which they yield identical values these ideas are illustrated by application of functional principal component regression a method for regressing scalars on functions to two chemometric data sets

the inelastic enskog equation with external force in this paper the cauchy problem for the inelastic enskog equation with external force is considered for near vacuum data under the assumptions on the bi characteristic we proved the global existence of mild solution

kernel regression when the boundary region is large with an application to testing the adequacy of polynomial models abstract it is well known that kernel regression estimators are subject to so called boundary or edge effects a phenomenon in which the bias of an estimator increases near the endpoints of the estimation interval when the regression curve is linear or nearly linear the requisite amount of smoothing is so great that the boundary region is effectively the entire estimation interval special boundary kernels are proposed here to deal with such cases it is shown that the proposed kernel estimator has a property also enjoyed by cubic smoothing splines namely as the estimator s smoothing parameter becomes large the estimator tends to a straight line the limiting straight line is essentially the least squares line when the design points are equally spaced a simple generalization of ideas in the linear case leads to kernel estimates that are polynomials of any given degree for large bandwidths such estimates are an important component of a proposed test for the adequacy of a polynomial model the test s

global existence in l 1 for the modified nonlinear enskog equation in ℝ 3 a global existence theorem with large initial data inl1 is given for the modified enskog equation in 3 the method which is based on the existence of a liapunov functional analog of theh boltzmann theorem utilizes a weak compactness argument inl1 in a similar way to the diperna lions proof for the boltzmann equation the existence theorem is obtained under certain condition on the behavior of the geometric factory the condition ony amounts to the fact that thel1 norm of the collision term grows linearly when the local density tends to infinity