analytic torsion and holomorphic determinant bundles i bott chern forms and analytic torsion we attach secondary invariants to any acyclic complex of holomorphic hermitian vector bundles on a complex manifold these were first introduced by bott and chern bot c our new definition uses quillen s superconnections we also give an axiomatic characterization of these classes these results will be used in bgs2 and bgs3 to study the determinant of the cohomology of a holomorphic vector bundle

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

asymptotic theory of generalized information criterion for geostatistical regression model selection information criteria such as akaike s information criterion and bayesian information criterion are often applied in model selection however their asymptotic behaviors for selecting geostatistical regression models have not been well studied particularly under the fixed domain asymptotic framework with more and more data observed in a bounded fixed region in this article we study the generalized information criterion gic for selecting geostatistical regression models under a more general mixed domain asymptotic framework via uniform convergence developments of some statistics we establish the selection consistency and the asymptotic loss efficiency of gic under some regularity conditions regardless of whether the covariance model is correctly or wrongly specified we further provide specific examples with different types of explanatory variables that satisfy the conditions for example in some situations gic is selection consistent even when some spatial covariance parameters cannot be estimated consistently on the other hand gic fails to select the true polynomial order consistently under the fixed domain asymptotic framework moreover the growth rate of the domain and the degree of smoothness of candidate regressors in space are shown to play key roles for model selection

efficient statistical inference procedures for partially nonlinear models and their applications motivated by an analysis of a real data set in ecology we consider a class of partially nonlinear models where both a nonparametric component and a parametric component are present we develop two new estimation procedures to estimate the parameters in the parametric component consistency and asymptotic normality of the resulting estimators are established we further propose an estimation procedure and a generalized f test procedure for the nonparametric component in the partially nonlinear models asymptotic properties of the newly proposed estimation procedure and the test statistic are derived finite sample performance of the proposed inference procedures are assessed by monte carlo simulation studies an application in ecology is used to illustrate the proposed methods

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

semiparametric inference in a partial linear model in a partial linear model the dependence of a response variate y on covariates w x is given by y w x e where e is independent of w x with densities g and f respectively in this paper an asymptotically efficient estimator of is constructed solely under mild smoothness assumptions on the unknown f and g thereby removing the assumption of finite residual variance on which all least squares type estimators available in the literature are based

positive shrinkage improved pretest and absolute penalty estimators in partially linear models shrinkage estimators of a partially linear regression parameter vector are constructed by shrinking estimators in the direction of the estimate which is appropriate when the regression parameters are restricted to a linear subspace we investigate the asymptotic properties of positive stein type and improved pretest semiparametric estimators under quadratic loss under an asymptotic distributional quadratic risk criterion their relative dominance picture is explored analytically it is shown that positive stein type semiparametric estimators perform better than the usual stein type and least square semiparametric estimators and that an improved pretest semiparametric estimator is superior to the usual pretest semiparametric estimator we also consider an absolute penalty type estimator for partially linear models and give a monte carlo simulation comparisons of positive shrinkage improved pretest and the absolute penalty type estimators the comparison shows that the shrinkage method performs better than the absolute penalty type estimation method when the dimension of the parameter space is much larger than that of the linear subspace

statistical estimation in generalized multiparameter likelihood models multiparameter likelihood models mlms with multiple covariates have a wide range of applications however they encounter the curse of dimensionality problem when the dimension of the covariates is large we develop a generalized multiparameter likelihood model that copes with multiple covariates and adapts to dynamic structural changes well it includes some popular models such as the partially linear and varying coefficient models as special cases we present a simple effective two step method to estimate both the parametric and the nonparametric components when the model is fixed the proposed estimator of the parametric component has the n 1 2convergence rate and the estimator of the nonparametric component enjoys an adaptivity property we suggest a data driven procedure for selecting the bandwidths and propose an initial estimator in profile likelihood estimation of the parametric part to ensure stability of the approach in general settings we further develop an automatic procedure to ide

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

second order approximation in the partially linear regression model we examine the second order properties of various quantities of interest in the partially linear regression model we obtain a stochastic expansion with remainder op n 2 4 where u 1 2 for the standardized semiparametric least squares estimator a standard error estimator and a studentized statistic we use the second order expansions to correct the standard error estimates for second order effects and to define a method of bandwidth choice a monte carlo experiment provides favorable evidence on our method of bandwidth choice

a unifying integral iss framework for stability of nonlinear cascades we analyze nonlinear cascades in which the driven subsystem is integral input to state stable iss and we characterize the admissible integral iss gains for stability this characterization makes use of the convergence speed of the driving subsystem and allows a larger class of gain functions when the convergence is faster we show that our integral iss gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem the result is used to develop a new observer based backstepping design in which the growth of the nonlinear damping terms is reduced

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

superconnections theta series and period domains abstract we use superconnections to define and study some natural differential forms on the period domain d that parametrizes polarized hodge structures of given type on a rational quadratic vector space v these forms depend on a choice of vectors v 1 v r v and have a gaussian shape that peaks on the locus where v 1 v r become hodge classes we show that they can be rescaled so that one can form theta series by summing over a lattice l r v r these series define differential forms on arithmetic quotients d we compute their cohomology class explicitly in terms of the cohomology classes of hodge loci in d when the period domain is a hermitian symmetric domain of type iv we show that the components of our forms of appropriate degree recover the forms introduced by kudla and millson in particular our results provide another way to establish the main properties of these forms

controller design for nonlinear affine systems by control lyapunov functions abstract this paper addresses the stabilization problems for nonlinear affine systems first of all the explicit feedback controller is developed for a nonlinear multiple input affine system by assuming that there exists a control lyapunov function next based upon the homogeneous property sufficient conditions for the continuity of the derived controller are developed and then the developed control design methodology is applied to stabilize a class of nonlinear affine cascaded systems it is shown that under some homogeneous assumptions on control lyapunov functions and the interconnection term the cascaded system can be globally stabilized finally some interesting results of finite time stabilization for nonlinear affine systems are also obtained

on two geometric theta lifts the theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type in this paper we establish for the orthogonal group o p 2 an adjointness result between borcherds s singular theta lift and the kudla millson lift we extend this result to arbitrary signature by introducing a new singular theta lift for o p q on the geometric side this lift can be interpreted as a differential character in the sense of cheeger and simons for the cycles under consideration

sparse estimators and the oracle property or the return of hodges estimator abstract we point out some pitfalls related to the concept of an oracle property as used in fan and li 2001 variable selection via nonconcave penalized likelihood and its oracle properties journal of the american statistical association 96 1348 1360 2002 variable selection for cox s proportional hazards model and frailty model annals of statistics 30 74 99 2004 new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis journal of the american statistical association 99 710 723 which are reminiscent of the well known pitfalls related to hodges estimator the oracle property is often a consequence of sparsity of an estimator we show that any estimator satisfying a sparsity property has maximal risk that converges to the supremum of the loss function in particular the maximal risk diverges to infinity whenever the loss function is unbounded for ease of presentation the result is set in the framework of a linear regression model but generalizes far beyond that setting in a monte carlo study we also assess the extent of the problem in finite samples for the smoothly clipped absolute deviation scad estimator introduced in fan and li 2001 variable selection via nonconcave penalized likelihood and its oracle properties journal of the american statistical association 96 1348 1360 we find that this estimator can perform rather poorly in finite samples and that its worst case performance relative to maximum likelihood deteriorates with increasing sample size when the estimator is tuned to sparsity

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

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

superconnection currents and complex immersions let i m m be an immersion of complex manifolds and let be a complex of holomorphic hermitian vector bundles on m which provides a projective resolution of the sheaf of sections of a holomorphic vector bundle on m we study the convergence as u of a class of superconnection currents u introduced by quillen and we calculate the limit microlocal estimates of the speed of convergence are also given

risk bounds for model selection via penalization performance bounds for criteria for model selection are devel oped using recent theory for sieves the model selection criteria are based on an empirical loss or contrast function with an added penalty term moti vated by empirical process theory and roughly proportional to the number of parameters needed to describe the model divided by the number of ob servations most of our examples involve density or regression estimation settings and we focus on the problem of estimating the unknown density or regression function we show that the quadratic risk of the minimum penal ized empirical contrast estimatoris bounded by an index of the accuracy of the sieve this accuracy index quanties the trade off among the candidate models between the approximation error and parameter dimension relative to sample size if we choose a list of models which exhibit good approximation prop erties with respect to different classes of smoothness the estimator can be simultaneously minimax rate optimal in each of those classes this is what is usually called adaptation the type of classes of smoothness in which one gets adaptation depends heavily on the list of models if too many models are involved in order to get accurate approximation of many wide classes of functions simultaneously it may happen that the estimator is only approx

robust stabilization of nonlinear cascaded systems this paper considers the problem of robust stabilization for an uncertain nonlinear system which is a cascaded interconnection of two subsystems both of the subsystems are allowed to be nonlinear multi variable and containing uncertain parameters we present a new approach to designing stabilizing controllers which assure both robust global asymptotic stability and local quadratic stability compared with existing results the assumptions required for such robust stabilizing controllers to exist are significantly simplified

quadratic stabilizability of linear systems with structural independent time varying uncertainties the author investigates the problem of designing a linear state feedback control to stabilize a class of single input uncertain linear dynamical systems the systems under consideration contain time varying uncertain parameters whose values are unknown but bounded in given compact sets the method used to establish asymptotical stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the author first shows that to ensure a stabilizable system some entries of the system matrices must be sign invariant he then derives necessary and sufficient conditions under which a system can be quadratically stabilized by a linear control for all admissible variations of uncertainties the conditions show that all uncertainties can only enter the system matrices in such a way as to form a particular geometrical pattern called an antisymmetric stepwise configuration for the systems satisfying the stabilizability conditions a computational control design procedure is also provided and illustrated via an example

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

on the large sample minimal coverage probability of confidence intervals after model selection we give a large sample analysis of the minimal coverage probability of the usual confidence intervals for regression parameters when the underlying model is chosen by a conservative or overconsistent model selection procedure we derive an upper bound for the large sample limit minimal coverage probability of such intervals that applies to a large class of model selection procedures including the akaike information criterion as well as various pretesting procedures this upper bound can be used as a safeguard to identify situations where the actual coverage probability can be far below the nominal level we illustrate that the asymptotic upper bound can be statistically meaningful even in rather small samples

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

variable selection for partially linear models with measurement errors this article focuses on variable selection for partially linear models when the covariates are measured with additive errors we propose two classes of variable selection procedures penalized least squares and penalized quantile regression using the nonconvex penalized principle the first procedure corrects the bias in the loss function caused by the measurement error by applying the so called correction for attenuation approach whereas the second procedure corrects the bias by using orthogonal regression the sampling properties for the two procedures are investigated the rate of convergence and the asymptotic normality of the resulting estimates are established we further demonstrate that with proper choices of the penalty functions and the regularization parameter the resulting estimates perform asymptotically as well as an oracle procedure as proposed by fan and li choice of smoothing parameters is also discussed finite sample performance of the proposed variable selection procedures is asse

robust global stabilization of a class of uncertain feedforward nonlinear systems abstract the problem of global asymptotically stabilizing a certain class of uncertain feedforward nonlinear systems is considered the control law is obtained by nesting saturation functions whose amplitude can be rendered arbitrarily small with respect to previous works on the subject the design procedure is able to deal with uncertain possibly time varying parameters ranging within the prescribed compact sets which can affect also the linear approximation of the system the small gain theorem for nonlinear systems which are input to state stable with restrictions is shown to be a key tool for designing a state feedback saturated control law

a note on smoothness priors and nonlinear regression abstract a generalization of a nonparametric estimator proposed by shiller 1984 is considered the estimator is shown to be directly related to penalized least squares estimation and spline smoothing some simplifications concerning the computation of shiller s estimator and corresponding posterior covariances are indicated

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

green forms and the arithmetic siegel weil formula we construct natural green forms for special cycles in orthogonal and unitary shimura varieties in all codimensions and for compact shimura varieties of type mathrm o p 2 and mathrm u p 1 we show that the resulting local archimedean height pairings are related to special values of derivatives of siegel eisentein series a conjecture put forward by kudla relates these derivatives to arithmetic intersections of special cycles and our results settle the part of his conjecture involving local archimedean heights

convergence rates for parametric components in a partly linear model consider the regression model y i x i beta g t i e i for i 1 cdots n here g is an unknown holder continuous function of known order p in r beta is a k times 1 parameter vector to be estimated and e i is an unobserved disturbance such a model is often encountered in situations in which there is little real knowledge about the nature of g a piecewise polynomial g n is proposed to approximate g the least squares estimator hat beta is obtained based on the model y i x i beta g n t i e i it is shown that hat beta can achieve the usual parametric rates n 1 2 with the smallest possible asymptotic variance for the case that x and t are correlated

the hodge conjecture and arithmetic quotients of complex balls let s be a closed shimura variety uniformized by the complex n ball associated with a standard unitary group the hodge conjecture predicts that every hodge class in h 2k s mathbb q k 0 dots n is algebraic we show that this holds for all degrees k away from the neighborhood bigl tfrac13n tfrac23n bigr of the middle degree we also prove the tate conjecture for the same degrees as the hodge conjecture and the generalized form of the hodge conjecture in degrees away from an interval depending on the codimension c of the subvariety centered at the middle dimension of s these results are derived from a general theorem that applies to all shimura varieties associated with standard unitary groups of any signature the proofs make use of arthur s endoscopic classification of automorphic representations of classical groups as such our results rely on the stabilization of the trace formula for the disconnected groups gl n rtimes langle theta rangle associated with base change

kernel smoothing in partial linear models on considere deux methodes d estimation l une reliee aux splines de lissage partiels l autre motivee par une analyse de residus partielle

consistent covariate selection and post model selection inference in semiparametric regression this paper presents a model selection technique of estimation in semiparametric regression models of the type y i x i f t i w i i 1 n the parametric and nonparametric components are estimated simultaneously by this procedure estimation is based on a collection of finite dimensional models using a penalized least squares criterion for selection we show that by tailoring the penalty terms developed for nonparametric regression to semiparametric models we can consistently estimate the subset of nonzero coefficients of the linear part moreover the selected estimator of the linear component is asymptotically normal

tuning parameter selectors for the smoothly clipped absolute deviation method summary the penalized least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method it not only automatically and consistently selects the important variables but also produces estimators which are as efficient as the oracle estimator however these attractive features depend on appropriate choice of the tuning parameter we show that the commonly used generalized crossvalidation cannot select the tuning parameter satisfactorily with a nonignorable overfitting effect in the resulting model in addition we propose a bic tuning parameter selector which is shown to be able to identify the true model consistently simulation studies are presented to support theoretical findings and an empirical example is given to illustrate its use in the female labor supply data

robust h control for a class of uncertain nonlinear switched systems with average dwell time this paper focuses on the robust h control problem for a class of nonlinear switched systems containing neutral uncertainties with average dwell time adt switching uncertainties are considered to be nonlinearly dependent on state and state derivative and allowed to appear in channels of state control input and disturbance input the robust h control problem of the switched system with stabilisable and unstabilisable subsystems is solvable if the stabilisable and unstabilisable subsystems satisfy certain conditions and admissible switching strategy among them adt and piecewise lyapunov function approaches are applied to achieve the control design a numerical example is provided to illustrate the effectiveness of the proposed approach

an asymptotic theory for model selection inference in general semiparametric problems summary hjort claeskens 2003 developed an asymptotic theory for model selection model averaging and subsequent inference using likelihood methods in parametric models along with associated confidence statements in this article we consider a semiparametric version of this problem wherein the likelihood depends on parameters and an unknown function and model selection averaging is to be applied to the parametric parts of the model we show that all the results of hjort claeskens hold in the semiparametric context if the fisher information matrix for parametric models is replaced by the semiparametric information bound for semiparametric models and if maximum likelihood estimators for parametric models are replaced by semiparametric efficient profile estimators our methods of proof employ le cam s contiguity lemmas leading to transparent results the results also describe the behaviour of semiparametric model estimators when the parametric component is misspecified and also have implications for pointwise consistent model selectors somekeywords akaike information criterion bayes information criterion efficient semiparametric estimation frequentist model averaging model averaging model selection profile likelihood semiparametric model

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

semiparametric regression in likelihood based models abstract a weighted likelihood is used to estimate the parameters in a semiparametric model involving two covariates and allowing an association between the covariates the development is for arbitrary but specified densities of the observations the estimators are consistent and asymptotically normal hypothesis testing of the parametric component can be performed using a wald test simulations and analysis of data with bernoulli observations demonstrate the estimators application speckman developed kernel estimators where the conditional density of the observations is normal with p parametric covariates speckman s estimators and the new estimators are asymptotically equivalent with the bias of speckman s estimators being smaller as an example we study the relationship between a binary response indicating the occurrence of an intraoperative cardiac complication icc in vascular surgery patients and two risk factors duration of the operation or and asa score which is an evaluation of the patien

minimax adaptive spectral estimation from an ensemble of signals we develop a statistical method for estimating the spectrum from a data set that consists of several signals all of which are realizations of a common random process we first find estimates of the common spectrum using each signal then we construct m partial aggregates each partial aggregate is a linear combination of m 1 of the spectral estimates the weights are obtained from the data via a least squares criterion the final spectral estimate is the average of these m partial aggregates we show that our final estimator is minimax rate adaptive if at least two of the estimators per signal attain the optimal rate n 2alpha 2alpha 1 for spectra belonging to a generalized lipschitz ball with smoothness index alpha our simulation study strongly suggests that our procedure works well in practice and in a large variety of situations is preferable to the simple averaging of the m spectral estimates