statistical inference for time changed levy processes via composite characteristic function estimation in this article the problem of semi parametric inference on the parameters of a multidimensional levy process lt with independent components based on the low frequency observations of the corresponding time changed levy process l mathcal t t where mathcal t is a nonnegative nondecreasing real valued process independent of lt is studied we show that this problem is closely related to the problem of composite function estimation that has recently gotten much attention in statistical literature under suitable identifiability conditions we propose a consistent estimate for the levy density of lt and derive the uniform as well as the pointwise convergence rates of the estimate proposed moreover we prove that the rates obtained are optimal in a minimax sense over suitable classes of time changed levy models finally we present a simulation study showing the performance of our estimation algorithm in the case of time changed normal inverse gaussian nig levy processes

a simple smooth backfitting method for additive models in this paper a new smooth backfitting estimate is proposed for additive regression models the estimate has the simple structure of nadaraya watson smooth backfitting but at the same time achieves the oracle property of local linear smooth backfitting each component is estimated with the same asymptotic accuracy as if the other components were known

adaptive estimation over anisotropic functional classes via oracle approach we address the problem of adaptive minimax estimation in white gaussian noise model under lp loss 1 p 1 on the anisotropic nikolskii classes we present the es timation procedure based on a new data driven selection scheme from the family of kernel estimators with varying bandwidths for proposed estimator we establish so called lp norm oracle inequality and use it for deriving minimax adaptive results we prove the existence of rate adaptive estimators and fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk in particular some new asymptotics of the minimax risk are discovered including necessary and sufficient conditions for existencea uniformly consistent estimator we provide also with detailed overview of existing methods and results and formulate open problems in adaptive minimax estimation

differentiability of multivalued functions on time scales and applications to multivalued dynamic equations abstract in this paper a class of new derivatives of multivalued functions on a time scale called the hukuhara hilger derivative suited to our study of multivalued dynamic equations is developed moreover some corresponding properties of the hukuhara hilger derivative are discussed the proposed approach forms the appropriate environment within which the study of multivalued dynamic inclusions on time scales can be developed a first example of multivalued dynamic equations is included

integrably bounded set valued stochastic integrals abstract the paper is devoted to properties of aumann and ito set valued stochastic integrals defined as some set valued random variables in particular the problem of integrable boundedness of the generalized ito set valued stochastic integrals is considered unfortunately ito set valued stochastic integrals defined by e j jung and j h kim in the paper 5 are not in general integrably bounded see 8 15 therefore in the present paper we consider generalized ito set valued stochastic integrals see 10 11 defined for absolutely summable and countable subsets of the space i l 2 i r i f i r d m of all square integrable i f nonanticipative matrix valued stochastic processes such integrals are integrably bounded and possess properties needed in the theory of set valued stochastic equations

the existence and asymptotic properties of a backfitting projection algorithm under weak conditions we derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function the procedure employs a recent projection interpretation of popular kernel estimators provided by mammen marron turlach and wand 1997 and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in bickel klaassen ritov and wellner 1993 our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components and in this sense improves on the method analysed in opsomer and ruppert 1997 we provide high level conditions independent of the sampling scheme we then verify that these conditions are satisfied in a regression and a time series autoregression under weak conditions

set valued functions in frechet spaces continuity hukuhara differentiability and applications to set differential equations abstract the set k c f of compact convex subsets of a frechet space f is studied in detail and is realized as a projective limit of metric spaces the notion of hausdorff metric on it is replaced by a family of corresponding semi metrics which provide the necessary background for the support of continuity and lipschitz continuity finally the notion of hukuhara derivative suited to our study is developed the proposed approach forms the appropriate environment within which the study of set differential equations for frechet spaces can be developed a first example on r is included

weak solutions of set valued stochastic differential equations abstract the paper is devoted to the existence of weak solutions of set valued stochastic differential equations such equations were considered in the authors paper 22 where existence and uniqueness of strong solutions have been investigated now apart from the existence of weak solutions the weak compactness in distribution of the set of all weak solutions of set valued stochastic differential equations is considered

the interrelation between stochastic differential inclusions and set valued stochastic differential equations abstract in this paper we connect the well established theory of stochastic differential inclusions with a new theory of set valued stochastic differential equations solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty bounded convex and closed subsets of the space l 2 consisting of square integrable random vectors we show that for the solution x to a set valued stochastic differential equation corresponding to a stochastic differential inclusion there exists a solution x for this inclusion that is a l 2 continuous selection of x this result enables us to draw inferences about the reachable sets of solutions for stochastic differential inclusions as well as to consider the viability problem for stochastic differential inclusions

multivariate locally weighted least squares regression nonparametric regression using locally weighted least squares was first discussed by stone and by cleveland recently it was shown by fan and by fan and gijbels that the local linear kernel weighted least squares regression estimator has asymptotic properties making it superior in certain senses to the nadaraya watson and gasser muller kernel estimators in this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables we are able to derive the leading bias and variance terms for general multivariate kernel weights using weighted least squares matrix theory this approach is especially convenient when analysing the asymptotic conditional bias and variance of the estimator at points near the boundary of the support of the predictors we also investigate the asymptotic properties of the multivariate local quadratic least squares regression estimator discussed by cleveland and devlin and in the univariate case higher order polynomial fits and derivative estimation

estimation of additive regression models with known links summary we consider estimation of an additive nonparametric regression model with known link function the asymptotic distribution of this regression estimate is given the practical performance is investigated via an application to the study of migration between east and west germany

local partitioned regression in this paper we introduce a kernel based estimation principle for nonparametric models named local partitioned regression lpr this principle is a nonparametric generalization of the familiar partition regression in linear models it has several key advantages first it generates estimators for a very large class of semi and nonparametric models a number of examples that are particularly relevant for economic applications will be discussed in this paper this class contains the additive partially linear and varying coefficient models as well as several other models that have not been discussed in the literature second lpr based estimators achieve optimality criteria they have optimal speed of convergence and are oracle efficient moreover they are simple in structure widely applicable and computationally inexpensive a monte carlo simulation highlights these advantages

yield curve estimation by kernel smoothing methods we introduce a new method for the estimation of discount functions yield curves and forward curves from government issued coupon bonds our approach is nonparametric and does not assume a particular functional form for the discount function although we do show how to impose various restrictions in the estimation our method is based on kernel smoothing and is defined as the minimum of some localized population moment condition the solution to the sample problem is not explicit and our estimation procedure is iterative rather like the backfitting method of estimating additive nonparametric models we establish the asymptotic normality of our methods using the asymptotic representation of our estimator as an infinite series with declining coefficients the rate of convergence is standard for one dimensional nonparametric regression we investigate the finite sample performance of our method in comparison with other well established methods in a small simulation experiment

on deep learning as a remedy for the curse of dimensionality in nonparametric regression assuming that a smoothness condition and a suitable restriction on the structure of the regression function hold it is shown that least squares estimates based on multilayer feedforward neural networks are able to circumvent the curse of dimensionality in nonparametric regression the proof is based on new approximation results concerning multilayer feedforward neural networks with bounded weights and a bounded number of hidden neurons the estimates are compared with various other approaches by using simulated data

estimation of a nonlinear panel data model with semiparametric individual effects abstract this paper investigates identification and estimation of a class of nonlinear panel data single index models the model allows for unknown time specific link functions and semiparametric specification of the individual specific effects we develop an estimator for the parameters of interest and propose a powerful new kernel based modified backfitting algorithm to compute the estimator we derive uniform rates of convergence results for the estimators of the link functions and show the estimators of the finite dimensional parameters are root n consistent with a gaussian limiting distribution we study the small sample properties of the estimator via monte carlo techniques

outlier tests for logistic regression a conditional approach summary we consider exact conditional methods for identifying outliers in logistic regression data tests for a single outlier and multiple outliers are developed assuming a logistic slippage model the p values for these tests are determined using an explicit enumeration of all possible responses consistent with the observed value of the sufficient statistic justifications are given for preferring this computationally intensive approach to standard methods based on asymptotic approximations the techniques are applied to two examples

data driven local bandwidth selection for additive models with missing data this paper deals in the nonparametric estimation of additive models in the presence of missing data in the response variable specifically in the case of additive models estimated by the backfitting algorithm with local polynomial smoothers 1 three estimators are presented one based on the available data and two based on a complete sample from imputation techniques we also develop a data driven local bandwidth selector based on a wild bootstrap approximation of the mean squared error of the estimators the performance of the estimators and the local bootstrap bandwidth selection method are explored through simulation experiments

testing for threshold effects in regression models in this article we develop a general method for testing threshold effects in regression models using sup likelihood ratio lr type statistics although the sup lr type test statistic has been considered in the literature our method for establishing the asymptotic null distribution is new and nonstandard the standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function the article provides an alternative novel method that can be used to establish the asymptotic null distribution even when the usual quadratic approximation is intractable we illustrate the usefulness of our approach in the examples of the maximum score estimation maximum likelihood estimation quantile regression and maximum rank correlation estimation we establish consistency and local power properties of the test we provide some simulation results and also an empirical application to tipping in racial segregation this ar

direct estimation of low dimensional components in additive models additive regression models have turned out to be a useful statistical tool in analyses of high dimensional data sets recently an estimator of additive components has been introduced by linton and nielsen which is based on marginal integration the explicit definition of this estimator makes possible a fast computation and allows an asymptotic distribution theory in this paper an asymptotic treatment of this estimate is offered for several models a modification of this procedure is introduced we consider weighted marginal integration for local linear fits and we show that this estimate has the following advantages i with an appropriate choice of the weight function the additive components can be efficiently estimated an additive component can be estimated with the same asymptotic bias and variance as if the other components were known ii application of local linear fits reduces the design related bias

estimation of nonparametric conditional moment models with possibly nonsmooth moments this paper studies nonparametric estimation of conditional moment models in which the residual functions could be nonsmooth with respect to the unknown functions of endogenous variables it is a problem of nonparametric nonlinear instrumental variables iv estimation and a difficult nonlinear ill posed inverse problem with an unknown operator we first propose a penalized sieve minimum distance smd estimator of the unknown functions that are identified via the conditional moment models we then establish its consistency and convergence rate in strong metric allowing for possibly non compact function parameter spaces possibly non compact finite or infinite dimensional sieves with flexible lower semicompact or convex penalty or finite dimensional linear sieves without penalty under relatively low level sufficient conditions and for both mildly and severely ill posed problems we show that the convergence rates for the nonlinear ill posed inverse problems coincide with the known minimax optimal rates for the nonparametric mean iv regression we illustrate the theory by two important applications root n asymptotic normality of the plug in penalized smd estimator of a weighted average derivative of a nonparametric nonlinear iv regression and the convergence rate of a nonparametric additive quantile iv regression we also present a simulation study and an empirical estimation of a system of nonparametric quantile iv engel curves

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

fitting a bivariate additive model by local polynomial regression while the additive model is a popular nonparametric regression method many of its theoretical properties are not well understood especially when the backfitting algorithm is used for computation of the estimators this article explores those properties when the additive model is fitted by local polynomial regression sufficient conditions guaranteeing the asymptotic existence of unique estimators for the bivariate additive model are given asymptotic approximations to the bias and the variance of a homoscedastic bivariate additive model with local polynomial terms of odd and even degree are computed this model is shown to have the same rate of convergence as that of univariate local polynomial regression

bandwidth selection for smooth backfitting in additive models the smooth backfitting introduced by mammen linton and nielsen ann statist 27 1999 1443 1490 is a promising technique to fit additive regression models and is known to achieve the oracle efficiency bound in this paper we propose and discuss three fully automated bandwidth selection methods for smooth backfitting in additive models the first one is a penalized least squares approach which is based on higher order stochastic expansions for the residual sums of squares of the smooth backfitting estimates the other two are plug in bandwidth selectors which rely on approximations of the average squared errors and whose utility is restricted to local linear fitting the large sample properties of these bandwidth selection methods are given their finite sample properties are also compared through simulation experiments

a mixture model for interval censored time to response quantal assay data various mixture models are proposed and fitted to a set of time to response quantal assay data the models provide a natural extension to the time dependent case of the classical threshold model for quantal assay data the approach deals simply with interval censoring and provides flexible families of distributions for both the mixing probability and the cumulative distribution function for time to response for data of the kind considered in this paper mixture models may provide a more suitable description than other models from survival analysis such as the proportional hazards model

least median of weighted squares in logistic regression with large strata summary one aim of robust regression is to find estimators with high finite sample breakdown points although various robust estimators have been proposed in logistic regression models their breakdown points are not yet known here it is shown for logistic regression models with binary data that there is no estimator with a high finite sample breakdown point provided the estimator has to fulfill a weak condition in logistic regression models with large strata however a modification of rousseeuw s least median of squares estimator is shown to have a finite sample breakdown point of approximately 2

model free variable selection in reproducing kernel hilbert space variable selection is popular in high dimensional data analysis to identify the truly informative variables many variable selection methods have been developed under various model assumptions whereas success has been widely reported in literature their performances largely depend on validity of the assumed models such as the linear or additive models this article introduces a model free variable selection method via learning the gradient functions the idea is based on the equivalence between whether a variable is informative and whether its corresponding gradient function is substantially non zero the proposed variable selection method is then formulated in a framework of learning gradients in a flexible reproducing kernel hilbert space the key advantage of the proposed method is that it requires no explicit model assumption and allows for general variable effects its asymptotic estimation and selection consistencies are studied which establish the convergence rate of the estimated sparse gradients and assure that the truly informative variables are correctly identified in probability the effectiveness of the proposed method is also supported by a variety of simulated examples and two real life examples

properties of set valued integrals and set valued stochastic equations driven by two parameter martingales abstract in the paper we study properties of aumann s stochastic integral driven by a two parameter increasing process and set valued ito s integral with respect to the two parameter martingale both types of integrals are understood as set valued processes next the existence uniqueness and convergence properties of solutions to set valued stochastic integral equations with respect to such integrators are investigated we present new types of such equations that generalize those studied earlier the results obtained in the paper present a set valued counterpart dealing with this topic known both in single valued deterministic and stochastic cases

smooth backfitting in practice summary compared with the classical backfitting of buja hastie and tibshirani the smooth backfitting estimator sbe of mammen linton and nielsen not only provides complete asymptotic theory under weaker conditions but is also more efficient robust and easier to calculate however the original paper describing the sbe method is complex and the practical as well as the theoretical advantages of the method have still neither been recognized nor accepted by the statistical community we focus on a clear presentation of the idea the main theoretical results and practical aspects like implementation and simplification of the algorithm we introduce a feasible cross validation procedure and apply it to the problem of data driven bandwidth choice for the sbe by simulations it is shown that the sbe and our cross validation work very well indeed in particular the sbe is less affected by sparseness of data in high dimensional regression problems or strongly correlated designs the sbe has reasonable performance even in 100 dimensional additive regression problems

estimation in semiparametric spatial regression nonparametric methods have been very popular in the last couple of decades in time series and regression but no such development has taken place for spatial models a rather obvious reason for this is the curse of dimensionality for spatial data on a grid evaluating the conditional mean given its closest neighbors requires a four dimensional nonparametric regression in this paper a semiparametric spatial regression approach is proposed to avoid this problem an estimation procedure based on combining the so called marginal integration technique with local linear kernel estimation is developed in the semiparametric spatial regression setting asymptotic distributions are established under some mild conditions the same convergence rates as in the one dimensional regression case are established an application of the methodology to the classical mercer and hall wheat data set is given and indicates that one directional component appears to be nonlinear which has gone unnoticed in earlier analyses

semiparametric estimation of a binary response model with a change point due to a covariate threshold this paper is concerned with semiparametric estimation of a threshold binary response model the estimation method considered in the paper is semiparametric since the parameters for a regression function are finite dimensional while allowing for heteroskedasticity of unknown form in particular the paper considers manski 1975 1985 s maximum score estimator the model in this paper is irregular because of a change point due to an unknown threshold in a covariate this irregularity coupled with the discontinuity of the objective function of the maximum score estimator complicates the analysis of the asymptotic behavior of the estimator sufficient conditions for the identification of parameters are given and the consistency of the estimator is obtained it is shown that the estimator of the threshold parameter is n consistent and the estimator of the remaining regression parameters is cube root n consistent furthermore we obtain the asymptotic distribution of the estimators it turns out that a suitably normalized estimator of the regression parameters converges weakly to the distribution to which it would converge weakly if the true threshold value were known and likewise for the threshold estimator

estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals this paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables this is a nonparametric nonlinear instrumental variables iv problem we propose a class of penalized sieve minimum distance psmd estimators which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space some of the psmd procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty others use large dimensional sieves with lower semicompact and or convex penalties we establish their consistency and the convergence rates in banach space norms such as a sup norm or a root mean squared norm allowing for possibly noncompact infinite dimensional parameter spaces for both mildly and severely ill posed nonlinear inverse problems our convergence rates in hilbert space norms such as a root mean squared norm achieve the known minimax optimal rate for the nonparametric mean iv regression we illustrate the theory with a nonparametric additive quantile iv regression we present a simulation study and an empirical application of estimating nonparametric quantile iv engel curves

smooth backfitting in generalized additive models generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non gaussian responses including binary and count data in this paper a new likelihood approach for fitting generalized additive models is proposed it aims to maximize a smoothed likelihood the additive functions are estimated by solving a system of nonlinear integral equations an iterative algorithm based on smooth backfitting is developed from the newton kantorovich theorem asymptotic properties of the estimator and convergence of the algorithm are discussed it is shown that our proposal based on local linear fit achieves the same bias and variance as the oracle estimator that uses knowledge of the other components numerical comparison with the recently proposed two stage estimator ann statist 32 2004 2412 2443 is also made

estimation of a regression function by maxima of minima of linear functions in this paper estimation of a regression function from independent and identically distributed random variables is considered estimates are defined by minimization of the empirical l2 risk over a class of functions which are defined as maxima of minima of linear functions results concerning the rate of convergence of the estimates are derived in particular it is shown that for smooth regression functions satisfying the assumption of single index models the estimate is able to achieve up to some logarithmic factor the corresponding optimal one dimensional rate of convergence hence under these assumptions the estimate is able to circumvent the so called curse of dimensionality the small sample behavior of the estimates is illustrated by applying them to simulated data

asymptotics for nonparametric and semiparametric fixed effects panel models abstract in this paper we investigate the problem of estimating nonparametric and semiparametric panel data models with fixed effects we focus on establishing the asymptotic results for estimators using smooth backfitting methods we consider two estimators for the smooth unknown function in nonparametric panel regressions one is a local linear estimator constructed similar as the one in mammen et al 2009 which was proposed for the additive nonparametric panel model the other is the local profile likelihood based estimator proposed by henderson et al 2008 hcl hereafter we build the link and compare the difference between these two estimators which are constructed under different sets of conditions we put both of these estimators in the smooth backfitting algorithm framework discussed in mammen et al 1999 following the recently developed theories on backfitting kernel estimates in mammen et al 2009 we establish the asymptotic normality of these estimators and hence verify the conjectures made by hcl and complement their paper further we consider a partially linear fixed effects panel data model with the nonparametric component estimated using the methods discussed in the first part of the paper we give the asymptotic result for the estimators of finite dimensional parameters which shows that the first step plug in estimators will not affect the asymptotic variance in the second step estimation

variable selection and identification of high dimensional nonparametric additive nonlinear systems this paper considers variable selection and identification of dynamic additive nonlinear systems via kernel based nonparametric approaches where the number of variables and additive functions may be large variable selection aims to find which additive functions contribute and which do not the proposed variable selection consists of two successive steps at the first step one estimates each additive function by kernel based nonparametric identification approaches without suffering from the curse of dimensionality at the second step a nonnegative garrote estimator is applied to identify which additive functions are nonzero by utilizing the obtained nonparametric estimates of each function under weak conditions the nonparametric estimates of each additive function can achieve the same asymptotic properties as for 1d nonparametric identification based on kernel functions it is also established that the nonnegative garrote estimator turns a consistent estimate for each additive function into a consistent variable selection with probability one as the number of samples tends to infinity two simulation examples are presented to verify the effectiveness of the variable selection and identification approaches proposed in the paper

convergence en loi des suites d integrales stochastiques sur l espace mathbb d 1 de skorokhod for sequences of stochastic integrals k n x n functional limit theorems are presented these results hold under simple natural conditions

nonlinear variation of parameters formula for set differential equations in a metric space nonlinear variation of parameters formula for set differential equations in a metric space is developed investigating necessary tools such as differentiability of solutions relative to initial values other needed results are also proven

semiparametric profile likelihood estimation for continuous outcomes with excess zeros in a random threshold damage resistance model continuous outcome data with a proportion of observations equal to zero often referred to as semicontinuous data arise frequently in biomedical studies typical approaches involve two part models with one part a logistic model for the probability of observing a zero and some parametric continuous distribution for modeling the positive part of the data we propose a semiparametric model based on a biological system with competing damage manifestation and resistance processes this allows us to derive a closed form profile likelihood based on the retro hazard function leading to a flexible procedure for modeling continuous data with a point mass at zero a simulation study is presented to examine the properties of the method in finite samples we apply the method to a data set consisting of pulmonary capillary hemorrhage area in lab rats subjected to diagnostic ultrasound copyright 2017 john wiley sons ltd

miscellanea efficient estimation of additive nonparametric regression models summary we define a new procedure for estimating additive nonparametric regression models we use the integration method of linton nielsen 1995 to provide starting values that are then used in a one step backfitting procedure we show that our new method is efficient in a certain sense and dominates the straight integration method according to mean squared error

observations on a stochastic model for quantal assay data ajustement de 2 modeles stochastiques pour decrire les donnees de dosage quantitatifs incorporant le temps de reponse a des jeux de donnees reels et simules application aux modeles mecanicistes

generalised structured models summary we present a general class of nonlinear regression and time series models that we call generalised structured models the class is a natural generalisation of generalised additive models and it includes generalised interaction models structured volatility models visual garch generalised autoregressive conditional heteroscedasticity models and varying coefficient models we discuss estimation principles including smoothing splines and a generalisation of the projection approach of mammen et al 1999 we finish the paper with some theoretical considerations about the asymptotic performance of the estimator for the general class of generalised structured models

a flexible semiparametric forecasting model for time series in this paper we propose a semiparametric procedure called the model averaging marginal regression mamar that is flexible for forecasting of time series this procedure considers approximating a multivariate regression function by an affine combination of one dimensional marginal regression functions the weight parameters involved in the approximation are estimated by least squares on the basis of the first stage nonparametric kernel estimates of the marginal regressions under some mild conditions we have established asymptotic normality for the estimated weights and the regression function in two cases case i considers that the number of the covariates is fixed while case ii allows the number of the covariates depending on the sample size and diverging as the observations are assumed to be stationary and near epoch dependent the approach developed is applicable to both the estimation and forecasting issues in time series analysis furthermore the method and result are augmented by a simulation study and illustrated by an application in forecasting the high frequency volatility of the ftse100 index

the monotone iterative technique for impulsive hybrid set valued integro differential equations abstract we develop the monotone method for impulsive hybrid set integro differential equations in all its generality some interesting observations are presented

semiparametric estimation in general repeated measures problems summary the paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function special cases in our approach include marginal models for longitudinal or clustered data conditional logistic regression for matched case control studies multivariate measurement error models generalized linear mixed models with a semiparametric component and many others we propose profile kernel and backfitting estimation methods for these problems derive their asymptotic distributions and show that in likelihood problems the methods are semiparametric efficient although generally not true it transpires that with our methods profiling and backfitting are asymptotically equivalent we also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm the methods proposed are evaluated by using simulation studies and applied to the kenya haemoglobin data

phase spaces and periodic solutions of set functional dynamic equations with infinite delay abstract very recently a new theory known as set dynamic equations on time scales has been built in this paper a phase space is built for set functional dynamic equations with infinite delay on time scales and sufficient criteria are established for the existence of periodic solutions of such equations which generalize and incorporate as special cases some known results for set differential equations and for set difference equations when the time scale is the real number set or the integer set respectively moreover for differential inclusions and difference inclusions if the variable under consideration is a single valued mapping our results show that one can unify the study of some continuous or discrete problems in the sense of set dynamic equations on general time scales

nonparametric matching and efficient estimators of homothetically separable functions for vectors z and w and scalar v let r v z w be a function that can be non parametrically estimated consistently and asymptotically normally such as a distribution density or conditional mean regression function we provide consistent asymptotically normal nonparametric estimators for the functions g and h where r v z w h vg z w and some related models this framework encompasses homothetic and homothetically separable functions and transformed partly additive models r v z w h v g z w for unknown functions g and h such models reduce the curse of dimensionality provide a natural generalization of linear index models and are widely used in utility production and cost function applications we also provide an estimator of g that is oracle efficient achieving the same performance as an estimator based on local least squares when h is known

estimating semiparametric arch models by kernel smoothing methods we investigate a class of semiparametric arch models that includes as a special case the partially nonparametric pnp model introduced by engle and ng 1993 and which allows for both flexible dynamics and flexible function form with regard to the news impact function we show that the functional part of the model satisfies a type ii linear integral equation and give simple conditions under which there is a unique solution we propose an estimation method that is based on kernel smoothing and profiled likelihood we establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model we also discuss efficiency of both the parametric part and the nonparametric part we investigate the performance of our procedures on simulated data and on a sample of s p500 index returns we find evidence of asymmetric news impact functions consistent with the parametric analysis

on kolmogorov s representation of functions of several variables by functions of one variable abstract this paper proposes a multivariate nonparametric regression estimator motivated by kolmogorov doklady 114 1957 679 we consider functions of the form k 1 t g k k 1 k x 1 k d k x d 1 t

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

consistent model selection for marginal generalized additive model for correlated data we consider the generalized additive model when responses from the same cluster are correlated incorporating correlation in the estimation of nonparametric components for the generalized additive model is important because it improves estimation efficiency and increases statistical power for model selection in our setting there is no specified likelihood function for the generalized additive model because the outcomes could be nonnormal and discrete which makes estimation and model selection very challenging problems we propose consistent estimation and model selection that incorporate the correlation structure we establish an asymptotic property with l2 norm consistency for the nonparametric components which achieves the optimal rate of convergence in addition the proposed model selection strategy is able to select the correct generalized additive model consistently that is with probability approaching to 1 the estimators for the zero function components converge to 0 almost surely we illus

nonparametric identification of nonlinear time series projections abstract we study the possibility of identifying general linear and nonlinear time series models using nonparametric methods the kernel estimators of the conditional mean and variance are used as a basis and the properties of these quantities as model indicators are briefly discussed some drawbacks are pointed out and motivated by these we introduce projections as tools of identification the projections are especially useful for additive modeling expressions for the asymptotic bias and variance are obtained the projection of the conditional variance is suggested as a tool for identifying heteroscedastic time series the results are illustrated by simulations for both the estimators of the projections and the estimators of the conditional mean and variance

consistent specification tests for semiparametric nonparametric models based on series estimation methods abstract this paper considers the problem of consistent model specification tests using series estimation methods the null models we consider in this paper all contain some nonparametric components a leading case we consider is to test for an additive partially linear model the null distribution of the test statistic is derived using a central limit theorem for hilbert valued random arrays the test statistic is shown to be able to detect local alternatives that approach the null models at the order of op n 1 2 we show that the wild bootstrap method can be used to approximate the null distribution of the test statistic a small monte carlo simulation is reported to examine the finite sample performance of the proposed test we also show that the proposed test can be easily modified to obtain series based consistent tests for other semiparametric nonparametric models

on connections between stochastic differential inclusions and set valued stochastic differential equations driven by semimartingales abstract in the paper we study properties of solutions to stochastic differential inclusions and set valued stochastic differential equations with respect to semimartingale integrators we present new connections between their solutions in particular we show that attainable sets of solutions to stochastic inclusions are subsets of values of multivalued solutions of certain set valued stochastic equations we also show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set valued stochastic equation the results obtained in the paper generalize results dealing with this topic known both in deterministic and stochastic cases

rate optimal estimation for a general class of nonparametric regression models with unknown link functions this paper discusses a nonparametric regression model that naturally generalizes neural network models the model is based on a finite number of one dimensional transformations and can be estimated with a one dimensional rate of convergence the model contains the generalized additive model with unknown link function as a special case for this case it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion

threshold dose response models in toxicology summary after a brief discussion of the threshold concept in toxicology we consider models for the estimation of thresholds in the case where the observed response is binary or quantal a generalization of the four parameter tukey lambda family of distributions is proposed as a useful class of models for threshold estimation properties of these models are discussed and the process of model fitting and evaluation is illustrated using a number of data sets the discussion includes consideration of background or spontaneous response and comparison with other models one of these is the linearplateau or hockey stick model which has been used in a number of toxicological studies

on two families of transformations to additivity for binary response data summary two families of power transformations for probabilities are introduced to model symmetric and asymmetric departures from the logistic model the aim is to provide in a comprehensive way a representation of alternative scales in terms of which to carry out the analysis of binary response data maximum likelihood methods are employed to estimate an appropriate transformation using glim tests for detection of symmetric and asymmetric departures are proposed

estimating regression models with unknown break points this paper deals with fitting piecewise terms in regression models where one or more break points are true parameters of the model for estimation a simple linearization technique is called for taking advantage of the linear formulation of the problem as a result the method is suitable for any regression model with linear predictor and so current software can be used threshold modelling as function of explanatory variables is also allowed differences between the other procedures available are shown and relative merits discussed simulations and two examples are presented to illustrate the method

threshold estimation based on a p value framework in dose response and regression settings we use p values to identify the threshold level at which a regression function leaves its baseline value a problem motivated by applications in toxicological and pharmacological dose response studies and environmental statistics we study the problem in two sampling settings one where multiple responses can be obtained at a number of different covariate levels and the other the standard regression setting involving limited number of response values at each covariate our procedure involves testing the hypothesis that the regression function is at its baseline at each covariate value and then computing the potentially approximate p value of the test an estimate of the threshold is obtained by fitting a piecewise constant function with a single jump discontinuity known as a stump to these observed p values as they behave in markedly different ways on the two sides of the threshold the estimate is shown to be consistent and its finite sample properties are studied through simulations our approach is computationally simple and extends to the estimation of the baseline value of the regression function heteroscedastic errors and to time series it is illustrated on some real data applications

set valued and fuzzy stochastic differential equations driven by semimartingales abstract in the paper we present set valued and fuzzy stochastic integrals with respect to semimartingale integrators as well as their main properties then we study the existence of solutions to set valued and fuzzy set valued stochastic differential equations driven by semimartingales the stability of solutions is also established

nonparametric estimation of an additive model with a link function this paper describes an estimator of the additive components of a nonparametric additive model with a known link function when the additive components are twice continuously differentiable the estimator is asymptotically normally distributed with a rate of convergence in probability of 2 5 n this is true regardless of the finite dimension of the explanatory variable thus in contrast to the existing asymptotically normal estimator the new estimator has no curse of dimensionality moreover the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty

a statistical method for assessing a threshold in epidemiological studies i describe a method for estimating and testing a threshold value in epidemiological studies a threshold effect indicates an association between a risk factor and a defined outcome above the threshold value but none below it an important field of application is occupational medicine where for a lot of chemical compounds and other agents which are non carcinogenic health hazards so called threshold limit values or tlvs are specified the method is presented within the framework of the logistic regression model which is widely used in the analysis of the relationship between some explanatory variables and a dependent dichotomous outcome in most available programs for this and also for other models the concept of a threshold is disregarded the method for assessing a threshold consists of an estimation procedure using the maximum likelihood technique and a test procedure based on the likelihood ratio statistic r following under the null hypothesis no threshold a quasi one sided chi 2 distribution with one degree of freedom this use of this distribution is supported by a simulation study the method is applied to data from an epidemiological study of the relationship between occupational dust exposure and chronic bronchitic reactions the results are confirmed by bootstrap resampling

asymptotic confidence bands for generalized nonlinear regression models asymptotic confidence bands for generalized nonlinear regression models are developed these are based on a combination of the s method of scheffe together with the delta method which is used to approximate the mean function by a linear combination of the parameters the approach can be used in any situation where large sample theory can be applied to yield asymptotically normal estimates of the parameters together with a consistent estimate of the large sample covariance matrix alternative formulations for various special cases allow the use of restricted range bands a number of examples are given including a pharmacokinetic model a logit model with a background response rate and a parametric survival model

existence and interrelation between set and fuzzy differential equations abstract an existence result is proved for set differential equation when the function involved is upper semicontinuous and the result is very general then the connection between the solutions of fuzzy differential equation and the set differential equation that is generated from it is studied

set valued assessments of solutions to stochastic differential equations with random set parameters abstract we consider stochastic differential equations depending on parameters whose uncertainty is modeled by random compact sets several approaches are discussed how to construct set valued stochastic processes from the solutions the induced lower and upper probabilities are compared to a set valued set function and a set of probability measures constructed from the distributions of the solutions and the selections of the random set

smooth backfitting of proportional hazards with multiplicative components smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression by projecting the data down onto the structured space of interest smooth backfitting

operational time and in sample density forecasting in this paper we consider a new structural model for in sample density forecasting in sample density forecasting is to estimate a structured density on a region where data are observed and then re use the estimated structured density on some region where data are not observed our structural assumption is that the density is a product of one dimensional functions with one function sitting on the scale of a transformed space of observations the transformation involves another unknown one dimensional function so that our model is formulated via a known smooth function of three underlying unknown one dimensional functions we present an innovative way of estimating the one dimensional functions and show that all the estimators of the three components achieve the optimal one dimensional rate of convergence we illustrate how one can use our approach by analyzing a real dataset and also verify the tractable finite sample performance of the method via a simulation study

dynamics and stability of impulsive hybrid setvalued integro differential equations with delay abstract we study the dynamics and stability theory for impulsive hybrid set integro differential equations with delay sufficient conditions for the stability of the null solution of impulsive hybrid set integro differential equations with delay are presented

nonparametric regression based on hierarchical interaction models in this paper we introduce the so called hierarchical interaction models where we assume that the computation of the value of a function m mathbb r d rightarrow mathbb r is done in several layers where in each layer a function of at most d inputs computed by the previous layer is evaluated we investigate two different regression estimates based on polynomial splines and on neural networks and show that if the regression function satisfies a hierarchical interaction model and all occurring functions in the model are smooth the rate of convergence of these estimates depends on d and not on d hence in this case the estimates can achieve good rate of convergence even for large d and are in this sense able to circumvent the so called curse of dimensionality

the dimensionality reduction principle for generalized additive models soit x y une paire de variables aleatoires telles que x x 1 x j s etende sur c 0 1 j la distribution conditionnelle de y etant donne x x est supposee appartenir a une famille exponentielle appropriee ayant pour parametre r f x denote la dependance de vis a vis de x et f l approximation additive de f ayant la log vraisemblance esperee maximum possible

nonparametric estimation of a generalized additive model with an unknown link function mean of a random scalar y conditional on a random vector x e rd let h x e yix x denote the conditional mean function this paper is concerned with estimating h under weak assumptions about its functional form when x is a multidimensional continuous random variable the paper describes a model that nests single index additive and multiplicative models and that can be estimated with a faster rate of convergence in probability than can a fully nonparametric model nonparametric estimation of h is usually unattractive when x is multidimensional the rate of convergence of nonparametric estimators decreases rapidly as the dimension of x increases and nonparametric estimates can be very imprecise with samples of practical size when x is multidimensional the curse of dimensionality this problem can be overcome through the use of dimension reduction methods they reduce the effective dimension of the estimation problem by making assumptions about the functional form of h that are stronger than those of a fully nonparametric estimator but weaker than those of a finite dimensional parametric model one method of dimension reduction is semiparametric single index modeling the best known and most easily estimated semiparametric single index model assumes that 1 1 h x g 3 x where 3 is an unknown d x 1 vector and g is an unknown function the vector 3 can be estimated with an n 1 2 rate of convergence in probability which is the rate that would be obtained if g were known han 1987 hardle and stoker 1989 horowitz and hardle 1996 ichimura 1993 klein and spady 1993 newey and stoker 1993 powell stock and stoker 1989 sherman 1993 stoker 1991 g can be estimated with the rate of convergence n r 2r 1 where r is an integer that depends on the smoothness of g but not on d dimension reduction can also be achieved by using a nonparametric generalized additive model in such a model