asymptotics for in sample density forecasting this paper generalizes recent proposals of density forecasting models and it develops theory for this class of models in density forecasting the density of observations is estimated in regions where the density is not observed identification of the density in such regions is guaranteed by structural assumptions on the density that allows exact extrapolation in this paper the structural assumption is made that the density is a product of one dimensional functions the theory is quite general in assuming the shape of the region where the density is observed such models naturally arise when the time point of an observation can be written as the sum of two terms e g onset and incubation period of a disease the developed theory also allows for a multiplicative factor of seasonal effects seasonal effects are present in many actuarial biostatistical econometric and statistical studies smoothing estimators are proposed that are based on backfitting full asymptotic theory is derived for them a practical example from the insurance business is given producing a within year budget of reported insurance claims a small sample study supports the theoretical results

multidimensional reaction diffusion equations with white noise boundary perturbations in this paper we study multidimensional stochastic reaction diffusion equations srde s with white noise boundary data more precisely we consider a general srde with robin data to be a white noise field because this boundary data is very irregular we formulate a set of conditions that a random field must satisfy to solve the srde we show that a unique solution exists and we study the boundary layer behavior of the solution this boundary layer analysis reveals some natural restrictions on the reaction term of the srde that ensure that the reaction term does not qualitatively affect the boundary layer the boundary layer analysis also leads to the definition of some functional banach spaces into which are encoded the boundary layer degeneracies and that would be the natural settings for other analyses of the srde of this paper e g large deviations and central limit theorems approximation theorems

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

efficient estimation of the partly linear additive cox model the partly linear additive cox model is an extension of the linear cox model and allows flexible modeling of covariate effects semiparametrically we study asymptotic properties of the maximum partial likelihood estimator of this model with right censored data using polynomial splines we show that with a range of choices of the smoothing parameter the number of spline basis functions required for estimation of the nonparametric components the estimator of the finite dimensional regression parameter is root n consistent asymptotically normal and achieves the semiparametric information bound rates of convergence for the estimators of the nonparametric components are obtained they are comparable to the rates in nonparametric regression implementation of the estimation approach can be done easily and is illustrated by using a simulated example

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

estimating multiplicative and additive hazard functions by kernel methods we propose new procedures for estimating the component functions in both additive and multiplicativen onparametricm arker dependenht azard models we work with a full counting process framework that allows for left truncation and right censoring and time varying covariates our procedures are based on kernel hazard estimation as developed by nielsen and linton and on the idea of marginal integration we provide a central limit theorem for the marginal integration estimator we then define estimators based on finite step backfitting in both additive and multiplicative cases and prove that these estimators are asymptotically normal and have smaller variance than the marginal integration method

optimal multivariable lqg control using a single diophantine equation the general solution of the optimal lqg problem using the polynomial equation approach involves the solution of a couple of two sided matrix polynomial equations the conditions under which a single one sided equation which is related to the original two the implied diophantine equation yields the unique optimal controller are derived in this paper the result has considerable relevance to aspects such as computation and self tuning control applications

kernel estimation in a nonparametric marker dependent hazard model we introduce a new kernel hazard estimator in a nonparametric model where the stochastic hazard depends on the current value of time and on the current value of a time dependent covariate or marker we establish the pointwise and global convergence of our estimator

exploring the nature of covariate effects in the proportional hazards model we discuss an exploratory technique for investigating the nature of covariate effects in cox s proportional hazards model this technique features an additive term sigma p1 fj chi ij in place of the usual linear term sigma p1 chi ij beta j where chi i1 chi i2 chi ip are covariate values for the ith individual the fj are unspecified smooth functions that are estimated using scatterplot smoothers these functions can be used for descriptive purposes or to suggest transformations of the covariates the estimation technique is a variation of the local scoring algorithm for generalized additive models hastie and tibshirani 1986 statistical science 1 297 318

diagnostic plots to reveal functional form for covariates in multiplicative intensity models abstract we show how plots based on the residuals from a proportional hazards model may be used to reveal the correct functional form for covariates in the model a smoothed plot of the martingale residues was suggested for this purpose by therneau grambsch and fleming 1990 biometrika 77 147 160 however its consistency required that the covariates be independent they also noted that the plot could be biased for large covariate effects we introduce two refinements which overcome these difficulties the first is based on a ratio of scatter plot smooths where the numerator is the smooth of the observed count plotted against the covariate and the denominator is a smooth of the expected count this is related to the arjas goodness of fit plot 1988 journal of the american statistical association 83 204 212 the second technique smooths the martingale residuals divided by the expected count using expected count as a weight this latter approach is related to a glm partial residual plot as well as to the iterative methods of hastie and tibshirani 1990 biometrics 46 1005 1016 and gentleman and crowley 1991 biometrics 47 1283 1296 applications to survival data sets are given

a general theory for the wiener hopf design of multivariable control systems multivariable control system design in a quadratic cost setting is treated for a completely general configuration the class of all controllers is determined for which the general configuration is internally asymptotically stable and a quadratic cost functional is finite this controller class is parameterized in terms of an arbitrary real rational strictly proper matrix z s which is analytic in the closed right hand side of the s plane the choice z identical to 0 gives the controller which minimizes the quadratic cost functional

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

comparative analysis of multiscale gaussian random field simulation algorithms abstract we analyze and compare the efficiency and accuracy of two simulation methods for homogeneous random fields with multiscale resolution we consider in particular the fourier wavelet method and three variants of the randomization method a without any stratified sampling of wavenumber space b with stratified sampling of wavenumbers with equal energy subdivision c with stratified sampling with a logarithmically uniform subdivision we focus primarily on fractal gaussian random fields with kolmogorov type spectra previous work has shown that variants a and b of the randomization method are only able to generate a self similar structure function over three to four decades with reasonable computational effort by contrast variant c along with the fourier wavelet method is able to reproduce accurate self similar scaling of the structure function over a number of decades increasing linearly with computational effort for our examples we will show that nine decades can be reproduced we provide some conceptual and numerical comparison of the various cost contributions to each random field simulation method we find that when evaluating ensemble averaged quantities like the correlation and structure functions as well as some multi point statistical characteristics the randomization method can provide good accuracy with less cost than the fourier wavelet method the cost of the randomization method relative to the fourier wavelet method however appears to increase with the complexity of the random field statistics which are to be calculated accurately moreover the fourier wavelet method has better ergodic properties and hence becomes more efficient for the computation of spatial rather than ensemble averages which may be important in simulating the solutions to partial differential equations with random field coefficients

regression splines in the cox model with application to covariate effects in liver disease abstract the cox proportional hazards model restricts the log hazard ratio to be linear in the covariates a smooth nonlinear covariate effect may go undetected in this model but can be well approximated by a spline function a survival model based on data from a clinical trial of primary biliary cirrhosis is developed using regression splines and the resulting log hazard ratio estimates are compared with those from nonparametric methods we remove the linear restriction on the log hazard ratio by transforming a continuous covariate into a vector of fixed knot basis splines b splines b splines are known to produce better conditioned systems of equations than the truncated power basis when used as interpolants and show similar behavior when fitting proportional hazards models we describe the procedures for and the issues arising in the estimation and the testing of the b spline coefficients although inference is not well developed for some nonparametric methods that estimate covariate effects the

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

numerical simulation of randomly forced turbulent flows several authors have proposed studying randomly forced turbulent flows e g e a novikov soviet physics jetp 20 5 1290 1965 more recently theoretical investigations e g renormalization group have focused on white noise forced navier stokes equations v yakhot and s a orszag j sci comput 1 1 3 1986 the present article aims to provide an appropriate numerical method for the simulation of randomly forced turbulent systems the spatial discretization is based on the classical fourier spectral method the time integration is performed by a second order runge kutta scheme the consistency of an extension of this scheme to treat additive noise stochastic differential equations is proved the random number generator is based on lagged fibonacci series results are presented for two randomly forced problems the burgers and the incompressible navier stokes equations with a white noise in time forcing term characterized by a power law correlation function in spectral space a variety of statistics are computed for both problems including the structure functions the third order structure functions are compared with their exact expressions in the inertial subrange the influence of the dissipation mechanism viscous or hyperviscous on the inertial subrange is discussed in particular probability density functions of velocity increments are computed for the navier stokes simulation finally for both burgers and navier stokes problems our results support the view that random sweeping is the dominant effect of the large scale motion on the small scales

a feedback theory of two degree of freedom optimal wiener hopf design the design of linear two degree of freedom stabilizing controllers is treated in a quadratic cost setting the class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance tracking cost sensitivity and stability margins is discussed

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

in sample forecasting with local linear survival densities in this paper in sample forecasting is defined as forecasting a structured density to sets where it is unobserved the structured density consists of one dimensional in sample components that identify the density on such sets we focus on the multiplicative density structure which has recently been seen as the underlying structure of non life insurance forecasts in non life insurance the in sample area is defined as one triangle and the forecasting area as the triangle that 20 added to the first triangle produces a square recent approaches estimate two one dimensional components by projecting an unstructured two dimensional density estimator onto the space of multiplicatively separable functions we show that time reversal reduces the problem to two one dimensional problems where the one dimensional data are left truncated and a one dimensional survival density estimator is needed this paper then uses the local linear density smoother with 25 weighted cross validated and do validated bandwidth selectors full asymptotic theory is provided with and without time reversal finite sample studies and an application to non life insurance are included

the lqg ltr procedure for multivariable feedback control design this paper provides a tutorial overview of the lqg ltr design procedure for linear multivariable feedback systems lqg ltr is interpreted as the solution of a specific weighted h2 tradeoff between transfer functions in the frequency domain properties of this solution are examined for both minimum phase and nonminimum phase systems this leads to a formal weight augmentation procedure for the minimum phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights while such arbitrary specifications are not possible for nonminimum phase problems a direct relationship between weights and sensitivities is developed for nonminimum phase siso and certain nonminimum phase mimo cases which guides the weight selection process

stochastic analysis of an elastic 3d half space respond to random boundary displacements exact results and karhunen loeve expansion a stochastic response of an elastic 3d half space to random displacement excitations on the boundary plane is studied we derive exact results for the case of white noise excitations which are then used to give convolution representations for the case of general finite correlation length fluctuations of displacements prescribed on the boundary solutions to these elasticity problem are random fields which appear to be horizontally homogeneous but inhomogeneous in the vertical direction this enables us to construct explicitly the karhunen loeve k l series expansion by solving the eigen value problem for the correlation operator simulation results are presented and compared with the exact representations derived for the displacement correlation tensor this paper is a complete 3d generalization of the 2d case study we presented in sabelfeld and shalimova j stat phys 132 6 1071 1095 2008

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

general polynomial solution to the optimal feedback feedforward stochastic tracking problem a general solution to the optimal stochastic tracking problem in the presence of both measurable and immeasurable disturbances is obtained using polynomial techniques the plant under consideration includes a coloured measurement noise signal in addition all disturbance and reference sub systems may be unstable the problem formulation involves a cost function which has dynamic weighting elements a feedforward compensator is incorporated in the optimization procedure for the rejection of the measurable disturbance

extension of linear quadratic optimal control theory for mixed backgrounds the problem of finding an optimal controller while both deterministic and stochastic signals are present in the feedback system is addressed a general framework is developed to solve the above problem and to unify conventional frequency domain lq and lqg optimal control theories both the system transient and steady state behaviours are considered and the exact tracking of the arbitrary reference signal is guaranteed the decomposition of a mixed signal into the deterministic and stochastic parts gives a chance to investigate the effect of the weighting factors which were specified in the cost function on the compromise between transient and steady state system performance the solution which characterizes the structure of the optimal controller results in a set of independent diophantine equations instead of a set of coupled ones moreover the number of equations can be reduced under weak conditions finally both transient command tracking and steady state noise rejection capabilities can be op

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

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

elastic half plane under random displacement excitations on the boundary we study in this paper a respond of an elastic half plane to random boundary excitations we treat both the white noise excitations and more generally homogeneous random fluctuations of displacements prescribed on the boundary solutions to these problems are inhomogeneous random fields which are however homogeneous with respect to the longitudinal coordinate this is used to represent the displacements as series expansions involving a complete set of deterministic functions with corresponding random coefficients we construct the karhunen loeve k l series expansion which is based on the eigen decomposition of the correlation operator the k l expansion can be used to calculate the statistical characteristics of other functionals of interest in particular the strain and stress tensors and the elastic energy tensor