gridding with continuous curvature splines in tension a gridding method commonly called minimum curvature is widely used in the earth sciences the method interpolates the data to be gridded with a surface having continuous second derivatives and minimal total squared curvature the minimum curvature surface has an analogy in elastic plate flexure and approximates the shape adopted by a thin plate flexed to pass through the data points minimum curvature surfaces may have large oscillations and extraneous inflection points which make them unsuitable for gridding in many of the applications where they are commonly used these extraneous inflection points can be eliminated by adding tension to the elastic plate flexure equation it is straightforward to generalize minimum curvature gridding algorithms to include a tension parameter the same system of equations must be solved in either case and only the relative weights of the coefficients change therefore solutions under tension require no more computational effort than minimum curvature solutions and any algorithm which can solve the minimum curvature equations can solve the more general system we give common geologic examples where minimum curvature gridding produces erroneous results but gridding with tension yields a good solution we also outline how to improve the convergence of an iterative method of solution for the gridding equations

some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

splines in statistics abstract this is a survey article that attempts to synthesize a broad variety of work on splines in statistics splines are presented as a nonparametric function estimating technique after a general introduction to the theory of interpolating and smoothing splines splines are treated in the nonparametric regression setting the method of cross validation for choosing the smoothing parameter is discussed and the general multivariate regression surface estimation problem is addressed an extensive discussion of splines as nonparametric density estimators is followed by a discussion of their role in time series analysis a comparison of the spline and isotonic regression methodologies leads to a formulation of a hybrid estimator the closing section provides a brief overall summary and formulates a number of open unsolved problems relating to splines in statistics

brief optimal trajectory planning and smoothing splines in this paper some of the relationships between optimal control and trajectory planning are examined when planning trajectories for linear control systems a demand that arises naturally in air traffic control or noise contaminated data interpolation is that the curve passes close to given points or through intervals at given times in this paper we produce these curves by solving an optimal control problem for linear control systems while driving the output of the system close to the waypoints we furthermore show how this optimal control problem reduces to a finite quadratic programming problem and we thus provide a constructive yet theoretically sound framework for producing a rich set of curves called smoothing splines

nonlinear modeling of time series using multivariate adaptive regression splines mars abstract multivariate adaptive regression splines mars is a new methodology due to friedman for nonlinear regression modeling mars can be conceptualized as a generalization of recursive partitioning that uses spline fitting in lieu of other simple fitting functions given a set of predictor variables mars fits a model in the form of an expansion in product spline basis functions of predictors chosen during a forward and backward recursive partitioning strategy mars produces continuous models for high dimensional data that can have multiple partitions and predictor variable interactions predictor variable contributions and interactions in a mars model may be analyzed using an anova style decomposition by letting the predictor variables in mars be lagged values of a time series one obtains a new method for nonlinear autoregressive threshold modeling of time series a significant feature of this extension of mars is its ability to produce models with limit cycles when modeling time series data that

assessing time by covariate interactions in proportional hazards regression models using cubic spline functions proportional hazards or cox regression is a popular method for modelling the effects of prognostic factors on survival use of cubic spline functions to model time by covariate interactions in cox regression allows investigation of the shape of a possible covariate time dependence without having to specify a specific functional form cubic spline functions allow one to graph such time by covariate interactions to test formally for the proportional hazards assumption and also to test for non linearity of the time by covariate interaction the functions can be fitted with existing software using relatively few parameters the regression coefficients are estimated using standard maximum likelihood methods

numerical solution of differential equations with colored noise using the general theory of numerical integration of stochastic differential equations a constructive approach to numerical methods for a system with colored noise is proposed efficient methods up to the 5 2 strong order and up to the third weak order including runge kutta and implicit schemes are presented the algorithms are tested on the kubo oscillator

a semiparametric approach to density estimation abstract one method of fitting a parametric density function f x is first to estimate by maximum likelihood say and then to estimate f x by on the other hand when the parametric model does not hold the true density f x may be estimated nonparametrically as in the case of a kernel estimate the key idea proposed is to fit a combination of the parametric and nonparametric estimates namely where 0 1 is unknown the parameter is estimated from the data and its estimate is then used in as the proposed density estimate the main point is that we expect to be close to unity when the parametric model prevails and close to zero when it does not hold we show that under certain conditions converges to the parametric density when the parametric model holds and approaches the true f x when the parametric model does not hold the procedure was applied to a number of actual data sets in each case the maximum likelihood estimate was readily obtained and the semiparametric density es

interpolation methods comparison abstract in many fields spatial interpolation is used to evaluate physical data in a continuous domain the many different techniques offer different performances according to the characteristics of initial data points the aim of this paper is to provide help in choosing and evaluating the technique that best suits the data set a few indices measure the quality of interpolation by different viewpoints an extensive test case is reported involving four different interpolation methods data sets are generally connected with environmental topics or taken from literature

non parametric survival analysis of infectious disease data this paper develops nonparametric methods based on contact intervals for the analysis of infectious disease data the contact interval from person i to person j is the time between the onset of infectiousness in i and infectious contact from i to j where we define infectious contact as a contact sufficient to infect a susceptible individual the hazard function of the contact interval distribution equals the hazard of infectious contact from i to j so it provides a summary of the evolution of infectiousness over time when who infects whom is observed the nelson aalen estimator produces an unbiased estimate of the cumulative hazard function of the contact interval distribution when who infects whom is not observed we use an em algorithm to average the nelson aalen estimates from all possible combinations of who infected whom consistent with the observed data this converges to a nonparametric maximum likelihood estimate of the cumulative hazard function that we call the marginal nelson aalen estimate we study the behavior of these methods in simulations and use them to analyze household surveillance data from the 2009 influenza a h1n1 pandemic

a cubic spline extension of the durbin watson test summary we propose a new test for model misspecification in linear regression based on a measure of smoothness of the regression residuals this curvature statistic is related to a property of cubic splines and leads to a convenient powerful test for patterns the distribution of the curvature statistic may be derived from assumptions of normality for equally spaced data the calculations are simplified and a table of significance points of the distribution is given smoothness considerations also lead to a natural generalization of the durbin watson or mean square successive differences statistic for unequally spaced observations this generalized mean squared successive differences statistic arises when linear splines are substituted for cubic splines in the development of the curvature statistic the power of the curvature statistic is investigated by simulation compared to several other commonly used tests for patterns the curvature test is shown to be more powerful where noise levels are small and the complexity of the underlying pattern is moderate the calculation and use of this statistic is illustrated on a problem involving nonlinear regression residuals

inverse passive learning of an input output map through update spline smoothing this paper presents a robust method of learning passively a one dimensional input output map when receiving only indirect information about the correct input output map e g only the sign of the deviation between the actual estimated output value and the correct output value is obtained this information is obtained for only one input output combination per updating cycle the approach is to increment or decrement step by step the output values of the actually stored map and then to apply global or local cubic spline smoothing in order to avoid adaptation holes at points which are never updated or less frequently updated than other points this method works with noisy measurements as well as slowly time varying systems even discontinuous changes of the desired input output relation do not result in instability problems of convergence and stability are treated and design rules are given

multi level repeated measures growth modelling using extended spline functions this paper explores the fitting of multi level models to growth data over a wide age range using a new class of extended spline models these extend conventional splines based on a function representation by allowing variable order functions and by including fractional polynomial terms the work focuses on modelling human growth in height and head circumference with example data sets the procedures can be used with covariates and for comparing population parameters

extended hazard regression for censored survival data with covariates a spline approximation for the baseline hazard function a regression model for censored survival data with covariates is introduced and termed extended hazard regression ehr ehr includes the proportional hazards ph and the accelerated failure time aft models as special cases by approximating the baseline hazard function with quadratic splines we develop a maximum likelihood estimation procedure to provide a simultaneous estimate of both the hazard function and the regression coefficients the aft and ph assumptions can then be compared by likelihood ratio tests within the more general ehr model several examples based on artificial and real data are discussed

flexible regression models with cubic splines we describe the use of cubic splines in regression models to represent the relationship between the response variable and a vector of covariates this simple method can help prevent the problems that result from inappropriate linearity assumptions we compare restricted cubic spline regression to non parametric procedures for characterizing the relationship between age and survival in the stanford heart transplant data we also provide an illustrative example in cancer therapeutics

numerical treatment of stochastic river quality models driven by colored noise 1 monte carlo simulation is a popular method of risk and uncertainty analysis in oceanographic atmospheric and environmental applications it is common practice to introduce a stochastic part to an already existing deterministic model and after many simulations to provide the user with statistics of the model outcome the underlying deterministic model is often a discretization of a set of partial differential equations describing physical processes such as transport turbulence buoyancy effects and continuity much effort is also put into deriving numerically efficient schemes for the time integration the resulting model is often quite large and complex in sharp contrast the stochastic extension used for monte carlo experiments is usually achieved by adding white noise unfortunately the order of time integration in the stochastic model is reduced compared to the deterministic model because white noise is not a smooth process instead of completely replacing the old numerical scheme and implementing a higher order scheme for stochastic differential equations we suggest a different approach that is able to use existing numerical schemes the method uses a smooth colored noise process as the driving force resulting in a higher order of convergence we show promising results from numerical experiments including parametric uncertainty

a tension approach to controlling the shape of cubic spline surfaces on fvs triangulations we propose a parametric tensioned version of the fvs macro element to control the shape of the composite surface and remove artificial oscillations bumps and other undesired behaviour in particular this approach is applied to c 1 cubic spline surfaces over a four directional mesh produced by two stage scattered data fitting methods

a two stage algorithm for discontinuity preserving surface reconstruction a two stage algorithm for visual surface reconstruction from scattered data while preserving discontinuities is presented the first stage consists of a robust local approximation algorithm the moving least median of squares mlms of error to clean the data and create a grid from the original scattered data points this process is discontinuity preserving the second stage introduces a weighted bicubic spline wbs as a surface descriptor the wbs has a factor in the regularizing term that adapts the behavior of the spline across discontinuities the weighted bicubic approximating spline can approximate data with step discontinuities with no discernible distortion in the approximating surface the combination of robust surface fitting and wbss removes outliers and reduces gaussian noise either stage by itself would not effectively remove both kinds of noise experimental results with the two stage algorithm are presented

vector splines and the estimation of filter functions in this paper we consider the estimation of vector valued periodic functions by use of splines an error criterion is constructed and it is shown that the vector spline is simply the vector of univariate splines the vector valued spline is shown to be an approach to the estimation of the spectral density matrix in a multivariate setting two approaches are given for estimation of filter related functions including gain transfer function coherency and so on some results on consistency are given and an application is made to sonar systems

influence diagnostics for the cross validated smoothing parameter in spline smoothing abstract this article addresses the problem of influence in estimating the smoothing parameter when fitting a univariate smoothing spline diagnostics are presented that can identify observations that locally influence the choice of smoothing parameter by generalized cross validation either through their case weights or observed responses generalized cross validation and the diagnostic methods are given a frequency interpretation and illustrated with examples

field theory for function fields of plane quartic curves abstract let c be a smooth plane quartic curve over a field k and k c be a rational function field of c we develop a field theory for k c in the following method let p be the projection from c to a line l with a center p p 2 the p induces an extension field k c k p 1 where k p 1 is a maximal rational subfield in this paper we study the extension k c k p 1 from several points of view for example we consider the following questions when is the extension k c k p 1 galois what is the galois closure of k c k p 1

flexible modeling of the effects of continuous prognostic factors in relative survival relative survival methods permit separating the effects of prognostic factors on disease related excess mortality from their effects on other causes natural mortality even when individual causes of death are unknown as in conventional crude survival accurate assessment of prognostic factors requires testing and possibly modeling of non proportional effects and for continuous covariates of non linear relationships with the hazard we propose a flexible extension of the additive hazards relative survival model in which the observed all causes mortality hazard is represented by a sum of disease related excess and natural mortality hazards in our flexible model the three functions representing i the baseline hazard for excess mortality ii the time dependent effects and iii for continuous covariates non linear effects on the logarithm of this hazard are all modeled by low dimension cubic regression splines non parametric likelihood ratio tests are proposed to test the time dependent and non linear effects the accuracy of the estimated functions is evaluated in multivariable simulations to illustrate the new insights offered by the proposed model we apply it to re assess the effects of patient age and of secular trends on disease related mortality in colon cancer

minimizing the laplacian of a function squared with prescribed values on interior boundaries theory of polysplines in this paper we consider the minimization of the integral of the laplacian of a real valued function squared and more general functionals with prescribed values on some interior boundaries r with the integral taken over the domain d we prove that the solution is a biharmonic function in d except on the interior boundaries r and satisfies some matching conditions on r there is a close analogy with the one dimensional cubic splines which is the reason for calling the solution a polyspline of order 2 or biharmonic polyspline similarly when the quadratic functional is the integral of qf 2 q a positive integer then the solution is a polyharmonic function of order 2q 2qf x o for x e d r satisfying matching conditions on r and is called a polyspline of order 2q uniqueness and existence for polysplines of order 2q provided that the interior boundaries r are sufficiently smooth surfaces arld ad c r is proved three examples of data sets r possessing symmetry are considered in which the computation of polysplines is reduced to computation of onedimensional l splines

reproducing kernel hilbert space method for optimal interpolation of potential field data the rkhs based optimal image interpolation method presented by chen and de figueiredo 1993 is applied to scattered potential field measurements the rkhs which admits only interpolants consistent with laplace s equation is defined and its kernel derived the algorithm is compared to bicubic spline interpolation and is found to yield vastly superior results

fitting time dependent multicompartment models a case study a multicompartment model with time dependent transfer rates is fitted to data on ovarian follicle dynamics in mice the fitted model arises from an interplay between parametric and nonparametric approaches to fitting curves to these data nonparametric regression estimates in the form of spline smoothers are used in conjunction with the biologically meaningful general class of multicompartment models to suggest refinements to the parametric model one result of this interplay is the suggestion of using three stage step functions for the compartmental transition rates the resulting curves mimic closely the nonparametric regression estimates

multiresolution parameterization for geophysical inverse problems a model parameterization based on a multiresolution wavelet representation is proposed for geophysical inverse problems in this study the matrix equation for the wavelet representation of the model is constructed by dual wavelet transforms of a readily built matrix based on the pixel parameterization we demonstrate the merits of the proposed parameterization using the simple examples of geophysical data gridding and 3d seismic tomography and comparing the results with those obtained by the conventional pixel parameterization it is shown that for the conventional damped least squares solutions of pixel parameterized models regularization by norm damping deteriorates the underlying model correlation due to sparse and heterogeneous sampling whereas roughness damping schemes impose a priori arbitrary correlation length irrespective of the heterogeneous sampling the scale hierarchy embedded in the proposed multiresolution parameterization facilitates the compromise between the dual spatial and scale resolution depending on the local richness of the data constraints across different scales at a site model variation of various scale spectra can be robustly resolved through the scale hierarchy there is thus no need to invoke additional smoothness regularization

application of the pocs inversion method to cross borehole imaging cross borehole tomography suffers from a well known problem of data incompleteness the limited ray coverage dictated by the poor experimental geometry implies that certain features of the velocity field are not determined by the data construction of a tomographic image of the velocity field therefore requires the addition of prior constraints to the inversion in the fourier wavenumber domain assuming straight line rays the process of adding prior constraints is equivalent to specifying unmeasured wavenumber coefficients the projection onto convex sets pocs algorithm can impose physically plausible constraints that allow high quality tomographic images to be produced each constraint is viewed as defining a set in function space of images that satisfy that particular constraint the pocs method finds one or more images in the intersection of the constraining sets which is equivalent to finding an image that simutaneously satisfies a number of constraints including the observed data the sets of

a green s function based bi dimensional empirical mode decomposition a new git bemd algorithm is developed based on green s function with tension much faster than canonical bemd algorithms easy to implement and very robust superior performance tested on artificial and real images bidimensional empirical mode decomposition bemd interprets an image as a superposition of bidimensional intrinsic mode functions bimfs they are extracted by a process called sifting which encompasses two dimensional surface interpolations connecting a set of local maxima or minima to form corresponding envelope surfaces existing surface interpolation schemes are computationally very demanding and often induce artifacts in the extracted modes this paper suggests a novel method of envelope surface interpolation based on green s functions including surface tension greatly improves the stability of the new method which we call green s function in tension based bemd git bemd simulation results using toy images with various textures facial images and functional neuroimages demonstrate the superior performance of the new method when compared to its canonical bemd counterpart git bemd strongly speeds up computations and achieves a higher quality of the extracted bimfs furthermore git bemd can be extended simply to an ensemble based variant git beemd if needed in summary the study suggests the new variant git bemd as a highly competitive fast and stable alternative to existing bemd techniques for image analysis

diagnostics for smoothing splines summary diagnostic measures appropriate for use with smoothing splines are derived and their properties are investigated the proposed measures focus on detection of observations which substantially influence the fit and provide additional information over that obtained from examination of residuals alone a numerical example illustrates the technique

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

flexible estimation of survival curves conditional on non linear and time dependent predictor effects prognostic studies often estimate survival curves for patients with different covariate vectors but the validity of their results depends largely on the accuracy of the estimated covariate effects to avoid conventional proportional hazards and linearity assumptions flexible extensions of cox s proportional hazards model incorporate non linear nl and or time dependent td covariate effects however their impact on survival curves estimation is unclear our primary goal is to develop and validate a flexible method for estimating individual patients survival curves conditional on multiple predictors with possibly nl and or td effects we first obtain maximum partial likelihood estimates of nl and td effects and use backward elimination to select statistically significant effects into a final multivariable model we then plug the selected nl and td estimates in the full likelihood function and estimate the baseline hazard function and the resulting survival curves conditional on individual covariate vectors the td and nl functions and the log hazard are modeled with unpenalized regression b splines in simulations our flexible survival curve estimates were unbiased and had much lower mean square errors than the conventional estimates in real life analyses of mortality after a septic shock our model improved significantly the deviance likelihood ratio test 84 8 df 20 p 0 0001 and changed substantially the predicted survival for several subjects

algebraic phase unwrapping based on two dimensional spline smoothing over triangles two dimensional 2d phase unwrapping is an estimation problem of a continuous phase function over a 2d domain from its wrapped samples in this paper we propose a novel approach for high resolution 2d phase unwrapping in the first step spline smoothing sps we construct a pair of the smoothest spline functions which minimize the energies of their local changes while interpolating respectively the cosine and the sine of given wrapped samples if these functions have no common zero over the domain the proposed estimate of the continuous phase function can be obtained by algebraic phase unwrapping in the second step algebraic phase unwrapping apu to avoid the occurrence of common zeros in sps due to phase noise in the observed wrapped samples we also propose a denoising step denoising by selective smoothing dss as preprocessing which selectively smooths unreliable wrapped samples by using convex optimization the smoothness of the proposed unwrapped phase function is guaranteed globally over the domain without losing any desired consistency with all reliable wrapped samples numerical experiments for terrain height estimation demonstrate the effectiveness of the proposed 2d phase unwrapping scheme

singular plane curves with infinitely many galois points for a plane curve c we call a point p p2 a galois point with respect to c if the point projection from p induces a galois extension of function fields we give an example of a singular plane curve having infinitely many inner and outer galois points we also classify plane curves whose general points are inner galois points before our results known examples in the theory of galois points have only finitely many galois points except trivial cases

principal components analysis of sampled functions this paper describes a technique for principal components analysis of data consisting ofn functions each observed atp argument values this problem arises particularly in the analysis of longitudinal data in which some behavior of a number of subjects is measured at a number of points in time in such cases information about the behavior of one or more derivatives of the function being sampled can often be very useful as for example in the analysis of growth or learning curves it is shown that the use of derivative information is equivalent to a change of metric for the row space in classical principal components analysis the reproducing kernel for the hilbert space of functions plays a central role and defines the best interpolating functions which are generalized spline functions an example is offered of how sensitivity to derivative information can reveal interesting aspects of the data

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

a hierarchical model for aggregated functional data in many areas of science one aims to estimate latent subpopulation mean curves based only on observations of aggregated population curves by aggregated curves we mean linear combination of functional data that cannot be observed individually we assume that several aggregated curves with linearly independent coefficients are available and each aggregated curve is an independent partial realization of a gaussian process with mean modeled through a weighted linear combination of the disaggregated curves the mean of the gaussian process is modeled using b splines basis expansion methods we propose a semiparametric valid covariance function that is modeled as the product of a nonparametric variance function by a correlation function the variance function is described as the square of a function that is expanded using b splines basis functions this results in a nonstationary covariance function and includes constant variance models as special cases inference is performed following the bayesian paradig

a least squares smooth fitting for irregularly spaced data finite element approach using the cubic b spline basis a new method of multivariate smooth fitting of scattered noisy data using cubic b splines was developed an optimum smoothing function was defined to minimize the x1d4c1 2 norm composed of the data residuals and the first and the second derivatives which represent the total misfit fluctuation and roughness of the function respectively the function is approximated by a cubic b spline expansion with equispaced knots the solution can be interpreted in three ways from the stochastic viewpoint it is the maximum likelihood estimate among the admissible functions under the a priori information that the first and second derivatives are zero everywhere due to random errors i e white noise from the physical viewpoint it is the finite element approximation for a lateral displacement of a bar or a plate under tension which is pulled to the data points by springs from a technical viewpoint it is an improved spline fitting algorithm the additional condition of minimizing the derivative norms stabilizes the l

monotone nonparametric regression in monotone regression procedures one utilizes only the monotonicity of the regression function in nonparametric regression one utilizes only the assumed smoothness the analytic and asymptotic properties of the estimator are superior in the latter case however monotonicity is not guaranteed we study a hybrid procedure that produces monotone estimators with properties similar to those of nonparametric regression estimators

numerical treatment of stochastic differential equations we define general runge kutta approximations for the solution of stochastic differential equations sde these approximations are proved to converge in quadratic mean to the solution of an sde with a corrected drift the explicit form of the correction term is given concerning the order of convergence we show that in general it is impossible for the quadratic mean of the one step error to be of an order greater than o h 3 this order is attained e g by the stochastic analogue of heun s method in the n dimensional case the highest order of convergence is in general only o h 2 attained by euler s method the order o h 3 can only be reached if nabla x sigma r sigma s nabla x sigma s sigma r for the diffusion matrix

penalized partial likelihood for frailties and smoothing splines in time to first insemination models for dairy cows in many epidemiological studies time to event data are clustered and the physiological relationship between time dependent covariates and the log hazard is often not linear as assumed in the cox model introducing frailties in the cox model can account for the clustering of the data and smoothing splines can be used to describe nonlinear relations these two extensions of the cox model are introduced jointly and it is shown how penalized partial likelihood techniques can be used to fit the extended model we demonstrate the need for such a model to study the relation between the physiological covariates milk ureum and protein concentration and the log hazard of first insemination in dairy cows with the farms as clusters

spline estimation of paths using bearings only tracking data abstract in many applications bearings are measured to a moving object with the goal of estimating the object s course of movement if movement is appropriately modeled as a smooth deterministic curve in the plane then a cubic spline is a reasonable representation of the curve maximum likelihood estimators are presented for parameters of regression splines assuming that observation errors follow a von mises distribution location estimates are obtainable even when data are sparse path estimation error number and placement of knots and outlier detection are discussed examples including both simulated paths and observations from a wildlife radio tracking study are presented

multicategorical spline model for item response theory additional information contained in incorrect responses calls for a multicategorical rather than a binary analysis of multiple choice data a nonparametric divided by total model for joint maximum likelihood estimation of probability of choice functions for particular responses and of latent ability is proposed the model approximates probability functions by rational splines some illustrative examples of real test data analysis and the results of a monte carlo study are presented

uniqueness and eventual uniqueness of optimal designs in some time series models abstract earlier results on the uniqueness and eventual uniqueness of optimal designs for certain time series models are extended to a wider class of processes which includes those with covariance structures such as that of multiple integrals of brownian motion and brownian bridge processes the relationship between the problems of regression design for time series and piecewise polynomial approximation with free breakpoints is discussed and consequently asymptotic results obtained by sacks and ylvisaker 1970 are seen to hold under weaker assumptions for these processes

galois points on singular plane quartic curves abstract we study the structure of function fields of plane curves following our method developed in k miura h yoshihara field theory for function fields of plane quartic curves j algebra 226 2000 283 294 especially we study galois points on singular plane quartic curves and determine the number of galois points on them furthermore we give concrete defining equations when the curve has a galois point

nonparametric maximum likelihood estimation by the method of sieves maximum likelihood estimation often fails when the parameter takes values in an infinite dimensional space for example the maximum likelihood method cannot be applied to the completely nonparametric estimation of a density function from an operatorname iid sample the maximum of the likelihood is not attained by any density in this example as in many other examples the parameter space positive functions with area one is too big but the likelihood method can often be salvaged if we first maximize over a constrained subspace of the parameter space and then relax the constraint as the sample size grows this is grenander s method of sieves application of the method sometimes leads to new estimators for familiar problems or to a new motivation for an already well studied technique we will establish some general consistency results for the method and then we will focus on three applications

function field theory of plane curves by dual curves we study the structure of function fields of plane curves following our method developed previously k miura and h yoshihara 2000 j algebra226 283 294 let k be the function field of a smooth plane curve c of degree d 4 and let kp be a maximal rational subfield of k for p p2 we study the field extension k kp from a geometrical viewpoint especially we give a sufficient condition that the galois group of the galois closure of k kp becomes a full symmetric group

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

the restricted cubic spline as baseline hazard in the proportional hazards model with step function time dependent covariables we incorporate a cubic spline function where the tails are linearly constrained as the baseline hazard into the proportional hazards model we show estimation of covariable coefficients and survival probabilities with this model to be as efficient statistically as with the cox proportional hazards model when covariables are fixed examples show that the inclusion of time dependent covariables defined as step functions into the restricted cubic spline proportional hazards model reduces computation time by a factor of 213 over the cox model advantages of the spline model also include flexibility of the hazard smooth survival curves and confidence limits for the survival and hazard estimates when there are time dependent covariables present

segmented polynomials for incidence rate estimation from prevalence data the study considers the problem of estimating incidence of a non remissible infection or disease with possibly differential mortality using data from a several cross sectional prevalence survey s fitting segmented polynomial models is proposed to estimate the incidence as a function of age using the maximum likelihood method the approach allows automatic search for optimal position of knots and model selection is performed using the akaike information criterion the method is applied to simulated data and to estimate hiv incidence among men in zimbabwe using data from both the nimh project accept hptn 043 and zimbabwe demographic health surveys 2005 2006 copyright 2016 john wiley sons ltd

a method for fitting regression splines with varying polynomial order in the linear mixed model the linear mixed model has become a widely used tool for longitudinal analysis of continuous variables the use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses exploratory analyses and hypothesis driven confirmatory analyses we propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and or random effects of the linear mixed model the polynomial segments are explicity constrained by side conditions for continuity and some smoothness at the points where they join by using a reparameterization of this explicitly constrained linear mixed model an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed knot regression splines the proposed approach is relatively simple handles splines in one variable or multiple variables and can be easily programmed using existing commercial software such as sas or s plus the method is illustrated using two examples an analysis of longitudinal viral load data from a study of subjects with acute hiv 1 infection and an analysis of 24 hour ambulatory blood pressure profiles copyright 2005 john wiley sons ltd

smoothing methods for epidemiologic analysis the development of techniques for fitting non parametric smooth curves has resulted in less restrictive regression models we discuss the ideas underlying such smoothing algorithms develop their application to epidemiologic studies and address specific issues such as coping with correlated errors an example illustrates a particular smoothing approach as applied to pulmonary function data the method provides new insight into the effect of smoking on pulmonary function the discussion offers some qualitative comparisons between smoothing methods and conventional linear models