approximation orders and shape preserving properties of the multiquadric trigonometric b spline quasi interpolant the purpose of the paper is to derive some properties of the multiquadric trigonometric b spline quasi interpolant firstly the paper captures its approximation orders for high order derivatives based on the error estimate one can choose the shape parameter properly such that the quasi interpolant gives optimal approximations to high order derivatives moreover the approximation orders also show that from the theoretical point of view the considered quasi interpolant can be applied when the approximation of high order derivatives is needed i e numerical solution of some pdes construction of lyapunov function etc secondly the paper derives some shape preserving properties of the quasi interpolant these properties suggest that the quasi interpolant may be used in the geometric modeling cad cam for instance that requires shape preservation finally to illustrate the validity of the results some numerical examples are presented both theoretical and numerical results demonstrate that the quasi interpolant cannot only provide excellent approximations to high order derivatives but also preserve the shapes well

total positivity and its applications preface i spline functions total positivity of the spline kernel and its applications b bojanov total positivity properties of lb splines t lyche l l schumaker total positivity and splines k morken totally positive systems and interpolation by subspaces of generalized splines m sommer h strauss ii matrix theory preservation of total nonnegativity under the hadamard product and related topics j garloff d g wagner vertex implications for totally nonnegative under the hadamard product and related topics j garloff on factorizations of totally positive matrices j garloff on factorizations of totally positive matrices m gasca j m pena iii geometric modeling total positivity and optimal bases j m carnicer j m pena total positivity and the shape of curves t n t goodman tchebycheff curves m l mazure h pottmann iv probability and mathematical biology analytical and probabilistic methods for totally positive matrices g s goodman some inequalities of total positivity in pure and applied mathematics s karlin z ziegler new directions and problems of multivariate total positivity motivated by genetic recombination probabilities s karlin v approximation theory tchebycheff spaces and total positivity j m carnicer j m pena cebysev and weak cebysev systems r a zalik vi complex analysis zero sets of entire fourier transforms of multiply positive density functions o m katkova vii statistics total nonnegativity of moment matrices and its application to e optimal designs in polynomial regression b heiligers analysis of regression dependence in 2 xn bivariate distributions and some applications in contingency tables s kasala m b rao viii real analysis total positivity and nonlinear analysis r q jia solutions of certain functional equations s karlin alternance and snakes in the nonlinear finite moment problem k tatalian ix combinatorics the applications of total positivity to combinatorics and conversely f brenti x integral equations spectral properties of totally positive kernels and matrices a pinkus index

an intermediate distribution between gaussian and cauchy distributions abstract in this paper we construct an intermediate distribution linking the gaussian and the cauchy distribution we provide the probability density function and the corresponding characteristic function of the intermediate distribution because many kinds of distributions have no moment we introduce weighted moments specifically we consider weighted moments under two types of weighted functions the cut off function and the exponential function through these two types of weighted functions we can obtain weighted moments for almost all distributions we consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory moreover we utilize the intermediate distribution to the problem of the stock market return in quantitative finance

limit shape of minimal difference partitions and fractional statistics the class of minimal difference partitions text mdp q with gap q is defined by the condition that successive parts in an integer partition differ from one another by at least q ge 0 in a recent series of papers by a comtet and collaborators the text mdp q ensemble with uniform measure was interpreted as a combinatorial model for quantum systems with fractional statistics that is interpolating between the classical bose einstein q 0 and fermi dirac q 1 cases this was done by formally allowing values q in 0 1 using an analytic continuation of the limit shape of the corresponding young diagrams calculated for integer q to justify this replica trick we introduce a more general model based on a variable mdp type condition encoded by an integer sequence mathfrak q q i whereby the limiting gap q is naturally interpreted as the cesaro mean of mathfrak q in this model we find the family of limit shapes parameterized by q in 0 infty confirming the earlier answer and also obtain the asymptotics of the number of parts

classes of nonseparable spatio temporal stationary covariance functions abstract suppose that a random process z s t indexed in space and time has spatio temporal stationary covariance c h u where h d d 1 is a spatial lag and u is a temporal lag separable spatio temporal covariances have the property that they can be written as a product of a purely spatial covariance and a purely temporal covariance their ease of definition is counterbalanced by the rather limited class of random processes to which they correspond in this article we derive a new approach that allows one to obtain many classes of nonseparable spatio temporal stationary covariance functions and fit several such classes to spatio temporal data on wind speed over a region in the tropical western pacific ocean

growth factors of pivoting strategies associated with neville elimination neville elimination is a direct method for solving linear systems several pivoting strategies for neville elimination including pairwise pivoting are analyzed bounds for two different kinds of growth factors are provided finally an approximation of the average normalized growth factor associated with several pivoting strategies is computed and analyzed using random matrices

a quasi interpolation scheme for periodic data based on multiquadric trigonometric b splines abstract multiquadric mq quasi interpolation has been studied extensively in the literature however the mq quasi interpolant is not well defined for periodic data since its kernel the mq function itself is not periodic note that in many applications the data may arise from a closed curve surface and thus possess some kind of periodicity for example analysis of geodetic and meteorological data constructing active contours estimating the region of attraction of dynamical systems and so on therefore it is meaningful to construct a quasi interpolant whose kernel itself is periodic for periodic data combining the construction techniques of the mq quasi interpolant and the trigonometric b spline quasi interpolant the paper constructs such a quasi interpolant the quasi interpolant couples together the periodicity of the trigonometric b spline quasi interpolant and the smoothness of the mq quasi interpolant moreover both the quasi interpolant and its derivatives are periodic the quasi interpolant covers the trigonometric b spline quasi interpolant as a special case in addition the error estimate shows that a proper shape parameter can be chosen such that the quasi interpolant provides the same approximation order as a trigonometric b spline quasi interpolant for a periodic function furthermore the quasi interpolant gives better approximations to high order derivatives than the trigonometric b spline quasi interpolant as illustrated by numerical examples presented at the end of the paper

radial basis function approximations as smoothing splines radial basis function methods for interpolation can be interpreted as roughness minimizing splines although this relationship has already been established for radial basis functions of the form g r r a and g r r alog r it is extended here to include a much larger class of functions this class includes the multiquadric g r r 2 c 2 1 2 and inverse multiquadric g r r 2 c 2 1 2 functions as well as the gaussian exp r 2 d the crucial condition is that the fourier transform of g x be positive except possibly at the origin the appropriate measure of roughness is defined in terms of this fourier transform to allow for possibility of noisy data the analysis is presented within the general framework of smoothing splines of which interpolation is a special case two diagnostic quantities the cross validation function and the sensitivity indicate the accuracy of the approximation

nonseparable stationary covariance functions for space time data geostatistical approaches to spatiotemporal prediction in environmental science climatology meteorology and related fields rely on appropriate covariance models this article proposes general classes of nonseparable stationary covariance functions for spatiotemporal random processes the constructions are directly in the space time domain and do not depend on closed form fourier inversions the model parameters can be associated with the data s spatial and temporal structures respectively and a covariance model with a readily interpretable space time interaction parameter is fitted to wind data from ireland

matern cross covariance functions for multivariate random fields we introduce a flexible parametric family of matrix valued covariance functions for multivariate spatial random fields where each constituent component is a matern process the model parameters are interpretable in terms of process variance smoothness correlation length and colocated correlation coefficients which can be positive or negative both the marginal and the cross covariance functions are of the matern type in a data example on error fields for numerical predictions of surface pressure and temperature over the north american pacific northwest we compare the bivariate matern model to the traditional linear model of coregionalization

self similarity part ii optimal estimation of fractal processes in a companion paper see self similarity part i splines and operators we characterized the class of scale invariant convolution operators the generalized fractional derivatives of order gamma we used these operators to specify regularization functionals for a series of tikhonov like least squares data fitting problems and proved that the general solution is a fractional spline of twice the order we investigated the deterministic properties of these smoothing splines and proposed a fast fourier transform fft based implementation here we present an alternative stochastic formulation to further justify these fractional spline estimators as suggested by the title the relevant processes are those that are statistically self similar that is fractional brownian motion fbm and its higher order extensions to overcome the technical difficulties due to the nonstationary character of fbm we adopt a distributional formulation due to gel fand this allows us to rigorously specify an innovation model for these fractal processes which rests on the property that they can be whitened by suitable fractional differentiation using the characteristic form of the fbm we then derive the conditional probability density function pdf p bh t y where y bh k n k kisinz are the noisy samples of the fbm bh t with hurst exponent h we find that the conditional mean is a fractional spline of degree 2h which proves that this class of functions is indeed optimal for the estimation of fractal like processes the result also yields the optimal minimum mean square error mmse parameters for the smoothing spline estimator as well as the connection with kriging and wiener filtering

a valid matern class of cross covariance functions for multivariate random fields with any number of components we introduce a valid parametric family of cross covariance functions for multivariate spatial random fields where each component has a covariance function from a well celebrated matern class unlike previous attempts our model indeed allows for various smoothnesses and rates of correlation decay for any number of vector components we present the conditions on the parameter space that result in valid models with varying degrees of complexity we discuss practical implementations including reparameterizations to reflect the conditions on the parameter space and an iterative algorithm to increase the computational efficiency we perform various monte carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging the application of the proposed multivariate matern model is illustrated on two meteorological datasets temperature pressure over the pacific northwest bivariate and wind temperature pressure in oklahoma trivariate in the latter case our flexi

integer partitions and exclusion statistics we provide a combinatorial description of exclusion statistics in terms of minimal difference p partitions we compute the probability distribution of the number of parts in a random minimal p partition it is shown that the bosonic point p 0 is a repulsive fixed point for which the limiting distribution has a gumbel form for all positive p the distribution is shown to be gaussian

a general modelling framework for multivariate disease mapping this paper deals with multivariate disease mapping we propose a novel framework that encompasses most of the models already proposed our framework starts with a simple identity reformulating kronecker products of covariance matrices as simple matrix products this formula is computationally convenient and its generalizations reproduce most of the proposals in the disease mapping literature use of the identity leads to a flexible general and computationally convenient modelling framework making it possible to combine spatial dependence structures and different relationships between diseases with limited effort moreover as the proposed modelling framework covers most of the gaussian markov random field based multivariate disease mapping models in the literature it allows comparison of all these models in a common context thus helping us to understand them better copyright 2013 oxford university press

sign regular matrices and neville elimination abstract a pivoting strategy of o n operations for the neville elimination of n n nonsingular sign regular matrices is introduced among other nice properties it is proved that it preserves sign regularity it is also shown its relationship with scaled partial pivoting strategies for neville elimination

generalized smoothing splines and the optimal discretization of the wiener filter we introduce an extended class of cardinal l sup l splines where l is a pseudo differential operator satisfying some admissibility conditions we show that the l sup l spline signal interpolation problem is well posed and that its solution is the unique minimizer of the spline energy functional spl par ls spl par sub l2 sup 2 subject to the interpolation constraint next we consider the corresponding regularized least squares estimation problem which is more appropriate for dealing with noisy data the criterion to be minimized is the sum of a quadratic data term which forces the solution to be close to the input samples and a smoothness term that privileges solutions with small spline energies here too we find that the optimal solution among all possible functions is a cardinal l sup l spline we show that this smoothing spline estimator has a stable representation in a b spline like basis and that its coefficients can be computed by digital filtering of the input signal we describe an efficient recursive filtering algorithm that is applicable whenever the transfer function of l is rational which corresponds to the case of exponential splines we justify these algorithms statistically by establishing an equivalence between l sup l smoothing splines and the minimum mean square error mmse estimation of a stationary signal corrupted by white gaussian noise in this model based formulation the optimum operator l is the whitening filter of the process and the regularization parameter is proportional to the noise variance thus the proposed formalism yields the optimal discretization of the classical wiener filter together with a fast recursive algorithm it extends the standard wiener solution by providing the optimal interpolation space we also present a bayesian interpretation of the algorithm

partition asymptotics from one dimensional quantum entropy and energy currents we give an alternative method to that of hardy ramanujan rademacher to derive the leading exponential term in the asymptotic approximation to the partition function p n a defined as the number of decompositions of a positive integer n into integer summands with each summand appearing at most a times in a given decomposition the derivation involves mapping to an equivalent physical problem concerning the quantum entropy and energy currents of particles flowing in a one dimensional 1d channel connecting thermal reservoirs and which obey gentile s intermediate statistics with statistical parameter a the method is also applied to partitions associated with haldane s fractional exclusion statistics

space time radial basis functions abstract radial basis functions are isotropic i e under a rotation the basis function is left unchanged and is obtained as a function of a distance on the space for euclidean space this is not a problem since there is a natural metric to extend radial basis functions to space time i e rm t either a zonal anisotropy has to be incorporated or a metric must be defined on space time while the sum of two valid radial basis functions defined on different dimensional spaces is generally only semidefinite on the product space the product of two positive definite functions on lower dimensional spaces is positive definite on the product space this construction can be extended in several ways including a product sum integrated product and the integrated product sum examples are given for each construction and an application is given the constructions are equally applicable to extending from space to space time or for splitting higher dimensional euclidean spaces into the product of several lower dimensional spaces

on the problem of permissible covariance and variogram models the covariance and variogram models ordinary or generalized are important statistical tools used in various estimation and simulation techniques which have been recently applied to diverse hydrologic problems for example the efficacy of kriging a method for interpolating filtering or averaging spatial phenomena depends to a large extent on the covariance or variogram model chosen the aim of this article is to provide the users of these techniques with convenient criteria that may help them to judge whether a function which arises in a particular problem and is not included among the known covariance or variogram models is permissible as such a model this is done by investigating the properties of the candidate model in both the space and frequency domains in the present article this investigation covers stationary random functions as well as intrinsic random functions i e nonstationary functions for which increments of some order are stationary then based on the theoretical results obtained a procedure is outlined and successfully applied to a number of candidate models in order to give to this procedure a more practical context we employ stereological equations that essentially transfer the investigations to one dimensional space together with approximations in terms of polygonal functions and fourier bessel series expansions there are many benefits and applications of such a procedure polygonal models can be fit arbitrarily closely to the data also the approximation of a particular model in the frequency domain by a fourier bessel series expansion can be very effective this is shown by theory and by example

a new method for derivation of statistical weight of the gentile statistics abstract we present a new method for obtaining the statistical weight of the gentile statistics in a recent paper perez and tun presented an approximate combinatoric and an exact recursive formula for the statistical weight of gentile statistics beginning from bosonic and fermionic cases respectively hernandez perez and tun 2007 in this paper we obtain two exact one combinatoric and one recursive formulae for the statistical weight of gentile statistics by another approach the combinatoric formula is valid only for special cases whereas recursive formula is valid for all possible cases moreover for a given q maximum number of particles that can occupy a level for gentile statistics the recursive formula we have derived gives the result much faster than the recursive formula presented in hernandez perez and tun 2007 when one uses a computer program moreover we obtained the statistical weight for the distribution proposed by dai and xie 2009

decoherence free subspaces of anyon states abstract in this paper we propose decoherence free subspaces dfss of anyon states under two kinds of noises the forms of collective dephasing and collective rotation noises are introduced the invariance requirement under these noises give some restrictions of the winding number of anyons we put forward a scheme to realize the dfs of anyon states in the kitaev spin lattice model and give some discussion of general kinds of anyons

kriging cokriging radial basis functions and the role of positive definiteness abstract there are at least three developments for interpolators that lead to the same functional form for the interpolator the thin plate spline radial basis functions and the regression method known as kriging the key to the interrelationship lies in the positive definiteness of the kernel function micchelli has known that a weak form of positive definiteness is sufficient to ensure a unique solution to the system of equations determining the coefficients in the interpolator both the positive definiteness and the interpolator can be extended to vector valued functions via the kriging approach which is also independent of the dimension of the underlying space the kriging approach leads naturally to various methods for simulation as well

vectorial interpolation using radial basis like functions this paper deals with vector field interpolation i e the data are r3 values located in scattered r3 points while the interpolating function is a function from r3 into r3 in order to take into account possible connections between the components of the interpolant we derive it by solving a variational spline problem involving the rotational and the divergence of the interpolant and depending on a parameter significative of the balance of the rotational part and of the divergence part and on the order m of derivatives of the rotational and divergence involved in the minimized seminorm we so obtain interpolants whose expression is x ni 1 x xi ai pm 1 x where is some 3 3 matrix function pm 1 is a degree m 1 vectorial polynomial and where the ai are r3 vectors besides the ai meet a relation generalizing the usual orthogonality to all polynomials of degree at most m 1 for 1 we find the usual m harmonic splines in each component of numerical examples show the interest of the method and we compare the so obtained functions with the ones obtained by matlab s procedures

cross covariance functions for multivariate random fields based on latent dimensions summary the problem of constructing valid parametric cross covariance functions is challenging we propose a simple methodology based on latent dimensions and existing covariance models for univariate random fields to develop flexible interpretable and computationally feasible classes of cross covariance functions in closed form we focus on spatio temporal cross covariance functions that can be nonseparable asymmetric and can have different covariance structures for instance different smoothness parameters in each component we discuss estimation of these models and perform a small simulation study to demonstrate our approach we illustrate our methodology on a trivariate spatio temporal pollution dataset from california and demonstrate that our cross covariance performs better than other competing models

a bivariate bayes method for improving the estimates of mortality rates with a twofold conditional autoregressive model a bivariate bayes method is proposed for estimating the mortality rates of a single disease for a given population using additional information from a second disease the information on the two diseases is assumed to be from the same population groups or areas the joint frequencies of deaths for the two diseases for given populations are assumed to have a bivariate poisson distribution with joint means proportional to the population sizes the relationship between the mortality rates of the two different diseases if formulated through the twofold conditional autoregressive car model where spatial effects as well as indexes of spatial dependence are introduced to capture the structured clusterings among areas this procedure is compared to a univariate hierarchical bayes procedure that uses information from one disease only comparisons of two procedures are made by the optimal property a monte carlo study real data and the bayes factor all of the methods that we consider demonstrate a substantial

the relation between properties of gentile statistics and fractional statistics of anyon abstract in this paper we discuss the relationship of two kinds of intermediate statistics the gentile statistics and the fractional statistics of anyons the anyon winding number representation is introduced we construct the transformation between anyon winding number representation and the occupation number representation of particles of gentile statistics we study intermediate statistics quantum bracket and coherent states for anyons in the winding number representation we demonstrate that anyons can be simulated by gentile statistics with a geometric phase

variation diminishing transformations a direct approach to total positivity and its statistical applications abstract karlin has shown that the variation diminishing property possessed by totally positive distributions allows a unified and straightforward presentation of many basic properties of hypothesis tests his work in fact reveals that total positivity is equivalent to a suitably formulated variation diminishing property this largely expository article begins with the latter concept and consequently gives a more direct account of the theory this approach avoids the extensive mathematical preliminaries previously required and isolates the more important statistical property

a representation of angular momentum su 2 algebra abstract this paper seeks to construct a representation of the algebra of angular momentum su 2 algebra in terms of the operator relations corresponding to gentile statistics in which one quantum state can be occupied by n particles first we present an operator realization of gentile statistics then we propose a representation of angular momenta the result shows that there exist certain underlying connections between the operator realization of the gentile statistics and the angular momentum su 2 algebra

almost strictly sign regular matrices and neville elimination with two determinant pivoting in 2007 cortes and pena introduced a pivoting strategy for the neville elimination of nonsingular sign regular matrices and called it two determinant pivoting neville elimination has been very useful for obtaining theoretical and practical properties for totally positive negative matrices and other related types of matrices a real matrix is said to be almost strictly sign regular if all its nontrivial minors of the same order have the same strict sign in this paper some nice properties related with the application of neville elimination with two determinant pivoting strategy to almost strictly sign regular matrices are presented

comparing pivoting strategies for almost strictly sign regular matrices abstract in this paper some properties of two determinant pivoting for neville elimination are presented in particular we consider a zero increasing property and we show an optimal normwise growth factor comparisons with other pivoting strategies for neville elimination and with gaussian elimination with partial pivoting of almost strictly sign regular matrices are performed numerical examples are included

why should anyone care about computing with anyons in this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation we give an overview of the concept of anyons and their exotic statistics present various models that exhibit topological behaviour and establish their relation to quantum computation possible directions for the physical realization of topological systems and the detection of anyonic behaviour are elaborated

backward stability with almost strictly sign regular matrices a sign regular matrix is almost strictly sign regular if all its nontrivial minors of the same order have the same strict sign these matrices form a subclass of sign regular matrices matrices whose minors of the same order have the same sign in this paper the backward stability for almost strictly sign regular matrices is studied when neville elimination with two determinant pivoting strategy is applied in addition several numerical experiments are also presented

quasi interpolation for linear functional data quasi interpolation has been studied extensively in the literature however most studies of quasi interpolation are usually only for discrete function values or a finite linear combination of discrete function values note that in practical applications more commonly we can sample the linear functional data the discrete values of the right hand side of some differential equations rather than the discrete function values e g remote sensing seismic data etc therefore it is more meaningful to study quasi interpolation for the linear functional data the main result of this paper is to propose such a quasi interpolation scheme error estimate of the scheme is also given in the paper based on the error estimate one can find a quasi interpolant that provides an optimal approximation order with respect to the smoothness of the right hand side of the differential equation the scheme can be applied in many situations such as the numerical solution of the differential equation construction of the lyapunov function and so on respective examples are presented in the end of this paper

multivariate spatial covariance models a conditional approach multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of locations in a continuously indexed domain multivariate spatial covariance models need to be built with care since any covariance matrix that is derived from such a model must be nonnegative definite in this article we develop a conditional approach for spatial model construction whose validity conditions are easy to check we start with bivariate spatial covariance models and go on to demonstrate the approach s connection to multivariate models defined by networks of spatial variables in some circumstances such as modelling respiratory illness conditional on air pollution the direction of conditional dependence is clear when it is not the two directional models can be compared more generally the graph structure of the network reduces the number of possible models to compare model selection then amounts to finding possible causative links in the network we demonstrate our conditional approach on surface temperature and pressure data where the role of the two variables is seen to be asymmetric

complete state counting for gentile s generalization of the pauli exclusion principle in the present work we perform the complete state counting for gentile s approach to the generalized pauli exclusion principle gpep which has been lacking in the literature we count the total number of ways to allocate n identical particles occupying a group of g states with up to q particles in each state in order to derive an exact expression for the statistical weight our obtained expression for the statistical weight gives the fermionic one for q 1 and for q41 it tends fast to a bosonic weight moreover we perform a numerical comparison between our state counting and wu s corresponding to the haldane wu s formulation of the gpep which implies that gentile s formulation gives rise to more boson like behavior while haldane wu s approach to more fermion like behavior this difference lies on the fact that each formulation has its own state occupation rules on which correlation plays a key role r 2007 published by elsevier b v pacs 05 30 d

nonsingular almost strictly sign regular matrices abstract the class of nonsingular almost strictly totally positive matrices has been characterized m gasca j m pena characterizations and decompositions of almost strictly positive matrices siam j matrix anal appl 28 2006 1 8 in this paper we discuss the class of almost strictly sign regular matrices that includes almost strictly totally positive matrices a characterization is provided for these matrices in terms of their nontrivial minors using consecutive rows and consecutive columns in particular we present a characterization of certain almost strictly sign regular matrices in terms of a very reduced number of boundary almost trivial minors

aggregation cokriging for highly multivariate spatial data best linear unbiased prediction of spatially correlated multivariate random processes often called cokriging in geostatistics requires the solution of a large linear system based on the covariance and cross covariance matrix of the observations for many problems of practical interest it is impossible to solve the linear system with direct methods we propose an efficient linear unbiased predictor based on a linear aggregation of the covariables the primary variable together with this single meta covariable is used to perform cokriging we discuss the optimality of the approach under different covariance structures and use it to create reanalysis type high resolution historical temperature fields

polyharmonic smoothing splines and the multidimensional wiener filtering of fractal like signals motivated by the fractal like behavior of natural images we develop a smoothing technique that uses a regularization functional which is a fractional iterate of the laplacian this type of functional was initially introduced by duchon for the approximation of nonuniformily sampled multidimensional data he proved that the general solution is a smoothing spline that is represented by a linear combination of radial basis functions rbfs unfortunately this is tedious to implement for images because of the poor conditioning of rbfs and their lack of decay here we present a much more efficient method for the special case of a uniform grid the key idea is to express duchon s solution in a fractional polyharmonic b spline basis that spans the same space as the rbfs this allows us to derive an algorithm where the smoothing is performed by filtering in the fourier domain next we prove that the above smoothing spline can be optimally tuned to provide the mmse estimation of a fractional brownian field corrupted by white noise this is a strong result that not only yields the best linear filter wiener solution but also the optimal interpolation space which is not bandlimited it also suggests a way of using the noisy data to identify the optimal parameters order of the spline and smoothing strength which yields a fully automatic smoothing procedure we evaluate the performance of our algorithm by comparing it against an oracle wiener filter which requires the knowledge of the true noiseless power spectrum of the signal we find that our approach performs almost as well as the oracle solution over a wide range of conditions