weighted estimates for the helmholtz equation and some applications we characterize the radial functionsvin rnfor which the a priori inequality u1 2 2 k uv1 2 2 c v 1 2 k2 u 2holds with constant independent ofk the condition is forvto have the x rays transform everywhere bounded we apply these estimates to the well posedness of evolution schrodinger equations with time dependent drift terms and to the restriction of the fourier transform to euclidean spheres

toeplitz operators on herglotz wave functions abstract the space of herglotz wave functions in r 2 consists of all the solutions of the helmholtz equation that can be represented as the fourier transform in r 2 of a measure supported in the circle and with density in l 2 s 1 this space has a structure of a hilbert space with reproducing kernel the purpose of this article is to study toeplitz operators with nonnegative radial symbols defined on this space we study the symbols defining bounded and compact toeplitz operators as well as the toeplitz operators belonging to the schatten classes s p

large deviations in taylor dispersion we establish a link between the phenomenon of taylor dispersion and the theory of empirical distributions using this connection we derive upon applying the theory of large deviations an alternative and much more precise description of the long time regime for taylor dispersion

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

on hp convergence of prolate spheroidal wave functions and a new well conditioned prolate collocation scheme the first purpose of this paper is to provide further illustrations from both theoretical and numerical perspectives for the nonconvergence of h refinement in hp approximation by the prolate spheroidal wave functions pswfs a surprising convergence property that was first discovered by boyd et al 2013 3 the second purpose is to offer a new basis that leads to prolate collocation systems with condition numbers independent of c n the intrinsic bandwidth parameter and the number of collocation points we highlight that the collocation scheme together with a very practical rule for pairing up c n significantly outperforms the legendre polynomial based method and likewise other jacobi polynomial based methods in approximating highly oscillatory bandlimited functions

semiparametric instrumental variable estimation of simultaneous equation sample selection models the identification and estimation of a semiparametric simultaneous equation model with selectivity have been considered the identification of structural parameters from reduced form parameters in the semiparametric model requires stronger conditions than the usual rank condition in the classical simultaneous equation model or the parametric simultaneous equation sample selection model with normal disturbances the necessary order condition for identification in the semiparametric model corresponds to the overidentification condition in the classical model semiparametric two stage estimation methods which generalize the two stage least squares method and the generalized two stage least squares method for the parametric model are introduced the semiparametric generalized two stage least squares estimator is shown to be asymptotically efficient in a class of semiparametric instrumental variable estimators

estimating the errors on measured entropy and mutual information abstract information entropy and the related quantity mutual information are used extensively as measures of complexity and to identify nonlinearity in dynamical systems expressions for the probability distribution of entropies and mutual informations calculated from finite amounts of data exist in the literature but the expressions have seldom been used in the field of nonlinear dynamics in this paper formulae for estimating the errors on observed information entropies and mutual informations are derived using the standard error analysis familiar to physicists their validity is demonstrated by numerical experiment for illustration the formulae are then used to evaluate the errors on the time lagged mutual information of the logistic map

the heun racah and heun bannai ito algebras the heun racah and heun bannai ito algebras are introduced specializations of these algebras are seen to be realized by the operators obtained by applying the algebraic heun construct to the bispectral operators of the racah and bannai ito polynomials the study supplements the results on the heun askey wilson algebra and completes the description of the heun algebras associated with the polynomial families at the top of the askey scheme its q analog and the bannai ito one

asymptotic efficiency in semi parametric models with censoring abstract we consider a regression model subject to bivariate censoring in which the errors are independent of the explanatory variables our objective is to drop the assumption of bivaraite normality and obtain an information bound on asymptotic efficiency when the error distribution is unrestricted except for smoothness and regularity conditions this bound has simple form if there are no exclusion restrictions on the selection equation then positive information requires a restriction on the regression slope parameters and a continuous distribution for a component of the explanatory variables we also consider a binary choice model under the weak assumption that the error distribution has zero median conditional on the explanatory variables here the semi parametric information bound is zero hence although a consistent estimator exists it is not possible to attain covergence at rate 1 n

persistent random motion with maximally correlated fluctuations how often should a random walker change its direction of motion in order to maximize correlation in velocity fluctuations over a finite time interval we address this optimal diffusion problem in the context of the one dimensional persistent random walk where we evaluate the correlation and mutual information in velocity trajectories as a function of the persistence level and the observation time we find the optimal persistence level corresponds to the average number of direction reversals asymptotically scaling as the square root of the observation time this square root scaling law makes the relative growth between the average number of direction reversals and the persistence length invariant with respect to changes in the overall time duration of the random walk

some comments on fourier analysis uncertainty and modeling investigation of the problem of simultaneously concentrating a function and its fourier transform has led to some interesting special functions that have widespread applications in engineering they provide a means of proving a rigorous version of an engineering folk theorem called the 2wt theorem many generalizations of these ideas seem to possess a similar elegant mathematical structure a brief descriptive review is given of these developments

generalized strichartz estimates and scattering for 3d zakharov system we obtain scattering for the 3d zakharov system with non radial small data in the energy space with angular regularity of degree one the main ingredient is a generalized strichartz estimate for the schrodinger equation in the space of l2 angular integrability

time frequency localization operators a geometric phase space approach the author defines a set of operators which localize in both time and frequency these operators are similar to but different from the low pass time limiting operator the singular functions of which are the prolate spheroidal wave functions the author s construction differs from the usual approach in that she treats the time frequency plane as one geometric whole phase space rather than as two separate spaces for disk shaped or ellipse shaped domains in time frequency plane the associated localization operators are remarkably simple their eigenfunctions are hermite functions and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions

universal role of correlation entropy in critical phenomena in statistical physics if we divide successively an equilibrium system into two parts we will face a situation that to a certain length the physics of a subsystem is no longer the same as the original one the extensive property of the thermal entropy s a boolean or b s a s b is then violated this observation motivates us to introduce a concept of correlation entropy between two points as measured by the mutual information in information theory to study the critical phenomena a rigorous relation is established to display some drastic features of the non vanishing correlation entropy of a subsystem formed by any two distant particles with long range correlation this relation actually indicates a universal role played by the correlation entropy for understanding the critical phenomena we also verify these analytical studies in terms of two well studied models for both the thermal and quantum phase transitions the two dimensional ising model and the one dimensional transverse field ising model therefore the correlation entropy provides us with a new physical intuition of the critical phenomena from the point of view of information theory

some aspects of measurement error in a censored regression model abstract when a linear model with a censored dependent variable is written as a regression model the model is nonlinear in the explanatory variables this means that when the explanatory variables are measured with error estimation by instrumental variables will not lead to consistent estimates of the parameters my approach to the problem involves assuming that the variables measured with error can be represented by a reduced form equation and estimating the parameters of the censored regression model by the least absolute deviations estimator this estimator is based on the median of the distribution of the dependent variable rather than the mean and the median is not affected by censoring in the lower tail hence the estimator is consistent under general conditions i also consider the problem of testing for the presence of measurement error

a donoho stark criterion for stable signal recovery in discrete wavelet subspaces abstract we derive a sufficient condition by means of which one can recover a scale limited signal from the knowledge of a truncated version of it in a stable manner following the canvas introduced by donoho and stark 1989 4 the proof follows from simple computations involving the zak transform well known in solid state physics geometric harmonics in the terminology of coifman and lafon 2006 22 for scale limited subspaces of l 2 r are also displayed for several test cases finally some algorithms are studied for the treatment of zero angle problems

diffusion coefficients for multi step persistent random walks on lattices we calculate the diffusion coefficients of persistent random walks on lattices where the direction of a walker at a given step depends on the memory of a certain number of previous steps in particular we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with a two step memory on different classes of one two and higher dimensional lattices

differential equations in the spectral parameter we determine all the potentialsv x for the schrodinger equation 2 v x k2 such that some family of eigenfunctions satisfies a differential equation in the spectral parameterk of the formb k k o x o for each suchv x we determine the algebra of all possible operatorsb and the corresponding functions x

radial multipliers and restriction to surfaces of the fourier transform in mixed norm spaces in this article we revisit some classical conjectures in harmonic analysis in the setting of mixed norm spaces l rad p l ang 2 left mathbb r n right we produce sharp bounds for the restriction of the fourier transform to compact hypersurfaces of revolution in the mixed norm setting and study an extension of the disc multiplier we also present some results for the discrete restriction conjecture and state an intriguing open problem

rank estimation of a location parameter in the binary choice model abstract this paper proposes a rank based estimator for a location parameter in the binary choice model under a monotonic index and symmetry condition given an initial n consistent estimator for the slope parameter the estimator converges at the usual parametric rate compared with existing estimators no nonparametric smoothing is needed here a small monte carlo study illustrates the usefulness of the estimator we also point out that the location and slope parameters can be jointly estimated

band limited functions lp convergence we consider the set bp q functions of lp tl whose fourier spectrum lies in i2 i2 we prove that the prolate spheroidal wave func tions constitute a basis of this space if and only if 4 3 p 4 the result is obtained as a consequence of the analogous problem for the spherical bessel functions the proof rely on a weighted inequality for the hubert transform

efficient estimation of limited dependent variable models with endogenous explanatory variables abstract this paper discusses asymptotically efficient estimation of the parameters of limited dependent variable models with endogenous explanatory variables general results on asymptotic efficiency of two stage and amemiya gls estimators are derived and used to obtain a simple asymptotically efficient estimator of the structural coefficients this estimator can be calculated by applying gls to estimates of the reduced form coefficients that are obtained by using reduced form residuals as additional explanatory variables it is also shown that it is possible to obtain asymptotically efficient estimators of the other coefficients by a modified minimum chi square method

steady diffusion in a drift field a comparison of large deviation techniques and multiple scale analysis a particle with internal unobserved states diffusing in a force field will generally display effective advection diffusion the drift velocity is proportional to the mobility averaged over the internal states or effective mobility while the effective diffusion has two terms one is of the equilibrium type and satisfies an einstein relation with the effective mobility while the other is quadratic in the applied force in this contribution we present two new methods to obtain these results on the one hand using large deviation techniques and on the other by a multiple scale analysis and compare the two we consider both systems with discrete internal states and continuous internal states we show that the auxiliary equations in the multiple scale analysis can also be derived in second order perturbation theory in a large deviation theory of a generating function discrete internal states or generating functional continuous internal states we discuss that measuring the two components of the effective diffusion give a way to determine kinetic rates from only first and second moments of the displacement in steady state

eigenvalue estimates and mutual information for the linear time varying channel we consider linear time varying channels with additive white gaussian noise for a large class of such channels we derive rigorous estimates of the eigenvalues of the correlation matrix of the effective channel in terms of the sampled time varying transfer function and thus provide a theoretical justification for a relationship that has been frequently observed in the literature we then use this eigenvalue estimate to derive an estimate of the mutual information of the channel our approach is constructive and is based on a careful balance of the tradeoff between approximate operator diagonalization signal dimension loss and accuracy of eigenvalue estimates

entropy estimates of small data sets estimating entropies from limited data series is known to be a non trivial task naive estimations are plagued with both systematic bias and statistical errors here we present a new balanced estimator for entropy functionals shannon renyi and tsallis specially devised to provide a compromise between low bias and small statistical errors for short data series this new estimator outperforms other currently available ones when the data sets are small and the probabilities of the possible outputs of the random variable are not close to zero otherwise other well known estimators remain a better choice the potential range of applicability of this estimator is quite broad specially for biological and digital data series

fluctuation dynamics thermodynamic analogies and ergodic behavior for nonequilibrium independent rate processes with dynamical disorder abstract the stochastic properties of the sojourn times attached to a markov process in continuous time and with a finite number of states are described by using a statistical ensemble approach this approach is applied for investigating the large time behavior of independent rate processes with dynamical disorder the large time behavior of the system is described in terms of an effective transport operator which can be expressed as a static average with respect to the stochastic properties of the sojourn times the method is illustrated by the generalization of the van den broeck approach to the generalized taylor diffusion explicit formulas for the effective transport coefficients and for the fluctuations of the concentration fields are derived the results are used for extending the non equilibrium generalized thermodynamic formalisms suggested by keizer and by ross hunt and hunt to systems with dynamical disorder it is shown that the logarithm of the probability density functional of concentration fluctuations is a lyapunov functional of the effective transport equation this lyapunov functional plays the role of a generalized nonequilibrium thermodynamic potential which may serve as a basis for a thermodynamics description of the average behavior of the system the existence and stability of a steady state can be expressed as an extremum condition for the lyapunov functional for taylor diffusion in an external electric field different from zero the generalized potential has a structure similar to the helmholtz free energy rather than to the entropy a generalized chemical potential is derived as the functional derivative of the lyapunov functional with respect to the concentration field the gradient of this generalized chemical potential is the driving force which determines the structure of the effective transport equation

quantile regression with censoring and endogeneity in this paper we develop a new censored quantile instrumental variable cqiv estimator and describe its properties and computation the cqiv estimator combines powell 1986 censored quantile regression cqr to deal with censoring with a control variable approach to incorporate endogenous regressors the cqiv estimator is obtained in two stages that are nonadditive in the unobservables the first stage estimates a nonadditive model with infinite dimensional parameters for the control variable such as a quantile or distribution regression model the second stage estimates a nonadditive censored quantile regression model for the response variable of interest including the estimated control variable to deal with endogeneity for computation we extend the algorithm for cqr developed by chernozhukov and hong 2002 to incorporate the estimation of the control variable we give generic regularity conditions for asymptotic normality of the cqiv estimator and for the validity of resampling methods to approximate its asymptotic distribution we verify these conditions for quantile and distribution regression estimation of the control variable our analysis covers two stage uncensored quantile regression with nonadditive first stage as an important special case we illustrate the computation and applicability of the cqiv estimator with a monte carlo numerical example and an empirical application on estimation of engel curves for alcohol

treatment effects with censoring and endogeneity this article develops a nonparametric approach to identification and estimation of treatment effects on censored outcomes when treatment may be endogenous and have arbitrarily heterogenous effects identification is based on an instrumental variable that satisfies the exclusion and monotonicity conditions standard in the local average treatment effects framework the article proposes a censored quantile treatment effects estimator derives its asymptotic distribution and illustrates its performance using monte carlo simulations even in the exogenous case the estimator performs better in finite samples than existing censored quantile regression estimators and performs nearly as well as maximum likelihood estimators in cases where their distributional assumptions hold an empirical application to a subsidized job training program finds that participation significantly and dramatically reduced the duration of jobless spells especially at the right tail of the distribution

radial weights and mixed norm inequalities for the disc multiplier in this paper we show that the l2 weighted inequalities with radial weights of the multiplier for the ball are controlled by the maximal function defined by averages on arbitrary rectangles this solves the case of radial weights of a problem proposed by e stein in 1978 it also gives an elegant and simple proof of the boundedness of the multiplier for the ball on the spaces of mixed norm lradp lang2 for 2n n 1 p 2n n 1 obtained by a cordoba and by g mockenhaupt additional work is presented in order to extend these mixed norm estimates to the end points 2n n 1 and 2n n 1 in the sharp form of restricted weak type inequalities

some applications of persistent random walks and the telegrapher s equation abstract a persistent random walk can be regarded as a multidimensional markov process the bias free telegraphers equation is 2 p t 2 1 t p t v 2 2 p it can be regarded as interpolating between the wave equation t and the diffusion equation t 0 previously it has found application in thermodynamics cf the review in rev mod phys 61 1989 41 62 1990 375 more recent applications are reviewed in the present article

limited information estimators and exogeneity tests for simultaneous probit models a two step maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators conditions under which each estimator attains the cramer rao lower bound are obtained simple tests for exogeneity based on the new two step estimator are proposed and are shown to be asymptotically equivalent to one another and to have the same local asymptotic power as classical tests based on the limited information maximum likelihood estimator finite sample comparisons between the new and alternative estimators are presented based on some monte carlo evidence the performance of the proposed tests for exogeneity is also assessed

hierarchical construction of orientation and velocity selective filters as a step towards the early measurement of visual primitives the authors outline design criteria for the extraction of orientation and velocity information and present a variety of tools useful in the construction of simple linear filters a hierarchical parallel processing scheme is used in which nodes compute a weighted sum of inputs from within a small spatio temporal neighborhood the resulting scheme is easily analyzed and provides mechanisms sensitive to narrow ranges of both image velocity and orientation the hierarchical approach in combination with separability in the first levels yields an efficient implementation

endogenous selection or treatment model estimation in a sample selection or treatment effects model common unobservables may affect both the outcome and the probability of selection in unknown ways this paper shows that the distribution function of potential outcomes conditional on covariates can be identified given an observed variable v that affects the treatment or selection probability in certain ways and is conditionally independent of the error terms in a model of potential outcomes selection model estimators based on this identification are provided which take the form of simple weighted averages gmm or two stage least squares these estimators permit endogenous and mismeasured regressors empirical applications are provided to estimation of a firm investment model and a schooling effects on wages model

ode solvers using band limited approximations we use generalized gaussian quadratures for exponentials to develop a new ode solver nodes and weights of these quadratures are computed for a given bandlimit c and user selected accuracy e so that they integrate functions e i b x for all b

singular integrals maximal functions and fourier restriction to spheres the disk multiplier revisited abstract several estimates for singular integrals maximal functions and spherical summation operator are given in the spaces l rad p l ang 2 r n n 2

spatio spectral concentration of convolutions differential equations may possess coefficients that vary on a spectrum of scales because coefficients are typically multiplicative in real space they turn into convolution operators in spectral space mixing all wavenumbers however in many applications only the largest scales of the solution are of interest and so the question turns to whether it is possible to build effective coarse scale models of the coefficients in such a manner that the large scales of the solution are left intact here we apply the method of numerical homogenisation to deterministic linear equations to generate sub grid scale models of coefficients at desired frequency cutoffs we use the fourier basis to project filter and compute correctors for the coefficients the method is tested in 1d and 2d scenarios and found to reproduce the coarse scales of the solution to varying degrees of accuracy depending on the cutoff we relate this method to mode elimination renormalisation group rg and discuss the connection between accuracy and the cutoff wavenumber the tradeoff is governed by a form of the uncertainty principle for convolutions which states that as the convolution operator is squeezed in the spectral domain it broadens in real space as a consequence basis sparsity is a high virtue and the choice of the basis can be critical

estimating mutual information we present two classes of improved estimators for mutual information m x y from samples of random points distributed according to some joint probability density mu x y in contrast to conventional estimators based on binnings they are based on entropy estimates from k nearest neighbor distances this means that they are data efficient with k 1 we resolve structures down to the smallest possible scales adaptive the resolution is higher where data are more numerous and have minimal bias indeed the bias of the underlying entropy estimates is mainly due to nonuniformity of the density at the smallest resolved scale giving typically systematic errors which scale as functions of k n for n points numerically we find that both families become exact for independent distributions i e the estimator m x y vanishes up to statistical fluctuations if mu x y mu x mu y this holds for all tested marginal distributions and for all dimensions of x and y in addition we give estimators for redundancies between more than two random variables we compare our algorithms in detail with existing algorithms finally we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis ica for improving ica and for estimating the reliability of blind source separation

mutual information functions versus correlation functions this paper studies one application of mutual information to symbolic sequences the mutual information functionm d this function is compared with the more frequently used correlation function d an exact relation betweenm d and d is derived for binary sequences for sequences with more than two symbols no such general relation exists in particular d 0 may or may not lead tom d 0 this linear but not general independence between symbols separated by a distance is studied for ternary sequences also included is the estimation of the finite size effect on calculating mutual information finally the concept of symbolic noise is discussed

two step estimation of panel data models with censored endogenous variables and selection bias this paper presents some two step estimators for a wide range of parametric panel data models with censored endogenous variables and sample selection bias our approach is to derive estimates of the unobserved heterogeneity responsible for the endogeneity selection bias to include as additional explanatory variables in the primary equation these are obtained through a decomposition of the reduced form residuals the panel nature of the data allows adjustment and testing for two forms of endogeneity and or sample selection bias furthermore it incorporates roles for dynamics and state dependence in the reduced form finally we provide an empirical illustration which features our procedure and highlights the ability to test several of the underlying assumptions

a comparison of the amemiya gls and the lee maddala trost g2sls in a simultaneous equations tobit model abstract this paper proposes a class of gls estimators for the structural parameters of a simultaneous equations tobit model and shows that this class contains an estimator which is asymptotically more efficient than an alternative estimator proposed by lee maddala and trost in 1980

mean convergence of prolate spheroidal series and their extensions abstract the aim of this paper is to establish the range of p s for which the expansion of a function f l p in a generalized prolate spheroidal wave function pswfs basis converges to f in l p two generalizations of pswfs are considered here the circular pswfs introduced by d slepian and the weighted pswfs introduced by wang and zhang both cases cover the classical pswfs for which the corresponding results have been previously established by barcelo and cordoba to establish those results we prove a general result that allows to extend mean convergence in a given basis e g jacobi polynomials or bessel basis to mean convergence in a second basis here the generalized pswfs

mutual information identifies spurious hurst phenomena in resting state eeg and fmri data long range memory in time series is often quantified by the hurst exponent h a measure of the signal s variance across several time scales we analyze neurophysiological time series from electroencephalography eeg and functional magnetic resonance imaging fmri resting state experiments with two standard hurst exponent estimators and with the time lagged mutual information function applied to discretized versions of the signals a confidence interval for the mutual information function is obtained from surrogate markov processes with equilibrium distribution and transition matrix identical to the underlying signal for eeg signals we construct an additional mutual information confidence interval from a short range correlated tenth order autoregressive model we reproduce the previously described hurst phenomenon h 0 5 in the analytical amplitude of alpha frequency band oscillations in eeg microstate sequences and in fmri signals but we show that the hurst phenomenon occurs without long range memory in the information theoretical sense we find that the mutual information function of neurophysiological data behaves differently from fractional gaussian noise fgn for which the hurst phenomenon is a sufficient condition to prove long range memory two other well characterized short range correlated stochastic processes ornstein uhlenbeck cox ingersoll ross also yield h 0 5 whereas their mutual information functions lie within the markovian confidence intervals similar to neural signals in these processes which do not have long range memory by construction a spurious hurst phenomenon occurs due to slow relaxation times and heteroscedasticity time varying conditional variance in summary we find that mutual information correctly distinguishes long range from short range dependence in the theoretical and experimental cases discussed our results also suggest that the stationary fgn process is not sufficient to describe neural data which seem to belong to a more general class of stochastic processes in which multiscale variance effects produce hurst phenomena without long range dependence in our experimental data the hurst phenomenon and long range memory appear as different system properties that should be estimated and interpreted independently

persistent random walk approach to anomalous transport of self propelled particles the motion of self propelled particles is modeled as a persistent random walk an analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk s displacement it is shown that the interplay of step length and turning angle distributions and self propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients the crossover from the anomalous short time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented

a new property of reproducing kernels for classical orthogonal polynomials abstract we exhibit a second order differential operator commuting with the reproducing kernel n 0 t n n h n each time that n is one of the classical orthogonal polynomials jacobi laguerre hermite and bessel this is the analog of a known property in the study of time and band limited signals

mean and almost everywhere convergence of fourier neumann series abstract let j denote the bessel function of order the functions x 2 2 1 2j 2n 1 x1 2 n 0 1 2 form an orthogonal system in l2 0 x dx when 1 in this paper we analyze the range of p and for which the fourier series with respect to this system converges in the lp 0 x dx norm also we describe the space in which the span of the system is dense and we show some of its properties finally we study the almost everywhere convergence of the fourier series for functions in such spaces

approximate factorizations of fourier matrices with nonequispaced knots abstract we propose a new algorithm for the multiplication of vectors with fourier matrices of the form a tf e 2 i x k v j n n 2 1 j k n 2 where both x k and v j are arbitrary knots in n 2 n 2 the algorithm is based on an approximate factorization of the transform matrix a tf into sparse matrices which entries are chosen to minimize the frobenius norm of certain error matrices numerical experiments demonstrate that the approximation error introduced by our new algorithm is about 10 2 times smaller than the approximation error of previously reported algorithms with the gaussian or b splines as window functions and as good as a previous algorithm with the kaiser bessel function as window function

semiparametric estimation of binary response models with endogenous regressors abstract in this paper we propose a two step semiparametric maximum likelihood sml estimator for the coefficients of a single index binary choice model with endogenous regressors when identification is achieved via a control function approach the first step consists of estimating a reduced form equation for the endogenous regressors and extracting the corresponding residuals in the second step the latter are added as control variates to the outcome equation which is in turn estimated by sml we establish the estimator s n consistency and asymptotic normality in a simulation study we compare the properties of our estimator with those of existing alternatives highlighting the advantages of our approach

optimal search strategies of space time coupled random walkers with finite lifetimes we present a simple paradigm for detection of an immobile target by a space time coupled random walker with a finite lifetime the motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed we call these walkers mortal creepers a mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate m while still alive the creeper has a finite mean frequency of change of the direction of motion in particular we consider the efficiency of the target search process characterized by the probability that the creeper will eventually detect the target analytic results confirmed by numerical results show that there is an m dependent optimal frequency opt that maximizes the probability of eventual target detection we work primarily in one dimensional d 1 domains and examine the role of initial conditions and of finite domain sizes numerical results in d 2 domains confirm the existence of an optimal frequency of change of direction thereby suggesting that the observed effects are robust to changes in dimensionality in the d 1 case explicit expressions for the probability of target detection in the long time limit are given in the case of an infinite domain we compute the detection probability for arbitrary times and study its early and late time behavior we further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time we also consider a version of the standard target problem in which many creepers start at random locations at the same time

distribution free estimation of the random coefficient dummy endogenous variable model this paper considers the estimation of the random coefficient dummy endogenous variable model under a symmetry and index condition for the error distribution we follow a two step approach the selection equation is estimated first in the second step an instrumental variables estimator is proposed for the ourcome equation through a pairwise comparison method our approach can be readily extended to the general switching regression model in constrast to the existing literature on sample selection models the exclusion restriction is not needed here for model identification furthermore the intercept term for the outcome equation can be estimated at the usual parametric rate

rapid prolate pseudospectral differentiation and interpolation with the fast multipole method pseudospectral methods utilizing prolate spheroidal wave functions as basis functions have been shown to possess advantages over the conventional pseudospectral methods based on trigonometric and orthogonal polynomials however the spectral differentiation and interpolation steps of the prolate pseudospectral method involve matrix vector products which if evaluated directly entail o n2 memory requirement and computational complexity where n is the number of unknowns utilized for discretization and interpolation in this work we show that the fast multipole method fmm can be used to reduce the memory requirement and computational complexity of the prolate pseudospectral method to o n example simulation results demonstrate the speed and accuracy of the resulting fast prolate pseudospectral solver

optimal search strategies of run and tumble walks the run and tumble walk consisting of randomly reoriented ballistic excursions models phenomena ranging from gas kinetics to bacteria motility we evaluate the mean time required for this walk to find a fixed target within a two or three dimensional spherical confinement we find that the mean search time admits a minimum as a function of the mean run duration for various types of boundary conditions and run duration distributions exponential power law deterministic our result stands in sharp contrast to the pure ballistic motion which is predicted to be the optimal search strategy in the case of poisson distributed targets

linear adjoint restriction estimates for paraboloid we prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices this result generalizes the paraboloid restriction estimate in radial case from shao rev mat iberoam 25 2009 1127 1168 as well as the result from miao et al proc ams 140 2012 2091 2102 as an application we show a local smoothing estimate for a solution of the linear schrodinger equation under the assumption that the initial datum has additional angular regularity

the surprising almost everywhere convergence of fourier neumann series for most orthogonal systems and their corresponding fourier series the study of the almost everywhere convergence for functions in l p requires very complicated research harder than in the case of the mean convergence for instance for trigonometric series the almost everywhere convergence for functions in l 2 is the celebrated carleson theorem proved in 1966 and extended to l p by hunt in 1967 in this paper we take the system j n a x 2 a 2n 1 j a 2 n 1 x x a 1 n 0 1 2 with j m being the bessel function of the first kind and of the order m which is orthonormal in l 2 0 x 2 a 1dx and whose fourier series are the so called fourier neumann series we study the almost everywhere convergence of fourier neumann series for functions in l p 0 x 2 a 1dx and we show that surprisingly the proof is relatively simple inasmuch as the mean convergence has already been established

an energy approach to space time galerkin bem for wave propagation problems in this paper we consider dirichlet or neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential starting from a natural energy identity a space time weak formulation for 1d integral problems is briefly introduced and continuity and coerciveness properties of the related bilinear form are proved then a theoretical analysis of an extension of the introduced formulation for 2d problems is proposed pointing out the novelty with respect to existing literature results at last various numerical simulations will be presented and discussed showing unconditional stability of the space time galerkin boundary element method applied to the energetic weak problem copyright 2009 john wiley sons ltd

entropy estimation of very short symbolic sequences while entropy per unit time is a meaningful index to quantify the dynamic features of experimental time series its estimation is often hampered in practice by the finite length of the data we here investigate the performance of entropy estimation procedures relying either on block entropies or lempel ziv complexity when only very short symbolic sequences are available heuristic analytical arguments point at the influence of temporal correlations on the bias and statistical fluctuations and put forward a reduced effective sequence length suitable for error estimation numerical studies are conducted using as benchmarks the wealth of different dynamic regimes generated by the family of logistic maps and stochastic evolutions generated by a markov chain of tunable correlation time practical guidelines and validity criteria are proposed for instance block entropy leads to a dramatic overestimation for sequences of low entropy whereas it outperforms lempel ziv complexity at high entropy as a general result the quality of entropy estimation is sensitive to the sequence temporal correlation hence self consistently depends on the entropy value itself thus promoting a two step procedure lempel ziv complexity is to be preferred in the first step and remains the best estimator for highly correlated sequences

random convex hulls and extreme value statistics in this paper we study the statistical properties of convex hulls of n random points in a plane chosen according to a given distribution the points may be chosen independently or they may be correlated after a non exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem we present a unifying approach based on the notion of support function of a closed curve and the associated cauchy s formulae that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics as an example of correlated points we study here in detail the case when the points represent the vertices of n independent random walks in the continuum time limit this reduces to n independent planar brownian trajectories for which we compute exactly for all n the mean perimeter and the mean area of their global convex hull our results have relevant applications in ecology in estimating the home range of a herd of animals some of these results were announced recently in a short communication phys rev lett 103 140602 2009

toeplitz matrices commuting with tridiagonal matrices abstract we prove that if r is a nonscalar toeplitz matrix ri j r i j which commutes with a tridiagonal matrix with simple spectrum then r k r 1 u k 1 r 2 r 1 cos p u k 1 cos p k 4 5 with uk the chebychev polynomial of the second kind where p is determined from cos p 1 2 r 2 1 r 1 r 3 r 2 2 r 1 r 3

specification tests for distributional assumptions in the tobit model abstract the recent development of distribution robust estimators for the censored regression model allows for the construction of specification tests of the normality and homoskedasticity assumption of the tobit model this paper considers hausman 1978 specification tests for the tobit model that are based on powell s 1986 symmetrically censored least squares estimator testing for models with explanatory variables that are endogeneous is considered as well as the simpler case where the explanatory variables are exogenous testing of the maintained conditional symmetry assumption of the symmetrically censored least squares estimator is also considered the tests are implemented in an empirical example of a model of female labor supply

spectral analysis of the finite hankel transform and circular prolate spheroidal wave functions in this paper we develop two practical methods for the computation of the eigenvalues as well as the eigenfunctions of the finite hankel transform operator these different eigenfunctions are called circular prolate spheroidal wave functions cpswfs this work is motivated by the potential applications of the cpswfs as well as the development of practical methods for computing their values also in this work we should prove that the cpswfs form an orthonormal basis of the space of hankel band limited functions an orthogonal basis of l 2 0 1 and an orthonormal system of l 2 0 our computation of the cpswfs and their associated eigenvalues is done by the use of two different methods the first method is based on a suitable matrix representation of the finite hankel transform operator the second method is based on the use of an efficient quadrature method based on a special family of orthogonal polynomials also we give two maple programs that implement the previous two methods finally we present some numerical results that illustrate the results of this work

efficient estimation of binary choice models under symmetry abstract this paper proposes a semiparametric maximum likelihood estimator for both the intercept and slope parameters in a binary choice model under symmetry and index restrictions the estimator attains the semiparametric efficiency bound in cosslett 1987 under the symmetry and independence restrictions compared with the estimator of klein and spady 1993 which attains the semiparametric efficiency bound in chamberlain 1986 and cosslett 1987 under the independence restriction we show that there are possible efficiency gains in estimating the slope parameters by imposing the additional symmetry restriction a small monte carlo study is carried out to illustrate the usefulness of our estimator

efficiency bounds for distribution free estimators of the binary choice and the censored regression models we derive lower bounds on the asymptotic variances for regular distribution free estimators of the parameters of the binary choice model and the censored regression tobit model a distribution free or semiparametric estimator is one that does not require any assumption about the distribution of the stochastic error term in the model apart from regularity conditions for the binary choice model we obtain an explicit lower bound for the asymptotic variance for the slope parameters or more generally the parameters of a nonlinear regression function in the underlying latent variable model but we find that there is no regular semiparametric estimator of the constant term identified by requiring the error distribution to have zero median lower bounds are also obtained under the further assumption that the error distribution is symmetric and in this case there is a finite lower bound for the constant term too comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution we give the conditions for equality of the parametric and semiparametric lower bounds in which case adaptive estimation may be possible both with and without the assumption of a symmetric error distribution in general adaptive estimation is not possible but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution the tobit model considered here is the censored nonlinear regression model with a fixed censoring point we again give an explicit lower bound for the asymptotic variance for the regression parameters this time including a constant term if the error term has zero median comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model

on landau s eigenvalue theorem and information cut sets a variation of landau s eigenvalue theorem describing the phase transition of the eigenvalues of a time frequency limiting self adjoint operator is presented the total number of degrees of freedom of square integrable multidimensional bandlimited functions is defined in terms of kolmogorov s n width and computed in some limiting regimes where the original theorem cannot be directly applied results are used to characterize up to order the total amount of information that can be transported in time and space by multiple scattered electromagnetic waves rigorously addressing a question originally posed in the early works of toraldo di francia and gabor applications in the context of wireless communication and electromagnetic sensing are discussed

a markov chain approach to renormalization group transformations abstract we aim at an explicit characterization of the renormalized hamiltonian after decimation transformation of a one dimensional ising type hamiltonian with a nearest neighbor interaction and a magnetic field term to facilitate a deeper understanding of the decimation effect we translate the renormalization flow on the ising hamiltonian into a flow on the associated markov chains through the markov gibbs equivalence two different methods are used to verify the well known conjecture that the eigenvalues of the linearization of this renormalization transformation about the fixed point bear important information about all six of the critical exponents this illustrates the universality property of the renormalization group map in this case