noncoherent capacity of underspread fading channels we derive bounds on the noncoherent capacity of wide sense stationary uncorrelated scattering wssus channels that are selective both in time and frequency and are underspread i e the product of the channel s delay spread and doppler spread is small the underspread assumption is satisfied by virtually all wireless communication channels for input signals that are peak constrained in time and frequency we obtain upper and lower bounds on capacity that are explicit in the channel s scattering function are accurate for a large range of bandwidth and allow to coarsely identify the capacity optimal bandwidth as a function of the peak power and the channel s scattering function we also obtain a closed form expression for the first order taylor series expansion of capacity in the infinite bandwidth limit and show that our bounds are tight in the wideband regime for input signals that are peak constrained in time only and hence allowed to be peaky in frequency we provide upper and lower bounds on the infinite bandwidth capacity our lower bound is closely related to a result by viterbi 1967 we find cases where the bounds coincide and hence the infinite bandwidth capacity is characterized exactly the analysis in this paper is based on a discrete time discrete frequency approximation of wssus time and frequency selective channels this discretization takes the underspread property of the channel explicitly into account

conditional scores and optimal scores for generalized linear measurement error models abstract this paper studies estimation of the parameters of generalized linear models in canonical form when the explanatory vector is measured with independent normal error for the functional case i e when the explanatory vectors are fixed constants unbiased score functions are obtained by conditioning on certain sufficient statistics this work generalizes results obtained for logistic regression in the case that the explanatory vectors are independent and identically distributed with unknown distribtuion efficient score functions are obtained using the theory developed in begun et al 1983 keywords conditional score function efficient score function functional model generalized linear model measurement error structural model

structural modeling and psychometrika an historical perspective on growth and achievements the field of linear structural equation modeling with continuous variables is reviewed trends in psychometric theory and data analysis across the five decades of publication ofpsychometrika are discussed especially the clarification of concepts of population and sample explication of the parametric structure of models delineation of concepts of exploratory and confirmatory data analysis expansion of statistical theory in psychometrics estimation via optimization of an explicit objective function and implementation of general function minimization methods developments in the ideas of factor analysis latent variables as well as structural and causal modeling are noted some major conceptual achievements involving general covariance structure representations multiple population models and moment structures are reviewed the major statistical achievements of normal theory generalized least squares estimation elliptical and distribution free estimation and higher moment estimation are discussed computer programs that implement some of the theoretical developments are described

global solutions of initial value problems for nonlinear second order impulsive integro differential equations of mixed type in banach spaces in this paper we develop a theorem for the existence of global solutions of an initial value problems for a class of second order impulsive integro differential equations of mixed type in a real banach space the results obtained are the generalizations and improvements of various recent results as an application of the theorem the existence of global solutions of two mixed boundary value problems for two classes of fourth order impulsive differential equations are established

efficient estimation in the errors in variables model we consider efficient estimation of the slope in the errors in variables model with normal error when either the ratio of error variances is known and the distribution of the independent is arbitrary and unknown or the distribution of the independent variable is not gaussian or degenerate we calculate information bounds and exhibit estimates achieving these bounds using an initial minimum distance estimate and suitable estimates of the efficient score function

linear unmixing of multivariate observations in many fields of science there are multivariate observations that may be assumed to be generated by a physical linear mixing process of contributions from different sources if the compositions of the sources are constant for different observations then these observations are up to a random error term nonnegative linear combinations of a fixed set of so called source profiles that characterize the sources the goal of linear unmixing is to recover both the source profiles and the source activities also called scores from a multivariate dataset we present a new parametric mixing model that assumes a multivariate lognormal distribution for the scores this model is proved to be identifiable moreover consistency and asymptotic normality of the maximum likelihood estimator mle are established in special cases to calculate the mle we propose the combination of two variants of the monte carlo em algorithm the proposed model is applied to simulated datasets and to a set of air pollution measure

global solutions of nonlinear second order impulsive integro differential equations of mixed type in banach spaces abstract in this paper by using the generalization of darbo s fixed point theorem we establish the existence of global solutions of an initial value problem for a class of second order impulsive integro differential equations of mixed type in a real banach space our results generalize and improve on the results of guo et al f guo l s liu y h wu p siew global solutions of initial value problems for nonlinear second order impulsive integro differential equations of mixed type in banach spaces nonlinear anal 61 2005 1363 1382 in the sense that the conditions for existence of global solution in our theorem is simpler and less strict to demonstrate the application of the theorem we give the global solutions of two mixed boundary value problems for two classes of fourth order impulsive integro differential equations

nonlinear autoregressive and nonlinear autoregressive moving average model parameter estimation by minimizing hypersurface distance the least squares ls can be used for nonlinear autoregressive nar and nonlinear autoregressive moving average narma parameter estimation however for nonlinear cases the ls results in biased parameter estimation due to its assumption that the independent variables are noise free the total least squares tls is another method that can used for nonlinear parameter estimation to increase the accuracy of the ls because it specifically accounts for the fact that the independent variables are noise corrupted tls has its own limitations however mainly because it is difficult for the method to isolate noise from the signal components we present a new method that is based on minimization of hypersurface distance for accurate parameter estimation for nar and narma models computer simulation examples show that the new method results in far more accurate nar and narma model parameter estimates than do either the ls and tls with noise that is either white or colored and retains its high accuracy even when the signal to noise ratio snr is as low as 10 db

statistical behavior of joint least square estimation in the phase diversity context the images recorded by optical telescopes are often degraded by aberrations that induce phase variations in the pupil plane several wavefront sensing techniques have been proposed to estimate aberrated phases one of them is phase diversity for which the joint least square approach introduced by gonsalves et al is a reference method to estimate phase coefficients from the recorded images in this paper we rely on the asymptotic theory of toeplitz matrices to show that gonsalves technique provides a consistent phase estimator as the size of the images grows no comparable result is yielded by the classical joint maximum likelihood interpretation e g as found in the work by paxman et al finally our theoretical analysis is illustrated through simulated problems

on the number of zeros of abelian integrals a constructive solution of the infinitesimal hilbert sixteenth problem we prove that the number of limit cycles generated from nonsingular energy level ovals periodic trajectories in a small non conservative perturbation of a hamiltonian polynomial vector field on the plane is bounded by a double exponential of the degree of the fields this solves the long standing infinitesimal hilbert 16th problem

existence theorems of global solutions for nonlinear volterra type integral equations in banach spaces in this paper first a new fixed point theorem is established and then by the use of it the existence theorems of global solutions for nonlinear volterra type integral equations in banach spaces are investigated the results obtained in this paper generalize and improve the results corresponding to those obtained by others

cramer rao lower bound for point based image registration with heteroscedastic error model for application in single molecule microscopy the cramer rao lower bound for the estimation of the affine transformation parameters in a multivariate heteroscedastic errors in variables model is derived the model is suitable for feature based image registration in which both sets of control points are localized with errors whose covariance matrices vary from point to point with focus given to the registration of fluorescence microscopy images the cramer rao lower bound for the estimation of a feature s position e g of a single molecule in a registered image is also derived in the particular case where all covariance matrices for the localization errors are scalar multiples of a common positive definite matrix e g the identity matrix as can be assumed in fluorescence microscopy then simplified expressions for the cramer rao lower bound are given under certain simplifying assumptions these expressions are shown to match asymptotic distributions for a previously presented set of estimators theoretical results are verified with simulations and experimental data

a novel power bearing approach and asymptotically optimum estimator for target motion analysis the problem of target motion analysis tma has been extensively investigated using bearing only bo doppler bearing db and other measurement data for radio frequency rf emitters signal powers follow the well known path loss law that can be utilized to aid localization and target tracking in bo tma leading to the novel power bearing pb approach as proposed in this paper our main contribution lies in the proof of the asymptotic optimality of the total least squares tls algorithm for pb tma under some mild condition the cramer rao lower bound crlb is employed to demonstrate the performance improvements of the pb tma over the bo tma our work shows the promise of the pb tma approach for rf signals

asymptotic eigenvalue distribution of block toeplitz matrices and application to blind simo channel identification szego s 1984 theorem states that the asymptotic behavior of the eigenvalues of a hermitian toeplitz matrix is linked to the fourier transform of its entries this result was later extended to block toeplitz matrices i e covariance matrices of multivariate stationary processes the present work gives a new proof of szego s theorem applied to block toeplitz matrices we focus on a particular class of toeplitz matrices those corresponding to covariance matrices of single input multiple output simo channels they satisfy some factorization properties that lead to a simpler form of szego s theorem and allow one to deduce results on the asymptotic behavior of the lowest nonzero eigenvalue for which an upper bound is developed and expressed in terms of the subchannels frequency responses this bound is interpreted in the context of blind channel identification using second order algorithms and more particularly in the case of band limited channels

asymptotic generalized eigenvalue distribution of block multilevel toeplitz matrices in many detection and estimation problems associated with processing of second order stationary random processes the observation data are the sum of two zero mean second order stationary processes the process of interest and the noise process in particular the main performance criterion is the signal to noise ratio snr after linear filtering the optimal snr corresponds to the maximal value of a rayleigh quotient which can be interpreted as the largest generalized eigenvalue of the covariance matrices associated with the signal and noise processes which are block multilevel toeplitz structured for m dimensional vector valued second order stationary p dimensional random processes xi1 i2 ip isin bbr m in this paper an extension of szego s theorem to the generalized eigenvalues of hermitian block multilevel toeplitz matrices is given providing information about the asymptotic distribution of those generalized eigenvalues and in particular of the optimal snr after linear filtering a simple proof of this theorem under the hypothesis of absolutely summable elements is given the proof is based on the notion of multilevel asymptotic equivalence between block multilevel matrix sequences derived from the celebrated gray approach finally a short example in wideband space time beamforming is given to illustrate this theorem

multivariate methods for quantitative and qualitative data abstract in this paper several multivariate analysis methods are analyzed by means of the errors in variables model two specifications viz the principal relations and the principal factors model for the set of unobserved latent variables are introduced and shown to be complementary for particular choices of the error covariance matrix the general model reduces to several well known multivariate techniques including ordinary least squares principal components orthogonal regression and canonical correlations the same apparatus is used to arrive at a set of multivariate techniques in case the data is qualitative instead of quantitative the relationship with optimal scaling techniques for qualitative data is shown an empirical example is given of a regression involving a dependent latent variable having two ordered categorical indicator variables

triple positive solutions of a boundary value problem for nonlinear singular second order differential equations of mixed type with p laplacian in this paper we establish the existence of triple positive solutions of a two point boundary value problem for the nonlinear singular second order differential equations of mixed type with a p laplacian operator we also demonstrate that the results obtained can be applied to study certain higher order mixed boundary value problems finally an example is given to demonstrate the use of the main results of this paper

new algorithm for a class of nonlinear integro differential equations in the reproducing kernel space this paper is concerned with the new algorithm for giving the approximate solution of a class of nonlinear integro differential equations in the reproducing kernel space two integro differential equations are solved using the algorithm it turns out that this algorithm is valid

initial value problems for nonlinear second order impulsive integro differential equations of mixed type in banach spaces in this paper through solving equations step by step without any assumption of compactness type conditions we obtain unique solution of initial value problems of nonlinear second order impulsive integral differential in banach spaces the results obtained generalize and improve the corresponding results of guo and chai in papers d j guo initial value problems for nonlinear second order impulsive integro differential equations in banach spaces j math anal appl 200 1996 1 13 g q chai initial value problems for nonlinear second order impulsive integro differential equations in banach space acta math sinica 20 3 2000 351 359 in chinese

a note on g r dolby s unreplicated ultrastructural model it is demonstrated that maximum likelihood estimators exist for the intercept slope and unknown error variance in dolby s 1976 unreplicated ultrastructural model with known error variance ratio even when the ratio of the variability of the measured variables to the variability of the measurement errors is unknown this corrects an assertion in dolby s paper patefield s 1978 adjusted maximum likelihood estimators for this model are shown to be strongly consistent and jointly asymptotically normal and also best in fisher s sensewithin a broad class of asymptotically normal estimators finally it is noted that patefield s adjusted estimators are asymptotically equivalent to the maximum likelihood estimators in a certain related structural model

asymptotic eigenvalue distribution of block toeplitz matrices the need for approximating block toeplitz with toeplitz block matrices by means of block circulant with circulant block matrices with the objective of transforming an inherently ill posed image deconvolution problem to a well posed one motivated a surge of papers on the analysis of the quality as well as the speed of convergence of the algorithms that produce such approximants to serve as preconditioners for conjugate gradient methods this correspondence contributes to that surge by giving a simple proof of the fact that the sequence of eigenvalues of the hermitian block toeplitz with toeplitz block matrices are asymptotically equidistributed to do this weyl s 1916 results on the distribution properties of multidimensional sequences are exploited inferences to related results are made

robust parametric transfer function estimation using complex logarithmic frequency response data the statistical properties of a logarithmic least squares frequency domain estimator are analyzed in an error in variables framework it is shown that contrary to most frequency domain estimators the logarithmic least squares estimator remains practically consistent when the variances of the frequency domain data are not a priori known if available the variance at each spectral line of the logarithmic frequency response data can be used to weight the logarithmic least squares estimator resulting in parameter estimates with a smaller variability an estimate of these variances can be derived from the residual errors at the excited spectral lines besides its robustness to lack of prior noise information it is demonstrated that the logarithmic estimator behaves remarkably well in the presence of outliers

functions of banded hermitian block toeplitz matrices in signal processing the paper deals with the entries of functions of large banded hermitian block toeplitz matrices and their perturbations for general continuous functions convergence results are established and for analytic functions these results are accompanied by estimates of the convergence speed the applications to signal processing include among others the direct derivation of a closed form solution of the minimum mean square error mmse for a double sided infinite length linear equalizer for mimo channels from the finite length mmse expression and the derivation of a formula for the contribution of each channel input to the overall mmse

a new approach to variable selection using the tls approach the problem of variable selection is one of the most important model selection problems in statistical applications it is also known as the subset selection problem and arises when one wants to explain the observations or data adequately by a subset of possible explanatory variables the objective is to identify factors of importance and to include only variables that contribute significantly to the reduction of the prediction error numerous selection procedures have been proposed in the classical multiple linear regression model we extend one of the most popular methods developed in this context the backward selection procedure to a more general class of models in the basic linear regression model errors are present on the observations only if errors are present on the regressors as well one gets the errors in variables model which for gaussian noise becomes the total least squares tls model this is the context considered here

algebraic relationships between classical regression and total least squares estimation abstract the total least squares tls technique which is well known in numerical linear algebra and able to compute strongly consistent estimators of the parameters in a linear errors in variables model is compared algebraically with the classical regression estimators using the singular value decomposition and geometric concepts algebraic equivalences and important relationships between the classical regression techniques and tls estimation are established with special reference to problems of collinearity the equivalence between principal component and latent root regression in collinearity problems is proven and the difference between latent root regression and tls estimation is clarified

effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable we consider three commonly used statistical tests for assessing the association between an explanatory variable and a measured binary or survival time response variable and investigate the loss in efficiency from mismodelling or mismeasuring the explanatory variable with respect to mismodelling we examine the consequences of using an incorrect dose metameter in a test for trend of mismodelling a continuous explanatory variable and of discretizing a continuous explanatory variable we also examine the consequences of classification errors for a discrete explanatory variable and of measurement errors for a continuous explanatory variable for all three statistical tests the asymptotic relative efficiency are corresponding to each type of mis specification equals the square of the correlation between the correct and fitted form of the explanatory variable this result is evaluated numerically for the different types of mis specification to provide insight into the selection of tests the interpretation of results and the design of studies where the correct explanatory variable cannot be measured exactly

on the polynomial functional relationship summary a method for obtaining consistent estimators of the coefficients in a polynomial functional relationship model with normal errors is proposed when the error covariance matrix is either completely known or known up to a proportionality factor for quadratic functional relationships with possibly non normal errors we present a consistent estimator when the error covariance matrix is known a large sample test of the quadratic against the linear functional relationship is also suggested in this case

the singular value decomposition and long and short spaces of noisy matrices using geometrical algebraic and statistical arguments it is clarified why and when the singular value decomposition is successful in so called subspace methods first the concepts of long and short spaces are introduced and a fundamental asymmetry in the consistency properties of the estimates is discussed the model which is associated with the short space can be estimated consistently but the estimates of the original data which follow from the long space are always inconsistent an expression is found for the asymptotic bias in terms of canonical angles which can be estimated from the data this allows all equivalent reconstructions of the original signals to be described as a matrix ball the center of which is the minimum variance estimate remarkably the canonical angles also appear in the optimal weighting that is used in weighted subspace fitting approaches the results are illustrated with a numerical simulation a number of examples are discussed

existence theorems of global solutions of initial value problems for nonlinear integrodifferential equations of mixed type in banach spaces and applications abstract this paper investigates the existence of global solutions for initial value problems of the nonlinear integrodifferential equations in banach spaces we obtain the existence of global solutions by schauder s fixed point theorem our results are the generalizations and improvements of recent results as applications of our results the existence of global solutions of two classes of third order mixed boundary value problem is obtained and an example of infinite system for nonlinear integrodifferential equations is worked out to illustrate our main results

the constrained total least squares technique and its applications to harmonic superresolution the constrained total least squares ctls method is a natural extension of tls to the case when the noise components of the coefficients are algebraically related the ctls technique is developed and some of its applications to superresolution harmonic analysis are presented the ctls problem is reduced to an unconstrained minimization problem over a small set of variables a perturbation analysis of the ctls solution is derived and from it the root mean square error rmse of the ctls solution which is valid for small noise levels is obtained in closed form the complex version of the newton method is derived and applied to determine the ctls solution it is also shown that the ctls problem is equivalent to a constrained parameter maximum likelihood problem the ctls technique is applied to estimate the frequencies of sinusoids in white noise and the angle of arrival of narrowband wavefronts at a linear uniform array in both cases the ctls method shows superior or similar accuracy to other advanced techniques

periodic solutions of abel equations with jumps abstract we study for given t 0 the abel like equation f 0 j 1 m f j j k 1 n a k j k where each f j 0 t r j 0 m is a t periodic function of bounded variation and each term a k j k k 1 n is a jump in of state dependent amplitude a k at state dependent instant k 0 t under appropriate conditions the equation is shown to admit an absolutely continuous t periodic solution with derivative of bounded variation having preassigned jumps a k j k by the contraction principle a bound is obtained for the rate of point wise convergence to the solution of a sequence of picard iterates an algorithm to calculate iterated convolutions is developed and applied to a riccati equation and to an abel equation from cosmology

instrumental variable estimator for the nonlinear errors in variables model abstract estimation for the nonlinear errors in variables model is considered it isassumed that additional information is available in the form of observations on instrumental variables an estimation procedure is presented for the parameters of the model asymptotic properties of the estimator are investigated

center conditions at infinity for abel differential equations an abel differential equation y p x y 2 q x y 3 is said to have a center at a set a a 1 a r of complex numbers if y a 1 y a 2 y a r for any solution y x with the initial value y a 1 small enough the polynomials p q are said to satisfy the polynomial composition condition on a if there exist polynomials p q and w such that p p and q q are representable as p x p w x q x q w x and w a 1 w a 2 w a r we show that for wide ranges of degrees of p and q restricted only by certain assumptions on the common divisors of these degrees the composition condition provides a very accurate approximation of the center one up to a finite number of configurations not accounted for to our best knowledge this is the first general i e not restricted to small degrees of p and q or to a very special form of these polynomials result in the center problem for abel equations as an important intermediate result we show that at infinity according to an appropriate projectivization of the parameter space the center conditions are given by a system of the moment equations of the form as a1 p k q 0 s 2 r k 0 1

asymptotically equivalent sequences of matrices and multivariate arma processes the present paper considers a special class of vector random processes that we call multivariate asymptotically wide sense stationary wss processes a multivariate random process is said to be asymptotically wss if it has constant mean and the sequence of its autocorrelation matrices is asymptotically equivalent a e to the sequence of autocorrelation matrices of some multivariate wss process it is shown that this class of processes contains meaningful processes other than multivariate wss processes in particular we give sufficient conditions for multivariate moving average ma processes multivariate autoregressive ar processes and multivariate autoregressive moving average arma processes to be asymptotically wss furthermore in order to solve multiple input multiple output mimo problems in communications and signal processing involving this kind of processes we extend the gray definition of a e sequences of matrices and his main results on these sequences to non square matrices as an example the derived results on a e sequences of non square matrices are applied to compute the differential entropy rate and the minimum mean square error mmse for a linear predictor of a multivariate asymptotically wss process

comparison of least squares and errors in variables regression with special reference to randomized analysis of covariance abstract in an errors in variables regression model the least squares estimate is generally inconsistent for the complete regression parameter but can be consistent for certain linear combinations of this parameter we explore the conjecture that when the least squares estimate is consistent for a linear combination of the regression parameter it will be preferred to an errors in variables estimate at least asymptotically the conjecture is false in general but it is true for some important classes of problems one such problem is a randomized two group analysis of covariance upon which we focus

using principal component analysis and correspondence analysis for estimation in latent variable models abstract correspondence analysis ca and principal component analysis pca are often used to describe multivariate data in certain applications they have been used for estimation in latent variable models the theoretical basis for such inference is assessed in generalized linear models where the linear predictor equals j xi j or aj bj xi xi j 2 i 1 n j 1 m and xi is treated as a latent fixed effect the pca and ca eigenvectors column scores are evaluated as estimators of j and uj and as estimators of uj with m fixed and n consistent estimators cannot be obtained due to the incidental parameters problem unless sufficient moment conditions are imposed on xi pca is equivalent to maximum likelihood estimation for the linear gaussian model and gives a consistent estimator of j up to a scale change when the second sample moment of xi is positive and finite in the limit it is inconsistent for poisson and bernoulli distributions but when bj is constant its first and or sec

brief paper on the asymptotic eigenvalue distribution of block toeplitz matrices related to the generalized orthonormal basis functions model in this paper we study the asymptotic distribution of the eigenvalues of a family of hermitian block toeplitz matrices generated by the internal signals of the so called generalized orthonormal basis functions models our results are a generalization of a well known theorem of szego which addresses only the case of hermitian toeplitz matrices

relationship between geometric translations and tls estimation bias in bearings only target localization this paper analyzes the effects of local coordinate translations and rotations on the bias and mean squared error performance of the total least squares tls bearings only target localization algorithm the tls estimator was originally proposed to alleviate the severe bias problems associated with the traditional pseudolinear estimator an interesting property of the tls estimator which is not shared by the pseudolinear estimator is that its bias is sensitive to where the origin of the local cartesian coordinates is placed the paper provides a formal proof of this observation discusses its implication on bias minimization and proposes a simple and effective method for tls bias reduction the findings of the paper are illustrated with comprehensive simulation examples

iterative method for solutions and coupled quasi solutions of nonlinear integro differential equations of mixed type in banach spaces we consider in this paper the existence of solutions coupled minimal and maximal quasi solutions and iterative approximation of the unique solution for the following initial value problems ivp of the nonlinear integro di erential equations of mixed type in ordered banach spaces e u f t u u tu su t i u t0 x0 1 where i t0 t0 a a 0 x0 e f c i e e e e e and

a new result on impulsive differential equations involving non absolutely convergent integrals in this paper we obtain as an application of a darbo type theorem global solutions for differential equations with impulse effects under the assumption that the function on the right hand side is integrable in the henstock sense we thus generalize several previously given results in literature for ordinary or impulsive equations

efficient inversion of toeplitz block toeplitz matrix an iterative algorithm for the inversion of a toeplitz block toeplitz matrix consisting of m m blocks of size p p is described the algorithm presented exploits the structure of the toeplitz block toeplitz matrix and outperforms akaike s algorithm by a factor of max 2 p m 2 the use of this algorithm for an iterative solution of a toeplitz block toeplitz set of linear equations is also presented

a theorem on the asymptotic eigenvalue distribution of toeplitz block toeplitz matrices we extend szego s eigenvalue distribution theorem to block toeplitz matrices a sequence of such matrices arises from the autocorrelation of a 2 d discrete random process we show that the eigenvalues of the matrix sequence are asymptotically distributed like the samples of the random process 2 d power spectrum

implicitly weighted total least squares abstract in a total least squares tls problem we estimate an optimal set of model parameters x so that a a x b b where a is the model matrix b is the observed data and a and b are corresponding corrections when b is a single vector rao 1997 and paige and strakos 2002 suggested formulating standard least squares problems for which a 0 and data least squares problems for which b 0 as weighted and scaled tls problems in this work we define an implicitly weighted tls formulation itls that reparameterizes these formulations to make computation easier we derive asymptotic properties of the estimates as the number of rows in the problem approaches infinity handling the rank deficient case as well we discuss the role of the ratio between the variances of errors in a and b in choosing an appropriate parameter in itls we also propose methods for computing the family of solutions efficiently and for choosing the appropriate solution if the ratio of variances is unknown we provide experimental results on the usefulness of the itls family of solutions

spatial filtering in ambient noise interferometry theoretically the empirical green s function between a pair of receivers can be extracted from the cross correlation of the received diffuse noise the diffuse noise condition rarely is met in the ocean and directional sources may bias the green s function here matrix based spatial filters are used for removing unwanted contributions in the cross correlations two methods are used for solving the matrix filter design problem first a matrix least square problem is solved with a low rank approximation of the pseudo inverse here derived for linear and planar arrays second a convex optimization approach is used to solve the design problem reformulated with ad hoc constraints the spatial filter is applied to real data cross correlations of elements from a linear array to attenuate the contribution of a discrete interferer in the case of a planar array and simulated data a spatial filter enables a passive upgoing downgoing wavefield separation along with an efficient rejection of horizontally propagating noise the impact of array size and frequency band on the filtered cross correlations is discussed

uniform upper bounds for the cyclicity of the zero solution of the abel differential equation abstract given two polynomials p q we consider the following question how large can the index of the first non zero moment m k a b p k q be assuming the sequence is not identically zero the answer k to this question is known as the moment bautin index and we provide the first general upper bound k 2 deg q 3 deg p 1 2 the proof is based on qualitative analysis of linear odes applied to cauchy type integrals of certain algebraic functions the moment bautin index plays an important role in the study of bifurcations of periodic solution in the polynomial abel equation y p y 2 e q y 3 for p q polynomials and e 1 in particular our result implies that for p satisfying a well known generic condition the number of periodic solutions near the zero solution does not exceed 5 deg q 3 deg 2 p this is the first such bound depending solely on the degrees of the abel equation

fast solutions of the 2d inverse scattering problem based on a tsvd approximation of the internal field for the forward model an alternative formulation of the microwave tomography problem is proposed in order to reduce the computation time of the inversion procedure the well known multiplicative regularized contrast source inversion method is used as reference algorithm our formulation is based on a truncated singular value decomposition of the matrix involved in the most computationally intensive operations of the inversion algorithm after theoretical and practical investigation of the behavior of the singular values it is shown that the corresponding approximation does not yield any significant degradation of the quality of the solutions even for large complex permittivity contrasts while the computation times are reduced by a factor ranging between 1 1 and 6 with respect to the original method

on well posedness of an initial value problem for nonlinear second order impulsive integro differential equations of volterra type in banach spaces in this paper we develop an existence and uniqueness theorem of the solution to an initial value problems for a class of second order impulsive integro differential equations of volterra type in a real banach space by using the generalized banach fixed point theorem an explicit iterative scheme for the solution and an error estimate of the approximation sequence for the initial value problem are also derived two examples are presented to demonstrate the application of our results

on the accuracy of total least squares and least squares techniques in the presence of errors on all data abstract every linear parameter estimation problem gives rise to an overdetermined set of linear equations ax b which is usually solved with the ordinary least squares ls method often both a and b are inaccurate for these cases a more general fitting technique called total least squares tls is devised this paper investigates via simulations how perturbations on both a and b affect the accuracy of the tls and ls solution several important factors are discussed as well as the consistency properties of the tls solution in the presence of uncorrelated and equally sized errors

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models the estimation of the parameters of a transfer function model is considered relationships between the total least squares tls and instrumental variable iv approaches are outlined both methods

on sprent s generalized least squares estimator summary this paper studies the asymptotic properties of sprent s 1966 generalized leastsquares estimator of the slope parameter in a functional relationship model which allows errors at different data points be correlated consistency is established and the asymptotic variance derived when the joint distribution of the errors is normal in which case sprent s estimator coincides with the maximum likelihood estimator the asymptotic variance formula is further simplified and the limiting distribution of the estimator is also shown to be normal the variance expression obtained under the normality assumption differs from that of dolby 1972 derived by inver ting the information matrix and the latter procedure is known to be generally invalid in functional relationship problems due to the presence of incidental parameters patefield 1978 an estimator of the asymptotic variance is also suggested

a robust matched detector we address the matched detector problem in the case the signal to be detected is imperfectly known while in the standard detector the signal is known to lie along a particular direction we consider the case where this direction is known up to additive white gaussian noise this somehow amounts to assuming that the signal lies in a cone the aperture of which depends upon the level of uncertainty we build the associated generalized likelihood ratio glr analyze its statistical properties indicate how to set the threshold to achieve a given false alarm rate and how to predict the associated probability of detection the so obtained detector reduces to the conventional one when the uncertainty vanishes and we analyze its behavior when the level of uncertainty which has to be known a priori is mis evaluated it appears that the sensitivity of the detector is quite low with respect to this kind of errors more importantly several realistic examples are presented that indicate that the proposed detector remains quite efficient when the true signals are far from being of the assumed model and whatever the model of the uncertainty actually is it is this robustness that makes the detector valuable

analysis of point based image registration errors with applications in single molecule microscopy we present an asymptotic treatment of errors involved in point based image registration where control point cp localization is subject to heteroscedastic noise a suitable model for image registration in fluorescence microscopy assuming an affine transform cps are used to solve a multivariate regression problem with measurement errors existing for both sets of cps this is an errors in variable problem and linear least squares is inappropriate the correct method being generalized least squares to allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration for a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix including the case where covariance matrices are multiples of the identity we provide closed form solutions to estimators and derive their distribution we consider the target registration error tre and define a new measure called the localization registration error lre believed to be useful especially in microscopy registration experiments assuming gaussianity of the cp localization errors it is shown that the asymptotic distribution for the tre and lre are themselves gaussian and the parameterized distributions are derived results are successfully applied to registration in single molecule microscopy to derive the key dependence of the tre and lre variance on the number of cps and their associated photon counts simulations show asymptotic results are robust for low cp numbers and non gaussianity the method presented here is shown to outperform gls on real imaging data

seismic velocity and polarization estimation for wavefield separation we address the problem of estimating the shape parameters of seismic wavefields using linear arrays of three component 3c vector sensors with uncertain acquisition geometry the goal is to separate the different seismic waves which is of practical need for oil exploration and geophysics we present a parametric model for multiple wideband polarized signals received by an array of three component sensors with positional and rotational calibration errors and derive the cramer rao lower bounds on the performance of the model parameters for both the exact physical model and the model with uncertain acquisition geometry we propose a method for jointly estimating the velocity and polarization parameters based on the shift invariance properties of multiple wavefields impinging on the linear array we then remove the interfering surface waves by using a beamforming filter designed to exploit the velocity and polarization diversity of the different seismic waves after clustering of the shape parameter estimates examples using simulated and experimental data illustrate the applicability of the proposed methodology