extrapolation algorithms for discrete signals with application in spectral estimation in this paper we present some new algorithms useful for extrapolation and spectral estimation of band limited sequences in one and two dimensions first we show that many of the existing extrapolation algorithms for noiseless observations are unified under the criterion of minimum norm least squares mnls extrapolation for example the iterative algorithms proposed in 2 and 8 10 are shown to be special cases of a one step gradient algorithm which has linear convergence convergence and other numerical properties are improved by going to a conjugate gradient algorithm for noisy observations these algorithms could be extended by considering a mean square extrapolation criterion which gives rise to a mean square extrapolation filter and also to a recursive extrapolation filter examples and application of these methods are given extension of these algorithms is made for problems where the signal is known to be periodic a new set of functions called the periodic discrete prolate spheroidal sequences p dpss analogous to dpss 21 22 are introduced and their properties are studied finally several of these algorithms are generalized to two dimensions and the relevant equations are given

a multicarrier architecture based upon the affine fourier transform recently innovative multicarrier schemes have been proposed that exploit the transmission of chirp shaped waves e sup j2 spl pi ct2 by optimally choosing the chirp parameter c on the basis of the channel characteristics and are more robust to time varying channels than ordinary ofdm schemes this concept was applied to continuous time and to discrete time systems in the present paper we aim at developing those ideas using the affine fourier transform aft which is a very general formulation of chirp transforms we present a multicarrier modulation based upon the discrete form of the aft that is therefore inherently discrete and strictly invertible moreover it allows to define a circular prefix concept that is coherent with the chirp nature of the transmission the system can be efficiently implemented by adding a simple phase correction block to standard ofdm modulators demodulators and can effectively combat interchannel interference when the propagation channel is made of few multipath components affected by independent frequency offsets our discrete time multicarrier scheme is an improved version of martone s approach as we also show by simulation results and exhibits analogous characteristics to barbarossa s continuous time system

asymptotic properties of the product limit estimate under random truncation on donne une description precise du comportement asymptotique de l estimateur limite produit incluant une forme explicite simple de la structure de covariance asymptotique

on the convergence theory of trust region based algorithms for equality constrained optimization in a recent paper dennis el alem and maciel proved global convergence to a stationary point for a general trust region based algorithm for equality constrained optimization this general algorithm is based on appropriate choices of trust region subproblems and seems particularly suitable for large problems this paper shows global convergence to a point satisfying the second order necessary optimality conditions for the same general trust region based algorithm the results given here can be seen as a generalization of the convergence results for trust regions methods for unconstrained optimization obtained by more and sorensen the behavior of the trust radius and the local rate of convergence are analyzed some interesting facts concerning the trust region subproblem for the linearized constraints the quasi normal component of the step and the hard case are presented it is shown how these results can be applied to a class of discretized optimal control problems

on the convegence of a sequential penalty function method for constrained minimization the convergence behaviour of a class of iterative methods for solving the constrained minimization problem is analysed the methods are based on the sequential minimization of a simple differentiable penalty function they are sufficiently general to ensure global convergence of the iterates to the solution of the problem at an asymptotic two step q superlinear rate

an analysis of reduced hessian methods for constrained optimization we study the convergence properties of reduced hessian successive quadratic programming for equality constrained optimization the method uses a backtracking line search and updates an approximation to the reduced hessian of the lagrangian by means of the bfgs formula two merit functions are considered for the line search thel1 function and the fletcher exact penalty function we give conditions under which local and superlinear convergence is obtained and also prove a global convergence result the analysis allows the initial reduced hessian approximation to be any positive definite matrix and does not assume that the iterates converge or that the matrices are bounded the effects of a second order correction step a watchdog procedure and of the choice of null space basis are considered this work can be seen as an extension to reduced hessian methods of the well known results of powell 1976 for unconstrained optimization

noniterative and fast iterative methods for interpolation and extrapolation in this correspondence we study the band limited interpolation and extrapolation problems for finite dimensional signals we show that these problems can be easily reduced to the solution of a set of linear equations with a real symmetric positive definite matrix s with spectral radius spl rho s

two channel paraunitary filter banks based on linear canonical transform in this correspondence we propose a two channel paraunitary filter bank which is based on linear canonical transform lct instead of the fourier transform input output relations for such a filter bank are derived in terms of polyphase matrices and modulation matrices it is shown that like conventional filter banks the lct based paraunitary filter banks need only one filter to be designed and the rest of the filters can be obtained from it it is also shown that lct based paraunitary filter banks can be designed by using conventional power symmetric filter design in the fourier domain

nonparametric estimation from cross sectional survival data abstract in many follow up studies survival data are often observed according to a cross sectional sampling scheme data of this type are subject to left truncation in addition to the usual right censoring a number of characteristics and properties of the product limit estimate for left truncated and right censored data have been explored and found to be similar to those of the kaplan meier estimate under the stationarity assumption however it is believed that an alternative estimate has much better efficiency in this article the conditional maximum likelihood estimate mle property of the product limit estimate is visited the non parametric mle of the truncation distribution is derived use of this estimate includes testing the stationarity assumption estimating the proportion of truncated data and other applications in prevalent cohort studies the analysis of the estimation is based on a working data approach the asymptotic properties of the proposed estimates are developed through nonpar

properties of a representation of a basis for the null space given a rectangular matrix a x that depends on the independent variables x many constrained optimization methods involve computations with z x a matrix whose columns form a basis for the null space of a sup t x when a is evaluated at a given point it is well known that a suitable z satisfying a sup t z 0 can be obtained from standard matrix factorizations however coleman and sorensen have recently shown that standard orthogonal factorization methods may produce orthogonal bases that do not vary continuously with x they also suggest several techniques for adapting these schemes so as to ensure continuity of z in the neighborhood of a given point this paper is an extension of an earlier note that defines the procedure for computing z here we first describe how z can be obtained by updating an explicit qr factorization with householder transformations the properties of this representation of z with respect to perturbations in a are discussed including explicit bounds on the change in z we then introduce regularized householder transformations and show that their use implies continuity of the full matrix q the convergence of z and q under appropriate assumptions is then proved finally we indicate why themore chosen form of z is convenient in certain methods for nonlinearly constrained optimization less

convergence theory for nonconvex stochastic programming with an application to mixed logit monte carlo methods have extensively been used and studied in the area of stochastic programming their convergence properties typically consider global minimizers or first order critical points of the sample average approximation saa problems and minimizers of the true problem and show that the former converge to the latter for increasing sample size however the assumption of global minimization essentially restricts the scope of these results to convex problems we review and extend these results in two directions we allow for local saa minimizers of possibly nonconvex problems and prove under suitable conditions almost sure convergence of local second order solutions of the saa problem to second order critical points of the true problem we also apply this new theory to the estimation of mixed logit models for discrete choice analysis new useful convergence properties are derived in this context both for the constrained and unconstrained cases and associated estimates of the simulation bias and variance are proposed

a note on the computation of an orthonormal basis for the null space of a matrix a highly regarded method to obtain an orthonormal basis z for the null space of a matrix a t is the qr decomposition of a where q is the product of householder matrices in several optimization contexts a x varies continuously with x and it is desirable the z x vary continuously also in this note we demonstrate that the standard implementation of the qr decomposition does not yield an orthonormal basis z x whose elements vary continuously with x we suggest three possible remedies

nonparametric estimation of the probability of illness in the illness death model under cross sectional sampling cross sectional sampling is an attractive design that saves resources but results in biased data for proper inference one should first discover the bias function and then weigh observations appropriately we consider cross sectioning of the illness death model with the aim of estimating the probability of visiting the illness state before death we develop simple consistent and asymptotically normal estimators under various assumptions on the model and data collection and in particular compare designs with and without a follow up these designs are common in surveillance of hospital acquired infections but estimators currently in use do not properly correct the bias

signal extrapolation in wavelet subspaces the papoulis gerchberg pg algorithm is well known for band limited signal extrapolation the authors consider the generalization of the pg algorithm to signals in the wavelet subspaces in this research the uniqueness of the extrapolation for continuous time signals is examined and sufficient conditions on signals and wavelet bases for the generalized pg gpg algorithm to converge are given a discrete gpg algorithm is proposed for discrete time signal extrapolation and its convergence is investigated numerical examples are given to illustrate the performance of the discrete gpg algorithm

a fast convergence algorithm for band limited extrapolation by sampling in this paper an algorithm for band limited extrapolation is presented this uses shannon s sampling theorem and fourier series error analysis is given by proof the convergence rate is much faster than that of the papoulis gerchberg algorithm the procedure of the fast convergence algorithm is described in detail the result is demonstrated by numerical examples

method for defining a class of fractional operations the fractional fourier transform frt permits a variety of associated fractional operations this correspondence proposes a systematic method based on the structure of the frt which not only provides unambiguous extensions of ordinary operations but permits writing the applicable expressions simply by inspection the approach also exposes the possible paths for implementing such operations

extrapolation of bandlimited signals in linear canonical transform domain the linear canonical transform lct has been shown to be a powerful analyzing tool in signal processing many results of this transform are already known including bandlimited extrapolation the existing algorithm for solving the problem of lct bandlimited extrapolation is based on signal expansion into a series of generalized prolate spheroidal wave functions gpswfs however the requirement to compute and store the gpswfs and the errors due to the series truncation render this algorithm ill suitable for a practical implementation in this correspondence we first propose a new formulation of the gerchberg papoulis gp algorithm for lct bandlimited extrapolation then we present a fast convergence algorithm for the new formulation the classical gp algorithm related to fourier bandlimited signals is noted as a special case moreover the comparison between the proposed algorithm and the one based on gpswfs expansion is provided and the validity of the theoretical derivations is demonstrated via simulations several potential applications of the achieved theory are also presented

testing goodness of fit of a uniform truncation model several goodness of fit tests of a lifetime distribution have been suggested in the literature many take into account censoring and or truncation of event times in some contexts a goodness of fit test for the truncation distribution is of interest in particular better estimates of the lifetime distribution can be obtained when knowledge of the truncation law is exploited in cross sectional sampling for example there are theoretical justifications for the assumption of a uniform truncation distribution and several studies have used it to improve the efficiency of their survival estimates the duality of lifetime and truncation in the absence of censoring enables methods for testing goodness of fit of the lifetime distribution to be used for testing goodness of fit of the truncation distribution however under random censoring this duality does not hold and different tests are required in this article we introduce several goodness of fit tests for the truncation distribution and investigate their performance in the presence of censored event times using simulation we demonstrate the use of our tests on two data sets

estimating a distribution function with truncated data let mathscr p be a finite population with n geq 1 elements for each e in mathscr p let x e and y e be independent positive random variables with unknown distribution functions f and g and suppose that the pairs x e y e are i i d we consider the problem of estimating f g and n when the data consist of those pairs x e y e for which e in mathscr p and y e leq x e the nonparametric maximum likelihood estimators mles of f and g are described and their asymptotic properties as n rightarrow infty are derived it is shown that the mles are consistent against pairs f g for which f and g are continuous g 1 0 leq f 1 0 and g 1 1 leq f 1 1 sqrt n times estimation error for f converges in distribution to a gaussian process if int infty 0 1 g df infty but may fail to converge if this integral is infinite

on the convergence of constrained optimization methods with accurate hessian information on a subspace this paper analyzes methods of the type proposed by coleman and conn for nonlinearly constrained optimization it is shown that if the reduced hessian approximation is sufficiently accurate then the method generates a sequence of iterates that converges one step superlinearly this result applies to a quasi newton implementation if the reduced exact hessian is used the method has an r order equal to that of the secant method a similar result for a modified version of successive quadratic programming is also proved finally some parallels between convergence results for methods that approximate the reduced hessian method and multiplier methods that use the reduced hessian inverse are pointed out

large sample theory of empirical distributions in biased sampling models vardi 1985a introduced an s sample model for biased sampling gave conditions which guarantee the existence and uniqueness of the nonparametric maximum likelihood estimator mathbb g n of the common underlying distribution g and discussed numerical methods for calculating the estimator here we examine the large sample behavior of the npmle mathbb g n including results on uniform consistency of mathbb g n convergence of sqrt n mathbb g n g to a gaussian process and asymptotic efficiency of mathbb g n as an estimator of g the proofs are based upon recent results for empirical processes indexed by sets and functions and convexity arguments we also give a careful proof of identifiability of the underlying distribution g under connectedness of a certain graph mathbf g examples and applications include length biased sampling stratified sampling enriched stratified sampling choice based sampling in econometrics and case control studies in biostatistics a final section discusses design issues and further problems

uncertainty principle for real signals in the linear canonical transform domains the linear canonical transform lct is a generalization of the fractional fourier transform frft having applications in several areas of signal processing and optics in this paper we extend the uncertainty principle for real signals in the fractional fourier domains to the linear canonical transform domains giving us the tighter lower bound on the product of the spreads of the signal in two specific lct domains than the existing lower bounds in the lct domains it is seen that this lower bound can be achieved by a gaussian signal the effect of time shifting and scaling the signal on the uncertainty principle is also discussed it is shown here that a signal bandlimited in one lct domain can be bandlimited in some other lct domains also the exceptions to the uncertainty principle in the lct domains arising out of this are also discussed

relations between fractional operations and time frequency distributions and their applications the fractional fourier transform frft is a useful tool for signal processing it is the generalization of the fourier transform many fractional operations such as fractional convolution fractional correlation and the fractional hilbert transform are defined from it in fact the frft can be further generalized into the linear canonical transform lct and we can also use the lct to define several canonical operations in this paper we discuss the relations between the operations described above and some important time frequency distributions tfds such as the wigner distribution function wdf the ambiguity function af the signal correlation function and the spectrum correlation function first we systematically review the previous works in brief then some new relations are derived and listed in tables then we use these relations to analyze the applications of the frpt lct to fractional canonical filter design fractional canonical hilbert transform beam shaping and then we analyze the phase amplitude problems of the frft lct for phase amplitude problems we find as with the original fourier transform that in most cases the phase is more important than the amplitude for the frft lct we also use the wdf to explain why fractional canonical convolution can be used for space variant pattern recognition

continuity of the null space basis and constrained optimization many constrained optimization algorithms use a basis for the null space of the matrix of constraint gradients recently methods have been proposed that enable this null space basis to vary continuously as a function of the iterates in a neighborhood of the solution this paper reports results from topology showing that in general there is no continuous function that generates the null space basis of all full rank rectangular matrices of a fixed size thus constrained optimization algorithms cannot assume an everywhere continuous null space basis we also give some indication of where these discontinuities must occur we then propose an alternative implementation of a class of constrained optimization algorithms that uses approximations to the reduced hessian of the lagrangian but is independent of the choice of null space basis this approach obviates the need for a continuously varying null space basis

generalized prolate spheroidal wave functions associated with linear canonical transform time limited and a b c d band limited signals are of great interest not only in theory but also in real applications in this paper we use the sampling theorem associated with linear canonical transform to investigate an operator whose effect on a signal is to produce its first time limited then b b c d band limited version first the eigenvalue problem for the operator is shown to be equivalent to a discrete eigenvalue problem for an infinite matrix then the eigenfunctions of the operator which are referred to as generalized prolate spheroidal wave functions gpswfs are shown to be first orthogonal over finite as well as infinite intervals and second complete over l2 l l and the class of a b c d band limited signals a simple method based on sampling theorem for computing gpswfs is presented and the definite parity of gpswfs is also given finally based on the dual orthogonality and completeness of gpswfs several applications of gpswfs to the representation of time limited and a b c d band limited signals are presented

nonlinear programming via an exact penalty function asymptotic analysis in this paper we consider the final stage of a global method to solve the nonlinear programming problem we prove 2 step superlinear convergence in the process of analyzing this asymptotic behavior we compare our method theoretically to the popular successive quadratic programming approach

sampling and reconstruction in arbitrary measurement and approximation spaces associated with linear canonical transform the linear canonical transform lct which generalizes many classical transforms has been shown to be a powerful tool for signal processing and optics sampling theory of the lct for bandlimited signals has blossomed in recent years however in practice signals are never perfectly bandlimited and in many cases measurement devices are nonideal the objective of this paper is to develop a sampling theorem for the lct from general measurements which can provide a suitable and realistic model of sampling and approximation for real world applications we first describe a general class of approximation spaces for the lct and provide a full characterization of their basis functions then we propose a generalized sampling theorem for arbitrary measurement and approximation spaces associated with the lct several properties of the proposed sampling theorem are also discussed furthermore the approximation error is estimated finally numerical results and several applications of the derived results are presented