an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

a shamanskii like self adaptive levenberg marquardt method for nonlinear equations abstract in this paper we are concerned with the shamanskii like self adaptive levenberg marquardt methods for nonlinear equations we consider two choices of levenberg marquardt parameter one of them is the standard self adaptive levenberg marquardt parameter the other is nonmonotone self adaptive levenberg marquardt parameter by using the nonmonotone technique of grippo lampariello and lucidi under the error bound condition which is weaker than nonsingularity we show that the shamanskii like self adaptive levenberg marquardt methods converge with q order m 1 numerical experiments show the new algorithms are efficient and promising

on the global convergence of the bfgs method for nonconvex unconstrained optimization problems this paper is concerned with the open problem of whether the bfgs method with inexact line search converges globally when applied to nonconvex unconstrained optimization problems we propose a cautious bfgs update and prove that the method with either a wolfe type or an armijo type line search converges globally if the function to be minimized has lipschitz continuous gradients

variable metric methods for unconstrainted optimization and nonlinear least squares variable metric or quasi newton methods are well known and commonly used in connection with unconstrained optimization since they have good theoretical and practical convergence properties although these methods were originally developed for small and moderate size dense problems their modifications based either on sparse partitioned or limited memory updates are very efficient on large scale sparse problems very significant applications of these methods also appear in nonlinear least squares approximation and nonsmooth optimization in this contribution we give an extensive review of variable metric methods and their use in various optimization fields

global convergence of a cass of quasi newton methods on convex problems we study the global convergence properties of the restricted broyden class of quasi newton methods when applied to a convex objective function we assume that the line search satisfies a standard sufficient decrease condition and that the initial hessian approximation is any positive definite matrix we show global and superlinear convergence for this class of methods except for dfp this generalizes powell s well known result for the bfgs method the analysis gives us insight into the properties of these algorithms in particular it shows that dfp lacks a very desirable self correcting property possessed by bfgs

a tool for the analysis of quasi newton methods with application to unconstrained minimization the bfgs update formula is shown to have an important property that is inde pendent of the algorithmic context of the update and that is relevant to both constrained and unconstrained optimization the bfgs method for unconstrained optimization using a variety of line searches including backtracking is shown to be globally and superlinearly convergent on uniformly convex problems the analysis is particularly simple due to the use of some new tools introduced in this paper

a nonlinear conjugate gradient method with a strong global convergence property conjugate gradient methods are widely used for unconstrained optimization especially large scale problems the strong wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods this paper presents a new version of the conjugate gradient method which converges globally provided the line search satisfies the standard wolfe conditions the conditions on the objective function are also weak being similar to those required by the zoutendijk condition

application of gradient descent method to the sedimentary grain size distribution fitting existence of a least squares solution for a sum of several weighted normal functions is proved the gradient descent gd method is used to fit the measured data i e the laser grain size distribution of the sediments with a sum of three weighted lognormal functions the numerical results indicate that the gd method is not only easy to operate but also could effectively optimize the parameters of the fitting function with the error decreasing steadily meanwhile the overall fitting results are satisfactory as a new way of data fitting the gd method could also be used to solve other optimization problems

nonlinear conjugate gradient methods with structured secant condition for nonlinear least squares problems in this paper we deal with conjugate gradient methods for solving nonlinear least squares problems several newton like methods have been studied for solving nonlinear least squares problems which include the gauss newton method the levenberg marquardt method and the structured quasi newton methods on the other hand conjugate gradient methods are appealing for general large scale nonlinear optimization problems by combining the structured secant condition and the idea of dai and liao 2001 20 the present paper proposes conjugate gradient methods that make use of the structure of the hessian of the objective function of nonlinear least squares problems the proposed methods are shown to be globally convergent under some assumptions finally some numerical results are given

on the partial realization problem abstract in this paper we take a unified approach to the partial realization problem in which we seek to incorporate ideas from numerical linear algebra most of which were originally developed in other contexts we approach the partial realization problem from several different angles and explore the connections to such topics as factoriza tion of hankel matrices block tridiagonalization generalizations of the lanczos process for biorthogonalization the euclidean algorithm and the principal part con tinued fractions of arne magnus the pade table and the berlekamp masseyalgo rithm in this way we are able to clarify some previous results by rissanen kalman and others and place them in a broader context this leads to several results and concepts which we think are new our analysis is restricted to the scalar case but some definitions and formulations have been rigged to facilitate an extension to the matrix case

a family of scaled factorized broyden like methods for nonlinear least squares problems in this paper a family of scaled factorized broyden like methods for unconstrained nonlinear least squares problems with zero or nonzero residual is presented this family is based on a full rank factorized form of a structured quasi newton update and a scaled approximation of the second order term using given information the resulting algorithms yield a q quadratic convergence for the zero residual case and a q superlinear convergence for the nonzero residual case and maintain at least locally the positive definiteness of the approximate hessian matrices

on the behavior of broyden s class of quasi newton methods this paper analyzes algorithms from the broyden class of quasi newton methods for nonlinear unconstrained optimization this class depends on a parameter phi k for which the choices phi k 0 and phi k 1 give the well known bfgs and dfp methods this paper examines algorithms that allow for negative values of the parameter phi k it shows that severe restrictions have to be imposed on the selection of phi k to guarantee q superlinear convergence it is argued that negative values of phi k are desirable and conditions on phi k that guarantee superlinear convergence are given however practical algorithms that preserve the excellent properties of the bfgs method are not easy to design

convergence properties of the bfgs algoritm the bfgs method is one of the most famous quasi newton algorithms for unconstrained optimization in 1984 powell presented an example of a function of two variables that shows that the polak ribiere polyak prp conjugate gradient method and the bfgs quasi newton method may cycle around eight nonstationary points if each line search picks a local minimum that provides a reduction in the objective function in this paper a new technique of choosing parameters is introduced and an example with only six cyclic points is provided it is also noted through the examples that the bfgs method with wolfe line searches need not converge for nonconvex objective functions

a semiparametric single index model with heterogeneous impacts on an unobserved variable this paper proposes a single index semiparametric model in which the unknown function has cross sectional unit specific weights the initial motivation comes from the search for a better measure of liquidity in stock trading which is captured by the unknown function here the model is estimated by semiparametric least squares developed by ichimura 1993 and ichimura and lee 1991 the proposed technique differs from theirs in at least two aspects first i show that the estimator has desirable asymptotic properties under less restrictive assumptions on data second the form of the unknown function is fixed however the coefficients are allowed to differ across the cross sectional units

the global convergence of partitioned bfgs on problems with convex decompositions and lipschitzian gradients the main purpose of this paper is the extension of powell s 1976 global convergence result to the partitioned bfgs method introduced by griewank and toint 1982 even in the unpartitioned case the original result is strengthened because the search directions need not be computed exactly and the gradient is only required to be lipschitzian rather than differentiable using the functional of byrd and nocedal 1987 a strong form of r superlinear convergence is obtained if the element functions are uniformly convex and their gradients are strictly differentiable at the minimizerx only in order to deal with the possibility of singular functions we utilize a damping of the bfgs update that becomes inactive if the problem turns out to be regular nearx

the leading root of the partial theta function abstract i study the leading root x 0 y of the partial theta function 0 x y n 0 x n y n n 1 2 considered as a formal power series i prove that all the coefficients of x 0 y are strictly positive indeed i prove the stronger results that all the coefficients of 1 x 0 y after the constant term 1 are strictly negative and all the coefficients of 1 x 0 y 2 after the constant term 1 are strictly negative except for the vanishing coefficient of y 3

on a necessary condition for an entire function with the increasing second quotients of taylor coefficients to belong to the laguerre polya class abstract for an entire function f z k 0 a k z k a k 0 we show that f does not belong to the laguerre polya class if the quotients a n 1 2 a n 2 a n are increasing in n and c lim n a n 1 2 a n 2 a n is smaller than an absolute constant q q 3 2336

on the convergence of the modified levenberg marquardt method with a nonmonotone second order armijo type line search recently fan j fan the modified levenberg marquardt method for nonlinear equations with cubic convergence math comput 81 2012 447 466 proposed a modified levenberg marquardt mlm method for nonlinear equations using a trust region technique global and cubic convergence of the mlm method is proved by fan 2012 12 under the local error bound condition which is weaker than nonsingularity the purpose of the paper is to investigate the convergence properties of the mlm method with a line search technique since the search direction of the mlm method may be not a descent direction standard line searches can not be used directly in this paper we propose a nonmonotone second order armijo line search which guarantees the global convergence of the mlm method moreover we prove that the unit step will be always accepted finally then cubic convergence of the mlm method is preserved under the local error bound condition some preliminary numerical results are also reported

on the use of product structure in secant methods for nonlinear least squares problems the problem of adjusting the second order term in secant methods for nonlinear least squares problems with zero residual is addressed the author uses the framework of structured secant methods to derive and investigate a new way to resize the approximation of the second order term using some exact information the resulting method is a self adjusting structured secant method for nonlinear least squares problems yielding a q quadratic convergence rate for zero residual and a q superlinear convergence rate for nonzero residual problems

a modified bfgs type quasi newton method with line search for symmetric nonlinear equations problems abstract in this paper using approximate gradient of the norm square metric function we present an inexact mbfgs method with line search for solving symmetric nonlinear equations which is a generalization of the mbfgs method proposed by li and fukushima 2001 for solving smooth unconstrained optimization the used approximate gradient of the proposed method only requires computing two residuals at every iteration and is easy to obtain by utilizing symmetric structure of the system we establish global convergence of the proposed method and report some numerical results

global convergence properties of conjugate gradient methods for optimization this paper explores the convergence of nonlinear conjugate gradient methods without restarts and with practical line searches the analysis covers two classes of methods that are globally convergent on smooth nonconvex functions some properties of the fletcher reeves method play an important role in the first family whereas the second family shares an important property with the polak ribiere method numerical experiments are presented

convergence properties of algorithms for nonlinear optimization this paper reviews some of the most successful methods for unconstrained constrained and nondifferentiable optimization calculations particular attention is given to the contribution that theoretical analysis has made to the development of algorithms it seems that practical considerations provide the main new ideas and that subsequent theoretical studies give improvements to algorithms coherence to the subject and better understanding

properties and numerical performance of quasi newton methods with modified quasi newton equations quasi newton qn equation plays a core role in contemporary nonlinear optimization the usual qn equation employs only the gradients but ignores the available function value information in this paper we derive a class of modified qn equations with a vector parameter which use both available gradient and function value information the modified quasi newton methods maintain most properties of the usual quasi newton methods meanwhile they achieve a higher order accuracy in approximating the second order curvature of the problem functions than the usual ones do numerical experiments are reported which support the theoretical analyses and show the advantages of the modified qn methods over the usual ones

conjugate gradient methods based on secant conditions that generate descent search directions for unconstrained optimization conjugate gradient methods have been paid attention to because they can be directly applied to large scale unconstrained optimization problems in order to incorporate second order information of the objective function into conjugate gradient methods dai and liao 2001 proposed a conjugate gradient method based on the secant condition however their method does not necessarily generate a descent search direction on the other hand hager and zhang 2005 proposed another conjugate gradient method which always generates a descent search direction in this paper combining dai liao s idea and hager zhang s idea we propose conjugate gradient methods based on secant conditions that generate descent search directions in addition we prove global convergence properties of the proposed methods finally preliminary numerical results are given

global convergence of a new hybrid gauss newton structured bfgs method for nonlinear least squares problems in this paper we propose a hybrid gauss newton structured bfgs method with a new update formula and a new switch criterion for the iterative matrix to solve nonlinear least squares problems we approximate the second term in the hessian by a positive definite bfgs matrix under suitable conditions global convergence of the proposed method with a backtracking line search is established moreover the proposed method automatically reduces to the gauss newton method for zero residual problems and the structured bfgs method for nonzero residual problems in a neighborhood of an accumulation point a locally quadratic convergence rate for zero residual problems and a locally superlinear convergence rate for nonzero residual problems are obtained for the proposed method some numerical results are given to compare the proposed method with some existing methods

local and superlinear convergence for partially known quasi newton methods this paper develops a unified theory for establishing the local and q superlinear convergence of quasi newton methods from the convex class when part of the hessian matrix is known one first proves the bounded deterioration principle due to dennis and popularized by broyden dennis and more for the appropriate modifications of all update formulas in the convex broyden class using standard conditions on the quasi newton updates one then deduces local and q superlinear convergence particular cases of these methods are the sqp augmented scale bfgs and dfp secant methods for constrained optimization problems introduced by tapia and a generalization of the al baali and fletcher modification of the structured secant method considered by dennis gay and welsch for the nonlinear least squares problem in all cases bounded deterioration is proved for the approximate hessian not for its inverse

the first order necessary conditions for nonsmooth variational and control problems the first order necessary conditions for nonsmooth problems of lagrange bolza multiple integral and optimal control are given the necessary conditions are expressed in terms of differential inclusions we deal with some new differentials that generalize the differential of frechet in particular the pontryagin maximum principle is proved without the assumption of continuous differentiability

convergence properties of nonlinear conjugate gradient methods recently important contributions on convergence studies of conjugate gradient methods were made by gilbert and nocedal siam j optim 2 1992 pp 21 42 they introduce a sufficient descent condition to establish global convergence results although this condition is not needed in the convergence analyses of newton and quasi newton methods gilbert and nocedal hint that the sufficient descent condition which was enforced by their two stage line search algorithm may be crucial for ensuring the global convergence of conjugate gradient methods this paper shows that the sufficient descent condition is actually not needed in the convergence analyses of conjugate gradient methods consequently convergence results on the fletcher reeves and polak ribiere type methods are established in the absence of the sufficient descent condition to show the differences between the convergence properties of fletcher reeves and polak ribiere type methods two examples are constructed showing that neither the boundedness of the level set nor the restriction beta k geq 0 can be relaxed for the polak ribiere type methods

on the accuracy of solving confluent prony systems in this paper we consider several nonlinear systems of algebraic equations which can be called prony type these systems arise in various reconstruction problems in several branches of theoretical and applied mathematics such as frequency estimation and nonlinear fourier inversion consequently the question of stability of solution with respect to errors in the right hand side becomes critical for the success of any particular application we investigate the question of maximal possible accuracy of solving prony type systems putting stress on the local behavior which approximates situations with low absolute measurement error the accuracy estimates are formulated in very simple geometric terms shedding some light on the structure of the problem numerical tests suggest that global solution techniques such as prony s algorithm and the esprit method are suboptimal when compared to this theoretical best local behavior

fitting distribution like data to exponential sums with genetic algorithms conventional derivative based algorithms of fitting distribution like data to exponential sum functions can be easily trapped in some local minima this paper is concerned with the development of algorithms of fitting distribution like data to exponential sums with genetic algorithms both binary coding scheme and real valued coding scheme have been investigated in this research experimental results have shown that real valued coding scheme is more appropriate to the problem of fitting distribution like data to exponential sums testing with real engineering data it has been demonstrated that the fitting algorithm derived in this paper is quite promising the fitted exponential sum models using genetic algorithm can very well describe the measured data however for the data with wavy trends pure exponential sum functions may not be the best candidate models more generalized exponential sum models need to be studied

specification tests for binary choice models based on index quantiles abstract in testing choice models there are contexts in which it is important to focus on choice probabilities as opposed to the parameters of choice models this paper examines the former by formulating a distance measure between parametric choice probabilities under the null hypothesis and either a nonparametric or a semiparametric alternative to access where the parametric model is unsatisfactory we apply the distance measure to ordered data subsets index quantiles we establish the large sample distribution of the test statistics examine their asymptotic local power properties and apply the tests to a model of labor force participation

on the entire functions from the laguerre polya i class having the increasing second quotients of taylor coefficients abstract we prove that if f x k 0 a k x k a k 0 is an entire function such that the sequence q a k 2 a k 1 a k 1 k 1 is non decreasing and a 1 2 a 0 a 2 2 2 3 then all but a finite number of zeros of f are real and simple we also present a criterion in terms of the closest to zero roots for such a function to have only real zeros in other words for belonging to the laguerre polya class of type i under additional assumption on the sequence q

a review of the parameter estimation problem of fitting positive exponential sums to empirical data exponential sum models are used frequently in heat diffusion diffusion of chemical compounds time series in medicine economics physical sciences and technology thus it is important to find good methods for the estimation of parameters in exponential sums in this paper we review and discuss results from the last forty years of research there are many different ways of estimating parameters in exponential sums and model a fit criterion which gives a valid result from the fit we find that a good choice is a weighted two norm objective function with weights based on the maximum likelihood ml criterion if the number of exponential terms is unknown statistical methods based on an information criterion or cross validation can be used to determine the optimal number it is suitable to use hybrid gauss newton gn and quasi newton algorithms to find the unknown parameters in the constrained weighted nonlinear least squares nlls problem formulated using an maximal likelihood ml objective function the problem is highly ill conditioned and it is crucial to find good starting values for the parameters to find the initial parameter values a modified prony method or a method based upon rewriting partial sums as geometrical sums is proposed

multi step quasi newton methods for optimization abstract quasi newton methods update at each iteration the existing hessian approximation or its inverse by means of data deriving from the step just completed we show how multi step methods employing in addition data from previous iterations may be constructed by means of interpolating polynomials leading to a generalization of the secant or quasi newton equation the issue of positive definiteness in the hessian approximation is addressed and shown to depend on a generalized version of the condition which is required to hold in the original single step methods the results of extensive numerical experimentation indicate strongly that computational advantages can accrue from such an approach by comparison with single step methods particularly as the dimension of the problem increases

the bfgs method with exact line searches fails for non convex objective functions this work shows that the bfgs method and other methods in the broyden class with exact line searches may fail for non convex objective functions

an optimal positive definite update for sparse hessian matrices a hessian update is described that preserves sparsity and positive definiteness and satisfies a minimal change property the update reduces to the bfgs update in the dense case and generalises a recent result in siam j nnmer anal 26 1989 pp 727 739 relating to the byrd and nocedal measure function a surprising outcome is that a sparsity projection of the inverse hessian plays a major role it is shown that the hessian itself can be recovered from this information under mild assumptions the update is computed by solving a concave programming problem derived by using the wolfe dual the hessian of the dual is important and plays a similar role to the matrix q that arises in the sparse psb update of toint math comp 31 1977 pp 954 961 this matrix is shown to satisfy the same structural and definiteness conditions as toint s matrix the update has been implemented for tridiagonal systems and some numerical experiments are described these experiments indicate that there is potential for a

on the convergence of a modified regularized newton method for convex optimization with singular solutions in this paper we propose a modified regularized newton method for convex minimization problems whose hessian matrices may be singular the proposed method is proved to converge globally if the gradient and hessian of the objective function are lipschitz continuous under the local error bound condition we first show that the method converges quadratically which implies that x k x is equivalent to dist x k x where x is the solution set and x k x x then we in turn prove the cubic convergence of the proposed method under the same local error bound condition which is weaker than nonsingularity

application of a combination production function model abstract in the analysis of economic growth factors people often use the production function to analyze the contribution rate of the influencing factors of economic growth the commonly used production functions include c d production function ces production function and ves production function the analysis result of three production functions always differ a lot in order to reduce the difference and increase the reliability of the analysis this paper combines with three production function models utilizes the principal component regression and obtains the composite production function model based on the composite production function model a method which is used to calculate the contribution rate of the economic growth factors is proposed in this paper based on this method the deficiencies of solow s calculation formula are overcome and the precision estimation is improved finally according to the given method in this paper the empirical analysis is made on the contribution rate of the economic growth factors for the tertiary industry in china

on hager and zhang s conjugate gradient method with guaranteed descent abstract in this paper we point out that hager zhang family of conjugate gradient methods are based on the spectral scaling secant equation are really members of dai liao type of gradient methods with common constant parameters we propose a possible efficient parameter for hager zhang s conjugate gradient method with guaranteed descent cg descent and present a conjugate gradient method cg descent1 the cg descent1 method preserves the same global convergence properties as cg descent method of hager and zhang and is numerically tested compared with cg descent method and other conjugate gradient methods considering the difference of the search directions approximation to the search direction of the memoryless bfgs method we give the reason why the proposed method is more efficient than cg descent method under some conditions and further find an optimal conjugate gradient method and an approximation optimal conjugate method in hager zhang family of conjugate gradient methods

a modified prony algorithm for exponential function fitting a modification of the classical technique of prony for fitting sums of exponential functions to data is considered the method maximizes the likelihood for the problem unlike the usual implementation of prony s method which is not even consistent for transient signals proves to be remarkably effective in practice and is supported by an asymptotic stability result novel features include a discussion of the problem parametrization and its implications for consistency the asymptotic convergence proofs are made possible by an expression for the algorithm in terms of circulant divided difference operators

local and superlinear convergence for truncated iterated projections methods least change secant updates can be obtained as the limit of iterated projections based on other secant updates we show that these iterated projections can be terminated or truncated after any positive number of iterations and the local and the superlinear rate of convergence are still maintained the truncated iterated projections method is used to find sparse and symmetric updates that are locally and superlinearly convergent

approximate gauss newton methods for nonlinear least squares problems the gauss newton algorithm is an iterative method regularly used for solving nonlinear least squares problems it is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting the procedure consists of a sequence of linear least squares approximations to the nonlinear problem each of which is solved by an inner direct or iterative process in comparison with newton s method and its variants the algorithm is attractive because it does not require the evaluation of second order derivatives in the hessian of the objective function in practice the exact gauss newton method is too expensive to apply operationally in meteorological forecasting and various approximations are made in order to reduce computational costs and to solve the problems in real time here we investigate the effects on the convergence of the gauss newton method of two types of approximation used commonly in data assimilation first we examine truncated gauss newton methods where the inner linear least squares problem is not solved exactly and second we examine perturbed gauss newton methods where the true linearized inner problem is approximated by a simplified or perturbed linear least squares problem we give conditions ensuring that the truncated and perturbed gauss newton methods converge and also derive rates of convergence for the iterations the results are illustrated by a simple numerical example a practical application to the problem of data assimilation in a typical meteorological system is presented

simulation and the asymptotics of optimization estimators on demontre un theoreme de limite centrale general pour des estimateurs definis par minimisation de la longueur d une fonction de critere aleatoire a valeurs vectorielles aucune hypothese de regularite suffisante n est imposee sur la fonction de critere pour que les resultats puissent etre appliques a une classe d estimlateurs de simulation assez large des analyses completes de deux estimateurs de simulation l un introduit par pakes l autre par mcfadden illustrent l application des theoremes generaux

exponential interpolation theory and numerical algorithms we consider the problem of exponential interpolation and show that in some cases it can be solved with effective numerical procedures we show that the problem is closely related to gaussian quadrature and to the problem of partial realization in linear control theory

on the spectrum of a partial theta function the bivariate series defines a partial theta function for fixed q q is an entire function we show that for q 0 108 the function q has no multiple zeros

factorized quasi newton methods for nonlinear least squares problems this paper provides a modification to the gauss newton method for nonlinear least squares problems the new method is based on structured quasi newton methods which yield a good approximation to the second derivative matrix of the objective function in particular we propose bfgs like and dfp like updates in a factorized form which give descent search directions for the objective function we prove local and q superlinear convergence of our methods and give results of computational experiments for the bfgs like and dfp like updates

on the conditions for entire functions related to the partial theta function to belong to the laguerre polya class abstract in this paper we study entire functions of order zero with positive taylor coefficients and investigate sufficient or necessary conditions for such functions to have only real zeros we answer the following question for which values of a 1 and m 1 an entire function a m z k 0 z k a k 2 k m and its taylor sections belong to the laguerre polya class

on bandwidth variation in kernel estimates a square root law we consider kernel estimation of a smooth density f at a point but depart from the usual approach in admitting an adaptive dependence of the sharpness of the kernels on the underlying density proportionally varying the bandwidths like f 1 2 at the contributing readings lowers the bias to a vanishing fraction of the usual value and makes for performance seen in well known estimators that force moment conditions on the kernel and so sacrifice positivity of the curve estimate issues of equivariance and variance stabilitization are treated

hardy petrovitch hutchinson s problem and partial theta function in 1907 m petrovitch initiated the study of a class of entire functions all whose finite sections i e truncations are real rooted polynomials he was motivated by previous studies of e laguerre on uniform limits of sequences of real rooted polynomials and by an interesting result of g h hardy an explicit description of this class in terms of the coefficients of a series is impossible since it is determined by an infinite number of discriminant inequalities one for each degree however interesting necessary or sufficient conditions can be formulated in particular j i hutchinson has shown that an entire function p x a 0 a 1 x a n x n with strictly positive coefficients has the property that all of its finite segments a i x i a i 1 x i 1 a j x j have only real roots if and only if a i 2 a i 1 a i 1 4 for i 1 2 in the present paper we give sharp lower bounds on the ratios a i 2 a i 1 a i 1 i 1 2 for the class considered by m petrovitch in particular we show that the limit of these minima when i infinity equals the inverse of the maximal positive value of the parameter for which the classical partial theta function belongs to the laguerre polya class l pi we also explain the relation between newton s and hutchinson s inequalities and the logarithmic image of the set of all real rooted polynomials with positive coefficients

partitioned variable metric updates for large structured optimization problems this paper presents a minimization method based on the idea of partitioned updating of the hessian matrix in the case where the objective function can be decomposed in a sum of convex element functions this situation occurs in a large class of practical problems including nonlinear finite elements calculations some theoretical and algorithmic properties of the update are discussed and encouraging numerical results are presented

estimating a class of triangular simultaneous equations models without exclusion restrictions this paper provides a control function estimator to adjust for endogeneity in the triangular simultaneous equations model where there are no available exclusion restrictions to generate suitable instruments our approach is to exploit the dependence of the errors on exogenous variables e g heteroscedasticity to adjust the conventional control function estimator the form of the error dependence on the exogenous variables is subject to restrictions but is not parametrically specified in addition to providing the estimator and deriving its large sample properties we present simulation evidence which indicates the estimator works well

a modified bfgs method and its global convergence in nonconvex minimization in this paper we propose a modification of the bfgs method for unconstrained optimization a remarkable feature of the proposed method is that it possesses a global convergence property even without convexity assumption on the objective function under certain conditions we also establish superlinear convergence of the method

methods for estimating a conditional distribution function abstract motivated by the problem of setting prediction intervals in time series analysis we suggest two new methods for conditional distribution estimation the first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation it produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1 the second method involves an adjusted form of the nadaraya watson estimator it preserves the bias and variance properties of a class of second order estimators introduced by yu and jones but has the added advantage of always being a distribution itself our methods also have application outside the time series setting for example to quantile estimation for independent data this problem motivated the work of yu and jones

shift restrictions and semiparametric estimation in ordered response models we develop a n consistent and asymptotically normal estimator of the parameters regression coefficients and threshold points of a semiparametric ordered response model under the assumption of independence of errors and regressors the independence assumption implies shift restrictions allowing identification of threshold points up to location and scale the estimator is useful in various applications particularly in new product demand forecasting from survey data subject to systematic misreporting we apply the estimator to assess exaggeration bias in survey data on demand for a new telecommunications service

on the recovery and resolution of exponential relaxation rates from experimental data ii the optimum choice of experimental sampling points for laplace transform inversion in a previous paper bertero boccacci pike proc r soc lond a 383 15 1982 we investigated the benefits of a priori knowledge of finite support of the solution in the inversion of the laplace transform and determined the number of exponential components that could be recovered from given data in the presence of quantified amounts of noise the support of the data was assumed to be unrestricted in the present paper these calculations are extended to cover the case of a necessarily finite number of experimental data points we consider two cases uniform distribution and geometric distribution of data points in both cases the condition number of singular value inversions is minimized with respect to the placing of the data points for fixed numbers of data samples the results allow optimum placing of the experimental data points as a function of the ratio of given upper and lower bounds of the support of the solution the number of exponentials recoverable is less than in the unrestricted case but for 8 we find that with 32 linearly spaced data points optimally placed this reduction is rather small geometrical sampling of experimental data reduces further the number of sample points required for inversion for 8 we show that with 5 geometrically spaced data points points optimally placed the ill conditioning in the restoration of 2 to 4 exponential components is smaller than with 32 linearly spaced data samples this has important implications for the design of a number of scientific experiments and instruments