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

a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

efficient estimation for the proportional hazards model with interval censoring the maximum likelihood estimator mle for the proportional hazards model with case 1 interval censored data is studied it is shown that the mle for the regression parameter is asymptotically normal with n convergence rate and achieves the information bound even though the mle for the baseline cumulative hazard function only converges at n 1 3 rate estimation of the asymptotic variance matrix for the mle of the regression parameter is also considered to prove our main results we also establish a general theorem showing that the mle of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the mle of the infinite dimensional parameter converges at a rate slower than n the results are iliustrated by applying them to a data set from a tumorigenicity study

a geometric approach to root finding in gt q sup m the problem of finding roots in f of polynomials in f x for f gf q sup m where q is a prime or prime power and m is a positive integer greater than 1 is considered the problem is analyzed by making use of the finite affine geometry ag m q a new method is proposed for finding roots of polynomials over finite extension fields it is more efficient than previous algorithms when the degree of the polynomial whose roots are to be found is less than dimension m of the extension field implementation of the algorithm can be enhanced in cases in which optimal normal bases for the coefficient field are available

regression analysis for current status data using the em algorithm we propose new expectation maximization algorithms to analyze current status data under two popular semiparametric regression models the proportional hazards ph model and the proportional odds po model monotone splines are used to model the baseline cumulative hazard function in the ph model and the baseline odds function in the po model the proposed algorithms are derived by exploiting a data augmentation based on poisson latent variables unlike previous regression work with current status data our ph and po model fitting methods are fast flexible easy to implement and provide variance estimates in closed form these techniques are evaluated using simulation and are illustrated using uterine fibroid data from a prospective cohort study on early pregnancy copyright 2013 john wiley sons ltd

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

testing independence for bivariate current status data this article develops a nonparametric procedure for testing marginal independence based on bivariate current status data asymptotic properties of the proposed tests are derived and their finite sample performance is studied via simulations the method is applied to analyze data from a community based study of cardiovascular epidemiology in taiwan

accelerated solution of multivariate polynomial systems of equations we propose new las vegas randomized algorithms for the solution of a square nondegenerate system of equations with well separated roots the algorithms use oc delta csttn d 2 log d log b arithmetic operations in addition to the operations required to compute the normal form of the boundary monomials modulo the ideal to approximate all real roots of the system as well as all roots lying in a fixed n dimensional box or disc here d is an upper bound on the number of all complex roots of the system e g bezout or bernshtein bound delta is the number of real roots or the roots lying in the box or disc and epsilon 2 b is the required upper bound on the output errors for computing the normal form modulo the ideal the efficient practical algorithms of b mourrain and p trebuchet in proceedings of the international symposium on symbolic and algebraic computation acm new york 2000 pp 231 238 or j c faugere j pure appl algebra 139 1999 pp 61 88 can be applied we also yield the bound oc csttn d 2 log d on the complexity of counting the numbers of all roots in a fixed box disc and all real roots for a large class of inputs and typically in practical computations the factor delta is much smaller than d delta o d this improves by the order of magnitude the known complexity estimates of the order of at least 3n d4 d3 log b or d4 which so far are the record estimates even for the approximation of a single root of a system and for each of the cited counting problems respectively our progress relies on proposing several novel techniques in particular we exploit the structure of matrices associated to a given polynomial system and relate it to the associated linear operators dual space of linear forms and normal forms of polynomials in the quotient algebra furthermore our techniques support the new nontrivial extension of the matrix sign and quadratic inverse power iterations to the case of multivariate polynomial systems where we emulate the recursive splitting of a univariate polynomial into factors of smaller degree

a semiparametric proportional odds regression model for the analysis of current status data abstract an approach to covariate analysis of current status data is described the method is applicable when the logit of the conditional probability of survival given the covariates is some increasing function of time plus a linear combination of the covariates the approach is based on approximating the infinite dimensional nuisance parameter the baseline log odds of failure with a step function and carrying out a maximum likelihood procedure the resulting finite dimensional parameter estimates for the regression parameters are shown to be asymptotically normal and semiparametric efficient numerical studies with small and moderate samples are discussed

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

a neural root finder of polynomials based on root moments this letter proposes a novel neural root finder based on the root moment method rmm to find the arbitrary roots including complex ones of arbitrary polynomials this neural root finder nrf was designed based on feedforward neural networks fnn and trained with a constrained learning algorithm cla specifically we have incorporated the a priori information about the root moments of polynomials into the conventional backpropagation algorithm bpa to construct a new cla the resulting nrf is shown to be able to rapidly estimate the distributions of roots of polynomials we study and compare the advantage of the rmm based nrf over the previous root coefficient method based nrf and the traditional muller and laguerre methods as well as the mathematica roots function and the behaviors the accuracies of the resulting root finders and their training speeds of two specific structures corresponding to this fnn root finder the log and the fnn we also analyze the effects of the three controlling parameters p0 p with the cla on the two nrfs theoretically and experimentally finally we present computer simulation results to support our claims

constrained least absolute deviation neural networks it is well known that least absolute deviation lad criterion or norm used for estimation of parameters is characterized by robustness i e the estimated parameters are totally resistant insensitive to large changes in the sampled data this is an extremely useful feature especially when the sampled data are known to be contaminated by occasionally occurring outliers or by spiky noise in our previous works we have proposed the least absolute deviation neural network ladnn to solve unconstrained lad problems the theoretical proofs and numerical simulations have shown that the ladnn is lyapunov stable and it can globally converge to the exact solution to a given unconstrained lad problem we have also demonstrated its excellent application value in time delay estimation more generally a practical lad application problem may contain some linear constraints such as a set of equalities and or inequalities which is called constrained lad problem whereas the unconstrained lad can be considered as a special form of the constrained lad in this paper we present a new neural network called constrained least absolute deviation neural network cladnn to solve general constrained lad problems theoretical proofs and numerical simulations demonstrate that the proposed cladnn is lyapunov stable and globally converges to the exact solution to a given constrained lad problem independent of initial values the numerical simulations have also illustrated that the proposed cladnn can be used to robustly estimate parameters for nonlinear curve fitting which is extensively used in signal and image processing

regression with interval censored data summary interval censored data result when survival times are not known exactly but are only known to have occurred between intermittent examination times here the accelerated failure time model is treated for interval censored data a class of score statistics that may be used for estimation and confidence procedures is proposed an adaptive procedure based on estimating the optimal member of the class of score statistics is explored

nonlinear adaptive wavelet control using constructive wavelet networks in this paper an adaptive wavelet network based control approach is proposed for highly nonlinear uncertain dynamical systems wavelet network as a kind of universal approximator has two novel properties orthonormality and multiresolution the orthonormal property ensures that adding a new resolution new wavelets does not affect the existing wavelet network that may have been well tuned in the sequel the online adjustment of the structure of the nonlinear adaptive wavelet controller awc can be done in a constructive manner by gradually increasing the network resolution the multiresolution property on the other hand assures a guaranteed improvement of the approximation precision when a new resolution is added in real life problems we are unable to know the adequate size of a network either a neural network nn or a wavelet network to produce the required approximation precision by virtue of the novel wavelet network properties a coarse or very simple structure can be selected first if the system fails to converge after the elapse of a dwell time a new wavelet resolution is considered to be necessary and added directly in this manner the awc can be easily constructed and tuned from the coarse to finer levels until the performance requirement is satisfied the trial and error way of selecting the network structure which may lead to either an inadequate or a highly redundant structure can be avoided in this paper the proposed adaptive wavelet network is applied first to a class of nonlinear dynamical systems with a partially known model and an affine in input structure then the adaptive wavelet network is applied to a class of nonlinear nonaffine dynamical systems

maximum likelihood estimation in the proportional odds model abstract we consider maximum likelihood estimation of the parameters in the proportional odds model with right censored data the estimator of the regression coefficient is shown to be asymptotically normal with efficient variance the maximum likelihood estimator of the unknown monotonic transformation of the survival time converges uniformly at a parametric rate to the true transformation estimates for the standard errors of the estimated regression coefficients are obtained by differentiation of the profile likelihood and are shown to be consistent a likelihood ratio test for the regression coefficient is also considered

regression analysis of failure time data with informative interval censoring interval censoring arises when a subject misses prescheduled visits at which the failure is to be assessed most existing approaches for analysing interval censored failure time data assume that the censoring mechanism is independent of the true failure time however there are situations where this assumption may not hold in this paper we consider such a situation in which the dependence structure between the censoring variables and the failure time can be modelled through some latent variables and a method for regression analysis of failure time data is proposed the method makes use of the proportional hazards frailty model and an em algorithm is presented for estimation finite sample properties of the proposed estimators of regression parameters are examined through simulation studies and we illustrate the method with data from an aids study

assessing age at onset risk factors with incomplete covariate current status data under proportional odds models motivated by an epidemiological survey of fracture in elderly women we develop a semiparametric regression analysis of current status data with incompletely observed covariate under the proportional odds model to accommodate both the interval censored nature of current status failure time data and the incompletely observed covariate data we propose an analysis based on the validation likelihood vl which is derived from likelihood pertaining to the validation sample namely the subset of the sample where the data are completely observed the missing data mechanism is assumed to be missing at random and is explicitly modeled and estimated in the vl approach we propose implementing the vl method by integrating self consistency and newton raphson algorithms asymptotic normality and standard error estimation for the proposed estimator of the regression parameter are guaranteed simulation results reveal good performance of the vl estimator the vl method has some gain in efficiency compared with the naive complete case method but the vl method leads to unbiased estimators whereas the complete case method does not when missing covariates are not missing completely at random application of the vl approach to the fracture data confirms that osteoporosis low bone density is a strong risk factor for the age at onset of fracture in elderly women copyright 2012 john wiley sons ltd

bayesian models for multivariate current status data with informative censoring des donnees multivariees d etat consistent en un ensemble d indicatrices associees a la realisation de plusieurs evenements au moment d un examen nous nous interessons aux inferences sur les distributions jointes des temps d evenements les methodes conventionnelles d analyse des donnees de durees multiples ne peuvent etre utilisees parce que tous les temps d evenements sont censures et la censure peut etre informative nous prenons en compte la correlation des temps d evenements chez un sujet au moyen d une variable latente propre au sujet conditionnellement a laquelle les divers temps d evenements sont supposes independants nous supposons egalement que chaque evenement contribue independamment au risque de censure des fonctions en escalier non parametriques sont utilisees pour caracteriser les distributions de base des differents temps d evenements et des temps d examen les covariables et les effets specifiques du sujet sont incorpores grace au modele lineaire generalise un algorithme de monte carlo par chaines de markov est decrit pour l estimation des distributions a posteriori des inconnues les methodes sont illustrees par une application sur des donnees de sites multiples de tumeurs dans une etude de carcinogenicite animale

a hybrid learning algorithm combined with generalized rls approach for radial basis function neural networks in this paper a new hybrid learning method for radial basis function neural networks based on generalized recursive least square algorithm is proposed firstly the generalized recursive least square grls model including a general quadratic weight decay term in the energy function for the training of rbf neural networks is described then combined with the grls approach a new hybrid learning method is proposed to meet the design goals improving the generalization ability of the trained network finally experimental results demonstrate that our approach can achieve a significantly improved generalization performance of the rbf networks

improved constrained learning algorithms by incorporating additional functional constraints into neural networks in this paper two improved constrained learning algorithms that are able to guarantee to obtain better generalization performance are proposed these two algorithms are substantially on line learning ones the cost term for the additional functionality of the first improved algorithm is selected based on the first order derivatives of the neural activation at hidden layers while the one of the second improved algorithm is selected based on second order derivatives of the neural activation at hidden layers and output layer in the course of training the cost terms selected from these additional cost functions can penalize the input to output mapping sensitivity or high frequency components included in training data finally theoretical justifications and simulation results are given to verify the efficiency and effectiveness of the two proposed learning algorithms

locally efficient estimation with current status data and time dependent covariates abstract in biostatistical applications interest often focuses on the estimation of the distribution of a failure time variable t if one observes only whether or not t exceeds an observed monitoring time c then the data structure is called current status data also known as interval censored data case i we extend the data structure by allowing the presence of a possibly time dependent covariate process which is observed up till the monitoring time c we follow the approach of robins and rotnitzky by modeling the hazard of c conditional on the failure time variable and the covariate process i e the missingness or censoring process under the restriction that the missingness monitoring process satisfies coarsening at random because of the curse of dimensionality no globally efficient nonparametric estimators with a good practical performance at moderate sample sizes exist we introduce an inverse probability of censoring weighted estimator of the distribution and of smooth functionals of this di

on profile likelihood abstract we show that semiparametric profile likelihoods where the nuisance parameter has been profiled out behave like ordinary likelihoods in that they have a quadratic expansion in this expansion the score function and the fisher information are replaced by the efficient score function and efficient fisher information the expansion may be used among others to prove the asymptotic normality of the maximum likelihood estimator to derive the asymptotic chi squared distribution of the log likelihood ratio statistic and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance

on semi competing risks data summary we consider a variation of the competing risks problem in which a terminal event censors a non terminal event but not vice versa the joint distribution of the events is formulated via a gamma frailty model in the upper wedge where data are observable day et al 1997 with the marginal distributions unspecified an estimator for the association parameter is obtained from a concordance estimating function a novel plug in estimator for the marginal distribution of the non terminal event is shown to be uniformly consistent and to converge weakly to a gaussian process the assumptions on the joint distribution outside the upper wedge are weaker than those usually made in competing risks analyses simulations demonstrate that the methods work well with practical sample sizes the proposals are illustrated with data on morbidity and mortality in leukaemia patients

improved bounds on the supremum of autoconvolutions we give an improvement of the best known lower bound for the supremum of autoconvolutions of nonnegative functions supported in a compact interval also by means of explicit examples we disprove a long standing natural conjecture of schinzel and schmidt concerning the extremal function for such autoconvolutions

adaptive polynomial factorization by coefficient matching a polynomial factorization algorithm is presented which updates all roots simultaneously and efficiently in response to coefficient perturbations the algorithm requires approximately 2n sup 2 complex floating point operations to update all roots of nth order polynomial close to the true root vector the algorithm s convergence rate is quadratic the root update requires only the solution of two sets of structured linear equations and a convolution the algorithm can be used to track the roots of time varying polynomials which is useful for application in adaptive signal processing

regression with doubly censored current status data data from settings in which an initiating event and a subsequent event occur in sequence are called doubly censored current status data if the time of neither event is observed directly but instead it is determined at a random monitoring time whether either the initiating or subsequent event has yet occurred this paper is concerned with using doubly censored current status data to estimate the regression coefficient in an accelerated failure time model for the length of time between the initiating event and the subsequent event motivated by a problem in the epidemiology of acquired immune deficiency syndrome attention here is focused on a special case the case in which the initiating event given that it has occurred before the monitoring time may be assumed to follow a uniform distribution the main result is that the likelihood in the special case has the same structure as the likelihood in a simpler setting the setting in which the time of the initiating event is known the result allows methods developed for the simpler setting to be applied in the special case the results of the application of the approach to real data are reported

a generalized constraint neural network model associating partially known relationships for nonlinear regressions in an attempt to enhance the neural network technique so that it can evolve from a black box tool into a semi analytical one we propose a novel modeling approach of imposing generalized constraints on a standard neural network we redefine approximation problems by use of a new formalization with the aim of embedding prior knowledge explicitly into the model to the maximum extent a generalized constraint neural network gcnn model has therefore been developed which basically consists of two submodels one is constructed by the standard neural network technique to approximate the unknown part of the target function the other is formed from partially known relationships to impose generalized constraints on the whole model three issues arising after combination of the two submodels are discussed a the better approximation provided by the gcnn model compared with a standard neural network b the identifiability of parameters in the partially known relationships and c the discrepancy in the approximation due to removable singularities in the target function numerical studies of three benchmark problems show important findings that have not previously been reported in the literature significant benefits were observed from using the gcnn model in comparison with a standard neural network

sieve estimation for the proportional odds failure time regression model with interval censoring abstract estimation of the proportional odds failure time regression model with interval censoring is considered conditions that allow for positive information for the regression parameter are discussed the efficient score is characterized by a fredholm equation of the second kind the sieve maximum likelihood estimator for the finite dimensional regression parameter is shown to be asymptotically normal with n convergence rate and to achieve the information bound data analysis and simulations assist in clarifying our thoughts regarding the choice of sieve for finite sample problems

extremal results for random discrete structures we study thresholds for extremal properties of random discrete structures we determine the threshold for szemer edi s theorem on arithmetic progressions in random subsets of the integers and its multidimensional extensions and we determine the threshold for tur an type problems for random graphs and hypergraphs in particular we verify a conjecture of

a delayed neural network for solving linear projection equations and its analysis in this paper we present a delayed neural network approach to solve linear projection equations the lyapunov krasovskii theory for functional differential equations and the linear matrix inequality lmi approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network compared with the existing linear projection neural network theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems

threshold functions and poisson convergence for systems of equations in random sets we study threshold functions for the existence of solutions to linear systems of equations in random sets and present a unified framework which includes arithmetic progressions sum free sets b h g sets and hilbert cubes in particular we show that there exists a threshold function for the property mathcal a contains a non trivial solution of m cdot mathbf x mathbf 0 where mathcal a is a random set and each of its elements is chosen independently with the same probability from the interval of integers 1 dots n our study contains a formal definition of trivial solutions for any linear system extending a previous definition by ruzsa when dealing with a single equation furthermore we study the distribution of the number of non trivial solutions at the threshold scale we show that it converges to a poisson distribution whose parameter depends on the volumes of certain convex polytopes arising from the linear system under study as well as the symmetry inherent in the structures which we formally define and characterize

interval censored survival data with informative examination times parametric models and approximate inference we develop parametric methods for analysing interval censored data when examination and survival times are not independent the hazard function is modelled by introducing individual frailties related to the frequency of examinations model parameters may be obtained by direct maximization of the marginal log likelihood we develop a simpler approximate method in which the frailties are estimated by empirical bayes the two approaches are equivalent asymptotically as the number of examinations on each individual increases simulations suggest that the approximate method is adequate for estimating regression parameters even when the number of examinations on each individual is small the methods are used to estimate age and period effects on hiv incidence in a cohort of repeat attenders at genito urinary clinics in london u k

maximum likelihood estimation for semiparametric transformation models with interval censored data interval censoring arises frequently in clinical epidemiological financial and sociological studies where the event or failure of interest is known only to occur within an interval induced by periodic monitoring we formulate the effects of potentially time dependent covariates on the interval censored failure time through a broad class of semiparametric transformation models that encompasses proportional hazards and proportional odds models we consider nonparametric maximum likelihood estimation for this class of models with an arbitrary number of monitoring times for each subject we devise an em type algorithm that converges stably even in the presence of time dependent covariates and show that the estimators for the regression parameters are consistent asymptotically normal and asymptotically efficient with an easily estimated covariance matrix finally we demonstrate the performance of our procedures through simulation studies and application to an hiv aids study conducted in thailand

analysis of clustered interval censored data using a class of semiparametric partly linear frailty transformation models a flexible class of semiparametric partly linear frailty transformation models is considered for analyzing clustered interval censored data which arise naturally in complex diseases and dental research this class of models features two nonparametric components resulting in a nonparametric baseline survival function and a potential nonlinear effect of a continuous covariate the dependence among failure times within a cluster is induced by a shared unobserved frailty term a sieve maximum likelihood estimation method based on piecewise linear functions is proposed the proposed estimators of the regression dependence and transformation parameters are shown to be strongly consistent and asymptotically normal whereas the estimators of the two nonparametric functions are strongly consistent with optimal rates of convergence an extensive simulation study is conducted to study the finite sample performance of the proposed estimators we provide an application to a dental study for illustration

a semiparametric regression cure model for interval censored data motivated by medical studies in which patients could be cured of disease but the disease event time may be subject to interval censoring we present a semiparametric nonmixture cure model for the regression analysis of interval censored time to event data we develop semiparametric maximum likelihood estimation for the model using the expectation maximization method for interval censored data the maximization step for the baseline function is nonparametric and numerically challenging we develop an efficient and numerically stable algorithm via modern convex optimization techniques yielding a self consistency algorithm for the maximization step we prove the strong consistency of the maximum likelihood estimators under the hellinger distance which is an appropriate metric for the asymptotic property of the estimators for interval censored data we assess the performance of the estimators in a simulation study with small to moderate sample sizes to illustrate the method we also analyze a real dataset

proportional odds regression and sieve maximum likelihood estimation summary this paper introduces under a censoring mechanism an estimation procedure for the baseline function and the regression parameters in the proportional odds model based on the sieve maximum likelihood method the procedure uses monotone splines of variable orders and knots as approximations for the baseline function and an approximately unbiased estimator of the comparative kullback leibler risk to select the best approximation the procedure adapts to various unknown structures of the baseline function such as spatial structures and smoothness of an unknown degree the proposed procedure is implemented for right censored and so called case 2 interval censored data the estimated regression parameters are shown to be asymptotically normal and efficient the small sample operating characteristics of the proposed procedure are examined via simulations and are illustrated on a dataset from a study of breast cancer patients

semiparametric probit models with univariate and bivariate current status data summary multivariate current status data are frequently encountered in biomedical and public health studies semiparametric regression models have been extensively studied for univariate current status data but most existing estimation procedures are computationally intensive involving either penalization or smoothing techniques it becomes more challenging for the analysis of multivariate current status data in this article we study the maximum likelihood estimations for univariate and bivariate current status data under the semiparametric probit regression models we present a simple computational procedure combining the expectation maximization algorithm with the pool adjacent violators algorithm for solving the monotone constraint on the baseline function asymptotic properties of the maximum likelihood estimators are investigated including the calculation of the explicit information bound for univariate current status data as well as the asymptotic consistency and convergence rate for bivariate current status data extensive simulation studies showed that the proposed computational procedures performed well under small or moderate sample sizes we demonstrate the estimation procedure with two real data examples in the areas of diabetic and hiv research

on assessing the association for bivariate current status data assuming that the two failure times of interest with bivariate current status data follow a bivariate copula model we propose a two stage estimation procedure to estimate the association parameter which is related to kendall s tau asymptotic properties of the proposed semiparametric estimator show that although the first stage marginal estimators have a convergence rate of only n 1 3 the resulting parameter estimator still converges to a normal random variable with the usual n 1 2 rate the variance of the proposed estimator can be consistently estimated simulation results are presented and a community based study of cardiovascular diseases in taiwan provides an illustrative example

generalized sidon sets we give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number we then use this to obtain an analogous result for sets of integers answering an old question of simon sidon

determining the number of real roots of polynomials through neural networks the ability of feedforward neural networks to identify the number of real roots of univariate polynomials is investigated furthermore their ability to determine whether a system of multivariate polynomial equations has real solutions is examined on a problem of determining the structure of a molecule the obtained experimental results indicate that neural networks are capable of performing this task with high accuracy even when the training set is very small compared to the test set

modified constrained learning algorithms incorporating additional functional constraints into neural networks in this paper two modified constrained learning algorithms are proposed to obtain better generalization performance and faster convergence rate the additional cost terms of the first algorithm are selected based on the first order derivatives of the activation functions of the hidden neurons and the second order derivatives of the activation functions of the output neurons while the additional cost terms of the second one are selected based on the first order derivatives of the activation functions of the output neurons and the second order derivatives of the activation functions of the hidden neurons in the course of training the additional cost terms of the proposed algorithms can penalize the input to output mapping sensitivity and the high frequency components simultaneously so that the better generalization performance can be obtained finally theoretical justifications and simulation results are given to verify the efficiency and effectiveness of our proposed learning algorithms

regression analysis of case k interval censored failure time data in the presence of informative censoring summary interval censored failure time data occur in many fields such as demography economics medical research and reliability and many inference procedures on them have been developed sun 2006 chen sun and peace 2012 however most of the existing approaches assume that the mechanism that yields interval censoring is independent of the failure time of interest and it is clear that this may not be true in practice zhang et al 2007 ma hu and sun 2015 in this article we consider regression analysis of case k interval censored failure time data when the censoring mechanism may be related to the failure time of interest for the problem an estimated sieve maximum likelihood approach is proposed for the data arising from the proportional hazards frailty model and for estimation a two step procedure is presented in the addition the asymptotic properties of the proposed estimators of regression parameters are established and an extensive simulation study suggests that the method works well finally we apply the method to a set of real interval censored data that motivated this study

on the accelerated failure time model for current status and interval censored data and tianxi cai this paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time model for current status and interval censored data the estimator is constructed by inverting a wald type test for testing a null proportional hazards model a numerically efficient markov chain monte carlo based resampling method is proposed for obtaining simultaneously the point estimator and a consistent estimator of its variance covariance matrix we illustrate our approach with interval censored datasets from two clinical studies extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators

a new image thresholding method based on gaussian mixture model in this paper an efficient approach to search for the global threshold of image using gaussian mixture model is proposed firstly a gray level histogram of an image is represented as a function of the frequencies of gray level then to fit the gaussian mixtures to the histogram of image the expectation maximization em algorithm is developed to estimate the number of gaussian mixture of such histograms and their corresponding parameterization finally the optimal threshold which is the average of these gaussian mixture means is chosen and the experimental results show that the new algorithm performs better

analysis of covariance with incomplete data via semiparametric model transformations we propose a method for fitting semiparametric models such as the proportional hazards ph additive risks ar and proportional odds po models each of these semiparametric models implies that some transformation of the conditional cumulative hazard function at each t depends linearly on the covariates the proposed method is based on nonparametric estimation of the conditional cumulative hazard function forming a weighted average over a range of t values and subsequent use of least squares to estimate the parameters suggested by each model an approximation to the optimal weight function is given this allows semiparametric models to be fitted even in incomplete data cases where the partial likelihood fails e g left censoring right truncation however the main advantage of this method rests in the fact that neither the interpretation of the parameters nor the validity of the analysis depend on the appropriateness of the ph or any of the other semiparametric models in fact we propose an integrated method for data analysis where the role of the various semiparametric models is to suggest the best fitting transformation a single continuous covariate and several categorical covariates factors are allowed simulation studies indicate that the test statistics and confidence intervals have good small sample performance a real data set is analyzed

zeroing polynomials using modified constrained neural network approach this paper proposes new modified constrained learning neural root finders nrfs of polynomial constructed by backpropagation network bpn the technique is based on the relationships between the roots and the coefficients of polynomial as well as between the root moments and the coefficients of the polynomial we investigated different resulting constrained learning algorithms clas based on the variants of the error cost functions ecfs in the constrained bpn and derived a new modified cla mcla and found that the computational complexities of the cla and the mcla based on the root moment method rmm are the order of polynomial and that the mcla is simpler than the cla further we also discussed the effects of the different parameters with the cla and the mcla on the nrfs in particular considering the coefficients of the polynomials involved in practice to possibly be perturbed by noisy sources thus we also evaluated and discussed the effects of noises on the two nrfs finally to demonstrate the advantage of our neural approaches over the nonneural ones a series of simulating experiments are conducted

asymptotic theory for the correlated gamma frailty model the frailty model is a generalization of cox s proportional hazard model where a shared unobserved quantity in the intensity induces a positive correlation among the survival times murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator npmle for the shared gamma frailty model without covariates in this paper we extend this result to the correlated gamma frailty model and we allow for covariates we discuss the definition of the nonparametric likelihood function in terms of a classical proof of consistency for the maximum likelihood estimator which goes back to wald our proof of the consistency for the npmle is essentially the same as the classical proof for the maximum likelihood estimator a new central limit theorem for processes of bounded variation is given furthermore we prove that a consistent estimator for the asymptotic variance of the npmle is given by the inverse of a discrete observed information matrix

semiparametric bayes proportional odds models for current status data with underreporting current status data are a type of interval censored event time data in which all the individuals are either left or right censored for example our motivation is drawn from a cross sectional study which measured whether or not fibroid onset had occurred by the age of an ultrasound exam for each woman we propose a semiparametric bayesian proportional odds model in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure the proposed approach has the advantage of being straightforward to implement using a simple and efficient gibbs sampler whereas alternative semiparametric bayes event time models encounter problems for current status data the model is generalized to allow systematic underreporting in a subset of the data and the methods are applied to an epidemiologic study of uterine fibroids

a constructive approach for finding arbitrary roots of polynomials by neural networks this paper proposes a constructive approach for finding arbitrary real or complex roots of arbitrary real or complex polynomials by multilayer perceptron network mlpn using constrained learning algorithm cla which encodes the a priori information of constraint relations between root moments and coefficients of a polynomial into the usual bp algorithm bpa moreover the root moment method rmm is also simplified into a recursive version so that the computational complexity can be further decreased which leads the roots of those higher order polynomials to be readily found in addition an adaptive learning parameter with the cla is also proposed in this paper an initial weight selection method is also given finally several experimental results show that our proposed neural connectionism approaches with respect to the nonneural ones are more efficient and feasible in finding the arbitrary roots of arbitrary polynomials

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

sieve maximum likelihood regression analysis of dependent current status data current status data occur in contexts including demographic studies and tumorigenicity experiments in such cases each subject is observed only once and the failure time of interest is either left or right censored kalbfleisch prentice 2002 many methods have been developed for the analysis of such data huang 1996 sun 2006 most of which assume that the failure time and the observation time are independent completely or given covariates in this paper we present a sieve maximum likelihood approach for current status data when independence does not hold a copula model and monotone i splines are used and the asymptotic properties of the resulting estimators are established in particular the estimated regression parameters are shown to be semiparametrically efficient an illustrative example is provided

a new partitioning neural network model for recursively finding arbitrary roots of higher order arbitrary polynomials a new partitioning feedforward neural network fnn root finder model for recursively finding the arbitrary including complex roots of higher order arbitrary polynomials is proposed in this paper moreover an efficient complex version of constrained learning algorithm cla which incorporates the a priori information i e the constrained relation between the original polynomial coefficients and the remaining polynomial coefficients plus the partitioned roots out from the original polynomial is constructed to train the corresponding partitioning neural root finder network for finding the arbitrary roots of arbitrary polynomials finally the experimental results are given to show the efficiency and effectiveness of our proposed neural model with respect to traditional non neural root finders

an algebraic approach to the estimation of the order of fir filters from complete and partial magnitude and phase specifications the problems addressed by this paper is the following given a set of measurements over the range of normalized frequencies thetas1 thetas2 on the magnitude and or phase of a real fir but otherwise unknown filter to estimate the order of the fir filter the range thetas1 thetas2 may be partial or it may cover the entire range of frequencies the purpose of the paper is to propose a new algebraic approach to solve the above collection of problems specific new results include fir order estimation from partial or complete noiseless measurements for a real system from a phase alone from b magnitude alone not necessarily piece wise constant and from c joint magnitude and phase the proposed approach is not only capable of dealing with specifications that go beyond the conventional formulas for the standard piece wise constant magnitude fir filter order estimation but it also furnishes a nexus for order estimation from phase or group delay specifications areas which have remained hitherto unaddressed the approach is based on the use of root moments in this context the novel concept of fractional root moments is used in a key fashion to provide an estimate on the number of zeros inside the unit circle open problems and new directions of exploration and research are mentioned in the body of the paper

combinatorial theorems in sparse random sets we develop a new technique that allows us to show in a unified way that many well known combinatorial theorems including turan s theorem szemeredi s theorem and ramsey s theorem hold almost surely inside sparse random sets for instance we extend turan s theorem to the random setting by showing that for every 0 and every positive integer t 3 there exists a constant c such that if g is a random graph on n vertices where each edge is chosen independently with probability at least cn 2 t 1 then with probability tending to 1 as n tends to infinity every subgraph of g with at least 1 1 t 1 e g edges contains a copy of kt this is sharp up to the constant c we also show how to prove sparse analogues of structural results giving two main applications a stability version of the random turan theorem stated above and a sparse hypergraph removal lemma many similar results have recently been obtained independently in a different way by schacht and by friedgut rodl and schacht

finding the zeros of linear phase fir frequency sampling digital filters the need for finding the zeros of fir filters often arises in digital signal processing applications if we want to convert linear phase finite impulse response fir filters into minimum phase fir filters 1 2 the problem of finding the zeros of the filter is encountered this problem has been addressed in 3 but not solved here we introduce the idea of using frequency sampling filters for obtaining its zeros the advantage of using this kind of filter resides in the fact that all the zeros on the unit circle are known furthermore the zeros off the unit circle can be obtained with some simple processing this type of filter is especially useful when high order narrow band filters are involved finding the zeros of very high order equirriple low pass filters can be a difficult if not impossible task

semiparametric transformation models with random effects for joint analysis of recurrent and terminal events we propose a broad class of semiparametric transformation models with random effects for the joint analysis of recurrent events and a terminal event the transformation models include proportional hazards intensity and proportional odds models we estimate the model parameters by the nonparametric maximum likelihood approach the estimators are shown to be consistent asymptotically normal and asymptotically efficient simple and stable numerical algorithms are provided to calculate the parameter estimators and to estimate their variances extensive simulation studies demonstrate that the proposed inference procedures perform well in realistic settings applications to two hiv aids studies are presented

semiparametric regression analysis of interval censored data with informative dropout interval censored data arise when the event time of interest can only be ascertained through periodic examinations in medical studies subjects may not complete the examination schedule for reasons related to the event of interest in this article we develop a semiparametric approach to adjust for such informative dropout in regression analysis of interval censored data specifically we propose a broad class of joint models under which the event time of interest follows a transformation model with a random effect and the dropout time follows a different transformation model but with the same random effect we consider nonparametric maximum likelihood estimation and develop an em algorithm that involves simple and stable calculations we prove that the resulting estimators of the regression parameters are consistent asymptotically normal and asymptotically efficient with a covariance matrix that can be consistently estimated through profile likelihood in addition we show how to consistently estimate the survival function when dropout represents voluntary withdrawal and the cumulative incidence function when dropout is an unavoidable terminal event furthermore we assess the performance of the proposed numerical and inferential procedures through extensive simulation studies finally we provide an application to data on the incidence of diabetes from a major epidemiological cohort study

a new approach for function approximation incorporating adaptive particle swarm optimization and a priori information in this paper a new approach coupling adaptive particle swarm optimization apso and a priori information for function approximation problem is proposed to obtain better generalization performance and faster convergence rate it is well known that gradient based learning algorithms such as backpropagation bp algorithm have good ability of local search whereas pso has good ability of global search therefore in the new approach first apso encoding the first order derivative information of the approximated function is applied to train network to near global minima second with the connection weights produced by apso the network is trained with a gradient based algorithm due to combining apso with local search algorithm and considering a priori information the new approach has better generalization performance and convergence rate than traditional learning ones finally simulation results are given to verify the efficiency and effectiveness of the proposed approach

the analysis of current status data on point processes abstract this article considers the analysis of event count data in which each subject is observed at only one time point and no information is available on subjects between their entry time and observation points this type of data often referred to as current status data arises frequently for example in demography epidemiology and reliability studies statistical methods for the analysis of current status data from point processes are proposed specifically a statistic for testing the equality of the mean functions of point processes is presented and its asymptotic distribution obtained for illustration the proposed method is used to analyze multiple tumor data from a tumorgenicity experiment with focus on the comparison of tumor growth rates in male and female rats the adequacy of the asymptotic distribution of the test statistic is evaluated in a small simulation study power comparisons with the usual parametric model are also obtained finally some possible directions for further research

a nonparametric test for current status data with unequal censoring nonparametric tests for the comparison of different treatments based on current status data are proposed for this problem most methods proposed in the literature require that observation times on all subjects follow the same distribution in other words censoring distributions are identical between the treatment groups in this paper we focus on the situation where the censoring distributions may be different for subjects in different treatment groups and the test that can take this unequal censoring into account is given the asymptotic distribution of the test proposed is derived the method proposed is applied to data arising from a tumorigenicity experiment

testing the proportional odds model under random censoring summary in practical applications it is not uncommon for the hazard functions of two groups to converge with time one approach that allows for converging hazard functions is the proportional odds model we develop a procedure for testing the proportional odds assumption when the available data consist of two independent random samples of ran domly right censored lifetimes asymptotic normality of the test statistic is proved and the procedure is applied to two well known datasets the effective significance level and power of the proposed test are assessed through a simulation study the objective of this paper is to develop a test for comparison of survival times under random censorship when the hazard functions for the two groups of interest are not proportional through time but their ratio appears to be tending to 1 such a situation is encountered for example when the initial effects of treatment or the differences between stages of the disease at diagnosis tend to diminish with time and the hazard rates of different groups of patients become more similar a decaying treatment effect was found in the analysis of university of california san francisco s kidney transplant data by dabrowska et al 1992 and in the analysis of malignant melanoma data by andersen et al 1993 ch 7 frequently converging hazard functions are modelled by extending cox s proportional hazards model to include time dependent explanatory variables or by introducing a frailty parameter we refer to andersen et al 1993 ch 7 9 hougaard 2000 ch 2 7 and klein moeschberger 2003 ch 9 13 for detailed discussion an alternative approach to the problem of converging hazard functions is through the pro portional odds model if fg t is the true survival function underlying the data for groupi i and fi t then qi t for i are the true odds of a group iindividual surviving beyond time t we say that the two groups satisfy a proportional odds model if b2 t for all t and some constant if aksk is the hazard

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

analysis of survival data by the proportional odds model a model is presented for the analysis of lifetime data in which the rates of mortality for separate groups of patients converge with time a non parametric estimate is given for the survivor function the theoretical basis for the model assumes that prognostic factors have a multiplicative effect on the odds against survival beyond any given time the model is fitted to data using maximum likelihood estimation and an example of its use in the analysis of a lung cancer trial is given

computationally simple accelerated failure time regression for interval censored data summary an approach is presented for fitting the accelerated failure time model to interval censored data that does not involve computing the nonparametric maximum likelihood estimate of the distribution function at the residuals the approach involves estimating equations computed with the examination times from the same individual treated as if they had actually been obtained from different individuals the dependence between different measurements obtained from the same individual is then accounted for in the calculation of the standard error of the regression coefficients the approach is applicable to interval censored data in settings in which examinations continue to occur regardless of whether the failure time has occurred simulations are presented to assess the behaviour of the approach and the methodology is illustrated through an application to data from an aids clinical trial

a refinement of the cameron erdős conjecture in this paper we study sum free subsets of the set 1 n that is subsets of the first n positive integers which contain no solution to the equation x y z and erdos conjectured in 1990 that the lumber of such sets is o 2 n 2 this conjecture was confirmed by green and independently by sapozhenko here we prove a refined version of their theorem by showing that the number of sum free subsets of n of size in is 2 o n m n 2 for every 1 to 17 21 for m root t this result is sharp up to the constant implicit in the oh our proof uses a general bound on the number of independent sets of size to in 3 uniform hypergraphs proved recently by the authors and new bounds on the number of integer partitions with small sumset