diffusion approximation of frequency sensitive competitive learning the focus of this paper is a convergence study of the frequency sensitive competitive learning fscl algorithm we approximate the final phase of fscl learning by a diffusion process described by the fokker plank equation sufficient and necessary conditions are presented for the convergence of the diffusion process to a local equilibrium the analysis parallels that by ritter schulten 1988 for kohonen s self organizing map we show that the convergence conditions involve only the learning rate and that they are the same as the conditions for weak convergence described previously our analysis thus broadens the class of algorithms that have been shown to have these types of convergence characteristics

linear objective function optimization with fuzzy relation equation constraints regarding max av composition in this paper an optimization model with a linear objective function subject to a system of the fuzzy relation equations with max av composition is presented the solution set of such a fuzzy relation equations is a non convex set in this paper firstly we discuss the feasible solution set with two schemes and secondly study relationship between maximum and minimum points and also the feasible points as well furthermore an algorithm and few concrete examples are presented in order to optimize linear objective function

a note on a paper by e khorram and a ghodousian abstract the aim of this short note is to show on a numerical example that one of the two optimization algorithms proposed in e khorram a ghodousian linear objective function optimization with fuzzy relation equation constraints regarding max av composition appl math comput 173 2006 872 886 may not lead to the optimal solution in some cases besides it will be pointed out that the other algorithm correct but unfortunately ineffective for larger problems proposed in e khorram a ghodousian linear objective function optimization with fuzzy relation equation constraints regarding max av composition appl math comput 173 2006 872 886 can be extended to a wider class of non convex optimization problems

maximum of the weighted kaplan meier tests with application to cancer prevention and screening trials summary a class of maximum weighted kaplan meier test statistics is described where the weight functions are chosen from a family of smooth functions the investigated test statistic is robust and sensitive to a variety of alternatives that are often observed in cancer prevention and screening trials a simulation study is performed to compare the size and power properties between the proposed test statistics and some existing ones we illustrate the procedure using data from a clinical trial of a breast cancer screening program

the jackknife estimate of a kaplan meier integral summary we derive an explicit formula for the jackknife estimate of a kaplan meier integral from this the asymptotic analysis of the jackknifed kaplan meier process becomes straightforward in a small simulation study it is demonstrated that jackknifing may lead to a considerable reduction of the bias

residual plots for the censored data linear regression model to be consistent censored data linear regression estimators typically require a correctly specified linear regression function and independent and identically distributed errors for uncensored data one can assess these model assumptions informally by examining plots of the residuals against the independent variables or fitted values in this paper i propose plots for censored data analogous to these uncensored data residual plots one can use such plots in the same way as their uncensored data counterparts for checking model assumptions if the model assumptions are correct then the plots should exhibit a random scatter i show that the proposed plots are useful in selecting a linear regression model for the stanford heart transplant data

linear life expectancy regression with censored data summary in the statistical literature life expectancy is usually characterised by the mean residual life function regression models are thus needed to study the association between the mean residual life functions and their covariates in this paper we consider a linear mean residual life model and develop inference procedures in the presence of potential censoring the new model and inference procedures are applied to the stanford heart transplant data semiparametric efficiency calculations and information bounds are also considered

method of medians for lifetime data with weibull models the weibull family of distributions is frequently used in failure time models the maximum likelihood estimator is very sensitive to occurrence of upper and lower outliers especially when the hazard function is increasing we consider the method of medians estimator for the two parameter weibull model as an m estimator it has a bounded influence function and is highly robust against outliers it is easy to compute as it requires solving only one equation instead of a pair of equations as for most other m estimators furthermore no assumptions or adjustments are needed for the estimator when there are some possibly censored observations at either end of the sample about 16 per cent of the largest observations and 34 per cent of the smallest observations may be censored without affecting the calculations we also present a simple criterion to choose between the maximum likelihood estimator and the method of medians estimator to improve on the finite sample efficiency of the weibull model robust inference on the shape parameter is also considered the usefulness with contaminated or censored samples is illustrated by examples on three lifetime data sets a simulation study was carried out to assess the performance of the proposed estimator and the confidence intervals of a variety of contaminated weibull models

estimation in linear models with censored data summary three methods for linear regression with censored data are considered that of buckley james 1979 a proposed simpler nonparametric method and a normal model for censored data a new estimator for the variance of the error term in buckley james s 1979 procedure is proposed and simulations comparing the three methods are described many methods have been proposed for handling regression problems in which the dependent variable may be censored we focus on three methods for the linear model y xt3 e two methods are nonparametric so that the distribution of e is unspecified while the third assumes that e is normally distributed the nonparametric methods are analogous to the expectation maximization em algorithm introduced by dempster laird rubin 1977 which is broadly applicable for computing maximum likelihood estimates in 2 we discuss each of these methods and propose a new estimator of the variance of e for the buckley james method in 3 we give simulation results which compare the three methods

high breakdown point robust regression with censored data in this paper we propose a class of high breakdown point estimators for the linear regression model when the response variable contains censored observations these estimators are robust against high leverage outliers and they generalize the lms least median of squares s mm and estimators for linear regression an important contribution of this paper is that we can define consistent estimators using a bounded loss function or equivalently a redescending score function since the calculation of these estimators can be computationally costly we propose an efficient algorithm to compute them we illustrate their use on an example and present simulation studies that show that these estimators also have good finite sample properties

regression with censored data summary there are four regression techniques currently available for use with censored data which do not assume particular parametric families of survival distributions they are due to i cox 1972 ii miller 1976 iii buckley james 1979 and iv koul susarla van ryzin 1981 these four methods are described and their performances compared on the updated stanford heart transplant data conclusions on the usefulness of the four procedures are drawn

censored regression local linear approximations and their applications abstract various statistical tools are available for modeling the relationship between response and covariate if the data are fully observable in the situation of censored data however those tools are no longer directly applicable this article provides an easily implemented methodology for modeling the association based on censored data the form of the regression relationship will be completely determined by the data no assumptions are made about this form basic ideas behind the methodology are to transform the observed data in an appropriate simple way and then to apply a locally weighted least squares regression the proposed estimator involves a variable bandwidth that automatically adapts to the design of the data points that the methodology is very easy to implement is illustrated by several examples including simulation studies and an analysis of the stanford heart transplant data and the primary biliary cirrhosis data several theoretical considerations are reflected in the examples fina

clustering based on conditional distributions in an auxiliary space we study the problem of learning groups or categories that are local in the continuous primary space but homogeneous by the distributions of an associated auxiliary random variable over a discrete auxiliary space assuming that variation in the auxiliary space is meaningful categories will emphasize similarly meaningful aspects of the primary space from a data set consisting of pairs of primary and auxiliary items the categories are learned by minimizing a kullback leibler divergence based distortion between implicitly estimated distributions of the auxiliary data conditioned on the primary data still the categories are defined in terms of the primary space an online algorithm resembling the traditional hebb type competitive learning is introduced for learning the categories minimizing the distortion criterion turns out to be equivalent to maximizing the mutual information between the categories and the auxiliary data in addition connections to density estimation and to the distributional clustering paradigm are outlined the method is demonstrated by clustering yeast gene expression data from dna chips with biological knowledge about the functional classes of the genes as the auxiliary data

doubly penalized buckley james method for survival data with high dimensional covariates recent interest in cancer research focuses on predicting patients survival by investigating gene recent interest in cancer research focuses on predicting patients survival by investigating gene expression profiles based on microarray analysis we propose a doubly penalized buckley james method for the semiparametric accelerated failure time model to relate high dimensional genomic data to censored survival outcomes which uses the elastic net penalty that is a mixture of l 1 and l 2 norm penalties similar to the elastic net method for a linear regression model with uncensored data the proposed method performs automatic gene selection and parameter estimation where highly correlated genes are able to be selected or removed together the two dimensional tuning parameter is determined by generalized crossvalidation the proposed method is evaluated by simulations and applied to the michigan squamous cell lung carcinoma study

on estimating equations with censored data summary general estimating equations based on independent identically distributed random variables which may be right censored are considered the equations which appear to be natural analogues of the uncensored equations require full distributional assumptions and a distribution free modification based on the product limit estimator is suggested it follows from self consistency that the resulting estimating functions are simply means obtained from the product limit estimator the asymptotic variances of the estimators obtained from the equations are derived and compared

the minmax k means clustering algorithm applying k means to minimize the sum of the intra cluster variances is the most popular clustering approach however after a bad initialization poor local optima can be easily obtained to tackle the initialization problem of k means we propose the minmax k means algorithm a method that assigns weights to the clusters relative to their variance and optimizes a weighted version of the k means objective weights are learned together with the cluster assignments through an iterative procedure the proposed weighting scheme limits the emergence of large variance clusters and allows high quality solutions to be systematically uncovered irrespective of the initialization experiments verify the effectiveness of our approach and its robustness over bad initializations as it compares favorably to both k means and other methods from the literature that consider the k means initialization problem 2014 elsevier ltd all rights reserved

large sample theory of a modified buckley james estimator for regression analysis with censored data this approach we introduce herein a slight modification of the buckley james estimator to get around the difficulties caused by the instability at the upper tail of the associated kaplan meier estimate of the underlying error distribution and show that the modified buckleyjames estimator is consistent and asymptotically normal under certain regularity conditions a simple formula for the asymptotic variance of the modified buckley james estimator is also derived and is used to study the asymptotic efficiency of the estimator extensions of these results to the multiple regression model are also given

large sample behaviour of the product limit estimator on the whole line weak convergence results are proved for the product limit estimator on the whole line applications are given to confidence band construction estimation of mean lifetime and to the theory of q functions the results are obtained using stochastic calculus and in probability linear bounds for empirical processes

renovated scatterplots for censored data summary in simple linear regression where the response variable has been subject to right censoring censored points in the scatterplot of observed data are moved vertically to create a renovated scatterplot where the bias of censoring is removed the relationship to least squares estimation and the effect on regression diagnostics are examined in the multiple regression context

bootstrapping the kaplan meier estimator abstract randomly censored data consist of iid pairs of observations xi i i 1 n if i 0 xi denotes a censored observation and if i 1 xi denotes an exact survival time which is the variable of interest for estimating the distribution f of the survival times the product limit estimator proposed by kaplan and meier 1958 has been studied extensively and it has been shown to enjoy a number of optimality properties wellner 1982 see gill 1980 chaps 1 4 1983 for a modern treatment and for references with censored data bootstrapping can be carried out using two different resampling plans introduced by efron 1981 and reid 1981 respectively with efron s plan one takes a random sample with replacement from x 1 xn n whereas with reid s plan one takes a random sample from the kaplan meier estimator the purpose of this article is to study the asymptotic behavior of the bootstrapped kaplan meier estimator with both resampling plans the approach adopted uses the

frequency sensitive competitive learning for scalable balanced clustering on high dimensional hyperspheres competitive learning mechanisms for clustering in general suffer from poor performance for very high dimensional 1000 data because of curse of dimensionality effects in applications such as document clustering it is customary to normalize the high dimensional input vectors to unit length and it is sometimes also desirable to obtain balanced clusters i e clusters of comparable sizes the spherical kmeans spkmeans algorithm which normalizes the cluster centers as well as the inputs has been successfully used to cluster normalized text documents in 2000 dimensional space unfortunately like regular kmeans and its soft expectation maximization based version spkmeans tends to generate extremely imbalanced clusters in high dimensional spaces when the desired number of clusters is large tens or more this paper first shows that the spkmeans algorithm can be derived from a certain maximum likelihood formulation using a mixture of von mises fisher distributions as the generative model and in fact it can be considered as a batch mode version of normalized competitive learning the proposed generative model is then adapted in a principled way to yield three frequency sensitive competitive learning variants that are applicable to static data and produced high quality and well balanced clusters for high dimensional data like kmeans each iteration is linear in the number of data points and in the number of clusters for all the three algorithms a frequency sensitive algorithm to cluster streaming data is also proposed experimental results on clustering of high dimensional text data sets are provided to show the effectiveness and applicability of the proposed techniques

sequential analysis for censored regression data abstract motivated by buckley and james modification of the least squares procedure for censored regression data we derive a score process that incorporates the time evolution and handles staggered entry data in a natural way by censored regression data we mean that the responses are subject to a possible right censorship such cases often arise from clinical trials and industrial life tests the score process can be interpreted as a weighted comparison of transformed survival times this is especially suitable for the accelerated failure time regression model by expressing it in an appropriate form so that the counting process and its associate martingale theory can be applied we show that the score process is approximated by a mean 0 multidimensional gaussian process a consistent estimator of its covariance matrix function is provided based on the covariance matrix estimator and the sequential test of slud and wei a repeated significance test is then proposed usefulness of the procedure is il

codeword distribution for frequency sensitive competitive learning with one dimensional input data we study the codeword distribution for a conscience type competitive learning algorithm frequency sensitive competitive learning fscl using one dimensional input data we prove that the asymptotic codeword density in the limit of large number of codewords is given by a power law of the form q x c spl middot p x sup spl alpha where p x is the input data density and spl alpha depends on the algorithm and the form of the distortion measure to be minimized we further show that the algorithm can be adjusted to minimize any l sub p distortion measure with p ranging in 0 2

small sample results for the kaplan meier estimator abstract whereas much is known about the asymptotic properties of the kaplan meier 1958 estimator kme of a survival function exact results for small samples have been difficult to obtain in this article we obtain an exact expression for the th moment 0 of the kme under a model of proportional hazards this enables us under proportional hazards to a study the bias of the kme and b compare the exact variance of the kme to its asymptotic variance

nonparametric estimation of the gap time distributions for serial events with censored data summary in many follow up studies each subject can potentially experience a series of events which may be repetitions of essentially the same event or may be events of entirely diverent natures this paper provides a simple nonparametric estimator for the multivariate distribution function of the gap times between successive events when the follow up time is subject to right censoring the estimator is consistent and upon proper normalisation converges weakly to a zero mean gaussian process with an easily estimated covariance function numerical studies demonstrate that both the distribution function estimator and its covariance function estimator perform well for practical sample sizes an application to a colon cancer study is presented

clustering on the unit hypersphere using von mises fisher distributions several large scale data mining applications such as text categorization and gene expression analysis involve high dimensional data that is also inherently directional in nature often such data is l2 normalized so that it lies on the surface of a unit hypersphere popular models such as mixtures of multi variate gaussians are inadequate for characterizing such data this paper proposes a generative mixture model approach to clustering directional data based on the von mises fisher vmf distribution which arises naturally for data distributed on the unit hypersphere in particular we derive and analyze two variants of the expectation maximization em framework for estimating the mean and concentration parameters of this mixture numerical estimation of the concentration parameters is non trivial in high dimensions since it involves functional inversion of ratios of bessel functions we also formulate two clustering algorithms corresponding to the variants of em that we derive our approach provides a theoretical basis for the use of cosine similarity that has been widely employed by the information retrieval community and obtains the spherical kmeans algorithm kmeans with cosine similarity as a special case of both variants empirical results on clustering of high dimensional text and gene expression data based on a mixture of vmf distributions show that the ability to estimate the concentration parameter for each vmf component which is not present in existing approaches yields superior results especially for difficult clustering tasks in high dimensional spaces

another modification from two papers of ghodousian and khorram and khorram et al abstract in this paper we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max min and the max average composition and the max star composition respectively they have been proposed by ghodousian and khorram a ghodousian e khorram solving a linear programming problem with the convex combination of the max min and the max average fuzzy relation equations appl math comput 180 2006 411 418 and khorram et al e khorram a ghodousian a abbasi molai solving linear optimization problems with max star composition equation constraints appl math comput 179 2006 654 661 respectively firstly we show that the tabular method algorithm in the first paper and the first procedure in the second paper may not lead to the optimal solutions of the two models in some cases secondly we generalize the proposed algorithm by abbasi molai and khorram a abbasi molai e khorram a modified algorithm for solving the proposed models by ghodousian and khorram and khorram and ghodousian appl math comput 190 2007 1161 1167 to solve the two models in fact it modifies the presented algorithms in the two papers finally some numerical examples are given to illustrate the purposes

a distribution free least squares estimator for censored linear regression models abstract this paper describes a method for estimating simultaneously the parameter vector of the systematic component and the distribution function of the random component of a censored linear regression model the estimator is obtained by minimizing the sum of the squares of the differences between the observed values of the dependent variable and the corresponding expected values of this variable according to the estimated parameter vector and distribution function the resulting least squares parameter estimator incorporates information on the distribution of the random component of the regression model that is available from the estimation sample hence it may often be more efficient than are parameter estimators that do not use such information the results of numerical experiments with the least squares estimator tend to support this hypothesis

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

an application of imputation to an estimation problem in grouped lifetime analysis tanner and wang in press have introduced the data augmentation algorithm for the analysis of parametric missing data problems in this article this paradigm is used to develop an algorithm for the nonparametric estimation of the hazard function from grouped and censored lifetime data this algorithm makes use of the notions of cross validation and multiple imputation to prescribe the appropriate degree of smoothing for the nonparametric hazard estimate a procedure for estimating the variance of the estimator is also proposed the nonparametric hazard estimate and corresponding variance formula are shown to perform well in a simulation study the algorithm is illustrated with a numerical example

a method for determining groups in multiple survival curves survival analysis includes a wide variety of methods for analyzing time to event data one basic but important goal in survival analysis is the comparison of survival curves between groups several nonparametric methods have been proposed in the literature to test for the equality of survival curves for censored data when the null hypothesis of equality of curves is rejected leading to the clear conclusion that at least one curve is different it can be interesting to ascertain whether curves can be grouped or if all these curves are different from each other a method is proposed that allows determining groups with an automatic selection of their number the validity and behavior of the proposed method was evaluated through simulation studies the applicability of the proposed method is illustrated using real data software in the form of an r package has been developed implementing the proposed method

asymptotically optimal bandwidth selection for kernel density estimators from randomly right censored samples abstract this paper makes two important contributions to the theory of bandwidth selection for kernel density estimators under right censorship first an asymptotic representation of the integrated squared error into easily understood variance and squared bias components is given second it is shown that if the bandwidth is chosen by the data based method of least squares cross validation then it is asymptotically optimal in a compelling sense a by product of the first part is an interesting comparison of the two most popular kernel estimators keywords nonparametric density estimation smoothing parameter

m estimation in censored linear models summary we propose a method of obtaining an m estimator in a linear model when the responses are subject to right censoring the central limit theorem for the estimator using squared error loss i e least squares is derived using counting process martingale techniques the estimation method is applied to the stanford heart transplant data for illustration

latticized linear optimization on the unit interval this paper considers the latticized linear optimization llo problem and its variants which are a special class of optimization problems constrained by fuzzy relational equations or inequalities we show that an optimal solution to such a problem can be obtained in polynomial time as long as the objective function is a max separable function with continuous monotone components we further show that the set of all optimal solutions is fully determined by one maximum optimal solution and a finite number of minimal optimal solutions the maximum optimal solution can be constructed in polynomial time once the optimal objective value is known while the detection of all minimal optimal solutions in an efficient manner remains as a challenging problem the relation between llo and max separable optimization and related issues are also investigated

weighted least squares method for right censored data in accelerated failure time model summary the classical accelerated failure time aft model has been extensively investigated due to its direct interpretation of the covariate effects on the mean survival time in survival analysis however this classical aft model and its associated methodologies are built on the fundamental assumption of data homoscedasticity consequently when the homoscedasticity assumption is violated as often seen in the real applications the estimators lose efficiency and the associated inference is not reliable furthermore none of the existing methods can estimate the intercept consistently to overcome these drawbacks we propose a semiparametric approach in this article for both homoscedastic and heteroscedastic data this approach utilizes a weighted least squares equation with synthetic observations weighted by square root of their variances where the variances are estimated via the local polynomial regression we establish the limiting distributions of the resulting coefficient estimators and prove that both slope parameters and the intercept can be consistently estimated we evaluate the finite sample performance of the proposed approach through simulation studies and demonstrate its superiority through real example on its efficiency and reliability over the existing methods when the data is heteroscedastic

fisher s information in terms of the hazard rate if g t is a regular family of probability densities on the real line with corresponding hazard rates h t then the fisher information for can be expressed in terms of the hazard rate as follows f g 2 g h h 2 g r where the dot denotes this identity shows that the hazard rate transform of a probability density has an unexpected length preserving property we explore this property is continuous and discrete settings some geometric consequences and curvature formulas its connection with martingale theory and its relation to statistical issues in the theory of life time distributions and censored data

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

inference on multivariate m estimators based on bivariate censored data consider two random variables subject to random right censoring for example the survival times of twins or two recurrence times of a certain disease recorded on the same individual of interest is the estimation of a multivariate m functional of these two random variables asymptotic results for the proposed estimator are established under general conditions on the criterion function of the m estimator the obtained results include the asymptotic normality of the estimator its local power and construction of a confidence region our primary example of interest is the bivariate l1 median we compare the small sample behavior of this estimator with that of the vector of marginal medians by means of a simulation study finally we consider a dataset on kidney dialysis patients and estimate the median time to two different infections for these individuals

a unified model for probabilistic principal surfaces principal curves and surfaces are nonlinear generalizations of principal components and subspaces respectively they can provide insightful summary of high dimensional data not typically attainable by classical linear methods solutions to several problems such as proof of existence and convergence faced by the original principal curve formulation have been proposed in the past few years nevertheless these solutions are not generally extensible to principal surfaces the mere computation of which presents a formidable obstacle consequently relatively few studies of principal surfaces are available we previously 2000 proposed the probabilistic principal surface pps to address a number of issues associated with current principal surface algorithms pps uses a manifold oriented covariance noise model based on the generative topographical mapping gtm which can be viewed as a parametric formulation of kohonen s self organizing map building on the pps we introduce a unified covariance model that implements pps 0 1 by varying the clamping parameter spl alpha then we comprehensively evaluate the empirical performance of pps gtm and the manifold aligned gtm on three popular benchmark data sets it is shown in two different comparisons that the pps outperforms the gtm under identical parameter settings convergence of the pps is found to be identical to that of the gtm and the computational overhead incurred by the pps decreases to 40 percent or less for more complex manifolds these results show that the generalized pps provides a flexible and effective way of obtaining principal surfaces

a nonparametric approach to the truncated regression problem abstract a description is given of a new method of estimating the regression parameters in the linear regression model from data where the dependent variable is subject to truncation the residual distribution is allowed to be unspecified the method is iterative and involves estimation of the residual distribution under the truncated sampling scheme the technique can be interpreted as an iterative bias adjustment of the observations in order to correct the regression relationship in the sampled population to match that of the model a simulation study compares the performance of various estimators including one suggested by bhattacharya chernoff and yang 1983 this truncation regression problem arises in many contexts of scientific and social research in economics tobin 1958 analyzed household expenditure on durable goods using a regression model that took account of the fact that the expenditure is always nonnegative a more general situation was studied by hausman and wise 1976 1977 in conn

nonparametric methods for factorial designs with censored data abstract nonparametric hypotheses of no main effects no simple effects and no interaction effects are considered in the context of factorial designs with censored observations to test these hypotheses the asymptotic distribution of quadratic forms of rank statistics is derived using the methodology of martingales for counting processes the weights used reduce to the usual logistic scores with uncensored data but are different from the weights commonly used for testing the equality of k samples the formulation of all results includes tied observations approximations to the small sample distributions of the test statistics are given the performance of the tests is examined via simulation studies the procedures are illustrated on a real dataset

extended quasi likelihood with fractional polynomials in the frame of the accelerated failure time model the accelerated failure time model is frequently used in survival analysis because of its direct physical interpretation semiparametric inference methods have been extensively investigated for this model however the accelerated failure time model and the existing inference methods assume homogeneity of the survival data after taking log transformation this assumption is not always appropriate because heterogeneous data are often encountered in practice in dealing with this heterogeneity yu yu and liu proposed a parametric quasi likelihood method by assuming a known variance function which may not be realistic for real data in this paper we extend the parametric quasi likelihood method to semiparametric via relaxing its assumption and approximating the unknown variance function by using fractional polynomials approach simulations show that this novel extension performs superior to other methods in statistical properties of unbiasedness efficiency and correct coverage probability in finite samples an application to real data set in primary biliary cirrhosis demonstrates the applicability of this new methodology

estimation in a linear regression model with censored data we consider the semiparametric linear regression model with censored data and with unknown error distribution we describe estimation equations of the buckley james type that admit n consistent and asymptotically normal solutions the derived estimator is efficient at a particular error distribution we show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by tsiatis an extension to an estimator that is efficient everywhere is discussed

confidence bands for survival functions with censored data a comparative study consider the problem of obtaining simultaneous confidence bands for the survival function s x when the data are arbitrarily right censored the usual pointwise confidence intervals based on greenwood s variance formula can be adapted to yield a large sample confidence band this band has in a certain sense equal precision at each point of s x it is compared with the censored versions of the kolmogorov band and the renyi band the comparisons are made in terms of the widths and the adequacy of large sample approximations and are carried out under various censoring models and degrees of censoring the bands are illustrated by applying them to data from a mechanical switch life test

two sided bias bound of the kaplan meier estimator we prove in this paper that the bias of the kaplan meier estimator functional which always under estimates the true value is decreasing at an exponential rate an application of the inequality is also given

product limit estimators of the survival function with twice censored data a model for competing resp complementary risks survival data where the failure time can be left resp right censored is proposed product limit estimators for the survival functions of the individual risks are derived we deduce the strong convergence of our estimators on the whole real half line without any additional assumptions and their asymptotic normality under conditions concerning only the observed distribution when the observations are generated according to the double censoring model introduced by turnbull the product limit estimators represent upper and lower bounds for turnbull s estimator

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

linear regression with doubly censored data linear regression with doubly censored responses is considered buckley james ritov type estimators are proposed semiparametric information and projective scores are discussed an expansion of the estimating equations is obtained under fairly general assumptions sufficient conditions are given for the asymptotic consistency and normality of the estimators

demographic incidence rates and estimation of intensities with incomplete information many population processes in demography epidemiology and other fields can be represented by a time continuous markov chain model with a finite state space if we have complete information on the life history of a cohort the intensities of the markov model may be estimated by the occurrence exposure rates or by nonparametric techniques in many situations however we have only incomplete information in this paper we consider the special but important case where the occurrences and the total exposure are known but not the distribution of the latter over the various separate statuses methods for handling such data so called demographic incidence rates and methods for estimating the intensities from this kind of data are known in the literature however their statistical properties are only vaguely known the present paper gives a thorough presentation of the theory of these methods and provide rigorous proofs of their statistical properties using stochastic process theory 1 introduction in demography and fields with a similar methodology a population process on the individual level can frequently be represented by a time continuous markov chain with a finite state space the states of the markov chain represent the demographic statuses and the jumps between the states correspond to the demographic events the time parameter of the markov process may be the age of an individual the time since a specific event or some such quantity we will call it seniority given this general framework the population phenomena may be described by the transition intensities of the model consequently it is of great interest to estimate these functions in principle this is an easy task if the individuals studied are watched continuously over some period of time one may then use the classical methods based on occurrence exposure rates for a review see hoem 1976 or for small populations or samples nonparametric techniques developed by aalen 1978 and others quite often however one does not obtain the sufficiently detailed data required to use any of these methods this fact has inhibited the use of markov chain models in demography and related fields the development and study of statistical methods for situations with incomplete data is therefore of considerable interest there seems to be no general solution to the problem of estimating the intensities of partially observed markov chains in the present paper we consider a special but important type of incomplete observation namely that transitions within a subset of states k are observed in detail while counts of transitions out

tests for location with k samples and censored data summary tests which are specific for location are developed in the k sample situation with right censored data the tests are based on general estimating functions and do not require full parametric assumptions for large samples but in general they are not based only on ranks one class of tests allows shapes to differ in the k populations and includes as a special case the median test of brookmeyer crowley 1982 if the distributions are assumed to differ at most in location modified tests are suggested in which survival function estimates are obtained by pooling the data from all samples prentice s 1978 median test with minor modifications is included in this class

estimating fecundability from data on waiting times to first conception abstract this article tests assumptions invoked in the demographic literature to estimate the population distribution of fecundability from data on waiting times to first conception in continuous time the key assumption is that waiting times are realizations from a mixture of exponentials distribution in discrete time the key assumption is that waiting times are realizations from a mixture of geometrics distribution the hutterite data analyzed by sheps 1965 are consistent with this assumption various models however have one representation in mixture of exponentials form a fundamental identification problem plagues the conventional estimation procedure our analysis calls into question the conventional practice of checking model specification by using goodness of fit tests the practical importance of the identification problem in duration models is demonstrated

functional laws of the iterated logarithm for the product limit estimator of a distribution function under random censorship or truncation functional laws of the iterated logarithm are established for a modified version of the classical product limit estimator of a distribution function when the data are subject to random censorship or truncation making use of stochastic integral representations and empirical process theory strong approximations involving i i d continuous parameter martingales are developed for the product limit estimator and these strong approximations are then applied to derive the functional laws

a comparison of estimators for regression with a censored response variable summary several methods of estimating parameters in a linear regression when the response variable is censored are compared the estimator of buckley james 1979 is preferred further it is shown that the strength of the regression the support and distribution of the censoring variable and the magnitude of the slope all have an effect on the relative performance of the estimators

on plotting renovated samples in this note we use the buckley james method for censored regression in the p sample problem where the samples are subject to right censoring the samples are reconstructed so as to remove the effect of censoring and graphical procedures based on quantiles such as boxplots may then be used as a standard data analytic tool to describe the variable being measured

a note on a paper by molai and khorram abstract the aim of this note is to show that the optimization algorithm proposed in 6 may not lead to the optimal solution in some cases in fact the optimization problem remains open if we do not apply the branch and bound method to solve it or compute all the objective values of minimal solutions of the feasible domain

modeling the manifolds of images of handwritten digits this paper describes two new methods for modeling the manifolds of digitized images of handwritten digits the models allow a priori information about the structure of the manifolds to be combined with empirical data accurate modeling of the manifolds allows digits to be discriminated using the relative probability densities under the alternative models one of the methods is grounded in principal components analysis the other in factor analysis both methods are based on locally linear low dimensional approximations to the underlying data manifold links with other methods that model the manifold are discussed

a correlation goodness of fit test for randomly censored data summary for testing a composite goodness of fit hypothesis with randomly censored data a correlation statistic which is an analogue of the shapiro francia statistic is presented the test for exponentiality in case of light censoring is asymptotically robust against departures from the koziol green model of random censorship the power of the test is compared with the total time on test procedure and the new better than used test using monte carlo simulation as an example the test is applied to some data with prostate cancer