convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings in this paper we consider the weak and strong convergence of an implicit iterative process with errors for two finite families of asymptotically nonexpansive mappings in the framework of banach spaces our results presented in this paper improve and extend the recent ones announced by many others

convergence of the new composite implicit iteration process with random errors abstract in this paper strong convergence theorems for approximation of common fixed points of a finite family of asymptotically demicontractive mappings are proved in banach spaces using the new composite implicit iteration scheme with errors our results of this paper improve and extend the corresponding results of chen song zhou r d chen y s song h y zhou convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings j math anal appl 314 2006 701 709 osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81 gu f gu the new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings j math anal appl 329 2007 766 776 and yang and hu l p yang g hu convergence of implicit iteration process with random errors acta math sinica chin ser 51 1 2008 11 22

implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps convergence theorems for approximation of common fixed points of strictly pseudocontractive mappings of browder petryshyn type are proved in banach spaces using an implicit iteration scheme recently introduced by xu and ori numer funct anal optim 22 2001 767 773

convergence theorems of implicit iterative sequences for a finite family of asymptotically quasi nonexpansive type mappings abstract in this paper we introduce a new implicit iteration process generated by a finite family of asymptotically quasi nonexpansive type mappings and prove the convergence theorems of the process in a banach space or uniformly convex banach spaces our results extend and improve some recent results

composite implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps abstract let e be a real banach space and let k be a nonempty closed convex subset of e let t i i 1 n be n strictly pseudocontractive self maps of k such that f i 1 n f t i where f t i x k t i x x and let n n 1 n n 1 0 1 be two real sequence satisfying the conditions i n 1 1 n ii n 1 1 n 2 iii n 1 1 n iv 1 n 1 n l 2 1 n 1 where l 1 is common lipschitz constant of t i i 1 n for x 0 k let x n n 1 be new implicit process defined by x n n x n 1 1 n t n y n y n n x n 1 1 n t n x n where t n t n mod n then i lim n x n p exists for all p f ii lim inf n x n t n x n 0 the results of this paper generalize and improve the results of osilike in 2004 in this paper the proof methods of the main results are also different from that of osilike

parameter estimates of general failure rate model a bayesian approach abstract the failure rate function plays an important role in studying the lifetime distributions in reliability theory and life testing models a study of the general failure rate model r t a b t 1 under squared error loss function taking a and b independent exponential random variables has been performed in the literature in this article we consider a and b not necessarily independent the estimates of the parameters a and b under squared error loss linex loss and entropy loss functions are obtained and further examined using simulated and real data sets

local full likelihood estimation for the proportional hazards model summary in this paper a new approach to local likelihood estimation for censored data is proposed this method employs the full likelihood and alternates between estimating the baseline hazard and estimating the covariate effect the proposed methodology incorporates multidimensional data via additive models some results regarding inference for the covariate effect are also presented in this paper we propose new methodology for estimating a general covariate effect when the data arise from a proportional hazards model the methodology uses the full likelihood rather than the partial likelihood and is iterative in nature we note that techniques relying on the partial likelihood do not agree with the modeling assumptions and hence may be less desirable to begin some notation is introduced the data are observed as independent identically distributed triples ti bi zi where t is the minimum of the true failure time and the true censoring time 6 is an indicator of failure and z is a covariate that may be vector valued the true possibly unobserved failure time is assumed to have distribution function f the survivor function is denoted x the hazard x t and the integrated hazard a t further it is assumed that the data arise from a proportional hazards model that is the hazard x t z is assumed to be the product of a baseline hazard xo t and a covariate effect v z

a new iteration process for finite families of generalized lipschitz pseudo contractive and generalized lipschitz accretive mappings abstract a new iteration process is introduced and proved to converge strongly to a common fixed point for a finite family of generalized lipschitz nonlinear mappings in a real reflexive banach space e with a uniformly g teaux differentiable norm if at least one member of the family is pseudo contractive it is also proved that a slight modification of the process converges to a common zero for a finite family of generalized lipschitz accretive operators defined on e results for nonexpansive families are obtained as easy corollaries finally the new iteration process and the method of proof are of independent interest

convergence theorems for common fixed points for finite families of nonexpansive mappings in reflexive banach spaces let e be a real reflexive banach space with a uniformly g teaux differentiable norm let k be a nonempty closed convex subset of e suppose that every nonempty closed convex bounded subset of k has the fixed point property for nonexpansive mappings let t1 t2 tn be a family of nonexpansive self mappings of k with f i 1nfix ti 0 f fix tntn 1 t1 fix t1tn t2 fix tn 1tn 2 t1tn let n be a sequence in 0 1 satisfying the following conditions c1 lim n 0 c2 n for a fixed 0 1 define sn k k by snx 1 x tnx x k where tn tnmodn for an arbitrary fixed u x0 k let b x k tntn 1 t1x x 1 u for some 1 be bounded and let the sequence xn be defined iteratively by xn 1 n 1u 1 n 1 sn 1xn for n 0 assume that limn tnxn tn 1xn 0 then xn converges strongly to a common fixed point of the family t1 t2 tn this convergence theorem is also proved for non self maps

local em estimation of the hazard function for interval censored data summary we propose a smooth hazard estimator for interval censored survival data using the method of local likelihood the model is fit using a local em algorithm the estimator is more descriptive than traditional empirical estimates in regions of concentrated information and takes on a parametric flavor in regions of sparse information we derive two different standard error estimates for the smooth curve one based on asymptotic theory and the other on the bootstrap we illustrate the local em method for times to breast cosmesis deterioration finkelstein 1986 biometrics42 845 854 and for times to hiv 1 infection for individuals with hemophilia kroner et al 1994 journal of aids7 279 286 our hazard estimates for each of these data sets show interesting structures that would not be found using a standard parametric hazard model or empirical survivorship estimates

global partial likelihood for nonparametric proportional hazards models as an alternative to the local partial likelihood method of tibshirani and hastie and fan gijbels and king a global partial likelihood method is proposed to estimate the covariate effect in a nonparametric proportional hazards model t x exp x 0 t the estimator x reduces to the cox partial likelihood estimator if the covariate is discrete the estimator is shown to be consistent and semiparametrically efficient for linear functionals of x moreover breslow type estimation of the cumulative baseline hazard function using the proposed estimator x is proved to be efficient the asymptotic bias and variance are derived under regularity conditions computation of the estimator involves an iterative but simple algorithm extensive simulation studies provide evidence supporting the theory the method is illustrated with the stanford heart transplant data set the proposed global approach is also extended to a partially linear proportional hazards model and found to provide efficien

quantile comparison functions in two sample problems with application to comparisons of diagnostic markers abstract in this article a control percentile test a chi squared test and a kolmogorov type test are proposed for comparing two distributions from incomplete survival data these tests are obtained by examining a vertical shift comparison function at a single point a finite number of points and an entire set of points on an interval the proposed methods also have applications in receiver operating characteristic roc analysis which has been widely used in such diverse fields as signal detection theory psychology epidemiology and medicine the results are derived under very general conditions that hold for the well known random censorship and random truncation models the performances of the proposed procedures are studied using monte carlo simulation the methods are applied to analyze mayo clinic ovarian carcinoma data

a characterization of the convergence of picard iteration to a fixed point for a continuous mapping and an application necessary and sufficient conditions for the convergence of picard iteration to a fixed point for a continuous mapping in metric spaces are established as application we prove the convergence theorem of ishikawa iteration to a fixed point for a nonexpansive mapping in banach spaces

strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi nonexpansive maps the aim of this paper is to prove strong convergence of a modified implicit iteration process to a common fixed point for a finite family of generalized asymptotically quasi nonexpansive mappings an immediate corollary of our theorems provides an affirmative response to a question raised by xu and ori h k xu r ori an implicit iterative process for nonexpansive mappings numer funct anal optim 22 2001 767 773

local partial likelihood estimation in proportional hazards regression fan gijbels and king ann statist 25 1997 1661 1690 considered the estimation of the risk function x in the proportional hazards model their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood they proved the large sample properties of the derivative function but the large sample properties of the estimator for the risk function itself were not established in this paper we consider direct estimation of the relative risk function x 2 x 1 for any location normalization point x 1 the main novelty in our approach is that we select observations in shrinking neighborhoods of both x 1 and x 2 when constructing a local version of the partial likelihood whereas fan gijbels and king ann statist 25 1997 1661 1690 only concentrated on a single neighborhood resulting in the cancellation of the risk function in the local likelihood function the asymptotic properties of our estimator are rigorously established and the variance of the estimator is easily estimated the idea behind our approach is extended to estimate the differences between groups a simulation study is carried out

relative risk trees for censored survival data a method is developed for obtaining tree structured relative risk estimates for censored survival data the first step of a full likelihood estimation procedure is used in a recursive partitioning algorithm that adopts most aspects of the widely used classification and regression tree cart algorithm of breiman et al 1984 classification and regression trees belmont california wadsworth the performance of the technique is investigated through stimulation and compared to the tree structured survival methods proposed by davis and anderson 1989 statistics in medicine 8 947 961 and therneau grambsch and fleming 1990 biometrika 77 147 160

bayes estimation of parameters in a three non independent component series system with time dependent failure rate in this paper we have presented a bayesian approach for estimating the parameters included in three non independent and non identical components of series system subjected to four sources of fatal shocks the failure rate of the components of the system is linearly dependent on time bayes estimators for the values of reliability components of the system is obtained gamma prior distributions are assumed for the unknown parameters to be estimated special cases of the obtained results are presented to show how the present results generalize the results in other literatures

convergence of an implicit iterative process for asymptotically pseudocontractive nonself mappings abstract in this work an implicit iterative process is considered for asymptotically pseudocontractive nonself mappings weak and strong convergence theorems for common fixed points of a family of asymptotically pseudocontractive nonself mappings are established in the framework of hilbert spaces

implicit iteration process for a finite family of asymptotically hemi contractive mappings in banach spaces abstract the purpose of this paper is to study the strong convergence of a process of implicit iteration to a common fixed point for a finite family of asymptotically hemi contractive mappings our results extend a recent result of m o osilike and b g akuchu common fixed points of a finite family of asymptotically pseudocontractive maps fixed point theory appl 2 2004 81 88 from hilbert spaces to p uniformly convex banach spaces with p 1

diagnostic plots to reveal functional form for covariates in multiplicative intensity models abstract we show how plots based on the residuals from a proportional hazards model may be used to reveal the correct functional form for covariates in the model a smoothed plot of the martingale residues was suggested for this purpose by therneau grambsch and fleming 1990 biometrika 77 147 160 however its consistency required that the covariates be independent they also noted that the plot could be biased for large covariate effects we introduce two refinements which overcome these difficulties the first is based on a ratio of scatter plot smooths where the numerator is the smooth of the observed count plotted against the covariate and the denominator is a smooth of the expected count this is related to the arjas goodness of fit plot 1988 journal of the american statistical association 83 204 212 the second technique smooths the martingale residuals divided by the expected count using expected count as a weight this latter approach is related to a glm partial residual plot as well as to the iterative methods of hastie and tibshirani 1990 biometrics 46 1005 1016 and gentleman and crowley 1991 biometrics 47 1283 1296 applications to survival data sets are given

bayesian estimation of the parameters in two non independent component series system with dependent time failure rate in this paper we have presented a bayesian approach for estimating the parameters included in a two non independent and non identical component series system with linear failure rate subjected to three sources of fatal shocks also the bayes estimators for the values of reliability functions of the system components are deduced estimations of the system s mean time to failure and the system s failure rate are derived uniform prior distributions are assumed for the unknown parameters to be estimated special cases of the present results are obtained to show how the current results generalize the results in other literatures

estimation of system components reliabilities using masked data consider a system of m independent and non identical components connected in series such system fails whenever at least one of the components has failed due to the cost and time constraints however the exact cause of system failure might be unknown instead it is assumed that the cause of system failure may be due to a component that belongs to a subset of the m components such type of observation is referred to as being masked confronted with this phenomenon we use the maximum likelihood procedure to estimate the parameters indexed to the lifetime distributions of the system components further the system component reliabilities at a specified time will be estimated we focused on series systems with two and three components the system components lifetimes are assumed to be weibull distributed we show that closed form solutions for the maximum likelihood estimates can be obtained under certain assumptions further numerical simulation study is presented

common fixed points noor iteration for a finite family of asymptotically quasi nonexpansive mappings in banach spaces in this paper we introduce a general iteration scheme for a finite family of asymptotically quasi nonexpansive mappings the new iterative scheme includes the modified mann and ishikawa iterations three step iterative scheme of xu and noor and khan and takahashi scheme as special cases our results are generalizations as well as refinement of several known results in the current literature

investigating the geometry of a p dimensional data set abstract this article concerns itself with exploratory data analysis in hyperspace and discusses a method of data reduction intended to allow insight into the geometry of a p dimensional data set where p 2 the essential idea is to examine various views through the data set using a suitably chosen line the baseline for defining a viewing direction for a given data point its distance from a suitable point on the baseline called the vertex and the angular separation between the baseline and the line connecting the vertex to the data point are taken as coordinates of an ordinary polar coordinate plot in two dimensions the bulk of the article discusses empirical evidence for the utility of such a plot which can be referred to as a coneplot because points are essentially identified with the intersection in p dimensions of a hypersphere and a ray of a hypercone

convergence theorems of fixed points for asymptotically hemi pseudocontractive mappings in this paper the concept of asymptotically hemi pseudocontractive mapping in banach space which is a proper generalization of asymptotically pseudocontractive mapping with nonempty fixed point set as shown by an example is introduced some sufficient and necessary conditions on the strong convergence of the modified ishikawa and the modified mann iteration sequences with mean errors for uniformly l lipshitzian asymptotically hemi pseudocontractive mappings are presented

on the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings abstract the purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in banach spaces the results presented in this paper extend and improve the corresponding results of h bauschke the approximation of fixed points of compositions of nonexpansive mappings in hilbert space j math anal appl 202 1996 150 159 b halpern fixed points of nonexpansive maps bull amer math soc 73 1967 957 961 p l lions approximation de points fixes de contractions c r acad sci paris ser a 284 1977 1357 1359 s reich strong convergence theorems for resolvents of accretive operators in banach spaces j math anal appl 75 1980 287 292 z h sun strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings j math anal appl 286 2003 351 358 r wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 h k xu m g ori an implicit iterative process for nonexpansive mappings numer funct anal optimiz 22 2001 767 773 y y zhou s s chang convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in banach spaces numer funct anal optimiz 23 2002 911 921

strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings in the present paper we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex banach space requiring one member t in the family to be semi compact our results extend and improve some recent results

some convergence theorems of non implicit iteration process with errors for a finite families of i asymptotically nonexpansive mappings the purpose of this paper is to study the weak and strong convergence of non implicit iteration process with errors to a common fixed point for a finite family of i asymptotically quasi nonexpansive mappings in banach spaces the results presented in this paper extend and improve the corresponding results of several authors 1 2 7 14 17 19 22 29

parameter estimations in linear failure rate model using masked data estimations of the parameters included in the lifetime distributions of the individual components in a series system with independent and nonidentical components are introduced in this paper by using masked system life data particularly we deduce the maximum likelihood and bayes estimates of these parameters when the failure rates of the system components are assumed to be linear with different parameters in bayes approach it is assumed that the unknown parameters to be estimated behave as independent random variables having symmetrical triangular prior distributions the problem is illustrated on a two component series system to show how one can apply the theoretical results obtained here numerical simulation study is introduced also in such simulation study a comparison between the procedures used is discussed

a graphical procedure for determining nonstationarity in time series abstract integrated processes as models for time series data have proved to be an important component of the highly flexible class of arima p d q models determining the amount of differencing d has been a difficult task too little and the process is not yet second order stationary too much and the process is more variable than it need be it is shown that by introducing the notion of generalized covariances developed by matheron 1973 for spatial processes the amount of differencing needed can be read easily from a sequence of graphs showing averages of squares of primary data increments formal inference to determine if the last difference really is necessary can then be carried out time series data are analyzed in this way and compared with the hypothesis testing approach illustrated by dickey bell and miller 1986 once the order of differencing has been diagnosed either the differenced time series can be analyzed or the generalized covariance of the undifferenced series can be estimated

hyperdimensional data analysis using parallel coordinates abstract this article presents the basic results of using the parallel coordinate representation as a high dimensional data analysis tool several alternatives are reviewed the basic algorithm for parallel coordinates is laid out and a discussion of its properties as a projective transformation is given several duality results are discussed along with their interpretations as data analysis tools permutations of the parallel coordinate axes are discussed and some examples are given some extensions of the parallel coordinate idea are given the article closes with a discussion of implementation and some of my experiences

approximation methods for common fixed points of nonexpansive mappings in hilbert spaces abstract the aim of this work is to propose implicit and explicit viscosity like methods for finding specific common fixed points of infinite countable families of nonexpansive self mappings in hilbert spaces two numerical approaches to solving this problem are considered an implicit anchor like algorithm and a nonimplicit one the considered methods appear to be of practical interests from the numerical point of view and strong convergence results are proved

convergence theorems for common fixed points of asymptotically quasi nonexpansive mappings in convex metric spaces abstract in this paper we consider an implicit iteration process to approximate the common fixed points of two finite families of asymptotically quasi nonexpansive mappings in convex metric spaces as a consequence of our result we obtain some related convergence theorems our results generalize some recent results of khan and ahmed 4 khan et al 6 sun 12 wittmann 14 and xu and ori 15

explicit averaging cyclic algorithm for common fixed points of asymptotically strictly pseudocontractive maps weak and strong convergence theorems for the approximation of common fixed points of a finite family of asymptotically strictly pseudocontractive mappings are proved in hilbert spaces using an explicit averaging cyclic algorithm

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

estimation of components reliability in a parallel system using masked system life data in this paper we estimate the reliability of the individual components that belong to a parallel system using masked system life test data in particular we compute the maximum likelihood and bayes estimates of component reliabilities the considered system consists of j independent components having non identical complementary exponential lifetime distributions it is assumed for bayes estimates that the unknown parameters are independent random variables having symmetrical triangle probability density functions the approaches are illustrated with a two component parallel system a numerical simulation study is introduced to show how one can use the present approaches to compute these estimations for a practical problem also in the numerical simulation study a comparison between bayes and maximum likelihood estimates is introduced

estimations of the parameters in a three non independent component series system subjected to sources of shocks bayes estimators for the parameters included in a three non independent and non identical component series system subjected to four sources of fatal shocks are presented in this paper also the bayes estimators for the values of reliability functions of the system components are deduced uniform prior distributions are assumed for the unknown parameters to be estimated numerical simulation study is made to explain how one can utilize the theoretical results obtained

bayesian estimation of the parameters in n non independent and non identical series system in this paper we have presented a bayesian approach for estimating the unknown parameters in a n non independent and non identical series system subjected to n 1 sources of fatal shocks also the estimators of the values of the survival functions are deduced the corresponding estimators of the similar system subjected to exponential fatal shocks are given and during this process the gamma prior density function is used special cases of the present results are obtained to show how the current results generalized the results in other literatures

the equivalence of the convergence of four kinds of iterations for a finite family of uniformly asymptotically o pseudocontractive mappings in this paper we prove the equivalences of the strong convergence each other the modified mann iterative process with errors the modified ishikawa iterative process with errors the implicit iterative process with errors and the composite implicit iterative process with errors for a finite family of uniformly asymptotically o pseudocontractive mappings in arbitrary real banach space the results presented in this paper generalize and improve the corresponding results of roades soltuz and huang

weak and strong convergence of the ishikawa iterative process for a finite family of asymptotically nonexpansive mappings abstract in this paper we introduce an ishikawa implicit iterative process with errors for a finite family of n asymptotically nonexpansive mappings as follows x n 1 n n x n 1 n t i n k n y n n u n y n 1 n n x n n t i n k n x n n v n n 1 where for any n n fixed k n 1 denotes the quotient of the division of n by n and i n the rest i e n k n 1 n i n i n 1 n the sequences n n n n are four real sequences in 0 1 satisfying n n 1 and n n 1 for all n 1 un vn are two bounded sequences and x0 is a given point in the setting of uniformly convex banach spaces we give some results of weak and strong convergence of the above iterative process the results presented here are situated on the line of research of the corresponding results of sun j math anal appl 286 1 2003 351 358 osilike j math anal appl 294 1 2004 73 81 chang et al j math anal appl 313 1 2006 273 283 gu j math anal appl 329 2 2007 766 776 huang and noor appl math comput 190 1 2007 356 361 su and qin appl math comput 186 1 2007 271 278 zhou et al appl math comput 173 1 2006 196 212 and some others

graphical methods for censored data abstract various methods of graphically portraying censored data are discussed these include smoothing and model checking many existing graphical methods may be expressed as functionals of the empirical distribution function when the data are subject to censoring the kaplan meier estimator of the distribution may replace the empirical distribution in these methods the plots and problems that arise from such a substitution will be discussed

a new approximation method for common fixed points of a finite family of asymptotically quasi nonexpansive mappings in banach spaces in this paper we consider a new iterative scheme to approximate a common fixed point for a finite family of asymptotically quasi nonexpansive mappings we prove several strong and weak convergence results of the proposed iteration in banach spaces these results generalize and refine many known results in the current literature

partially linear hazard regression for multivariate survival data this article studies estimation of partially linear hazard regression models for multivariate survival data a profile pseudo partial likelihood estimation method is proposed under the marginal hazard model framework the estimation on the parameters for the linear part is accomplished by maximization of a pseudo partial likelihood profiled over the nonparametric part this enables us to obtain consistent estimators of the parametric component asymptotic normality is obtained for the estimates of both the linear and nonlinear parts the new technical challenge is that the nonparametric component is indirectly estimated through its integrated derivative function from a local polynomial fit an algorithm of fast implementation of our proposed method is presented consistent standard error estimates using sandwich type ideas are also developed which facilitates inferences for the model it is shown that the nonparametric component can be estimated as well as if the parametric components were known and the

multivariate profile charts for statistical process control the multivariate profile mp chart is a new control chart for simultaneous display of univariate and multivariate statistics it is designed to analyze and display extended structures of statistical process control data for various cases of grouping reference distribution and use of nominal specifications for each group of observations the scaled deviations from reference values are portrayed together as a modified profile plot symbol the vertical location of the symbol is determined by the multivariate distance of the vector of means from the reference values the graphical display in the mp chart enjoys improved visual characteristics as compared with previously suggested methods moreover the perceptual tasks required by the use of the mp chart provide higher accuracy in retrieving the quantitative information this graphical display is used to display other combined univariate and multivariate statistics such as measures of dispersion principal components and cumulative sums

existence and multiplicity of solutions of semilinear elliptic equations the existence and multiplicity results of solutions are obtained by the reduction method and the minimax methods for nonautonomous semilinear elliptic dirichlet boundary value problem some well known results are generalized

approximation of common fixed points for finite families of total asymptotically nonexpansive mappings abstract let e be a real banach space k a closed convex nonempty subset of e let t 1 t 2 t m k k be m total asymptotically nonexpansive mappings an iterative sequence for approximation of common fixed points assuming existence of t 1 t 2 t m is constructed necessary and sufficient conditions for the convergence of the scheme to a common fixed point of the mappings are given furthermore in the case that e is uniformly convex a sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is established

bayesian estimation and prediction using asymmetric loss functions abstract estimators and predictors that are optimal relative to varian s asymmetric linex loss function are derived for a number of well known models their risk functions and bayes risks are derived and compared with those of usual estimators and predictors it is shown that some usual estimators for example a scalar sample mean or a scalar least squares regression coefficient estimator are inadmissible relative to asymmetric linex loss by providing alternative estimators that dominate them uniformly in terms of risk

graphical perception theory experimentation and application to the development of graphical methods abstract the subject of graphical methods for data analysis and for data presentation needs a scientific foundation in this article we take a few steps in the direction of establishing such a foundation our approach is based on graphical perception the visual decoding of information encoded on graphs and it includes both theory and experimentation to test the theory the theory deals with a small but important piece of the whole process of graphical perception the first part is an identification of a set of elementary perceptual tasks that are carried out when people extract quantitative information from graphs the second part is an ordering of the tasks on the basis of how accurately people perform them elements of the theory are tested by experimentation in which subjects record their judgments of the quantitative information on graphs the experiments validate these elements but also suggest that the set of elementary tasks should be expanded the theory provides a guideline for graph construction

adaptive regression splines in the cox model we develop a method for constructing adaptive regression spline models for the exploration of survival data the method combines cox s 1972 journal of the royal statistical society series b 34 187 200 regression model with a weighted least squares version of the multivariate adaptive regressi on spline mars technique of friedman 1991 annals of statistics 19 1 141 to adaptively select the knots and covariates the new technique can automatically fit models with terms that represent nonlinear effects and interactions among covariates applications based on simulated data and data from a clinical trial for myeloma are presented results from the myeloma application identified several important prognostic variables including a possible nonmonotone relationship with survival in one laboratory variable results are compared to those from the adaptive hazard regression hare method of kooperberg stone and truong 1995 journal of the american statistical association 90 78 94

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

parameter estimations in a general hazard rate model using masked data the general hazard rate model is a relevant model to specify the life time distributions in reliability theory and life testing in this paper we use masked data to obtain estimations of the unknown parameters included in life time distributions of the individual components belonging to a series system consists of j independent and non identical components it is assumed here that the failure rate of component j is general with the form h j t a j b jt c j 1 j 1 2 j where a j b j c j are non negative parameters maximum likelihood and bayes estimates of the parameters a j b j are obtained while c j are known symmetrical triangular prior distributions are assumed for the unknown parameters to be estimated in obtaining the bayes estimators for these parameters a large simulation study is done in order to i explain how one can utilize the theoretical results obtained and ii compare the two procedures used the problem of estimating the unknown parameters included in increasing linear failure rate model can be obtained as special case by setting c j 2 for all j 1 2 j

on the convergence theorems of implicit iteration process for a finite family of i asymptotically nonexpansive mappings in this paper we consider the weak and strong convergence of implicit iteration process to a common fixed point of i asymptotically nonexpansive mappings the main results extend to a finite family of i asymptotically nonexpansive mappings in a banach space

graphical exploration of covariate effects on survival data through nonparametric quantile curves kaplan meier curves provide an effective means of presenting the distributional pattern in a sample of survival data however in order to assess the effect of a covariate a standard scatterplot is often difficult to interpret because of the presence of censored observations several authors have proposed a running median as an effective way of indicating the effect of a covariate this article proposes a form of kernel estimation employing double smoothing that can be applied in a simple and efficient manner to construct an estimator of a percentile of the survival distribution as a function of one or two covariates permutations and bootstrap samples can be used to construct reference bands that help identify whether particular features of the estimates indicate real features of the underlying curve or whether this may be due simply to random variation the techniques are illustrated on data from a study of kidney transplant patients

on graphical tests for proportionality of hazards in two samples in this paper we present a class of graphical tests of the proportional hazards hypothesis for two sample censored survival data the proposed tests are improvements over some existing tests based on asymptotic confidence bands of certain functions of the estimated cumulative hazard functions the new methods are based on the comparison of unrestricted estimates of the said functions and their restricted versions under the hypothesis they combine the rigour of analytical tests with the descriptive value of plots monte carlo simulations suggest that the proposed asymptotic procedures have reasonable small sample properties the power is much higher than existing graphical tests and comparable with existing analytical tests the method is then illustrated through the analysis of a data set on bone marrow transplantation for leukemia patients

explicit iteration method for common fixed points of a finite family of nonself asymptotically nonexpansive mappings suppose that k is a nonempty closed convex subset of a real uniformly convex banach space e which is also a nonexpansive retract of e with nonexpansive retraction p let t i i i be n nonself asymptotically nonexpansive mappings from k to e such that f x k t ix x i i f where i 1 2 n from arbitrary x 0 k x n is defined by x n p 1 a n x n 1 a nt n pt n m 1x n 1 n 1 where n m 1 n i t n t n m o d n t i i i the modn function takes values in i a n is a real sequence in d 1 d for some d 0 1 some strong and weak convergence theorems of x n to some q f are obtained under some suitable conditions in real uniformly convex banach spaces