proportional means regression for censored medical costs summary the semiparametric proportional means model specifies that the mean function for the cumulative medical cost over time conditional on a set of covariates is equal to an arbitrary baseline mean function multiplied by an exponential regression function we demonstrate how to estimate the vector valued regression parameter using possibly censored lifetime costs the estimator is consistent and asymptotically normal with an easily estimable covariance matrix simulation studies show that the proposed methodology is appropriate for practical use an application to aids is provided

estimating medical costs with censored data incompleteness of follow up data is a common problem in estimating medical costs naive analysis using summary statistics on the collected data can result in severely misleading statistical inference this paper focuses on the problem of estimating the mean medical cost from a sample of individuals whose medical costs may be right censored a class of weighted estimators which account appropriately for censoring are introduced our estimators are shown to be consistent and asymptotically normal with easily estimated variances the efficiency of these estimators is studied with the goal of finding as efficient an estimator for the mean medical cost as is feasible extensive simulation studies are used to show that our estimators perform well in finite samples even with heavily censored data for a variety of circumstances the methods are applied to a set of cost data from a cardiology trial conducted by the duke university medical center extensions to other censored data problems are also discussed

plurality voting based multiple classifier systems statistically independent with respect to dependent classifier sets abstract the simultaneous use of multiple classifiers has been shown to provide performance improvement in classification problems the selection of an optimal set of classifiers is an important part of multiple classifier systems and the independence of classifier outputs is generally considered to be an advantage for obtaining better multiple classifier systems in this paper the need for the classifier independence is interrogated from classification performance point of view the performance achieved with the use of classifiers having independent joint distributions is compared to some other classifiers which are defined to have best and worst joint distributions these distributions are obtained by formulating the combination operation as an optimization problem the analysis revealed several important observations about classifier selection which are then used to analyze the problem of selecting an additional classifier to be used with the available multiple classifier system

learn mf a random subspace approach for the missing feature problem we introduce learn mf an ensemble of classifiers based algorithm that employs random subspace selection to address the missing feature problem in supervised classification unlike most established approaches learn mf does not replace missing values with estimated ones and hence does not need specific assumptions on the underlying data distribution instead it trains an ensemble of classifiers each on a random subset of the available features instances with missing values are classified by the majority voting of those classifiers whose training data did not include the missing features we show that learn mf can accommodate substantial amount of missing data and with only gradual decline in performance as the amount of missing data increases we also analyze the effect of the cardinality of the random feature subsets and the ensemble size on algorithm performance finally we discuss the conditions under which the proposed approach is most effective

iterative boolean combination of classifiers in the roc space an application to anomaly detection with hmms hidden markov models hmms have been shown to provide a high level performance for detecting anomalies in sequences of system calls to the operating system kernel using boolean conjunction and disjunction functions to combine the responses of multiple hmms in the roc space may significantly improve performance over a single best hmm however these techniques assume that the classifiers are conditional independent and their of roc curves are convex these assumptions are violated in most real world applications especially when classifiers are designed using limited and imbalanced training data in this paper the iterative boolean combination ibc technique is proposed for efficient fusion of the responses from multiple classifiers in the roc space it applies all boolean functions to combine the roc curves corresponding to multiple classifiers requires no prior assumptions and its time complexity is linear with the number of classifiers the results of computer simulations conducted on both synthetic and real world host based intrusion detection data indicate that the ibc of responses from multiple hmms can achieve a significantly higher level of performance than the boolean conjunction and disjunction combinations especially when training data are limited and imbalanced the proposed ibc is general in that it can be employed to combine diverse responses of any crisp or soft one or two class classifiers and for wide range of application domains

decision combination in multiple classifier systems a multiple classifier system is a powerful solution to difficult pattern recognition problems involving large class sets and noisy input because it allows simultaneous use of arbitrary feature descriptors and classification procedures decisions by the classifiers can be represented as rankings of classifiers and different instances of a problem the rankings can be combined by methods that either reduce or rerank a given set of classes an intersection method and union method are proposed for class set reduction three methods based on the highest rank the borda count and logistic regression are proposed for class set reranking these methods have been tested in applications of degraded machine printed characters and works from large lexicons resulting in substantial improvement in overall correctness

efficient estimation of the distribution of quality adjusted survival time quality of life is an important aspect in evaluation of clinical trials of chronic diseases such as cancer and aids quality adjusted survival analysis is a method that combines both the quantity and quality of a patient s life into one single measure in this paper we discuss the efficiency of weighted estimators for the distribution of quality adjusted survival time using the general representation theorem for missing data processes we are able to derive an estimator that is more efficient than the one proposed in zhao and tsiatis 1997 biometrika 84 339 348 simulation experiments are conducted to assess the small sample properties of this estimator and to compare it with the semiparametric efficiency bound the value of this estimator is demonstrated from an application of the method to a data set obtained from a breast cancer clinical trial

a statistical unified framework for rank based multiple classifier decision combination abstract this study presents a theoretical investigation of the rank based multiple classifier decision combination problem with the aim of providing a unified framework to understand a variety of such systems the combination of the decisions of more than one classifiers with the aim of improving overall system performance is a concept of general interest in pattern recognition as a viable alternative to designing a single sophisticated classifier the problem of combining the classifier decisions in the raw form of candidate class rankings is formulated as a discrete optimization problem the objective function to be maximized is selected as the overall probability of correct decision this formulation introduces a set of observation statistics about the joint behavior of the classifiers which are to be estimated by observing the classifiers operated on a cross validation test set the resulting binary programming problem is shown to have a simple and global optimum solution but which also necessitates a prohibitive number of observation statistics from the objective function expansion the problem observation space is defined and a method based on partitioning is introduced to reduce its prohibitive dimensionality within this partitioning formalism called as the partitioned observation space pos theory the number of behavior observation statistics can be reduced to levels which are feasible to estimate from the available cross validation test data it is shown by examples that such specific partitionings can be defined when reasonable assumptions or prior knowledge about the classifiers are incorporated into the problem domain it is also demonstrated that certain specific partitionings of the classifier observation space effectively lead to the highest rank borda count and logistic regression rank based decision combination methods from the literature the analysis presented is general and promises to lead to a class of algorithms for rank based decision combination the potential of the theory and practical issues in implementation are illustrated by applying it in a real life phonetic discrimination problem from speech pattern classification with encouraging results

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

semi parametric regression models for cost effectiveness analysis improving the efficiency of estimation from censored data in a cost effectiveness analysis using clinical trial data estimates of the between treatment difference in mean cost and mean effectiveness are needed several methods for handling censored data have been suggested one of them is inverse probability weighting and has the advantage that it can also be applied to estimate the parameters from a linear regression of the mean such regression models can potentially estimate the treatment contrast more precisely since some of the residual variance can be explained by baseline covariates the drawback however is that inverse probability weighting may not be efficient using existing results on semi parametric efficiency this paper derives the semi parametric efficient parameter estimates for regression of mean cost mean quality adjusted survival time and mean survival time the performance of these estimates is evaluated through a simulation study applying both the new estimators and the inverse probability weighted estimators to the results of the evaluate trial showed that the new estimators achieved a halving of the variance of the estimated treatment contrast for cost some practical suggestions for choosing an estimator are offered

estimating medical costs from incomplete follow up data estimation of the average total cost for treating patients with a particular disease is often complicated by the fact that the survival times are censored on some study subjects and their subsequent costs are unknown the naive sample average of the observed costs from all study subjects or from the uncensored cases only can be severely biased and the standard survival analysis techniques are not applicable to minimize the bias induced by censoring we partition the entire time period of interest into a number of small intervals and estimate the average total cost either by the sum of the kaplan meier estimator for the probability of dying in each interval multiplied by the sample mean of the total costs from the observed deaths in that interval or by the sum of the kaplan meier estimator for the probability of being alive at the start of each interval multiplied by an appropriate estimator for the average cost over the interval conditional on surviving to the start of the interval the resultant estimators are consistent if censoring occurs solely at the boundaries of the intervals in addition the estimators are asymptotically normal with easily estimated variances extensive numerical studies show that the asymptotic approximations are adequate for practical use and the biases of the proposed estimators are small even when censoring may occur in the interiors of the intervals an ovarian cancer study is provided

a note on approximation properties of q durrmeyer operators in this paper the approximation properties of q durrmeyer operators d n q f x for f c 0 1 are discussed the exact class of continuous functions satisfying approximation process lim n d n q f x f x is determined the results of the paper provide an elaboration of the previously known ones on operators d n q

a theoretical study on six classifier fusion strategies we look at a single point in feature space two classes and l classifiers estimating the posterior probability for class spl omega sub 1 assuming that the estimates are independent and identically distributed normal or uniform we give formulas for the classification error for the following fusion methods average minimum maximum median majority vote and oracle

theoretical bounds of majority voting performance for a binary classification problem a number of earlier studies that have attempted a theoretical analysis of majority voting assume independence of the classifiers we formulate the majority voting problem as an optimization problem with linear constraints no assumptions on the independence of classifiers are made for a binary classification problem given the accuracies of the classifiers in the team the theoretical upper and lower bounds for performance obtained by combining them through majority voting are shown to be solutions of the corresponding optimization problem the objective function of the optimization problem is nonlinear in the case of an even number of classifiers when rejection is allowed for the other cases the objective function is linear and hence the problem is a linear program lp using the framework we provide some insights and investigate the relationship between two candidate classifier diversity measures and majority voting performance

joint regression analysis of survival and quality adjusted survival summary in this paper a semiparametric bivariate linear regression model for survival and quality adjusted survival is investigated even with a parametric specification for the joint distribution maximum likelihood is not applicable because of induced informative censoring we propose inference procedures based on estimating functions the estimators are consistent and asymptotically normal hypothesis tests and confidence intervals may be constructed with easy to implement resampling techniques simultaneous regression modeling of survival and quality adjusted survival has not been studied formally our methodology gives parameter estimates that are highly interpretable in the context of a cost effectiveness analysis the usefulness of the proposal is illustrated with a breast cancer dataset

regression and ordered categorical variables read before the royal statistical society by professor r l plackett on behalf of the late professor anderson at a meeting organized by the research section on wednesday october 5th 1983 professor j b copas in the chair summary a general approach to regression modelling for ordered categorical response variables y is given which is equally applicable to ordered and unordered y the regressor variables xt xi x may be continuous or categorical the method is based on the logistic family which contains a hierarchy of regression models ranging from ordered to unordered models ordered properties of the former the stereotype model are established the choice between models is made empirically on the basis of model fit this is particularly important for assessed ordered categorical response variables where it is not obvious a priori whether or not the ordering is relevant to the regression relationship model simplification is investigated in terms of whether or not the response categories are distinguishable with respect to x the models are fitted iteratively using the method of maximum likelihood examples are given

q bernstein polynomials of the cauchy kernel due to the fact that in the case q 1 q bernstein polynomials are not positive linear operators on c 0 1 the study of their approximation properties is essentially more difficult than that for 0 1 is still open in this paper the q bernstein polynomials bn q fa z of the cauchy kernel fa 1 z a a c 0 1 are found explicitly and their properties are investigated in particular it is proved that if q 1 then polynomials bn q fa z converge to fa uniformly on any compact set k z z a the sequence bn q fa z is not even uniformly bounded

saturation of convergence for q bernstein polynomials in the case q 1 abstract in the note we discuss voronovskaya type theorem and saturation of convergence for q bernstein polynomials for a function analytic in the disc u r z z r r q for arbitrary fixed q 1 we give explicit formulas of voronovskaya type for the q bernstein polynomials for q 1 we show that the rate of convergence for the q bernstein polynomials is o q n q 1 for infinite number of points having an accumulation point on u r q if and only if f is linear

handwritten numerical recognition based on multiple algorithms abstract in this paper the authors combine two algorithms for application to the recognition of unconstrained isolated handwritten numerals the first algorithm employs a modified quadratic discriminant function utilizing direction sensitive spatial features of the numeral image the second algorithm utilizes features derived from the profile of the character in a structural configuration to recognize the numerals while both algorithms yield very low error rates the authors combine the two algorithms in different ways to study the best polling strategy and realize very low error rates 0 2 or less and rejection rates below 4

how large should ensembles of classifiers be we propose to determine the size of a parallel ensemble by estimating the minimum number of classifiers that are required to obtain stable aggregate predictions assuming that majority voting is used a statistical description of the convergence of the ensemble prediction to its asymptotic infinite size limit is given the analysis of the voting process shows that for most test instances the ensemble prediction stabilizes after only a few classifiers are polled by contrast a small but non negligible fraction of these instances require large numbers of classifier queries to reach stable predictions specifically the fraction of instances whose stable predictions require more than t classifiers for email protected 1 has a universal form and is proportional to t 1 2 the ensemble size is determined as the minimum number of classifiers that are needed to estimate the infinite ensemble prediction at an average confidence level a close to one this approach differs from previous proposals which are based on determining the size for which the prediction error not the predictions themselves stabilizes in particular it does not require estimates of the generalization performance of the ensemble which can be unreliable it has general validity because it is based solely on the statistical description of the convergence of majority voting to its asymptotic limit extensive experiments using representative parallel ensembles bagging and random forest illustrate the application of the proposed framework in a wide range of classification problems these experiments show that the optimal ensemble size is very sensitive to the particular classification problem considered

semiparametric efficiency in multivariate regression models with missing data abstract we consider the efficiency bound for the estimation of the parameters of semiparametric models defined solely by restrictions on the means of a vector of correlated outcomes y when the data on y are missing at random we show that the semiparametric variance bound is the asymptotic variance of the optimal estimator in a class of inverse probability of censoring weighted estimators and that this bound is unchanged if the data are missing completely at random for this case we study the asymptotic performance of the generalized estimating equations gee estimators of mean parameters and show that the optimal gee estimator is inefficient except for special cases the optimal weighted estimator depends on unknown population quantities but for monotone missing data we propose an adaptive estimator whose asymptotic variance can achieve the bound

on the analyticity of functions approximated by their q bernstein polynomials when q 1 abstract since in the case q 1 the q bernstein polynomials bn q are not positive linear operators on c 0 1 the investigation of their convergence properties for q 1 turns out to be much harder than the one for 0 1 create a serious obstacle for the numerical experiments with the q bernstein polynomials despite the intensive research conducted in the area lately the class of functions which are uniformly approximated by their q bernstein polynomials on 0 1 is yet to be described in this paper we prove that if f 0 1 c is analytic at 0 and can be uniformly approximated by its q bernstein polynomials q 1 on 0 1 then f admits an analytic continuation from 0 1 into z z

parametric modelling of cost data in medical studies the cost of medical resources used is often recorded for each patient in clinical studies in order to inform decision making although cost data are generally skewed to the right interest is in making inferences about the population mean cost common methods for non normal data such as data transformation assuming asymptotic normality of the sample mean or non parametric bootstrapping are not ideal this paper describes possible parametric models for analysing cost data four example data sets are considered which have different sample sizes and degrees of skewness normal gamma log normal and log logistic distributions are fitted together with three parameter versions of the latter three distributions maximum likelihood estimates of the population mean are found confidence intervals are derived by a parametric bca bootstrap and checked by mcmc methods differences between model fits and inferences are explored skewed parametric distributions fit cost data better than the normal distribution and should in principle be preferred for estimating the population mean cost however for some data sets we find that models that fit badly can give similar inferences to those that fit well conversely particularly when sample sizes are not large different parametric models that fit the data equally well can lead to substantially different inferences we conclude that inferences are sensitive to choice of statistical model which itself can remain uncertain unless there is enough data to model the tail of the distribution accurately investigating the sensitivity of conclusions to choice of model should thus be an essential component of analysing cost data in practice copyright 2004 john wiley sons ltd

the q bernstein polynomials of the cauchy kernel with a pole on 0 1 in the case q 1 the problem to describe the bernstein polynomials of unbounded functions goes back to lorentz the aim of this paper is to investigate the convergence properties of the q bernstein polynomials b n q f x of the cauchy kernel email protected with a pole email protected 0 1 for q 1 the previously obtained results allow one to describe these properties when a pole is different from q m for some email protected 0 1 2 in this context the focus of the paper is on the behavior of polynomials b n q f x for the functions of the form f m x 1 x q m x q m and f m q m a email protected r here the problem is examined both theoretically and numerically in detail

ssc a classifier combination method based on signal strength we propose a new classifier combination method the signal strength based combining ssc approach to combine the outputs of multiple classifiers to support the decision making process in classification tasks as ensemble learning methods have attracted growing attention from both academia and industry recently it is critical to understand the fundamental issues of the combining rule motivated by the signal strength concept our proposed ssc algorithm can effectively integrate the individual vote from different classifiers in an ensemble learning system comparative studies of our method with nine major existing combining rules namely geometric average rule arithmetic average rule median value rule majority voting rule borda count max and min rule weighted average and weighted majority voting rules is presented furthermore we also discuss the relationship of the proposed method with respect to margin based classifiers including the boosting method adaboost m1 and adaboost m2 and support vector machines by margin analysis detailed analyses of margin distribution graphs are presented to discuss the characteristics of the proposed method simulation results for various real world datasets illustrate the effectiveness of the proposed method

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

median regression with censored cost data because of the skewness of the distribution of medical costs we consider modeling the median as well as other quantiles when establishing regression relationships to covariates in many applications the medical cost data are also right censored in this article we propose semiparametric procedures for estimating the parameters in median regression models based on weighted estimating equations when censoring is present numerical studies are conducted to show that our estimators perform well with small samples and the resulting inference is reliable in circumstances of practical importance the methods are applied to a dataset for medical costs of patients with colorectal cancer

calibration regression of censored lifetime medical cost analysis of lifetime medical cost is challenged by its irregular distribution and by incomplete follow up particularly the latter with limited study duration as is typical in medical research this article proposes the so called calibration regression to address these issues by modeling not only lifetime medical cost but also survival time in a semiparametric fashion it is postulated that both outcomes on possibly transformed scales linearly relate to the covariates however the bivariate model error distribution is completely unspecified whereas this conceptually simple model is a natural multivariate generalization of the accelerated failure time model this article proposes an inference procedure by extending the weighted log rank estimating function to the marked point process framework the resulting estimators are consistent and asymptotically normal in addition robustness and efficiency issues are discussed furthermore a novel sample based variance estimation procedure is proposed for es

graphical methods for assessing logistic regression models abstract in ordinary linear regression graphical diagnostic displays can be very useful for detecting and examining anomalous features in the fit of a model to data for logistic regression models the discreteness of binary data makes it difficult to interpret such displays modifications and extensions of linear model displays lead to three methods for diagnostic checking of logistic regression models local mean deviance plots are useful for detecting overall lack of fit empirical probability plots help point out isolated departures from the fitted model partial residual plots when smoothed to show underlying structure help identify specific causes of lack of fit these methods are illustrated through the analyses of simulated and real data

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

multiclass from binary expanding one versus all one versus one and ecoc based approaches recently there has been a lot of success in the development of effective binary classifiers although many statistical classification techniques have natural multiclass extensions some such as the support vector machines do not the existing techniques for mapping multiclass problems onto a set of simpler binary classification problems run into serious efficiency problems when there are hundreds or even thousands of classes and these are the scenarios where this paper s contributions shine we introduce the concept of correlation and joint probability of base binary learners we learn these properties during the training stage group the binary leaner s based on their independence and with a bayesian approach combine the results to predict the class of a new instance finally we also discuss two additional strategies one to reduce the number of required base learners in the multiclass classification and another to find new base learners that might best complement the existing set we use these two new procedures iteratively to complement the initial solution and improve the overall performance this paper has two goals finding the most discriminative binary classifiers to solve a multiclass problem and keeping up the efficiency i e small number of base learners we validate and compare the method with a diverse set of methods of the literature in several public available datasets that range from small 10 to 26 classes to large multiclass problems 1000 classes always using simple reproducible scenarios