a fitting algorithm for markov modulated poisson processes having two arrival rates abstract point processes with fluctuating arrival rates arise in many current applications of queueing theory notably in communications modeling markov modulated poisson processes mmpp have been used to describe such processes because they incorporate a mechanism to account for the temporal inhomogeneity of the arrival rates yet yield analytically tractable queueing results an iterative statistical procedure is developed for fitting mmpp having two arrival rates to observational data the procedure is largely numerical experimental and is motivated by maximum likelihood estimation

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

interval number and fuzzy number linear programmings abstract in this paper we focus on two kinds of linear programmings with fuzzy numbers they are called interval number and fuzzy number linear programmings respectively the problems of linear programmings with interval number coefficients are approached by taking maximum value range and minimum value range inequalities as constraint conditions reduced it into two classical linear programmings and obtained an optimal interval solution to it the problems of fuzzy linear programming with fuzzy number coefficients are approached in two ways i e fuzzy decisive set approach and interval number linear programming approach for several membership levels finally we gave the numerical solutions of the illustrative examples

ranking engineering design concepts using a fuzzy outranking preference model abstract the conceptual design evaluation is important since the poor selection of a design concept can rarely be compensated at later design stages due to subjective and incomplete design information collected at the early design stage it is difficult to select the best design concepts from a number of alternatives to tackle this problem an outranking preference model based on the possibility theory is developed in this paper the fuzzy outranking relation is developed to model the imprecise preference relation between each pair of design concepts a design concept outranked others if and only if there is sufficient evidence to support that the concept is superior or at least equal to the others according to the fuzzy outranking relation identified between each pair of design concepts three types of indices are developed to determine the non dominated design concepts for continuous improvement or further development at later design stages moreover the sensitivity analysis is used to examine the robustness of the result the fuzzy outranking preference model developed is more suitable to be used for concept selection in the imprecise and uncertain design environment

discrete time expectation maximization algorithms for markov modulated poisson processes in this paper we consider parameter estimation markov modulated poisson processes via robust filtering and smoothing techniques using the expectation maximization algorithm framework our filters and smoothers can be applied to estimate the parameters of our model in either an online configuration or an offline configuration further our estimator dynamics do not involve stochastic integrals and our new formulas in terms of time integrals are easily discretized and are written in numerically stable forms in w p malcolm r j elliott and j van der hoek ldquoon the numerical stability of time discretized state estimation via clark transformations rdquo presented at the ieee conf decision control mauii hi dec 2003

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

universal classification for hidden markov models binary hypotheses testing using empirically observed statistics is studied in the neyman pearson formulation for the hidden markov model hmm an asymptotically optimal decision rule is proposed and compared to the generalized likelihood ratio test glrt which has been shown in earlier studies to be asymptotically optimal for simpler parametric families the proof of the main theorem is provided the result can be applied to several types of hmms commonly used in speech recognition and communication applications several applications are demonstrated

constructing membership functions using statistical data abstract determination of the membership functions is vital in practical applications of the fuzzy set theory this paper presents a guideline to construct the membership functions for fuzzy sets whose elements have a defining feature with a known probability density function pdf in the universe of discourse the method finds the smallest fuzzy set which assigns high average membership values to those objects with the defining features distributed according to the given pdf it is show that for any pdf the method is capable of generating membership functions in accordance with the possibility probability consistency principle membership functions derived from some of the well known pdfs and an application in solving noise contaminated linear system of equations are presented

the minimum sum of absolute errors regression a robust alternative to the least squares regression this paper concerns the minimum sum of absolute errors regression it is a more robust alternative to the popular least squares regression whenever there are outliers in the values of the response variable or the errors follow a long tailed distribution or the loss function is proportional to the absolute errors rather than their squared values we use data from a study of interstitial lung disease to illustrate the method interpret the findings and contrast with least squares regression we point out some of the problems with the least squares analysis and show how to avoid these with the minimum sum of absolute errors analysis

ranking multiple aspect alternatives fuzzy relational equations approach abstract the paper discusses a general approach to the algorithms of ranking multiple aspect alternatives constructed with the aid of fuzzy relational equations it is pointed out that the algorithms can be constructed by considering data sets provided by prototypical situations discriminating properties of the proposed method are also taken into consideration

l sub 1 and l sub infinity minimization via a variant of karmarkar s algorithm simple iterative algorithms are presented for l sub 1 and l sub infinity minimization regression based on a variant of karmarkar s linear programming algorithm although these algorithms are based on entirely different theoretical principles to the popular irls iteratively reweighted least squares algorithm they have almost identical matrix operations also presented are the results of a monte carlo study comparing the numerical convergence properties of the karmarkar algorithm for l sub 1 minimization to those of an irls and a simplex algorithm the test problem involves l sub 1 estimation of ar autoregressive model parameters the karmarkar algorithm outperformed irls by achieving higher numerical accuracy in fewer iterations techniques for reducing the computational cost per iteration of the karmarkar l sub 1 algorithm are discussed

multilevel quantile function modeling with application to birth outcomes summary infants born preterm or small for gestational age have elevated rates of morbidity and mortality using birth certicate records in texas from 2002 2004 and environmental protection agency air pollution estimates we relate the quantile functions of birth weight and gestational age to ozone exposure and multiple predictors including parental age race and education level we introduce a semi parametric bayesian quantile approach that models the full quantile function rather than just a few quantile levels our multilevel quantile function model establishes relationships between birth weight and the predictors separately for each week of gestational age and between gestational age and the predictors separately across texas public health regions we permit these relationships to vary nonlinearly across gestational age spatial domain and quantile level and we unite them in a hierarchical model via a basis expansion on the regression coefficients that preserves interpretability very low birth weight is a primary concern so we leverage extreme value theory to supplement our model in the tail of the distribution gestational ages are rounded into weekly values so we present methodology for modeling quantile functions of discrete response data in a simulation study we show that pooling information across gestational age and quantile level substantially reduces mse of predictor effects relative to standard frequentist quantile regression wend that ozone is negatively associated with the lower tail of gestational age in south texas and across the distribution of birth weight for high gestational ages our methods are available in the r package bsquare

recursive estimation in mixture models with markov regime a recursive algorithm is proposed for estimation of parameters in mixture models where the observations are governed by a hidden markov chain the often badly conditioned information matrix is estimated and its inverse is incorporated into the algorithm the performance of the algorithm is studied by simulations of a symmetric normal mixture the algorithm seems to be stable and produce approximately normally distributed estimates provided the adaptive matrix is kept well conditioned some numerical examples are included

off the beaten track a new linear model for interval data abstract we propose a new linear regression model for interval valued variables the model uses quantile functions to represent the intervals thereby considering the distributions within them in this paper we study the special case where the uniform distribution is assumed in each observed interval and we analyze the extension to the symmetric triangular distribution the parameters of the model are obtained solving a constrained quadratic optimization problem that uses the mallows distance between quantile functions as in the classical case a goodness of fit measure is deduced two applications on up to date fields are presented one predicting duration of unemployment and the other allowing forecasting burned area by forest fires

multiple criteria linear regression the unknown parameters in multiple linear regression models may be estimated using any one of a number of criteria such as the minimization of the sum of squared errors msse the minimization of the sum of absolute errors msae and the minimization of the maximum absolute error mmae at present the msse or the least squares criterion continues to be the most popular however at times the choice of a criterion is not clear from statistical practical or other considerations under such circumstances it may be more appropriate to use multiple criteria rather than a single criterion to estimate the unknown parameters in a multiple linear regression model we motivate the use of multiple criteria estimation in linear regression models with an example propose a few models and outline a solution procedure

estimating regression parameters with imprecise input data in an appraisal context traditional valuation models such as capitalization or comparative share the common principle of using exact information in their calculations however in the professional field it is difficult to find situations characterized by the wealth and precision of the information available within the professional context it is usually necessary to carry out estimates on some of the explanatory variables of pricing even though consciously introducing an important degree of subjectivity the model proposed in this paper which uses the goal programming optimization technique is capable of dealing with imprecise information since it allows to consider intervals to define the values of the explanatory variables additionally this paper presents and demonstrates several propositions that increase the informative capacity of the model presented

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

a finite smoothing algorithm for linear l_1 estimation in this paper a new method for solving the linear l 1 problem is described analysed and tested the method is based on smoothing the nondifferentiable l 1 function the smoothing can be done in a well onditioned manner since the method has finite convergence extensive numerical tests demonstrate significant superiority to existing simplex type codes furthermore the tests show that the new algorithm is very well suited for vector processing

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

a globally and quadratically convergent affine scaling method for linear e 1 problems recently various interior point algorithms related to the karmarkar algorithm have been developed for linear programming in this paper we first show how this interior point philosophy can be adapted to the linear l1 problem in which there are no feasibility constraints to yield a globally and linearly convergent algorithm we then show that the linear algorithm can be modified to provide aglobally and ultimatelyquadratically convergent algorithm this modified algorithm appears to be significantly more efficient in practise than a more straightforward interior point approach via a linear programming formulation we present numerical results to support this claim

bayesian empirical likelihood for quantile regression bayesian inference provides a flexible way of combining data with prior information however quantile regression is not equipped with a parametric likelihood and therefore bayesian inference for quantile regression demands careful investigation this paper considers the bayesian empirical likelihood approach to quantile regression taking the empirical likelihood into a bayesian framework we show that the resultant posterior from any fixed prior is asymptotically normal its mean shrinks toward the true parameter values and its variance approaches that of the maximum empirical likelihood estimator a more interesting case can be made for the bayesian empirical likelihood when informative priors are used to explore commonality across quantiles regression quantiles that are computed separately at each percentile level tend to be highly variable in the data sparse areas e g high or low percentile levels through empirical likelihood the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains by using an mcmc algorithm in the computation we avoid the daunting task of directly maximizing empirical likelihood the finite sample performance of the proposed method is investigated empirically where substantial efficiency gains are demonstrated with informative priors on common features across several percentile levels a theoretical framework of shrinking priors is used in the paper to better understand the power of the proposed method

fuzzy linear regression models for assessing risks of cumulative trauma disorders abstract cumulative trauma disorders ctds are a major problem in industry and today s office environments especially for keyboard users since comprehensive knowledge about individual or a combination of risk factors contributing to ctds of the hand and forearm is still lacking developing methodologies to quantify relationships of risk factors is greatly needed the purpose of this research was to build fuzzy linear regression models to reveal the relationship of ctd risk factors to predict the injuries and to evaluate risk levels of individuals twenty seven keyboard users twenty two for model building and five for model validation and three ctd experts participated in the model building four fuzzy models were built corresponding to four risk categories and a final fuzzy linear model was established using ahp pairwise comparisons multicolinearity effects were addressed and a partial standard deviation scaling method was used to eliminate the effects from a methodological point of view fuzzy linear regression models provide useful insight into risk factors ctd relationship

an overview of the variables selection methods for the minimum sum of absolute errors regression the minimum sum of absolute errors regression is a robust alternative to the least squares regression whenever the errors follow a distribution for which the sample median is a more efficient estimator of location parameter than the sample mean the errors follow a long tailed distribution there are outliers in the values of the response variable in the data or the absolute error loss function is more appropriate than the quadratic loss function often an initial model may contain a large number of variables however in many situations it is neither necessary nor important to include all the variables in the model the methods for variable selection for the minimum sum of absolute errors regression are not as well documented and known as for the least squares regression our objective is to present an overview of the procedures to fit models with fewer variables and some criteria for selecting a model

recursive estimation of parameters in markov modulated poisson processes a hidden markov regime is a markov process that governs the time or space dependent distributions of an observed stochastic process recursive algorithms can be used to estimate parameters in mixed distributions governed by a markov regime the authors derive a recursive algorithm for estimation of parameters in a markov modulated poisson process also called a cox point process by this the authors mean a doubly stochastic poisson process with a time dependent intensity that can take on a finite number of different values the intensity switches randomly between the possible values according to a markov process the authors consider two different ways to observe the markov modulated poisson process in the first model the observations consist of the observed time intervals between events and in the second model they use the total number of events in successive intervals of fixed length they derive an algorithm for recursive estimation of the poisson intensities and the switch intensities between the two states and illustrate the algorithm in a simulation study the estimates of the switch intensities are based on the observed conditional switch probabilities

real time fuzzy regression analysis a convex hull approach abstract in this study we present an enhancement of fuzzy regression analysis with regard to its aspect of real time processing let us recall that fuzzy regression generalizes the concept of classical numeric regression in the sense of bringing additional capabilities that allow the model to deal with fuzzy granular data we show that a convex hull method provides a useful vehicle to reduce computing time which becomes of particular relevance in case of real time data analysis our objective is to develop an efficient real time fuzzy regression analysis based on the use of convex hull specifically a beneath beyond algorithm in this algorithm the re construction of convex hull edges depends on incoming vertices while a re computing procedure can be realized in real time we demonstrate the use of the developed enhancement to application to unit performance assessment and air pollution data an important role of convex hull is contrasted with the limitations of linear programming used in the standard regression

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

quasi maximum likelihood estimation for conditional quantiles in this paper we derive the asymptotic distribution of a new class of quasi maximum likelihood estimators qmle based on a tick exponential family of densities we show that the tick exponential assumption is a necessary and sufficient condition for a qmle to be consistent for the parameters of a correctly specified model of a given conditional quantile hence the role of this family of densities in the conditional quantile estimation is analog to the role of the linear exponential family in the conditional mean estimation the tick exponential qmles are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form not seen in earlier work and which accounts for possible model misspecification for practical purposes we show that the maximization of the tick exponential quasi log likelihood can conveniently be carried out by using standard gradient based optimization techniques more importantly we provide a consistent estimator for the asymptotic covariance matrix based on the scores of the log likelihood which allows us to compute the conditional quantile confidence intervals

valuating residential real estate using parametric programming abstract when the estimation of the single equation multiple linear regression model is looked upon as an optimization problem we show how the principles and methods of optimization can assist the analyst in finding an attractive prediction model we illustrate this with the estimation of a linear prediction model for valuating residential property using regression quantiles we make use of the linear parametric programming formulation to obtain the family of regression quantile models associated with a data set we use the principle of dominance to reduce the number of models for consideration in the search for the most preferred property valuation model s we also provide useful displays that assist the analyst and the decision maker in selecting the final model s the approach is an interface between data analysis and operations research

evaluation of design alternatives in mechanical engineering abstract the paper gives a description of a structure dedicated to evaluation of design alternatives in mechanical engineering a list of particular features of the system such as its ability to cope with fuzziness and a uniform way of treating various criteria involved in design processes is given and discussed in length special attention is focused on empirical engineering oriented aspects of membership functions estimation with a particular emphasis on expressing achieved precision the paper re analyzes some existing methods of multiobjective decision making some original contributions of the study to this area are focussed on developing new indices significantly facilitating interpretation of results of ranking such as e g specificity of different alternatives as well as strength of dominance observed among them an illustration of the performance of the system is completed with the aid of an evaluation of different types of joints found in hydraulic cylinders