bayesian solutions to graduate admissions and related selection problems a graduate program has to decide how many offers of admission to make to achieve a targeted number of acceptances for its entering class given uncertainty about how many will accept such offers we first structure and solve selection problems under the assumption that probabilities associated with uncertain outcomes have assumed values using symmetric and asymmetric loss functions and show sensitivity of solutions to errors in these assumed values then we show how these problems can be solved when these probabilities are heterogeneous and have to be estimated from sample data

robust forecast combinations abstract forecast outliers commonly occur in economic financial and other areas of forecasting applications in the literature of forecast combinations there have been only a few studies exploring how to deal with outliers in this work we propose two robust combining methods based on the after algorithm yang 2004a our approach utilizes robust loss functions in order to reduce the influence of outliers oracle inequalities for certain versions of these methods are obtained which show that the combined forecasts automatically perform as well as the best individual among the pool of original forecasts systematic simulations and data examples show that the robust methods outperform the after algorithm when outliers are likely to occur and perform on par with after when there are no outliers comparison of the robust afters with some commonly used combining methods also shows their potential advantages

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

optimal forecast combinations under general loss functions and forecast error distributions existing results on the properties and performance of forecast combinations have been derived in the context of mean squared error loss under this loss function empirical studies have generally found that equally weighted combined forecasts lead to better performance than estimates of optimal forecast combination weights which in turn outperform the best individual predictions we show that this and other results can be overturned when asymmetries are introduced in the loss function and the forecast error distribution is skewed we characterize the optimal combination weights for the most commonly used alternatives to mean squared error loss and demonstrate how the degree of asymmetry in the loss function and skews in the underlying forecast error distribution can significantly change the optimal combination weights we also propose estimation methods and investigate their small sample properties in simulations and in an inflation forecasting exercise

bayesian estimation for nonstandard loss functions using a parametric family of estimators bayesian estimation with other loss functions than the standard hit or miss loss or the quadratic loss often yields optimal bayesian estimators obes that can only be formulated as optimization problems and which have to be solved for each new observation the contribution of this paper is to introduce a new parametric family of estimators to circumvent this problem by restricting the estimator to lie in this family we split the estimation problem into two parts in a first step we have to find the best estimator with respect to the bayes risk for a given nonstandard loss function which has to be done only once the second step then calculates the estimate for an observation using importance sampling the computational complexity of this second step is therefore comparable to that of an mmse estimator if the mmse estimator also uses monte carlo integration we study the proposed parametric family using two examples and show that the estimator family gives for both a good approximation of the obe

computing optimal confidence sets for pareto models under progressive censoring this paper presents two families of joint confidence sets for the pareto shape and precision parameters based on progressively censored data which include the existing regions in the literature as particular cases and derives explicit expressions for the corresponding areas upon using fiducial arguments an exact and quick computational method is then proposed in order to find the smallest area pareto region which depends on the minimal sufficient statistic with a specified confidence level shortest length confidence intervals for the pareto parameters are also provided the reduction in area of the minimal joint confidence region with respect to the existing sets is substantial in most situations and impressive in some cases for illustrative and comparative purposes two practical studies concerning device lifetimes and business failures are considered applications of the smallest confidence sets include uses in hypothesis testing and estimation in particular it is possible to construct confidence intervals for functions of the pareto parameters as well as pointwise and simultaneous confidence bands for the pareto reliability function

bayes risk reduction of estimators using artificial observation noise this paper studies noise enhanced ne estimators which are constructed from an original estimator by artificially adding noise to the observation and computing the expected estimator output by this expectation operation we take into account the neighbourhood of an observation and the resulting ne estimator often has a smaller bayes risk than the original one we derive some general properties of this estimator and also present a method to obtain a suitable approximation of the optimal ne estimator which can be computed numerically by solving a constrained optimization problem finally we study two examples to show the bayes risk improvement that we can obtain from the ne estimator and we compare it to the stochastic resonance estimator

optimal critical values of pre tests when estimating the regression error variance analytical findings under a general loss structure this paper re visits the problem of estimating the regression error variance in a linear multiple regression model after preliminary hypothesis tests for either linear restrictions on the coefficients or homogeneity of variances there is an extensive literature that discusses these problems particularly in terms of the sampling properties of the pre test estimators using various loss functions as the basis for risk analysis in this paper a unified framework for analysing the risk properties of these estimators is developed under a general class of loss structures that incorporates virtually all first order differentiable losses particular consideration is given to the choice of critical values for the pre tests analytical results indicate that an level substantially higher than those normally used may be appropriate for optimal risk properties under a wide range of loss functions the paper also generalizes some known analytical results in the pre test literature and proves other results only previously shown numerically

modeling concurrency with interval traces interval order structures are useful tools to model abstract concurrent histories i e sets of equivalent system runs when system runs are modeled with interval orders this paper shows how interval order structures can be modeled by partially commutative monoids called interval traces the model is then used to provide a semantics of petri nets with inhibitor arcs both in terms of interval traces and in terms of interval order structures

modelling concurrency with comtraces and generalized comtraces comtraces combined traces are extensions of mazurkiewicz traces that can model the not later than relationship in this paper we first introduce the novel notion of generalized comtraces extensions of comtraces that can additionally model the non simultaneously relationship then we study some basic algebraic properties and canonical representations of comtraces and generalized comtraces finally we analyze the relationship between generalized comtraces and generalized stratified order structures the major technical contribution of this paper is a proof showing that generalized comtraces can be represented by generalized stratified order structures

noninformative priors and frequentist risks of bayesian estimators of vector autoregressive models in this study we examine posterior properties and frequentist risks of bayesian estimators based on several noninformative priors in vector autoregressive var models we prove existence of the posterior distributions and posterior moments under a general class of priors using a variety of priors in this class we conduct numerical simulations of posteriors we find that in most examples bayesian estimators with a shrinkage prior on the var coefficients and the reference prior of yang and berger ann statist 22 1994 1195 on the var covariance matrix dominate mle bayesian estimators with the diffuse prior and bayesian estimators with the prior used in rats we also examine the informative minnesota prior and find that its performance depends on the nature of the data sample and on the tightness of the minnesota prior a tightly set minnesota prior is better when the data generating processes are similar to random walks but the shrinkage prior or constant prior can be better otherwise

pay phones parking meters vending machines and optimal bayesian decisions on collection times payphones parking meters and vending machines illustrate the modern business practice of substituting machinery for manpower they do not eliminate manual labor completely because full coin boxes still must be replaced and vending machines still must be stocked deciding when to replace a coin box is important with unequal losses resulting from underestimation and overestimation this article derives optimal methodology for this problem by incorporating collection history and specifying common prior distributions over average daily fill rate and standard deviation at each box the approach is implemented and analyzed on collection records from 11 308 pay phones over a large geographical region when the loss from overestimation is 19 times that from underestimation our methods outperform the one in current use at least 69 9 of the time translating into average potential collection cost reductions exceeding 21

reliability analysis of a class of exponential distribution under record values in this paper the estimation of the parameters as well as survival and hazard functions for a class of an exponential family are presented by using bayesian and non bayesian approaches under record values maximum likelihood and interval estimation are derived for the model parameters and bayes estimators of reliability performances are obtained under symmetric and asymmetric loss functions when the parameters have discrete and continuous priors respectively finally two numerical examples are presented to illustrate the proposed results an algorithm is introduced to generate record data then the numerical example is given by using monte carlo simulation and different estimates results are compared

bayesian and non bayesian approaches to statistical inference and decision making bayesian and non bayesian approaches to statistical inference and decision making are discussed and compared a pragmatic criterion success in practice as well as logical consistency are emphasized in comparing alternative approaches attention is given to learning models probability concepts prior information axiom systems and selected technical aspects of bayesian and non bayesian approaches

testing forecast optimality under unknown loss empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function in this article we establish new testable properties that hold when the forecaster s loss function is unknown but testable restrictions can be imposed on the data generating process trading off conditions on the data generating process against conditions on the loss function we propose flexible estimation of the forecaster s loss function in situations where the loss depends not only on the forecast error but also on other state variables such as the level of the target variable we apply our results to the problem of evaluating the federal reserve s forecasts of output growth forecast optimality is rejected if the fed s loss depends only on the forecast error however the empirical findings are consistent with forecast optimality provided that overpredictions of output growth are costlier to the fed than underpredictions particularly during per

properties of ordinary least squares estimators in regression models with nonspherical disturbances abstract a general discussion is presented of the properties of the ols estimator in regression models where the disturbances do not have a scalar identity covariance matrix several new and interesting characterizations are provided together with a synthesis of existing results a distinguishing feature of the paper is the unified treatment of the issues of efficiency and inference the theoretical material is illustrated by examples covering a wide range of models of interest to applied econometricians

composite binary losses we study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function we characterise when margin losses can be proper composite losses explicitly show how to determine a symmetric loss in full from half of one of its partial losses introduce an intrinsic parametrisation of composite binary losses and give a complete characterisation of the relationship between proper losses and classification calibrated losses we also consider the question of the best surrogate binary loss we introduce a precise notion of best and show there exist situations where two convex surrogate losses are incommensurable we provide a complete explicit characterisation of the convexity of composite binary losses in terms of the link function and the weight function associated with the proper loss which make up the composite loss this characterisation suggests new ways of surrogate tuning as well as providing an explicit characterisation of when bregman divergences on the unit interval are convex in their second argument finally in an appendix we present some new algorithm independent results on the relationship between properness convexity and robustness to misclassification noise for binary losses and show that all convex proper losses are non robust to misclassification noise

s step iterative methods for symmetric linear systems abstract in this paper we introduce s step conjugate gradient method for symmetric and positive definite spd linear systems of equations and discuss its convergence in the s step conjugate gradient method iteration s new directions are formed simultaneously from r i ar i a s 1 r i and the preceding s directions all s directions are chosen to be a orthogonal to the preceding s directions the approximation to the solution is then advanced by minimizing an error functional simultaneously in all s directions this intuitively means that the progress towards the solution in one iteration of the s step method equals the progress made over s consecutive steps of the one step method this is proven to be true

two conjugate gradient type methods for unsymmetric linear equations we propose two new conjugate gradient type methods for the solution of sparse unsymmetric linear systems we present a new tridiagonalization process for unsymmetric matrices that is closely related to the lanczos process we use orthogonal factorizations of the tridiagonal matrix to derive the new algorithms usymlq and usymqr in the same fashion as symmlq and minres c c paige and m a saunders solution of sparse indefinite systems of linear equations siam j numer anal 12 1975 pp 617 629 for symmetric matrices some numerical results for the new methods and comparisons with other methods are presented

convergence rate of empirical bayes estimation for two dimensional truncation parameters under linex loss this paper deals with the empirical bayes eb estimation for two dimensional truncation parameters under linex loss by using kernel estimation of density function we construct the eb estimation of parameters under some suitable conditions we prove that the constructed eb estimations is asymptotically optimal and we obtain its convergence rate

concurrent systems and inevitability abstract concurrent systems viewed as partially ordered sets of states are considered a property of system states is called inevitable if the system will eventually reach a state with this property this notion is discussed within the partial order framework

projection minimization methods for nonsymmetric linear systems abstract we consider projection minimization methods for solving systems of linear equations we transform these methods to new ones and show that they converge faster in some sense we present in particular the transform of the norm decomposition method of gastinel the new algorithm presents advantages over some known conjugate gradient like methods this new method is studied and numerical examples are given

an adaptive empirical bayes estimator of the multivariate normal mean under quadratic loss abstract for shrinkage estimators to achieve significant risk improvement over their traditional competitors one must identify the region or subspace where the unknown location vector lies or is thought likely to lie a priori when vague or conflicting priors suggest that a broad class of estimators may be effective under a squared error loss measure new minimax or near minimax empirical bayes estimators are proposed that make use of stein s unbiased estimator of the risk to identify the optimum risk effective shrinkage estimator

a graphical analysis of cost sensitive regression problems several efforts have been done to bring roc analysis beyond binary classification especially in regression however the mapping and possibilities of these proposals do not correspond to what we expect from the analysis of operating conditions dominance hybrid methods etc in this paper we present a new representation of regression models in the so called regression roc rroc space the basic idea is to represent over estimation on the x axis and under estimation on the y axis the curves are just drawn by adjusting a shift a constant that is added or subtracted to the predictions and plays a similar role as a threshold in classification from here we develop the notions of optimal operating condition convexity dominance and explore several evaluation metrics that can be shown graphically such as the area over the rroc curve aoc in particular we show a novel and significant result the aoc is equal to the error variance multiplied by a factor which does not depend on the model the derivation of rroc curves with non constant shifts and soft regression models and the relation with cost plots is also discussed

roc curves for regression receiver operating characteristic roc analysis is one of the most popular tools for the visual assessment and understanding of classifier performance in this paper we present a new representation of regression models in the so called regression roc rroc space the basic idea is to represent over estimation against under estimation the curves are just drawn by adjusting a shift a constant that is added or subtracted to the predictions and plays a similar role as a threshold in classification from here we develop the notions of optimal operating condition convexity dominance and explore several evaluation metrics that can be shown graphically such as the area over the rroc curve aoc in particular we show a novel and significant result the aoc is equivalent to the error variance we illustrate the application of rroc curves to resource estimation namely the estimation of software project effort

the finite sample properties of simultaneous equations estimates and estimators bayesian and non bayesian approaches abstract after discussing the need for good finite sample estimation procedures for simultaneous equations models and showing the inadequacies of asymptotically justified estimators it is shown how the bayesian method of moments bmom provides an exact finite sample analysis of unrestricted reduced form systems then optimal finite sample estimates of structural coefficients are derived using three standard loss functions and they are compared to traditional bayesian optimal estimates monte carlo experimental evidence from four studies on the relative performance of bayesian and non bayesian estimators is reviewed with the finding that the performance of bayesian estimators is better

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

sampling performance of some joint one sided preliminary test estimators under squared error loss in many areas of science when drawing conclusions concerning a set of phenomena individual or linear combinations of parameters are assumed to be nonnegative nonpositive or to lie between upper and lower bounds likewise many functions are assumed to be monotonic convex or quasiconvex consequently questions naturally arise as to the correctness of the assumptions and within the context of statistical inference how to evaluate the evidence against these assumptions and to use the data at hand to seek the appropriate statistical model and the corresponding method of estimation within the context of the general linear statistical model multivariate analogues of one sided inequality hypotheses tests have been explored by bartholomew 1959 kudo 1963 osterhoff 1969 barlow et al 1972 yancey judge and bock 1981 yancey bohrer and judge 1982 gourieroux holly and montfort ghm 1982 judge and yancey 1986 wolak 1987 and shapiro 1988 in general the likelihood ratio framework has been used in developing a test statistic and determining acceptance and rejection regions in order to facilitate the interpretation of these test results in econometric practice in this paper we evaluate under a squared error loss sel measure the risk characteristics of the preliminary test pt estimators that evolve when based on the data at hand an estimation decision is taken as a result of the outcomes of two one sided multivariate hypothesis tests

building cost functions minimizing to some summary statistics a learning machine or a model is usually trained by minimizing a given criterion the expectation of the cost function measuring the discrepancy between the model output and the desired output as is already well known the choice of the cost function has a profound impact on the probabilistic interpretation of the output of the model after training in this work we use the calculus of variations in order to tackle this problem in particular we derive necessary and sufficient conditions on the cost function ensuring that the output of the trained model approximates 1 the conditional expectation of the desired output given the explanatory variables 2 the conditional median and more generally the q quantile 3 the conditional geometric mean and 4 the conditional variance the same method could be applied to the estimation of other summary statistics as well we also argue that the least absolute deviations criterion could in some cases act as an alternative to the ordinary least squares criterion for nonlinear regression in the same vein the concept of regression quantile is briefly discussed

best median unbiased estimation in linear regression with bounded asymmetric loss functions abstract this article considers optimal median unbiased estimation in a linear regression model with the distribution of the errors lying in a subclass of the elliptically symmetric distributions the generalized least squares gls estimator is shown to be best for any monotone loss function that is any loss function that is nondecreasing as the magnitude of underestimation or overestimation increases this includes bounded asymmetric loss functions for the same loss functions a restricted gls estimator is shown to be best when the estimand is known to lie in an interval for the case of normal errors a best median unbiased estimator of the error variance 2 is given for restricted and unrestricted parameter spaces this estimator differs from the sample variance s 2 in comparison with best mean unbiased estimators of regression and variance parameters the best median unbiased estimators considered here take advantage of restrictions on the parameter space and are optimal with respect to a much wi

efficiency of a liu type estimator in semiparametric regression models in this paper we consider the semiparametric regression model y x b f e recently hu 11 proposed ridge regression estimator in a semiparametric regression model we introduce a liu type combined ridge stein estimator lte in a semiparametric regression model firstly liu type estimators of both b and f are attained without a restrained design matrix secondly the lte estimator of b is compared with the two step estimator in terms of the mean square error we describe the almost unbiased liu type estimator in semiparametric regression models the almost unbiased liu type estimator is compared with the liu type estimator in terms of the mean squared error matrix a numerical example is provided to show the performance of the estimators

semantics of inhibitor nets we discuss an abstract semantics of concurrent systems generalising causal partial orders the new semantics employs relational structures called stratified order structures which comprise causal partial orders and weak causal partial orders stratified order structures can be represented by certain equivalence classes of step sequences comtraces directly generalising mazurkiewicz traces we use elementary net systems with inhibitor arcs as a system model and show that stratified order structures can provide an abstract semantics which is consistent with their operational semantics expressed in terms of step sequences two different types of operational rules are considered we also construct occurrence nets to enable the generation of stratified order structures for a given run of the net

inadmissibility of the stein rule estimator under the balanced loss function in this paper the risk of the stein rule sr estimator is compared with that of the improved stein rule estimator using the stein variance srsv estimator under the balanced loss function it is shown that the srsv estimator dominates the sr estimator even if the loss function is extended to the blf also our numerical results show that the srsv estimator dominates the ols estimator when the weight of precision of estimation is larger than about half and vice versa

structure of concurrency abstract noninterleaving models of concurrency assume that behavioural properties of systems can be adequately modelled in terms of causal partial orders we claim that the structure of concurrency is richer with causality being only one of the invariants generated by a set of closely related executions or observations the model we propose supports three levels of abstraction the observation level invariant level and system level and we will proceed from the bottom observation level to the top system level this is in contrast to the way other models for concurrency are introduced as they essentially support two levels of abstraction the system level and behavioural level which includes both observations and invariants with the direction of development going from the system to behavioural level in this paper we first discuss the notion of an observation of a concurrent behaviour in particular we investigate the role played by interval partial orders we then introduce a general framework for dealing with invariants generated by sets of closely related observations this leads to the formulation of the notion of a concurrent history whose structural properties are subsequently studied