forecasting with the age period cohort model and the extended chain ladder model we consider forecasting from age period cohort models as well as from the extended chain ladder model the parameters of these models are known only to be identified up to linear trends forecasts from such models may therefore depend on arbitrary linear trends a condition for invariant forecasts is proposed a number of standard forecast models are analysed

asymptotics for in sample density forecasting this paper generalizes recent proposals of density forecasting models and it develops theory for this class of models in density forecasting the density of observations is estimated in regions where the density is not observed identification of the density in such regions is guaranteed by structural assumptions on the density that allows exact extrapolation in this paper the structural assumption is made that the density is a product of one dimensional functions the theory is quite general in assuming the shape of the region where the density is observed such models naturally arise when the time point of an observation can be written as the sum of two terms e g onset and incubation period of a disease the developed theory also allows for a multiplicative factor of seasonal effects seasonal effects are present in many actuarial biostatistical econometric and statistical studies smoothing estimators are proposed that are based on backfitting full asymptotic theory is derived for them a practical example from the insurance business is given producing a within year budget of reported insurance claims a small sample study supports the theoretical results

bayesian estimation of the receiver operating characteristic curve for a diagnostic test with a limit of detection in the absence of a gold standard the receiver operating characteristic roc curve is commonly used for evaluating the discriminatory ability of a biomarker measurements for a diagnostic test may be subject to an analytic limit of detection leading to immeasurable or unreportable test results ignoring the scores that are beyond the limit of detection of a test leads to a biased assessment of its discriminatory ability as reflected by indices such as the associated area under the curve auc we propose a bayesian approach for the estimation of the roc curve and its auc for a test with a limit of detection in the absence of gold standard based on assumptions of normally and gamma distributed data the methods are evaluated in simulation studies and a truncated gamma model with a point mass is used to evaluate quantitative real time polymerase chain reaction data for bovine johne s disease paratuberculosis simulations indicated that estimates of diagnostic accuracy and auc were good even for relatively small sample sizes n 200 exceptions were when there was a high per cent of unquantifiable results 60 per cent or when auc was or 0 6 which indicated a marked overlap between the outcomes in infected and non infected populations

a diagrammatic approach to hecke algebras of the reflection equation hecke algebra deformations of the wreath product cd sn arise in solutions to the yang baxter equations with boundary the reflection equation we use a simple diagrammatic approach to construct bases for these algebras we hence introduce quotient algebras suitable for constructing physical solutions to the reflection equation with a well defined thermodynamic large n limit for all d and n we determine the generic representation theory of these algebras developing a formalism suitable for the analysis of corresponding q spin chain hamiltonian and transfer matrix spectra

using smoothed receiver operating characteristic curves to summarize and compare diagnostic systems abstract receiver operating characteristic roc curves are used for summarizing the performance of imperfect diagnostic systems especially in biomedical research these curves are also appropriate for summarizing the performance of a discriminant analysis but are under utilized by statisticians this article is illustrates the use of these curves for comparing competing diagnostic systems develops new estimation methods based on kernel density estimation and studies the statistical performance of the new method a transform of the roc curve is further suggested based on the idea of local population separation this graphic is quite generally useful for displaying the differences between two populations the methods are applied to a dataset comprising the results of seven diagnostics for predicting cancer activity on 353 patients the distributions of these diagnostics are not well modeled parametrically and so either completely nonparametric or kernel density estimation seems appropriate construct

one sided cross validation abstract a new method of selecting the smoothing parameters of nonparametric regression estimators is introduced the method termed one sided cross validation oscv has the objectivity of cross validation and statistical properties comparable to those of a plug in rule the new method may be viewed as an application of the prequential model selection method of dawid as such our results identify a situation in which the prequential method is a more efficient model selector than cross validation an example simulations and theoretical results demonstrate the utility of oscv when used with local linear and kernel estimators

on decomposition matrices for graded algebras abstract we study the relations between the decomposition matrix of a module over a graded algebra and the decomposition matrix of its restriction to the grading subalgebra we show that under appropriate hypotheses if one of the decomposition matrices is stable unitriangular then so is the other a particular case is when one of them is square unitriangular then both are using these results we describe the decomposition matrices of the hecke algebras of the complex reflection groups g de e n with respect to the ones of the ariki koike algebras or the decomposition matrices of q schur algebras of type dn with respect to the ones of q schur algebras of type bn

blocks of cyclotomic hecke algebras abstract this paper classifies the blocks of the cyclotomic hecke algebras of type g r 1 n over an arbitrary field rather than working with the hecke algebras directly we work instead with the cyclotomic schur algebras the advantage of these algebras is that the cyclotomic jantzen sum formula gives an easy combinatorial characterization of the blocks of the cyclotomic schur algebras we obtain an explicit description of the blocks by analyzing the combinatorics of jantzen equivalence we remark that a proof of the classification of the blocks of the cyclotomic hecke algebras was announced in 1999 unfortunately cox has discovered that this previous proof is incomplete

isomorphisms between simple modules of degenerate cyclotomic hecke algebras abstract we give explicit isomorphisms between simple modules of degenerate cyclotomic hecke algebras defined via various cellular bases a special case gives a generalized mullineux involution in the degenerate case

schur weyl reciprocity between quantum groups and hecke algebras of type g p p n abstract let u q gl m p be the quantized universal enveloping algebra of gl m p let be the automorphism of u q gl m p which is defined on generators by e i e i m f i f i m k j k j m for any i z p m z 0 m p 1 m and any j z p m z let h p p n be the hecke algebra of type g p p n with parameters q e where e is a primitive pth root of unity in this paper we establish a schur weyl reciprocity between h p p n and a twisted tensor product of u q gl m p and the group algebra for a cyclic group of order p by using the results in j hu j algebra 274 2004 446 490

hecke algebras of classical type and their representation type the purpose of this article is to determine the representation type for all of the hecke algebras of classical type to do this we combine methods from our previous work which is used to obtain information on their gabriel quivers and recent advances in the theory of finite dimensional algebras the principal computation is for hecke algebras of type b with two parameters then we show that the representation type of hecke algebras is governed by their poincare polynomials

bayesian semi parametric roc analysis this paper describes a semi parametric bayesian approach for estimating receiver operating characteristic roc curves based on mixtures of dirichlet process priors mdp we address difficulties in modelling the underlying distribution of screening scores due to non normality that may lead to incorrect choices of diagnostic cut offs and unreliable estimates of prevalence of the disease mdp is a robust tool for modelling non standard diagnostic distributions associated with imperfect classification of an underlying diseased population for example when a diagnostic test is not a gold standard for posterior computations we propose an efficient gibbs sampling framework based on a finite dimensional approximation to mdp we show using both simulated and real data sets that mdp modelling for roc curve estimation closely parallels the frequentist kernel density estimation kde approach

an integrated bayesian nonparametric approach for stochastic and variability orders in roc curve estimation an application to endometriosis diagnosis in estimating roc curves of multiple tests some a priori constraints may exist either between the healthy and diseased populations within a test or between tests within a population in this article we proposed an integrated modeling approach for roc curves that jointly accounts for stochastic and variability orders the stochastic order constrains the distributional centers of the diseased and healthy populations within a test while the variability order constrains the distributional spreads of the tests within each of the populations under a bayesian nonparametric framework we used features of the dirichlet process mixture to incorporate these order constraints in a natural way we applied the proposed approach to data from the physician reliability study that investigated the accuracy of diagnosing endometriosis using different clinical information to address the issue of no gold standard in the real data we used a sensitivity analysis approach that exploited diagnosis from a panel of experts

on the action of ariki koike algebras on tensor space the action of the ariki koike algebra on tensor space is used to show an isomorphism theorem between the ariki koike algebra and a direct sum of matrix rings over tensorproducts of smaller ariki koike algebras as an application we get schur weyl duality for the action of the ariki koike algebra and the levi subalgebra of the q schur algebra when separation conditions holds mit hilfe der operation der ariki koike algebra auf dem tensorraum wird ein isomorphismus zwischen der ariki koike algebra und einer direkten summe von matrizenringen uber tensorprodukten kleinerer ariki koike algebren gezeigt als anwendung ergibt sich das die ariki koike algebra und die leviunteralgebra der q schur algebra schur weyl dualitat erfullen falls die separationsbedingung erfullt ist

modular representations of hecke algebras of type g p p n hecke algebras for the complex reflection groups g r p n where p 1 and p r were introduced in the work of ariki j algebra 177 1995 164 185 broue and malle asterisque 212 1993 119 189 in this paper we consider modular representation theory for these algebras in the case where r p we assume that the field k contains a primitive pth root of unity e our method is to study the restrictions of specht modules s for hecke algebras hp n of type g p 1 n with parameters q 1 e ep 1 suppose that f q e 0 in k see 4 7 for definition of f q e for any multipartition 1 p of n we prove that s hp p n s k hp p n for any 1 k p 1 where k k 1 k 2 p 1 2 k and if k is the smallest positive integer such that k hence k p we explicitly decompose s hp p n into a direct sum of p k smaller hp p n submodules with the same dimensions as a result when f q e 0 in k we show that hp p n is split over k and get a complete classification of all the absolutely irreducible hp p n modules this generalizes earlier work of c pallikaros j algebra 169 1994 20 48 and j hu manuscripta math 108 2002 409 430 on hecke algebras of type dn which are included as a special case of our main results

representations of ariki koike algebras and grobner shirshov bases in this paper we investigate the structure of ariki koike algebras and their specht modules using grobner shirshov basis theory and combinatorics of young tableaux for a multipartition lambda we find a presentation of the specht module s lambda given by generators and relations and determine its grobner shirshov pair as a consequence we obtain a linear basis of s lambda consisting of standard monomials with respect to the grobner shirshov pair we show that this monomial basis can be canonically identified with the set of cozy tableaux of shape lambda

do validation for kernel density estimation bandwidth selection in kernel density estimation is one of the fundamental model selection problems of mathematical statistics the study of this problem took major steps forward with the articles of hall and marron 1987 and hall and johnstone 1992 since then the focus seems to have been on various versions of implementing the so called plug in method aimed at estimating the minimum mean integrated squared error mise the most successful of these efforts still seems to be the plug in method of sheather and jones 1991 or park and marron 1990 that we also use as a benchmark in this article in this article we derive a new theorem deriving the asymptotic theory for linear combinations of bandwidths obtained from different selectors as for example direct and indirect cross validation and plug in where we take advantage of recent advances in the study of indirect cross validation see hart and yi 1998 hart and lee 2005 and savchuk hart and sheather 2008 2010 we conclude that the slow

indirect cross validation for density estimation a new method of bandwidth selection for kernel density estimators is proposed the method termed indirect cross validation icv makes use of so called selection kernels least squares cross validation lscv is used to select the bandwidth of a selection kernel estimator and this bandwidth is appropriately rescaled for use in a gaussian kernel estimator the proposed selection kernels are linear combinations of two gaussian kernels and need not be unimodal or positive a theory is developed showing that the relative error of icv bandwidths can converge to 0 at a rate of n 1 4 which is substantially better than the n 1 10 rate of lscv interestingly the selection kernels that are best for purposes of bandwidth selection are very poor if used to actually estimate the density function this property appears to be part of the larger and well documented paradox to the effect that the harder the estimation problem the better cross validation performs the icv method uniformly outperforms lscv in a simul

on the decomposition numbers of the hecke algebra of type dn when n is even abstract let n 4 be an even integer let k be a field with char k 2 and q an invertible element in k such that i 1 n 1 1 q i 0 in this paper we study the decomposition numbers over k of the iwahori hecke algebra h q d n of type d n we obtain some equalities which relate its decomposition numbers with certain schur elements and the decomposition numbers of various iwahori hecke algebras of type a with the same parameter q when char k 0 this completely determine all of its decomposition numbers the main tools we used are the morita equivalence theorem established in j hu a morita equivalence theorem for hecke algebra h q d n when n is even manuscripta math 108 2002 409 430 and certain twining character formulae of weyl modules over a tensor product of two q schur algebras

the number of simple modules for the hecke algebras of type g r p n with an appendix by xiaoyi cui abstract we derive a parameterization of simple modules for the cyclotomic hecke algebras of type g r p n with p 1 and n 3 over fields of any characteristic coprime to p we give explicit formulas for the number of simple modules over these cyclotomic hecke algebras

a semiparametric model for randomly truncated data abstract for randomly censored data it is known that the maximum likelihood estimate mle of the survival curve is not affected by parametric assumption on the censoring variable the kaplan meier 1958 estimate is the mle for both nonparametric and semiparametric models for randomly truncated data the truncation product limit estimate is the mle for nonparametric models this is not the case if the truncation mechanism is parameterized however specifically let x be a generic random variable and t be the truncation variable if the distribution of t is parameterized and the distribution of x is left unspecified it can be shown that the truncation product limit estimate is not the mle for this semiparametric model even though it is for the fully nonparametric model in this article the mle is characterized for the semiparametric model and the large sample properties of the estimate are established the results show that unlike censoring the parametric information from the truncation mechanism

estimation of the area under the roc curve the area under the receiver operating characteristic curve is frequently used as a measure for the effectiveness of diagnostic markers in this paper we discuss and compare estimation procedures for this area these are based on i the mann whitney statistic ii kernel smoothing iii normal assumptions iv empirical transformations to normality these are compared in terms of bias and root mean square error in a large variety of situations by means of an extensive simulation study overall we find that transforming to normality usually is to be preferred except for bimodal cases where kernel methods can be effective

an alternative method of cross validation for the smoothing of density estimates cross validation with kullback leibler loss function has been applied to the choice of a smoothing parameter in the kernel method of density estimation a framework for this problem is constructed and used to derive an alternative method of cross validation based on integrated squared error recently also proposed by rudemo 1982 hall 1983 has established the consistency and asymptotic optimality of the new method for small and moderate sized samples the performances of the two methods of cross validation are compared on simulated data and specific examples

bayesian semiparametric roc curve estimation and disease diagnosis we develop a novel semiparametric modeling framework involving mixtures of polya trees for screening data with the dual purpose of diagnosing infection or disease status and of assessing the accuracy of continuous diagnostic measures in this framework we obtain i predictive probabilities of disease based on continuous diagnostic test outcomes in conjunction with other information including relevant covariates and results from one or more independent binary diagnostic tests an example would be the modeling of a serum enzyme linked immunosorbent assay elisa procedure for detecting antibodies to an infectious agent when used in conjunction with culture for antigen detection our second goal is to ii characterize measures of diagnostic performance of continuous tests by estimating receiver operating characteristic curves and area under the curve primarily when such extra information is available when true disease status is unknown parametric and nonparametric analyses require sufficient separation between the distributions of outcome values for the diseased and nondiseased populations however this overlap becomes less problematic when additional information in the form of either an informative prior that is based on real preferably data based scientific input or when additional information or both are available the additional information can be used to distinguish diseased from nondiseased individuals we present an example using simulated data that illustrates this point we also present an example involving data from an animal health survey for johne s disease where the performance of a serum elisa is evaluated using additional information obtained from fecal culture issues related to identifiability and partial identifiability are also discussed

testing the assumption of independence of truncation time and failure time summary for data subject to random censorship it is well known that the assumption of independence between censoring time and failure time cannot be tested nonparametrically for data subject to random truncation however it is possible to test independence of truncation time and failure time a statistic generalizing kendall s tau is proposed for testing the independence assumption and asymptotic properties under the null hypothesis are derived a conditional permutation test is also derived for small data sets generalization to allow right censoring and an application to truncated linear regression are also briefly discussed

q tensor space and q weyl modules we obtain the irreducible representations of the q schur algebra motivated by the fact that these representations give all the irreducible representations of gln q in the nondescribing characteristic the irreducible polynomial representations of the general linear groups in the describing characteristic are a special case of this construction the theory of polynomial representations of general linear groups is equivalent to the representation theory of schur algebras see green s book 5 and the bibliography therein in 4 we defined q analogues of schur algebras when q 1 these are the usual schur algebras and when q is a prime power representations of q schur algebras give a substantial part of the representation theory of finite general linear groups in the nondescribing characteristic case including all irreducible representations of these groups and important information about decomposition numbers it is natural to ask what features of the classical schur algebras have qanalogues in this paper we define q analogues of tensor space of weyl modules and of weight spaces thereby generalizing the main reslllts which appear in green s book 5 for example we classify the irreducible modules for qschur algebras we determine bases for q weyl modules compatible with weight spaces and we give results on composition multiplicities of the irreducible modules in q weyl modules the proofs are largely self contained so by specializing q to 1 we recover the corresponding results in 5 this paper therefore is relevant to the representation theory of symmetric groups and to the representation theory of general linear groups in the describing and in the nondescribing characteristics 1 the q schur algebra let r be a natural number let r be an integral domain and let q be a unit in r we denote the symmetric group on r letters by er the hecke algebra z is the r free r algebra with basis twlw e er where the multiplication is determined by the following rule if a i i 1 is a basic transposition in received by the editors august 15 1989 1980 mathematics subject classification 198 5 revision primary 1 6a64 1 6a6 5 secondary 20c30 this research was supported in part by nsf grant no dms 8802290 the authors gratefully acknowledge support received from nato grant no 0222 87 r 1991 american mathematical society 0002 9947 91 1 00 25 per page

on the semisimplicity of the cyclotomic brauer algebras ii abstract in this paper we give a necessary and sufficient condition for the semisimplicity of cyclotomic brauer algebras b m n of types g m 1 n with m 2 this generalizes h rui a criterion on the semisimple brauer algebras j combin theory ser a 111 2005 78 88 1 2 1 3 and h rui m si a criterion on the semisimple brauer algebras ii j combin theory ser a 113 2006 1199 1203 2 5 on brauer algebras

the jantzen sum formula for cyclotomic schur algebras the cyclotomic q schur algebra was introduced by dipper james and mathas in order to provide a new tool for studying the ariki koike algebra we here prove an analogue of jantzen s sum formula for the cyclotomic q schur algebra among the applications is a criterion for certain specht modules of the ariki koike algebras to be irreducible

schur weyl duality for infinitesimal q schur algebras sq 2 r 1 abstract using the result of s r doty d k nakano k m peters polynomial representations of frobenius kernels of gl 2 in contemp math vol 194 1996 pp 57 67 s konig c xi when is a cellular algebra quasi hereditary math ann 315 1999 281 293 we prove that a non semisimple infinitesimal schur algebra s 2 r 1 is not cellular furthermore we determine the structure of the endomorphism ring of tensor space as a module for the infinitesimal schur algebra s 2 r 1 up to morita equivalence both results generalize to the quantum case

bayesian nonparametric inference on stochastic ordering we consider bayesian inference about collections of unknown distributions subject to a partial stochastic ordering to address problems in testing of equalities between groups and estimation of group specific distributions we propose classes of restricted dependent dirichlet process priors these priors have full support in the space of stochastically ordered distributions and can be used for collections of unknown mixture distributions to obtain a flexible class of mixture models theoretical properties are discussed efficient methods are developed for posterior computation using markov chain monte carlo simulation and the methods are illustrated using data from a study of dna damage and repair

cellular structures on hecke algebras of type b abstract the aim of this paper is to gather and try to unify several approaches for the modular representation theory of hecke algebras of type b we attempt to explain the connections between geck s cellular structures coming from kazhdan lusztig theory with unequal parameters and ariki s theorem on the canonical basis of the fock spaces

markov chain monte carlo in approximate dirichlet and beta two parameter process hierarchical models summary we present some easy to construct random probability measures which approximate the dirichlet process and an extension which we will call the beta two parameter process the nature of these constructions makes it simple to implement markov chain monte carlo algorithms for fitting nonparametric hierarchical models and mixtures of nonparametric hierarchical models for the dirichlet process we consider a truncation approximation as well as a weak limit approximation based on a mixture of dirichlet processes the same type of truncation approximation can also be applied to the beta two parameter process both methods lead to posteriors which can be fitted using markov chain monte carlo algorithms that take advantage of blocked coordinate updates these algorithms promote rapid mixing of the markov chain and can be readily applied to normal mean mixture models and to density estimation problems we prefer the truncation approximations since a simple device for monitoring the adequacy of the approximation can be easily computed from the output of the gibbs sampler furthermore for the dirichlet process the truncation approximation offers an exponentially higher degree of accuracy over the weak limit approximation for the same computational effort we also find that a certain beta two parameter process may be suitable for finite mixture modelling because the distinct number of sampled values from this process tends to match closely the number of components of the underlying mixture distribution

a new parametric method based on s distributions for computing receiver operating characteristic curves for continuous diagnostic tests receiver operating characteristic roc curves provides a method for evaluating the performance of a diagnostic test these curves represent the true positive ratio that is the true positives among those affected by the disease as a function of the false positive ratio that is the false positives among the healthy corresponding to each possible value of the diagnostic variable when the diagnostic variable is continuous the corresponding roc curve is also continuous however estimation of such curve through the analysis of sample data yields a step line unless some assumption is made on the underlying distribution of the considered variable since the actual distribution of the diagnostic test is seldom known it is difficult to select an appropriate distribution for practical use data transformation may offer a solution but also may introduce a distortion on the evaluation of the diagnostic test in this paper we show that the distribution family known as the s distribution can be used to solve this problem the s distribution is defined as a differential equation in which the dependent variable is the cumulative this special form provides a highly flexible family of distributions that can be used as models for unknown distributions it has been shown that classical statistical distributions can be represented accurately as s distributions and that they occur in a definite subspace of the parameter space corresponding to the whole s distribution family consequently many other distributional forms that do not correspond to known distributions are provided by the s distribution this property can be used to model observed data for unknown distributions and is very useful in constructing parametric roc curves in those cases after fitting an s distribution to the observed samples of diseased and healthy populations roc curve computation is straightforward a roc curve can be considered as the solution of a differential equation in which the dependent variable is the ratio of true positives and the independent variable is the ratio of false positives this equation can be easily obtained from the s distributions fitted to observed data using these results we can compute pointwise confidence bands for the roc curve and the corresponding area under the curve we shall compare this approach with the empirical and the binormal methods for estimating a roc curve to show that the s distribution based method is a useful parametric procedure

double one sided cross validation of local linear hazards this paper brings together the theory and practice of local linear kernel hazard estimation bandwidth selection is fully analysed including do validation that is shown to have good practical and theoretical properties insight is provided into the choice of the weighting function in the local linear minimization and it is pointed out that classical weighting sometimes lacks stability a new semiparametric hazard estimator transforming the survival data before smoothing is introduced and shown to have good practical properties

an algorithm for the computation of the decomposition matrices for ariki koike algebras abstract we give a purely combinatorial algorithm for the computation of the decomposition matrices for ariki koike algebras when the parameters are powers of the same root of unity

bayesian bootstrap estimation of roc curve receiver operating characteristic roc curve is widely applied in measuring discriminatory ability of diagnostic or prognostic tests this makes the roc analysis one of the most active research areas in medical statistics many parametric and semiparametric estimation methods have been proposed for estimating the roc curve and its functionals in this paper we propose the bayesian bootstrap bb a fully nonparametric estimation method for the roc curve and its functionals such as the area under the curve auc the bb method offers a bandwidth free smoothing approach to the empirical estimate and gives credible bounds the accuracy of the estimate of the roc curve in the simulation studies is examined by the integrated absolute error in comparison with other existing curve estimation methods the bb method performs well in terms of accuracy robustness and simplicity we also propose a procedure based on the bb approach to test the binormality assumption

nonparametric analysis of truncated survival data with application to aids summary one source of data for the induction distribution of aids arises from persons infected by the aids virus from contaminated blood transfusions analyses of these data are complicated because the number of individuals infected by transfusion is unknown information is available only for those who are infected and develop aids within a certain chronologic time interval the statistical problem is one of making inferences about a stochastic process of infection and disease for which realizations are right truncated in chronologic time by considering the process in reverse time we transform the problem to one of analysing survival data that are left truncated in internal time we develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions of several groups an important feature of the natural history and population dynamics of aids is the induction period between infection with the aids virus and the onset of clinical aids this time is sometimes referred to as the latency period or incubation period follow up studies of individuals at risk of being infected will provide direct observations from the induction distribution but most of these studies will not be completed for several years one alternative source of information arises from persons infected with the aids virus from a contaminated blood transfusion of persons infected in this way only those who develop aids by a certain date can be identified the total number who are infected is not known a similar sampling distribution arises in the study of pediatric aids children who contract aids as a result of being infected in utero or at birth can be identified but the total number infected in this way is unknown the statistical problem is one of making inferences about a stochastic process of infection and subsequent disease in which realizations are right truncated in chronologic time by considering the process in reverse time the problem can be transformed to one of survival data that are left truncated in internal time we use this relationship to develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions for

bayesian methods for partial stochastic orderings summary we discuss two methods of making nonparametric bayesian inference on probability measures subject to a partial stochastic ordering the first method involves a nonparametric prior for a measure on partially ordered latent observations and the second involves rejection sampling computational approaches are discussed for each method and interpretations of prior and posterior information are discussed an application is presented in which inference is made on the number of independently segregating quantitative trait loci present in an animal population

in sample forecasting with local linear survival densities in this paper in sample forecasting is defined as forecasting a structured density to sets where it is unobserved the structured density consists of one dimensional in sample components that identify the density on such sets we focus on the multiplicative density structure which has recently been seen as the underlying structure of non life insurance forecasts in non life insurance the in sample area is defined as one triangle and the forecasting area as the triangle that 20 added to the first triangle produces a square recent approaches estimate two one dimensional components by projecting an unstructured two dimensional density estimator onto the space of multiplicatively separable functions we show that time reversal reduces the problem to two one dimensional problems where the one dimensional data are left truncated and a one dimensional survival density estimator is needed this paper then uses the local linear density smoother with 25 weighted cross validated and do validated bandwidth selectors full asymptotic theory is provided with and without time reversal finite sample studies and an application to non life insurance are included

testing goodness of fit of a uniform truncation model several goodness of fit tests of a lifetime distribution have been suggested in the literature many take into account censoring and or truncation of event times in some contexts a goodness of fit test for the truncation distribution is of interest in particular better estimates of the lifetime distribution can be obtained when knowledge of the truncation law is exploited in cross sectional sampling for example there are theoretical justifications for the assumption of a uniform truncation distribution and several studies have used it to improve the efficiency of their survival estimates the duality of lifetime and truncation in the absence of censoring enables methods for testing goodness of fit of the lifetime distribution to be used for testing goodness of fit of the truncation distribution however under random censoring this duality does not hold and different tests are required in this article we introduce several goodness of fit tests for the truncation distribution and investigate their performance in the presence of censored event times using simulation we demonstrate the use of our tests on two data sets

tilting modules for cyclotomic schur algebras this paper investigates the tilting modules of the cycloto mic q schur alge bras the young modules of the ariki koike algebras and the interconnections between them the main tools used to understand the tilting modules are contragredient duality and the specht filtrations and dual specht filtrations of cert ain permutation modules sur prisingly weyl filtrations which are in general more power ful than specht filtrations play only a secondary role

on the number of constituents of induced modules of ariki koike algebras abstract we examine the crystal graph of the sl e module arising from an sl e categorification to study the defining endo functors of the categorification this yields lower bounds on the number of irreducible constituents of certain objects we use ariki s categorification result on ariki koike algebras to obtain a new lower bound on the number of constituents of their parabolically induced modules in particular this will imply reducibility of every induced module

nonparametric kernel estimation in counting processes with explanatory variables summary cox s proportional hazards model assumes that the duration hazard rate factors into a product of a baseline hazard rate and a nonnegative function of explanatory variables an estimate of the baseline hazard rate hence also of overall hazard rate is proposed based on a smoothing procedure using a kernel function it is shown that the proposed estimator is uniformly consistent and converges weakly to a gaussian process bandwidth selection issues are also discussed

on the classification of finite dimensional irreducible modules for affine bmw algebras in this paper we classify the finite dimensional irreducible modules for affine bmw algebra over an algebraically closed field with arbitrary characteristic

the mirabolic hecke algebra abstract the iwahori hecke algebra of the symmetric group is the convolution algebra of gl n invariant functions on the variety of pairs of complete flags over a finite field considering convolution on the space of triples of two flags and a vector we obtain the mirabolic hecke algebra r n which had originally been described by solomon in this paper we give a new presentation for r n which shows that it is a quotient of a cyclotomic hecke algebra as defined by ariki and koike from this we recover the results of siegel about the representations of r n we use jucys murphy elements to describe the center of r n and to give a gl structure on the grothendieck group of the category of its representations giving mirabolic analogues of classical results about the iwahori hecke algebra we also outline a strategy towards a proof of the conjecture that the mirabolic hecke algebra is a cellular algebra

an interpretation for the roc curve and inference using glm procedures the accuracy of a medical diagnostic test is often summarized in a receiver operating characteristic roc curve this paper puts forth an interpretation for each point on the roc curve as being a conditional probability of a test result from a random diseased subject exceeding that from a random nondiseased subject this interpretation gives rise to new methods for making inference about roc curves it is shown that inference can be achieved with binary regression techniques applied to indicator variables constructed from pairs of test results one component of the pair being from a diseased subject and the other from a nondiseased subject within the generalized linear model glm binary regression framework roc curves can be estimated and we highlight a new semiparametric estimator covariate effects can also be evaluated with the glm models the methodology is applied to a pancreatic cancer dataset where we use the regression framework to compare two different serum biomarkers asymptotic distribution theory is developed to facilitate inference and to provide insight into factors influencing variability of estimated model parameters

cyclotomic double affine hecke algebras and affine parabolic category o using the orbifold kz connection we construct a functor from an affine parabolic category o of type a to the category o of a cyclotomic rational double affine hecke algebra h then we give several results concerning this functor

the degenerate analogue of ariki s categorification theorem we explain how to deduce the degenerate analogue of ariki s categorification theorem over the ground field mathbb c as an application of schur weyl duality for higher levels and the kazhdan lusztig conjecture in finite type a we also discuss some supplementary topics including young modules tensoring with sign tilting modules and ringel duality

small area estimation of receiver operating characteristic curves for ordinal data under stochastic ordering there has been a recent increase in the diagnosis of diseases through radiographic images such as x rays magnetic resonance imaging and computed tomography the outcome of a radiological diagnostic test is often in the form of discrete ordinal data and we usually summarize the performance of the diagnostic test using the receiver operating characteristic roc curve and the area under the curve auc the roc curve will be concave and called proper when the outcomes of the diagnostic test in the actually positive subjects are higher than in the actually negative subjects the diagnostic test for disease detection is clinically useful when a roc curve is proper in this study we develop a hierarchical bayesian model to estimate the proper roc curve and auc using stochastic ordering in several domains when the outcome of the diagnostic test is discrete ordinal data and compare it with the model without stochastic ordering the model without stochastic ordering can estimate the improper roc curve with a nonconcave shape or a hook when the true roc curve of the population is a proper roc curve therefore the model with stochastic ordering is preferable over the model without stochastic ordering to estimate the proper roc curve with clinical usefulness for ordinal data

canonical basic sets in type bn more than 10 years ago dipper james and murphy developed the theory of specht modules for hecke algebras of type bn more recently using lusztig s a function geck and rouquier showed how to obtain parametrizations of the irreducible representations of hecke algebras of any finite type in terms of so called canonical basic sets for certain values of the parameters in type bn combinatorial descriptions of these basic sets were found by jacon based on work of ariki and foda leclerc okado thibon welsh here we consider the canonical basic sets for all the remaining choices of the parameters

smooth backfitting of proportional hazards with multiplicative components smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression by projecting the data down onto the structured space of interest smooth backfitting

nonparametric and semiparametric estimation of the receiver operating characteristic curve curve odc given by f g t first we consider nonparametric estimators based on empirical distribution functions and derive asymptotic properties next we consider the so called semiparametric binormal model in which it is assumed that the distributions f and g are normal after some unknown monotonic transformation of the measurement scale for this model we propose a generalized least squares procedure and compare it with the estimation algorithm of dorfman and alf which is based on grouped data asymptotic results are obtained small sample properties are examined via a simulation study finally we describe a minimum distance estimator for the roc curve which does not require grouping the data

categorifications and cyclotomic rational double affine hecke algebras varagnolo and vasserot conjectured an equivalence between the category mathcal o for crdaha s and a subcategory of an affine parabolic category o of type a we prove this conjecture as applications we prove a conjecture of rouquier on the dimension of simple modules of crdaha s and a conjecture of chuang miyachi on the koszul duality for the category mathcal o of crdaha s