a frobenius formula for the characters of ariki koike algebras abstract let h n r be the ariki koike algebra associated to the complex reflection group wn r g r 1 n in this paper we give a new presentation of h n r by making use of the schur weyl reciprocity for h n r established by m sakamoto and t shoji 1999 j algebra 221 293 314 this allows us to construct various non parabolic subalgebras of h n r we construct all the irreducible representations of h n r as induced modules from such subalgebras we show the existence of a partition of unity in h n r which is specialized to a partition of unity in the group algebra c wn r then we prove a frobenius formula for the characters of h n r which is an analogy of the frobenius formula proved by a ram 1991 invent math 106 461 488 for the iwahori hecke algebra of type a

morita equivalences of ariki koike algebras we prove that every ariki koike algebra is morita equivalent to a direct sum of tensor products of smaller ariki koike algebras which have q connected parameter sets a similar result is proved for the cyclotomic q schur algebras combining our results with work of ariki and uglov the decomposition numbers for the ariki koike algebras defined over fields of characteristic zero are now known in principle

schur weyl reciprocity for ariki koike algebras let g glm1 glmr be a levi subalgebra of glm with m ri 1mi and v the natural representation of the quantum group uq g we construct a representation of the ariki koike algebra hn r on the n fold tensor space of v commuting with the action of uq g and prove the schur weyl reciprocity for the actions of uq g and hn r on it

parametric bootstrap approximation to the distribution of eblup and related prediction intervals in linear mixed models empirical best linear unbiased prediction eblup method uses a linear mixed model in combining information from different sources of information this method is particularly useful in small area problems the variability of an eblup is traditionally measured by the mean squared prediction error mspe and interval estimates are generally constructed using estimates of the mspe such methods have shortcomings like under coverage or over coverage excessive length and lack of interpretability we propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled eblup the bootstrap histogram is highly accurate and differs from the true eblup distribution by only o d 3 n 3 2 where d is the number of parameters and n the number of observations this result is used to obtain highly accurate prediction intervals simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models

edgeworth expansions of suitably normalized sample mean statistics for atomic markov chains this paper is devoted to the problem of estimating functionals of type f fd from observations drawn from a positive recurrent atomic markov chain open image in new window with stationary distribution the properties of different estimators are studied beyond an accurate estimation of their bias the estimation of their asymptotic variance is considered we also show that the results of malinovskii 1987 on the validity of the formal edgeworth expansion for sample mean statistics of type t n n 1 n i 1 f x i extend to their studentized versions normalized by the asymptotic variance estimates we consider

on decomposition numbers of the cyclotomic q schur algebras abstract let s be the cyclotomic q schur algebra associated to the ariki koike algebra h we construct a certain subalgebra s 0 of s and show that it is a standardly based algebra in the sense of du and rui s 0 has a natural quotient s 0 which turns out to be a cellular algebra in the case where the modified ariki koike algebra h is defined s 0 coincides with the cyclotomic q schur algebra associated to h in this paper we discuss a relationship among the decomposition numbers of s s 0 and s 0 in particular we show that some important part of the decomposition matrix of s coincides with a part of the decomposition matrix of s 0

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

modified ariki koike algebras and cyclotomic q schur algebras the modified ariki koike algebra open image in new window is a variation of the original ariki koike algebra open image in new window over an integral domain r when r is a rational function field over the independent parameters open image in new window but for general r open image in new window is not isomorphic to open image in new window and has a simpler structure than open image in new window in this paper we construct a cellular basis of open image in new window which has a similar property as the cellular basis of open image in new window introduced by dipper james mathas by comparing these two cellular bases we obtain some estimate on the decomposition numbers of open image in new window in terms of the decomposition numbers of open image in new window we also prove the integral form of the schur weyl reciprocity between a certain quantum algebra u q and open image in new window on the tensor space open image in new window

high order contractive runge kutta methods for volterra functional differential equations a contractivity theory of runge kutta methods for stiff nonlinear volterra functional differential equations vfdes is established by means of which a family of high order contractive runge kutta methods for vfdes are identified the application of the general theory for stiff nonlinear vfdes to the special cases of stiff nonlinear delay differential equations and delay integro differential equations is also presented

on the bootstrap and confidence intervals we derive an explicit formula for the first term in an unconditional edgeworth type expansion of coverage probability for the nonparametric bootstrap technique applied to a very broad class of studentized statistics the class includes sample mean k sample mean sample correlation coefficient maximum likelihood estimators expressible as functions of vector means etc we suggest that the bootstrap is really an empiric one term edgeworth inversion with the bootstrap simulations implicitly estimating the first term in an edgeworth expansion this view of the bootstrap is reinforced by our discussion of the iterated bootstrap which inverts an edgeworth expansion to arbitrary order by simulating simulations

product formulas for the cyclotomic v schur algebra and for the canonical bases of the fock space abstract let f q s be the q deformed fock space of level l with multi charge s s 1 s l uglov defined canonical bases g s of f q s for l partitions and the polynomials q z q are defined as the coefficients of the transition matrix between the canonical bases and the standard basis of f q s in this paper we prove a product formula for q for certain l partitions which expresses q as a product of such polynomials related to various smaller fock spaces f q s i yvonne conjectures that q are related to the q decomposition numbers d q of the cyclotomic v schur algebra s where the parameters v q 1 q l are roots of unity in c determined from s in our earlier work we have proved a product formula for d q of s and the product formula for q is regarded as a counter part of that formula for the case of the fock space

balanced simultaneous confidence sets abstract suppose that t tu is a family of parametric functions indexed by the variable u for each u an approximate confidence set cn u for tu may be obtained by referring a function of tu and the sample to an estimated quantile dn u of that function s sampling distribution this approach is sometimes called the pivotal method for constructing a confidence set even when it is not based on a true pivot a simultaneous confidence set cn for t is then obtained by simultaneously asserting the individual confidence sets cn u the problem is to choose the critical values for the cn u in such a way that the overall coverage probability of cn is correct and the coverage probabilities of the individual confidence sets cn u are equal the second property is termed balance it means that the simultaneous confidence set cn treats each constituent confidence statement cn u fairly aside from a few special cases the problem just described is too difficult for analytical approaches whe

inference for smooth curves in longitudinal data with application to an aids clinical trial we discuss a longitudinal study where data for many subjects are collected at irregular intervals the study is a randomized trial of hiv infected subjects and the response variable of interest is serum neopterin the mean of the outcome variable taken over patients in each treatment group is assumed to follow a smooth curve piecewise cubic polynomials with a moderate number of knots are used to model the curves a general parametric form is assumed for the covariance structure maximum penalized likelihood estimation is used to smooth the over parameterized curves statistical inference for the mean curves including confidence bands and hypothesis tests is discussed two approaches one using a bayesian interpretation of the penalized likelihood and the other based on the asymptotic distribution of the maximum penalized likelihood estimates are discussed and contrasted the properties of the confidence bands obtained from these two approaches are evaluated by examining their coverage rates in a simulation study

accurate bootstrap confidence limits for the cumulative hazard and survivor functions under random censoring abstract in clinical trials and other settings confidence intervals for survival probabilities at a fixed point in time are often required typically such intervals are constructed on the cumulative hazard scale the quantiles required for computing these intervals are generally obtained using a first order normal theory approximation the appropriateness of such intervals for small sample sizes or under moderate to heavy censoring is suspect we demonstrate that significant improvement is possible for randomly censored data using the nonparametric bootstrap in particular using edgeworth expansion it is shown that the percentile t and bc a bootstrap methodologies based on the studentized nelson aalen estimator yield second order correct confidence limits for the cumulative hazard function at a fixed time point an explicit formula for the correction term of the edgeworth expansion is found easy to compute estimators for the components of the correction term are also found and lead to simple analytic

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

pairwise comparisons of trimmed means for two or more groups the paper takes up the problem of performing all pairwise comparisons amongj independent groups based on 20 trimmed means currently a method that stands out is the percentile t bootstrap method where the bootstrap is used to estimate the quantiles of a studentized maximum modulus distribution when all pairs of population trimmed means are equal however a concern is that in simulations the actual probability of one or more type i errors can drop well below the nominal level when sample sizes are small a practical issue is whether a method can be found that corrects this problem while maintaining the positive features of the percentile t bootstrap three new methods are considered here one of which achieves the desired goal another method which takes advantage of theoretical results by singh 1998 performs almost as well but is not recommended when the smallest sample size drops below 15 in some situations however it gives substantially shorter confidence intervals

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