affine geometric crystals and limit of perfect crystals for every non exceptional affine lie algebra we explicitly construct a positive geometric crystal associated with a fundamental representation we also show that its ultra discretization is isomorphic to the limit of certain perfect crystals of the langlands dual affine lie algebra

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

comparability of segmented line regression models segmented line regression models which are composed of continuous linear phases have been applied to describe changes in rate trend patterns in this article we propose a procedure to compare two segmented line regression functions specifically to test i whether the two segmented line regression functions are identical or ii whether the two mean functions are parallel allowing different intercepts a general form of the test statistic is described and then the permutation procedure is proposed to estimate the p value of the test the permutation test is compared to an approximate f test in terms of the p value estimation and the performance of the permutation test is studied via simulations the tests are applied to compare female lung cancer mortality rates between two registry areas and also to compare female breast cancer mortality rates between two states

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

iteratively reweighted partial least squares estimation for generalized linear regression i extend the concept of partial least squares pls into the framework of generalized linear models a spectroscopy example in a logistic regression framework illustrates the developments these models form a sequence of rank 1 approximations useful for predicting the response variable when the explanatory information is severely ill conditioned iteratively reweighted pls algorithms are presented with various theoretical properties connections to principal component and maximum likelihood estimation are made as well as suggestions for rules to choose the proper rank of the final model

generalized linear regression on sampled signals and curves a p spline approach we consider generalized linear regression with many highly correlated regressors for instance digitized points of a curve on a spatial or temporal domain we refer to this setting as signal regression which requires severe regularization because the number of regressors is large often exceeding the number of observations we solve collinearity by forcing the coefficient vector to be smooth on the same domain dimension reduction is achieved by projecting the signal coefficient vector onto a moderate number of b splines a difference penalty between the b spline coefficients further increases smoothness the p spline framework of eilers and marx the procedure is regulated by a penalty parameter chosen using information criteria or cross validation

modified sequentially rejective multiple test procedures abstract suppose that n hypotheses h 1 h 2 h n with associated test statistics t 1 t 2 t n are to be tested by a procedure with experimentwise significance level the probability of rejecting one or more true hypotheses smaller than or equal to some specified value a commonly used procedure satisfying this condition is the bonferroni b procedure which consists of rejecting h i for any i iff the associated test statistic t i is significant at the level n holm 1979 introduced a modified bonferroni procedure with greater power than the b procedure under holm s sequentially rejective bonferroni srb procedure if any hypothesis is rejected at the level n the denominator of for the next test is n 1 and the criterion continues to be modified in a stagewise manner with the denominator of reduced by 1 each time a hypothesis is rejected so that tests can be conducted at successively higher significance levels holm proved that the experimentwise significance level

clustering of trend data using joinpoint regression models in this paper we propose methods to cluster groups of two dimensional data whose mean functions are piecewise linear into several clusters with common characteristics such as the same slopes to fit segmented line regression models with common features for each possible cluster we use a restricted least squares method in implementing the restricted least squares method we estimate the maximum number of segments in each cluster by using both the permutation test method and the bayes information criterion method and then propose to use the bayes information criterion to determine the number of clusters for a more effective implementation of the clustering algorithm we propose a measure of the minimum distance worth detecting and illustrate its use in two examples we summarize simulation results to study properties of the proposed methods and also prove the consistency of the cluster grouping estimated with a given number of clusters the presentation and examples in this paper focus on the segmented line regression model with the ordered values of the independent variable which has been the model of interest in cancer trend analysis but the proposed method can be applied to a general model with design points either ordered or unordered copyright 2014 john wiley sons ltd

estimating average annual per cent change in trend analysis trends in incidence or mortality rates over a specified time interval are usually described by the conventional annual per cent change capc under the assumption of a constant rate of change when this assumption does not hold over the entire time interval the trend may be characterized using the annual per cent changes from segmented analysis sapcs this approach assumes that the change in rates is constant over each time partition defined by the transition points but varies among different time partitions different groups e g racial subgroups however may have different transition points and thus different time partitions over which they have constant rates of change making comparison of sapcs problematic across groups over a common time interval of interest e g the past 10 years we propose a new measure the average annual per cent change aapc which uses sapcs to summarize and compare trends for a specific time period the advantage of the proposed aapc is that it takes into account the trend transitions whereas capc does not and can lead to erroneous conclusions in addition when the trend is constant over the entire time interval of interest the aapc has the advantage of reducing to both capc and sapc moreover because the estimated aapc is based on the segmented analysis over the entire data series any selected subinterval within a single time partition will yield the same aapc estimate that is it will be equal to the estimated sapc for that time partition the capc however is re estimated using data only from that selected subinterval thus its estimate may be sensitive to the subinterval selected the aapc estimation has been incorporated into the segmented regression free software joinpoint which is used by many registries throughout the world for characterizing trends in cancer rates copyright 2009 john wiley sons ltd

monte carlo evaluation of resampling based hypothesis tests abstract monte carlo estimation of the power of tests that require resampling can be very computationally intensive it is possible to reduce the size of the inner resampling loop as long as the resulting estimator of power can be corrected for bias a simple linear extrapolation method is shown to perform well in correcting for bias and thus reduces computation time in monte carlo power studies

penalized discriminant methods for the classification of tumors from gene expression data en raison de l avancee des technologies de micropuces haut debit il est devenu possible de developper des systemes de classifications moleculaires pour differents types de cancer dans cet article nous proposons une methode fondee sur les modeles de regression regularisee pour la classification des tumeurs dans les experiences de micropuces les performances des modeles en composantes principales des moindres carres partiels et de la ridge regression sont etudiees ces procedures de regression sont adaptees aux techniques de classification utilisant l algorithme de score optimal nous developpons egalement une methode de classement des genes fondee sur les modeles de regression ajustee les methodes proposees sont appliquees a deux etudes de cancerologie utilisant les micropuces

principal component estimation for generalized linear regression summary the generalized linear model nelder wedderburn 1972 has become an elegant and practical option to classical least squares linear model building we consider the specific problem of generalized linear regression utilizing a set of continuous explanatory variables to model an exponential family response it is the objective of this paper to develop and present an asymptotically biased principal component parameter estimation technique as an option to traditional maximum likelihood estimation for generalized linear regression both iterative and one step principal component estimators are developed directly compared and can be particularly useful with the presence of an ill conditioned information matrix the bias variance and mean squared error of principal component estimation will be quantified generalizations for rules of deletion of components will be examined lastly an example employs principal component estimation for poisson response data

semiparametric comparison of regression curves the comparison of nonparametric regression curves is considered it is assumed that there are parametric possibly nonlinear transformations of the axes which map one curve into the other estimation and testing of the parameters in the transformations are studied the rate of convergence is n 1 2 although the nonparametric components of the model typically have a rate slower than that a statistic is provided for testing the validity of a given completely parametric model

bootstrap test for difference between means in nonparametric regression abstract a bootstrap test is proposed for detecting a difference between two mean functions in the setting of nonparametric regression error distributions in the regression model are permitted to be arbitrary and unequal the test enjoys power properties akin to those in a parametric setting in the sense that it can distinguish between regression functions distant only n 1 2 apart where n is the sample size it has exceptional level accuracy with level error of only n 2 and uses a very accurate estimate of the critical point of an exact test being in error by only n 3 2 under the null hypothesis the test admits several generalizations for example to the case of testing for differences between several regression means this is a nonparametric regression analog of analysis of variance a simulation study using n as small as 15 corroborates the asymptotic result on level accuracy of the bootstrap test applications are illustrated with an example involving acid rain data

permutation tests for joinpoint regression with applications to cancer rates the identification of changes in the recent trend is an important issue in the analysis of cancer mortality and incidence data we apply a joinpoint regression model to describe such continuous changes and use the grid search method to fit the regression function with unknown joinpoints assuming constant variance and uncorrelated errors we find the number of significant joinpoints by performing several permutation tests each of which has a correct significance level asymptotically each p value is found using monte carlo methods and the overall asymptotic significance level is maintained through a bonferroni correction these tests are extended to the situation with non constant variance to handle rates with poisson variation and possibly autocorrelated errors the performance of these tests are studied via simulations and the tests are applied to u s prostate cancer incidence and mortality rates

test of significance when data are curves abstract with modern technology massive data can easily be collected in a form of multiple sets of curves new statistical challenge includes testing whether there is any statistically significant difference among these sets of curves in this article we propose some new tests for comparing two groups of curves based on the adaptive neyman test and the wavelet thresholding techniques introduced earlier by fan we demonstrate that these tests inherit the properties outlined by fan and that they are simple and powerful for detecting differences between two sets of curves we then further generalize the idea to compare multiple sets of curves resulting in an adaptive high dimensional analysis of variance called hanova these newly developed techniques are illustrated by using a dataset on pizza commercials where observations are curves and an analysis of cornea topography in ophthalmology where images of individuals are observed a simulation example is also presented to illustrate the power of the adapti

testing for treatment and interaction effects in semi parametric analysis of covariance semi parametric regression models assume that the effects of covariates on the mean response are additive we propose a test of additivity when there is one continuous covariate and a group indicator at p fixed points the differences of the within group kernel estimates of the means are calculated and the likelihood ratio test that the p differences have a constant mean is formed the kernel bandwidth and the location of the p fixed points are chosen to give the test good power performance of the proposed test is compared with parametric and non parametric tests of additivity published in 2001 by john wiley sons ltd

infinite flag varieties and conjugacy theorems abstract we study the orbit of a highest weight vector in an integrable highest weight module of the group g associated to a kac moody algebra unk a we obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of unk a in particular we prove conjugacy theorems for cartan and borel subalgebras of unk a so that the cartan matrix a is an invariant of unk a

a penalized method for multivariate concave least squares with application to productivity analysis abstract we propose a penalized method for the least squares estimator of a multivariate concave regression function this estimator is formulated as a quadratic programing qp problem with o n2 constraints where n is the number of observations computing such an estimator is a very time consuming task and the computational burden rises dramatically as the number of observations increases by introducing a quadratic penalty function we reformulate the concave least squares estimator as a qp with only non negativity constraints this reformulation can be adapted for estimating variants of shape restricted least squares i e the monotonic concave convex least squares the experimental results and an empirical study show that the reformulated problem and its dual are solved significantly faster than the original problem the matlab and r codes for implementing the penalized problems are provided in the paper

geometric crystals on unipotent groups and generalized young tableaux abstract we define geometric unipotent crystal structure on maximal unipotent subgroups of semi simple algebraic groups we shall show that in a n case their ultra discretizations coincide with crystals obtained by generalizing young tableaux

crystal graphs for representations of the q analogue of classical lie algebras the explicit form of the crystal graphs for the finite dimensional representations of the q analogue of the universal enveloping algebras of type a b c and d is given in terms of semi standard tableaux and its analogues