yetter drinfeld modules and projections of weak hopf algebras abstract in this paper we prove that if g b h is a morphism of weak hopf algebras which is split as an algebra coalgebra morphism then the subalgebra of coinvariants b h of b is a hopf algebra in the category of yetter drinfeld modules associated to h

weak c cleft extensions weak entwining structures and weak hopf algebras abstract we formulate the concept of weak cleft extension for a weak entwining structure in a braided monoidal category c with equalizers and coequalizers we prove that if a is a weak c cleft extension then there is an isomorphism of algebras between a and a subobject of the tensor product of a c and c where a c is a subalgebra of a also we prove the corresponding dual results and linking the information of this two parts we obtain a general property for a pair morphisms f c a and g a c of algebras and coalgebras satisfying certain conditions finally as particular instances we get the results of fernandez and rodriguez the theorems of radford majid and bespalov in the case of hopf algebras with projection and the ones obtained by alonso and gonzalez for weak hopf algebras living in a symmetric category with split idempotents for example the weak theorem of blattner cohen and montgomery for weak hopf algebras with coalgebra splitting is one of them

adding one handle to half plane layers in this paper we build properly embedded singly periodic minimal surfaces which have infinite total curvature in the quotient by the period these surfaces are constructed by adding a handle to the toroidal half plane layers defined by h karcher the technics that use is to solve a jenkins serrin problem over a strip domain and to consider the conjugate minimal surface to the graph

estimation and inference in semiparametric quantile factor models we propose an estimation methodology for a semiparametric quantile factor panel model we provide tools for inference that are robust to the existence of moments and to the form of weak cross sectional dependence in the idiosyncratic error term we apply our method to crsp daily data

method of medians for lifetime data with weibull models the weibull family of distributions is frequently used in failure time models the maximum likelihood estimator is very sensitive to occurrence of upper and lower outliers especially when the hazard function is increasing we consider the method of medians estimator for the two parameter weibull model as an m estimator it has a bounded influence function and is highly robust against outliers it is easy to compute as it requires solving only one equation instead of a pair of equations as for most other m estimators furthermore no assumptions or adjustments are needed for the estimator when there are some possibly censored observations at either end of the sample about 16 per cent of the largest observations and 34 per cent of the smallest observations may be censored without affecting the calculations we also present a simple criterion to choose between the maximum likelihood estimator and the method of medians estimator to improve on the finite sample efficiency of the weibull model robust inference on the shape parameter is also considered the usefulness with contaminated or censored samples is illustrated by examples on three lifetime data sets a simulation study was carried out to assess the performance of the proposed estimator and the confidence intervals of a variety of contaminated weibull models

a multistep protein lysate array quantification method and its statistical properties the protein lysate array is an emerging technology for quantifying the protein concentration ratios in multiple biological samples statistical inference for a parametric quantification procedure has been inadequately addressed in the literature mainly because the appropriate asymptotic theory involves a problem with the number of parameters increasing with the number of observations in this article we develop a multistep procedure for the sigmoidal models ensuring consistent estimation of the concentration levels with full asymptotic efficiency the results obtained in the article justify inferential procedures based on large sample approximations simulation studies and real data analysis are used in the article to illustrate the performance of the proposed method in finite samples the multistep procedure is convenient to work with asymptotically and is recommended for its statistical efficiency in protein concentration estimation and improved numerical stability by focusing on optimization of lower dimensional objective functions

breakdown points of t type regression estimators summary to bound the influence of a leverage point generalised m estimators have been suggested however the usual generalised m estimator of regression has a breakdown point that is less than the inverse of its dimension this paper shows that dimension independent positive breakdown points can be attained by a class of well defined generalised mestimators with redescending scores the solution can be determined through optimisation of t type likelihood applied to properly weighted residuals the highest breakdown point of is attained by cauchy score these bounded influence and high breakdown estimators can be viewed as a fully iterated version of the one step generalised m estimates of simpson ruppert carroll 1992 with the two advantages of easier interpretability and avoidance of undesirable roots to estimating equations given the design dependent weights they can be computed via em algorithms empirical investigations show that they are highly competitive with other robust estimators of regression

on a likelihood approach for monte carlo integration the use of estimating equations has been a common approach for constructing monte carlo estimators recently kong et al proposed a formulation of monte carlo integration as a statistical model making explicit what information is ignored and what is retained about the baseline measure from simulated data the baseline measure is estimated by maximum likelihood and then integrals of interest are estimated by substituting the estimated measure for two different situations in which independent observations are simulated from multiple distributions we show that this likelihood approach achieves the lowest asymptotic variance possible by using estimating equations in the first situation the normalizing constants of the design distributions are estimated and meng and wong s bridge sampling estimating equation is considered in the second situation the values of the normalizing constants are known thereby imposing linear constraints on the baseline measure estimating equations including hesterberg s

a general bahadur representation of m estimators and its application to linear regression with nonstochastic designs we obtain strong bahadur representations for a general class of m estimators that satisfies sigma i psi x i theta o delta n where the x i s are independent but not necessarily identically distributed random variables the results apply readily to m estimators of regression with nonstochastic designs more specifically we consider the minimum l p distance estimators bounded influence gm estimators and regression quantiles under appropriate design conditions the error ratesobtained for the first order approximations are sharp in these cases we also provide weaker and more easily verifiable conditions that suffice for an error rate that is suboptimal but strong enough for deriving the asymptotic distribution of m estimators in a wide variety of problems

sufficient moment and truncated moment conditions for the law of the iterated logarithm various sufficient conditions for the law of the iterated logarithm are given extending the main result of the author s previous paper 16 and kolmogoroff s law of iterated logarithm as a byproduct we give a unified approach to various old and new stability results

markov chain marginal bootstrap markov chain marginal bootstrap mcmb is a new method for constructing confidence intervals or regions for maximum likelihood estimators of certain parametric models and for a wide class of m estimators of linear regression the mcmb method distinguishes itself from the usual bootstrap methods in two important aspects it involves solving only one dimensional equations for parameters of any dimension and produces a markov chain rather than a conditionally independent sequence it is designed to alleviate computational burdens often associated with bootstrap in high dimensional problems the validity of mcmb is established through asymptotic analyses and illustrated with empirical and simulation studies for linear regression and generalized linear models

strong representations for lad estimators in linear models consider the standard linear modely i z i e i i 1 2 n where zi denotes theith row of ann x p design matrix p is an unknown parameter to be estimated andei are independent random variables with a common distribution functionf the least absolute deviation lad estimate tilde beta of is defined as any solution of the minimization problem sum limits i 1 n left y i z i tilde beta right inf left sum limits i 1 n left y i z i beta right beta in mathbb r p right

local polynomial quantile regression with parametric features we propose a new approach to conditional quantile function estimation that combines both parametric and nonparametric techniques at each design point a global possibly incorrect pilot parametric model is locally adjusted through a kernel smoothing fit the resulting quantile regression estimator behaves like a parametric estimator when the latter is correct and converges to the nonparametric solution as the parametric start deviates from the true underlying model we give a bahadur type representation of the proposed estimator from which consistency and asymptotic normality are derived under an mixing assumption we also propose a practical bandwidth selector based on the plug in principle and discuss the numerical implementation of the new estimator finally we investigate the performance of the proposed method via simulations and illustrate the methodology with a data example

weak hopf bialgebras in this chapter the r bialgebroids and hopf algebroids of the previous chapter are investigated further in the particular case when the base algebra r carries a so called separable frobenius structure separable frobenius structures on some algebra r are shown to correspond to separable frobenius structures on the forgetful functor from the category of r bimodules to the category of vector spaces based on that the bijection of chap 5 is refined to bijections between three structures for any algebra a first monoidal structures on the category of a modules together with separable frobenius structures on the forgetful functor to the category of vector spaces second bialgebroid structures on a over some base algebra r together with separable frobenius structures on r finally weak bialgebra structures on a the r bialgebroid a is a hopf algebroid if and only if the corresponding weak bialgebra a is a weak hopf algebra

inference for censored quantile regression models in longitudinal studies we develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants we consider a semi parametric quantile regression model that makes no distributional assumptions our research is motivated by the lack of proper inference procedures for data from biomedical studies where measurements are censored due to a fixed quantification limit in such studies the focus is often on testing hypotheses about treatment equality to this end we propose a rank score test for large sample inference on a subset of the covariates we demonstrate the importance of accounting for both censoring and intra subject dependency and evaluate the performance of our proposed methodology in a simulation study we then apply the proposed inference procedures to data from an aids related clinical trial we conclude that our framework and proposed methodology is very valuable for differentiating the influences of predictors at different locations in the conditional distribution of a response variable

the strong law of large numbers for sequential decisions under uncertainty combines optimization and ergodic theory to characterize the optimum long run average performance that can be asymptotically attained by nonanticipating sequential decisions let x sub t be a stationary ergodic process and suppose an action b sub t must be selected in a space spl bscr with knowledge of the t past x sub 0 spl middot spl middot spl middot x sub t 1 at the beginning of every period t spl ges 0 action b sub t will incur a loss l b sub t x sub t at the end of period t when the random variable x sub t is revealed the author proves under mild integrability conditions that the optimum strategy is to select actions that minimize the conditional expected loss given the currently available information at each step the minimum long run average loss per decision can be approached arbitrarily closely by strategies that are finite order markov and under certain continuity conditions it is equal to the minimum expected loss given the infinite past if the loss l b x is bounded and continuous and if the space spl bscr is compact then the minimum can be asymptotically attained even if the distribution of the process x sub t is unknown a priori and must be learned from experience

a lack of fit test for quantile regression we propose an omnibus lack of fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector the test does not involve nonparametric smoothing but is consistent for all nonparametric alternatives without any moment conditions on the regression error in addition the test is suitable for detecting the local alternatives of any order arbitrarily close to n 1 2 from the null hypothesis the limiting distribution of the proposed test statistic is non gaussian but can be characterized by a gaussian process we propose a simple sequential resampling scheme to carry out the test whose nominal levels are well approximated in our empirical study for

multiply robust estimation in regression analysis with missing data doubly robust estimators are widely used in missing data analysis they provide double protection on estimation consistency against model misspecifications however they allow only a single model for the missingness mechanism and a single model for the data distribution and the assumption that one of these two models is correctly specified is restrictive in practice for regression analysis with possibly missing outcome we propose an estimation method that allows multiple models for both the missingness mechanism and the data distribution the resulting estimator is consistent if any one of those multiple models is correctly specified and thus provides multiple protection on consistency this estimator is also robust against extreme values of the fitted missingness probability which for most doubly robust estimators can lead to erroneously large inverse probability weights that may jeopardize the numerical performance the numerical implementation of the proposed method through a modified newton ra

on a geometric notion of quantiles for multivariate data abstract an extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered the approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles both of which have been extensively studied in the literature these geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other l estimates of multivariate location and they lead to a directional notion of central and extreme points in a multidimensional setup such quantiles can be defined as meaningful and natural objects even in infinite dimensional hilbert and banach spaces and they yield an effective generalization of quantile regression in multiresponse linear model problems desirable equivariance properties are shown to hold for these multivariate quantiles and issues related to their computation for data in finite dimensional spaces are discussed n 1 2 consistenc

multivariate quantiles and multiple output regression quantiles from l1 optimization to halfspace depth a new multivariate concept of quantile based on a directional version of koenker and bassett s traditional regression quantiles is introduced for multivariate location and multiple output regression problems in their empirical version those quantiles can be computed efficiently via linear programming techniques consistency bahadur representation and asymptotic normality results are established most importantly the contours generated by those quantiles are shown to coincide with the classical halfspace depth contours associated with the name of tukey this relation does not only allow for efficient depth contour computations by means of parametric linear programming but also for transferring from the quantile to the depth universe such asymptotic results as bahadur representations finally linear programming duality opens the way to promising developments in depth related multivariate rank based inference

comment on adaptive confidence intervals for the test error in classification inspired by the non regular framework studied in laber and murphy 2011 we propose a family of adaptive classifiers we discuss briefly their asymptotic properties and show that under the non regular framework these classifiers have an oracle property and consequently have smaller asymptotic variance and smaller asymptotic test error variance than those of the original classifier we also show that confidence intervals for the test error of the adaptive classifiers based on either normal approximation or centered percentile bootstrap are consistent

a general framework for quantile estimation with incomplete data quantile estimation has attracted significant research interests in recent years however there has been only a limited literature on quantile estimation in the presence of incomplete data in this paper we propose a general framework to address this problem our framework combines the two widely adopted approaches for missing data analysis the imputation approach and the inverse probability weighting approach via the empirical likelihood method the proposed method is capable of dealing with many different missingness settings we mainly study three of them i estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates ii estimating the conditional quantile of a fully observed response while the covariates are partially available and iii estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables the proposed method allows multiple models for both the missingness probability and the data distribution the resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified the asymptotic distributions are established using the empirical process theory

median regression for longitudinal data we review and compare three estimators of median regression in linear models with longitudinal data the estimators are constructed based on well known ideas of weighting decorrelating and the working assumption of independence both asymptotic efficiency calculations and finite sample monte carlo studies are used to assess the performance of these estimators we find that their relative performances depend on the nature of covariates the estimator under the working assumption of independence is computationally simple and yet has good relative performance when the covariates are invariant over time or when the within subject correlations are small its relative performance in finite samples is also found to be more favourable than suggested by the asymptotic comparisons

weak hopf algebras i integral theory and c structure we give an introduction to the theory of weak hopf algebras proposed as a coassociative alternative of weak quasi hopf algebras we follow an axiomatic approach keeping as close as possible to the classical theory of hopf algebras the emphasis is put on the new structure related to the presence of canonical subalgebras al and ar in any weak hopf algebra a that play the role of non commutative numbers in many respects a theory of integrals is developed in which we show how the algebraic properties of a such as the frobenius property or semisimplicity or innerness of the square of the antipode are related to the existence of non degenerate normalized or haar integrals in case of c weak hopf algebras we prove the existence of a unique haar measure h a and of a canonical grouplike element g a implementing the square of the antipode and factorizing into left and right elements g glg 1r gl al gr ar further discussion of the c case will be presented in part ii

weak hopf algebras with projection and weak smash bialgebra structures abstract in this paper we study weak hopf algebras with projection if f h b g b h are morphisms of weak hopf algebras such that g f idh we prove that it is possible to find an object bh in the new category of weak yetter drinfeld modules that verifies similar conditions to the ones include in the definition of weak hopf algebra finally we define weak smash bialgebra structures and prove that under central and cocentral conditions bh and h determine an example of them

rank based estimates in the linear model with high breakdown point abstract an estimator in the linear model is defined by minimizing an objective function the derivative of which is a signed rank statistic the scores are generated from a function h 0 1 0 which is not necessarily nondecreasing as is usually assumed it is shown that this estimator can be chosen with a maximal breakdown point of 5 moreover strong consistency and asymptotic normality with convergence rate n 1 2 of the proposed estimator are proved under various regularity conditions because the objective function generally is not convex in the regression parameters the usual proofs of asymptotic normality do not carry over instead the proof is based on an asymptotic linearity result similar to that obtained by huber for m estimates and some moment estimates for signed rank statistics numerical examples illustrate the behavior of the estimator

m estimation of linear models with dependent errors we study asymptotic properties of m estimates of regression parameters in linear models in which errors are dependent weak and strong bahadur representations of the m estimates are derived and a central limit theorem is established the results are applied to linear models with errors being short range dependent linear processes heavy tailed linear processes and some widely used nonlinear time series

on monte carlo methods for estimating ratios of normalizing constants recently estimating ratios of normalizing constants has played an important role in bayesian computations applications of estimating ratios of normalizing constants arise in many aspects of bayesian statistical inference in this article we present an overview and discuss the current monte carlo methods for estimating ratios of normalizing constants then we propose a new ratio importance sampling method and establish its theoretical framework we find that the ratio importance sampling method can be better than the current methods for example the bridge sampling method meng and wong and the path sampling method gelman and meng in the sense of minimizing asymptotic relative mean square errors of estimators an example is given for illustrative purposes finally we present two special applications and the general implementation issues for estimating ratios of normalizing constants

local linear quantile estimation for nonstationary time series we consider estimation of quantile curves for a general class of nonstationary processes consistency and central limit results are obtained for local linear quantile estimates under a mild short range dependence condition our results are applied to environmental data sets in particular our results can be used to address the problem of whether climate variability has changed an important problem raised by ipcc intergovernmental panel on climate change in 2001

the geometry of minimal surfaces of finite genus i curvature estimates and quasiperiodicity let mathcal m be the space of properly embedded minimal surfaces in 3 with genus zero and two limit ends normalized so that every surface m mathcal m has horizontal limit tangent plane at infinity and the vertical component of its flux equals one we prove that if a sequence m i i mathcal m has the horizontal part of the flux bounded from above then the gaussian curvature of the sequence is uniformly bounded this curvature estimate yields compactness results and the techniques in its proof lead to a number of consequences concerning the geometry of any properly embedded minimal surface in 3 with finite genus and the possible limits through a blowing up process on the scale of curvature of a sequence of properly embedded minimal surfaces with locally bounded genus in a homogeneously regular riemannian 3 manifold

weak hopf algebras and weak yang baxter operators abstract in this paper we introduce the notions of weak yang baxter operator and weak braided hopf algebra we prove that it is possible to obtain examples of these notions working with yetter drinfeld modules associated to a weak hopf algebra h with invertible antipode finally we complete the study of the structure of weak hopf algebras with a projection obtaining a categorical equivalence between the category of weak hopf algebra projections associated to h and the category of hopf algebras in the non strict braided monoidal category of left left yetter drinfeld modules over h

weak c cleft extensions and weak galois extensions abstract for a weak entwining structure a c we formulate the notion of weak c galois extension with normal basis and we show that these galois extensions are equivalent to the weak c cleft extensions introduced in j n alonso alvarez j m fernandez vilaboa r gonzalez rodriguez a b rodriguez raposo weak c cleft extensions weak entwining structures and weak hopf algebras j algebra 284 2005 679 704

l estimation for linear models abstract linear combinations of order statistics or l estimators have played an extremely important role in the development of robust methods for the one sample problem we suggest analogs of l estimators for the parameters of the linear model based on the p dimensional regression quantiles proposed by koenker and bassett 1978 a uniform bahadur type asymptotic representation of regression quantiles is established and this yields a general asymptotic theory of l estimators for the linear model a leading example of the proposed estimators is an analog of the trimmed mean trq which is asymptotically equivalent to the trimmed least squares estimator studied by ruppert and carroll 1980 but appears to be somewhat less sensitive to influential design observations this estimator is also asymptotically equivalent to the well known huber m estimator but offers the significant advantage that it is scale invariant we illustrate the methods by reconsidering a mid 18th century linear model analyzed b

on the law of the iterated logarithm for independent banach space valued random variables in this paper we establish some general forms of the law of the iterated logarithm for independent random variables xn with banach space values where xn is not necessarily identically distributed our results include the kolmogorov law of the iterated logarithm lil in both finite and infinite dimensional cases and they improve the wittmann lil as well as extend it to the vector setting the ledoux talagrand lil for an i i d sequence is also a simple corollary of our results

monotone b spline smoothing abstract estimation of growth curves or item response curves often involves monotone data smoothing methods that have been studied in the literature tend to be either less flexible or more difficult to compute when constraints such as monotonicity are incorporated built on the ideas of koenker ng and portnoy and ramsay we propose monotone b spline smoothing based on l 1 optimization this method inherits the desirable properties of spline approximations and the computational efficiency of linear programs the constrained fit is similar to the unconstrained estimate in terms of computational complexity and asymptotic rate of convergence through applications to some real and simulated data we show that the method is useful in a variety of applications the basic ideas utilized in monotone smoothing can be useful in some other constrained function estimation problems

the classification of doubly periodic minimal tori with parallel ends let k be the space of properly embedded minimal tori in quotients of r 3 by two independent translations with any fixed even number of parallel ends after an appropriate normalization we prove that k is a 3 dimensional real analytic manifold that reduces to the finite coverings of the examples defined by karcher meeks and rosenberg in 9 10 15 the degenerate limits of surfaces in k are the catenoid the helicoid and three 1 parameter families of surfaces the simply and doubly periodic scherk minimal surfaces and the riemann minimal examples

higher order infinitesimal robustness using the von mises expansion we study the higher order infinitesimal robustness of a general m functional and characterize its second order properties we show that second order robustness is equivalent to the boundedness of both the estimator s estimating function and its derivative with respect to the parameter it implies at the same time i variance robustness and ii robustness of higher order saddlepoint approximations to the estimator s finite sample density the proposed construction of second order robust m estimators is fairly general and potentially useful in a variety of relevant settings besides the theoretical contributions we discuss the main computational issues and provide an algorithm for the implementation of second order robust m estimators finally we illustrate our theory by monte carlo simulation and in a real data estimation of the maximal losses of nikkei 225 index returns our findings indicate that second order robust estimators can improve on other widely applied robus

a strongly consistent information criterion for linear model selection based on m estimation in this paper a linear model selection procedure based on m estimation is proposed which includes many classical model selection criteria as its special cases it is shown that the proposed criterion is strongly consistent under certain mild conditions for instance without assuming normality of the distribution of the random errors the results from a simulation study are also presented

multiple imputation in quantile regression summary we propose a multiple imputation estimator for parameter estimation in a quantile regression model when some covariates are missing at random the estimation procedure fully utilizes the entire dataset to achieve increased efficiency and the resulting coefficient estimators are root n consistent and asymptotically normal to protect against possible model misspecification we further propose a shrinkage estimator which automatically adjusts for possible bias the finite sample performance of our estimator is investigated in a simulation study finally we apply our methodology to part of the eating at american s table study data investigating the association between two measures of dietary intake

asymptotic distributions of principal components based on robust dispersions algebraically principal components can be defined as the eigenvalues and eigenvectors of a covariance or correlation matrix but they are statistically meaningful as successive projections of the multivariate data in the direction of maximal variability an attractive alternative in robust principal component analysis is to replace the classical variability measure i e variance by a robust dispersion measure this projection pursuit approach was first proposed in li chen 1985 as a method of constructing a robust scatter matrix recent unpublished work of c croux and a ruiz gazen provided the influence functions of the resulting principal components the present paper focuses on the asymptotic distributions of robust principal components in particular we obtain the asymptotic normality of the principal components that maximise a robust dispersion measure we also explain the need to use a dispersion functional with a continuous influence function

variable selection for partially linear models with measurement errors this article focuses on variable selection for partially linear models when the covariates are measured with additive errors we propose two classes of variable selection procedures penalized least squares and penalized quantile regression using the nonconvex penalized principle the first procedure corrects the bias in the loss function caused by the measurement error by applying the so called correction for attenuation approach whereas the second procedure corrects the bias by using orthogonal regression the sampling properties for the two procedures are investigated the rate of convergence and the asymptotic normality of the resulting estimates are established we further demonstrate that with proper choices of the penalty functions and the regularization parameter the resulting estimates perform asymptotically as well as an oracle procedure as proposed by fan and li choice of smoothing parameters is also discussed finite sample performance of the proposed variable selection procedures is asse

uniqueness of the spatial median on montre que si une mesure de probabilite sur un espace euclidien n est pas concentree sur une droite alors sa mediane spatiale est unique

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

on ranking and generalization bounds the problem of ranking is to predict or to guess the ordering between objects on the basis of their observed features in this paper we consider ranking estimators that minimize the empirical convex risk we prove generalization bounds for the excess risk of such estimators with rates that are faster than 1 n we apply our results to commonly used ranking algorithms for instance boosting or support vector machines moreover we study the performance of considered estimators on real data sets

an enhanced quantile approach for assessing differential gene expressions due to the small number of replicates in typical gene microarray experiments the performance of statistical inference is often unsatisfactory without some form of information sharing across genes in this article we propose an enhanced quantile rank score test eqrs for detecting differential expression in genechip studies by analyzing the quantiles of gene intensity distributions through probe level measurements a measure of sign correlation delta plays an important role in the rank score tests by sharing information across genes we develop a calibrated estimate of delta which reduces the variability at small sample sizes we compare the eqrs test with four other approaches for determining differential expression the gene specific quantile rank score test the quantile rank score test assuming a common delta a modified t test using summarized probe set level intensities and the mack skillings rank test on probe level data the proposed eqrs is shown to be favorable for preserving false discovery rates and for being robust against outlying arrays in addition we demonstrate the merits of the proposed approach using a genechip study comparing gene expression in the livers of mice exposed to chronic intermittent hypoxia and of those exposed to intermittent room air

measurement errors in quantile regression models abstract this paper develops estimation and inference for quantile regression models with measurement errors we propose an easily implementable semiparametric two step estimator when repeated measures for the covariates are available building on recent theory on z estimation with infinite dimensional parameters consistency and asymptotic normality of the proposed estimator are established we also develop statistical inference procedures and show the validity of a bootstrap approach to implement the methods in practice monte carlo simulations assess the finite sample performance of the proposed methods we apply the methods to the investment equation model using a firm level data with repeated measures of investment demand tobin s q we document strong heterogeneity in the sensitivity of investment to tobin s q and cash flow across the conditional distribution of investment the cash flow sensitivity is relatively larger at the lower part of the distribution providing evidence that these firms are more exposed to and dependent on fluctuations in internal finance

the classification of singly periodic minimal surfaces with genus zero and scherk type ends given an integer k 2 let s k be the space of complete embedded singly periodic minimal surfaces in r 3 which in the quotient have genus zero and 2k scherk type ends surfaces in s k can be proven to be proper a condition under which the asymptotic geometry of the surfaces is well known it is also known that s 2 consists of the 1 parameter family of singly periodic scherk minimal surfaces we prove that for each k 3 there exists a natural one to one correspondence between s k and the space of convex unitary nonspecial polygons through the map which assigns to each m s k the polygon whose edges are the flux vectors at the ends of m a special polygon is a parallelogram with two sides of length 1 and two sides of length k 1 as consequence s k reduces to the saddle towers constructed by karcher

inference for linear models with dependent errors summary the paper is concerned with inference for linear models with fixed regressors and weakly dependent stationary time series errors theoretically we obtain asymptotic normality for the m estimator of the regression parameter under mild conditions and establish a uniform bahadur representation for recursive m estimators methodologically we extend the recently proposed self normalized approach of shao from stationary time series to the regression set up where the sequence of response variables is typically non stationary in mean since the limiting distribution of the self normalized statistic depends on the design matrix and its corresponding critical values are case dependent we develop a simulation based approach to approximate the critical values consistently through a simulation study we demonstrate favourable finite sample performance of our method in comparison with a block bootstrap based approach empirical illustrations using two real data sets are also provided

two stage least absolute deviations estimators1 in this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model a class of estimators called two stage least absolute deviations estimators is defined their asymptotic properties are derived and the problem of finding the optimal member of the class is considered in this paper we apply the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model we define a class of estimators called two stage least absolute deviations estimators 2slad and derive their asymptotic properties they are so named as their relationship to the two stage least squares estimator 2sls is analogous to the relationship of the least absolute deviations estimator lad to the least squares estimator ls in the standard regression model the lad estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized in this paper we show that the advantage of 2slad over 2sls in the simultaneous equations model can be as great as that of lad over ls in the standard regression model if 2slad is properly defined this last clause is very important since the results of this paper indicate that the lad analogue of 2sls that has been considered before in the literature is not an appropriate method

prediction of functional status for the elderly based on a new ordinal regression model the functional mobility of the elderly is a very important factor in aging research and prognostic information is valuable in making clinical and health care policy decisions we develop a predictive model for the functional status of the elderly based on data from the second longitudinal study of aging lsoa ii the functional status is an ordinal response variable the ordered probit model has been moderately successful in analyzing such data however its reliance on the normal distribution for its latent variable hinders its accuracy and potential in this paper we focus on the prediction of conditional quantiles of the functional status based on a more general transformation model the proposed estimation procedure does not rely on any parametric specification of the conditional distribution functions aiming to reduce model misspecification errors in the prediction cross validation within the lsoa ii data shows that our prediction intervals are more informative than those from the ordered probit

locally weighted censored quantile regression censored quantile regression offers a valuable supplement to cox proportional hazards model for survival analysis existing work in the literature often requires stringent assumptions such as unconditional independence of the survival time and the censoring variable or global linearity at all quantile levels moreover some of the work uses recursive algorithms making it challenging to derive asymptotic normality to overcome these drawbacks we propose a new locally weighted censored quantile regression approach that adopts the redistribution of mass idea and employs a local reweighting scheme its validity only requires conditional independence of the survival time and the censoring variable given the covariates and linearity at the particular quantile level of interest our method leads to a simple algorithm that can be conveniently implemented with r software applying recent theory of m estimation with infinite dimensional parameters we establish the consistency and asymptotic normality of the pr

on rank estimators in increasing dimensions abstract the family of rank estimators including han s maximum rank correlation han 1987 as a notable example has been widely exploited in studying regression problems for these estimators although the linear index is introduced for alleviating the impact of dimensionality the effect of large dimension on inference is rarely studied this paper fills this gap via studying the statistical properties of a larger family of m estimators whose objective functions are formulated as u processes and may be discontinuous in increasing dimension set up where the number of parameters p n in the model is allowed to increase with the sample size n first we find that often in estimation as p n n 0 p n n 1 2 rate of convergence is obtainable second we establish bahadur type bounds and study the validity of normal approximation which we find often requires a much stronger scaling requirement than p n 2 n 0 third we state conditions under which the numerical derivative estimator of asymptotic covariance matrix is consistent and show that the step size in implementing the covariance estimator has to be adjusted with respect to p n all theoretical results are further backed up by simulation studies

spacelike hypersurfaces with prescribed boundary values and mean curvature we consider the boundary value problem for the mean curvature operator in minkowski space and give necessary and sufficient conditions for the existence of smooth strictly spacelike solutions our main results hold for non constant mean curvature and make no assumptions about the smoothness of the boundary or boundary data

asymptotic distributions of the maximal depth estimators for regression and multivariate location we derive the asymptotic distribution of the maximal depth regression estimator recently proposed in rousseeuw and hubert the estimator is obtained by maximizing a projection based depth and the limiting distribution is characterized through a max min operation of a continuous process the same techniques can be used to obtain the limiting distribution of some other depth estimators including tukey s deepest point based on half space depth results for the special case of two dimensional problems have been available but the earlier arguments have relied on some special geometric properties in the low dimensional space this paper completes the extension to higher dimensions for both regression and multivariate location models

the structure of hopf algebras with a projection the smash product algebra and the smash coproduct coalgebra are well known in the context of hopf algebras 1 5 and these notions can be viewed as being motivated by the semidirect product construction in the theory of groups and in the theory of afiine group schemes respectively let

a useful estimate in the multidimensional invariance principle an estimate of the convergence speed in the multidimensional invariance principle is obtained using this estimate we can prove strong invariance principles for partial sums of independent not necessarily identically distributed multidimensional random vectors

crossed products for weak hopf algebras with coalgebra splitting in this paper we prove that if g b h is a morphism of weak hopf algebras which is split as a coalgebra morphism then there exists a subalgebra bh of b morphisms bh h bh bh bh h h bh and an isomorphism of algebras and right h comodules bb b bh h being bh h a subobject of bh h with its algebra structure defined by a crossed product also we obtain the dual results and as a consequence we prove the radford s theorem for weak hopf algebras

a distributional approach for causal inference using propensity scores drawing inferences about the effects of treatments and actions is a common challenge in economics epidemiology and other fields we adopt rubin s potential outcomes framework for causal inference and propose two methods serving complementary purposes one can be used to estimate average causal effects assuming no confounding given measured covariates the other can be used to assess how the estimates might change under various departures from no confounding both methods are developed from a nonparametric likelihood perspective the propensity score plays a central role and is estimated through a parametric model under the assumption of no confounding the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution expectations from the joint distribution are estimated as weighted averages or equivalently to first order regression estimates the likelihood estimator is at least as efficient and the regression estimator is at least as efficient and r

concavity and estimation on donne des conditions simplifiees pour la consistance et la normalite asymptotique d estimations m deduites par maximisation de moyennes de fonctions concaves aleatoires identiquement distribuees et independantes des applications sont donnees pour l estimation de maximum de vraisemblance

empirical likelihood and quantile regression in longitudinal data analysis we propose a novel quantile regression approach for longitudinal data analysis which naturally incorporates auxiliary information from the conditional mean model to account for within subject correlations the efficiency gain is quantified theoretically and demonstrated empirically via simulation studies and the analysis of a real dataset

adaptive l estimation for linear models asymptotically efficient adaptive estimators for the slope parameters of the linear regression model are constructed based upon the regression quantile statistics suggested by koenker and bassett the estimators are natural analogues of the adaptive l estimators of location of sacks but employ kernel density type estimators of the optimal l estimator weight function

detecting differential expressions in genechip microarray studies a quantile approach in this article we consider testing for differentially expressed genes in genechip studies by modeling and analyzing the quantiles of gene expression through probe level measurements by developing a robust rank score test for linear quantile models with a random effect we propose a reliable test for detecting differences in certain quantiles of the intensity distributions by using a genomewide adjustment to the test statistic to account for within array correlation we demonstrate that the proposed rank score test is highly effective even when the number of arrays is small our empirical studies with real experimental data show that detecting differences in the quartiles for the probe level data is a valuable complement to the usual mixed model analysis based on gaussian likelihood the methodology proposed in this article is a first attempt to develop inferential tools for quantile regression in mixed models

weak hopf algebras ii representation theory dimensions and the markov trace abstract if a is a weak c hopf algebra then the category of finite dimensional unitary representations of a is a monoidal c category with its monoidal unit being the gns representation d e associated to the counit e this category has isomorphic left dual and right dual objects which leads as usual to the notion of a dimension function however if e is not pure the dimension function is matrix valued with rows and columns labeled by the irreducibles contained in d e this happens precisely when the inclusions a l a and a r a are not connected still there exists a trace on a which is the markov trace for both inclusions we derive two numerical invariants for each c wha of trivial hypercenter these are the common indices i and of the haar respectively markov conditional expectations of either one of the inclusions a l r a or a l r a in generic cases i in the special case of weak kac algebras we reproduce d nikshych s result 2000 j operator theory to appear by showing that i and is always an integer