conditional scores and optimal scores for generalized linear measurement error models abstract this paper studies estimation of the parameters of generalized linear models in canonical form when the explanatory vector is measured with independent normal error for the functional case i e when the explanatory vectors are fixed constants unbiased score functions are obtained by conditioning on certain sufficient statistics this work generalizes results obtained for logistic regression in the case that the explanatory vectors are independent and identically distributed with unknown distribtuion efficient score functions are obtained using the theory developed in begun et al 1983 keywords conditional score function efficient score function functional model generalized linear model measurement error structural model

metriques de carnot cartheodory et quasiisometries des espaces symetriques de rang un we exhibit a rigidity property of the simple groups sp n 1 and f7 20 which implies mostow rigidity this property does not extend to o n 1 and u n 1 the proof relies on quasiconformal theory applied in the cr setting extensions are given to a class of solvable lie groups as a byproduct a result on quasiisometries of infinite nilpotent groups is obtained dans cet article on etablit une propriete de rigidite des groupes simples de rang un sp n 1 n 2 2 et fqui entraine la rigidite de mostow 1 theoreme toute quasiisornwtrie de 1 espace hyperbolique quaternionien hhn n 2 resp du plan hyperbolique de cayley cah2 est d distance bornee d une isometrie i e differe d une isomnetrie par une application qui diplace les points d une distance bornee une application f entre espaces metriques est une quasiisometrie s il existe des constantes l et c telles que l image de f soit c dense et que pour tous x y c d x y d fx fy ld x y c l une quasiisometrie entre des g et g est une sorte d isomorphisme virtuel dans la categorie topologique en effet cela correspond a une action de g sur un fibre principal c de groupe g sur une base compacte cf ra un isomorphisme entre sous groupes cocompacts covolume fini suffit pour les groupes simples de rang un de groupes de lie s etend en une quasiisometrie des espaces symetriques ou des groupes de lie si celle ci est proche d une isometrie des espaces symetriques resp un isomorphisme des groupes de lie les sous groupes sont conjugues c est la rigidite de mostow m2 la propriete ci dessus ne s etend pas aux groupes o n 1 et u n 1 en effet paragraphe 11 7 ceux ci ont beaucoup de quasiisometries au moins this content downloaded from 207 46 13 92 on sun 20 nov 2016 04 26 46 utc all use subject to http about jstor org terms

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

optimal rates of convergence for deconvolving a density abstract suppose that the sum of two independent random variables x and z is observed where z denotes measurement error and has a known distribution and where the unknown density f of x is to be estimated one application is the estimation of a prior density for a sequence of location parameters a second application arises in the errors in variables problem for nonlinear and generalized linear models when one attempts to model the distribution of the true but unobservable covariates this article shows that if z is normally distributed and f has k bounded derivatives then the fastest attainable convergence rate of any nonparametric estimator of f is only log n k 2 therefore deconvolution with normal errors may not be a practical proposition other error distributions are also treated stefanski carroll 1987a estimators achieve the optimal rates the results given have versions for multiplicative errors where they imply that even optimal rates are exceptionally slow

errors in variables jump regression using local clustering errors in variables eiv regression is widely used in econometric models the statistical analysis becomes challenging when the regression function is discontinuous and the distribution of measurement error is unknown in the literature most existing jump regression methods either assume that there is no measurement error involved or require that jumps are explicitly detected before the regression function can be estimated in some applications however the ultimate goal is to estimate the regression function and to preserve the jumps in the process of estimation in this paper we are concerned with reconstructing jump regression curve from data that involve measurement error we propose a direct jump preserving method that does not explicitly detect jumps the challenge of restoring jump structure masked by measurement error is handled by local clustering theoretical analysis shows that the proposed curve estimator is statistically consistent a numerical comparison with an existing jump regression method highlights its jump preserving property finally we demonstrate our method by an application to a health tax policy study in australia

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

small time heat kernel asymptotics at the sub riemannian cut locus for a sub riemannian manifold provided with a smooth volume we relate the small time asymptotics of the heat kernel at a point y of the cut locus from x with roughly how much y is conjugate to x this is done under the hypothesis that all minimizers connecting x to y are strongly normal i e all pieces of the trajectory are not abnormal our result is a renement of the one of leandre 4t logpt x y d 2 x y for t 0 in which only the leading exponential term is detected our results are obtained by extending an idea of molchanov from the riemannian to the sub riemannian case and some details we get appear to be new even in the riemannian context these results permit us to obtain properties of the sub riemannian distance starting from those of the heat kernel and vice versa for the grushin plane endowed with the euclidean volume we get the expansion pt x y t 5 4 exp d 2 x y 4t where y is reached from a riemannian point x by a minimizing geodesic which is conjugate at y

the existence of a global fundamental solution for homogeneous hormander operators via a global lifting method we prove the existence of a global fundamental solution x y with pole x for any hormander operator l i 1mxi2 on rn which is homogeneous of degree 2 here homogeneity is meant with respect to a family of non isotropic diagonal maps of the form x 1x1 nxn with 1 1 n due to a global lifting method for homogeneous operators proved by folland comm partial differential equations 2 1977 161 207 there exists a carnot group g and a polynomial surjective map g rn such that l is related to a sub laplacian lg on g we show that it is always possible to perform a global change of variable on g such that the lifting map becomes the projection of g rn rp onto rn we prove that an integration argument over the non compact fibers of provides a fundamental solution for l indeed if g x x y y x y rn x y rp is the fundamental solution of lg we show that g x 0 y y is always integrable with respect to y rp and its y integral is a fundamental solution for l

the intrinsic hypoelliptic laplacian and its heat kernel on unimodular lie groups we present an invariant definition of the hypoelliptic laplacian on sub riemannian structures with constant growth vector using the popp s volume form introduced by montgomery this definition generalizes the one of the laplace beltrami operator in riemannian geometry in the case of left invariant problems on unimodular lie groups we prove that it coincides with the usual sum of squares we then extend a method first used by hulanicki on the heisenberg group to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular lie group of type i the main tool is the noncommutative fourier transform we then study some relevant cases su 2 so 3 sl 2 with the metrics inherited by the killing form and the group se 2 of rototranslations of the plane our study is motivated by some recent results about the cut and conjugate loci on these sub riemannian manifolds the perspective is to understand how singularities of the sub riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

slope estimation in the presence of informative right censoring modeling the number of observations as a geometric random variable summary a method is proposed for the estimation of rate of change from incomplete longitudinal data where the number of observations made for each subject is assumed to vary depending on the level of the response variable the proposed method involves a random slope model in which the number of observations is modeled as a geometric distribution with its mean dependent on the individual subject s rate of change the method adjusts for informative right censoring and provides estimates of the slopes of individual subjects as well as of the population under noninformative right censoring these estimators of the slopes are equivalent to bayes estimators fearn 1975 biometrika 62 89 100 the simulation study demonstrates that in cases where the censoring process is informative the proposed estimator is more efficient than either the unweighted or weighted estimator of slope the method is illustrated by the analysis of renal transplant data

nonparametric prediction in measurement error models predicting the value of a variable y corresponding to a future value of an explanatory variable x based on a sample of previously observed independent data pairs x1 y1 xn yn distributed like x y is very important in statistics in the error free case where x is observed accurately this problem is strongly related to that of standard regression estimation since prediction of y can be achieved via estimation of the regression curve e y x when the observed xis and the future observation of x are measured with error prediction is of a quite different nature here if t denotes the future contaminated available version of x prediction of y can be achieved via estimation of e y t in practice estimating e y t can be quite challenging as data may be collected under different conditions making the measurement errors on xi and x nonidentically distributed we take up this problem in the nonparametric setting and introduce estimators which allow a highly adaptive approach to smoothing

the effect of measurement error summary measurement error causes the distribution generating data to differ from the distribution that is of substantive interest to understand the effect of measurement error on the information produced by statistical procedures it is thus necessary to understand the distortions induced by measurement error this paper sheds light on this by providing small error variance approximations to the distribution of variates subject to contamination by measurement error these provide the basis for the analysis of the properties of estimators and tests and less formal procedures when measurement error is present and the basis for the development of tests to detect measurement error and of models which incorporate its influence

on some universal algebras associated to the category of lie bialgebras in our previous work math 0008128 we studied the set quant k of all universal quantization functors of lie bialgebras over a field k of characteristic zero compatible with the operations of taking duals and doubles we showed that quant k is canonically isomorphic to a product g0 k k where g0 k is a universal group and k is a quotient set of a set b k of families of lie polynomials by the action of a group g k we prove here that g0 k is equal to the multiplicative group 1 k so quant k is as close as it can be to k we also prove that the only universal derivations of lie bialgebras are multiples of the composition of the bracket with the cobracket finally we prove that the stabilizer of any element of b k is reduced to the 1 parameter subgroup generated by the corresponding square of the antipode

on the invertibility of quantization functors certain quantization problems are equivalent to the construction of morphisms from quantum to classical props once such a morphism is constructed hensel s lemma shows that it is in fact an isomorphism this gives a new simple proof that any etingof kazhdan quantization functor is an equivalence of categories between quantized universal enveloping que algebras and lie bialgebras over a formal series ring dequantization we apply the same argument to construct dequantizations of formal solutions of the quantum yang baxter equation and of quasitriangular que algebras we derive from there a classification of all twistors killing a given associator we also give structure results for the props involved in quantization of lie bialgebras which yield an associator independent proof that the prop of que algebras is a flat deformation of the prop of co poisson universal enveloping algebras

short time asymptotics of heat kernels for a class of hypoelliptic operators we compute the short time asymptotics of heat kernels for a family of hypoelliptic operators and we relate these to the value function of an associated variational problem previously investigated in the control theory literature these heat kernels generalize to the noncontact case a heat kernel that has been previously obtained for the contact hypoelliptic laplacian defined on the heisenberg group

instrumental variable estimation in binary regression measurement error models abstract we describe two approaches to instrumental variable estimation in binary regression measurement error models the methods entail constructing approximate mean models for the binary response as a function of the measured predictor the instrument and any covariates in the model estimates are obtained by exploiting relationships between regression parameters just as in linear instrumental variable estimation in the course of deriving the approximate mean models we obtain an alternative characterization of instrumental variable estimation in linear measurement error models

uniqueness of coxeter structures on kac moody algebras abstract let g be a symmetrizable kac moody algebra and u g the corresponding quantum group we showed in 1 2 that the braided coxeter structure on integrable category o representations of u g which underlies the r matrix actions arising from the levi subalgebras of u g and the quantum weyl group action of the generalized braid group b g can be transferred to integrable category o representations of g we prove in this paper that up to unique equivalence there is a unique such structure on the latter category with prescribed restriction functors r matrices and local monodromies this extends simplifies and strengthens a similar result of the second author valid when g is semisimple and is used in 3 to describe the monodromy of the rational casimir connection of g in terms of the quantum weyl group operators of u g our main tool is a refinement of enriquez s universal algebras which is adapted to the prop describing a lie bialgebra graded by the non negative roots of g

comprehensive definitions of breakdown points for independent and dependent observations summary we provide a new definition of breakdown in finite samples with an extension to asymptotic breakdown previous definitions centre on defining a critical region for either the parameter or the objective function if for a particular outlier configuration the critical region is entered breakdown is said to occur in contrast with the traditional approach we leave the definition of the critical region implicit our proposal encompasses previous definitions of breakdown in linear and non linear regression settings in some cases it leads to a different and more intuitive notion of breakdown than other procedures that are available an important advantage of our new definition is that it also applies to models for dependent observations where current definitions of breakdown typically fail we illustrate our suggestion by using examples from linear and non linear regression and time series

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

using simex for smoothing parameter choice in errors in variables problems simex methods are attractive for solving curve estimation problems in errors in variables regression using parametric or semiparametric techniques however nonparametric approaches are generally of quite a different type being based on for example kernels local linear modeling ridging orthogonal series or splines all of these techniques involve the challenging and not well studied issue of empirical smoothing parameter choice we show that simex can be used effectively for selecting smoothing parameters when applying nonparametric methods to errors in variable regression in particular we suggest an approach based on multiple error inflated or remeasured data sets and extrapolation

low order approximations in deconvolution and regression with errors in variables summary we suggest two new methods which are applicable to both deconvolution and regression with errors in explanatory variables for nonparametric inference the two approaches involve kernel or orthogonal series methods they are based on defining a low order approximation to the problem at hand and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently of course both techniques could be employed to construct consistent estimators but in many contexts of importance e g those where the errors are gaussian consistency is from a practical viewpoint an unattainable goal we rephrase the problem in a form where an explicit interpretable low order approximation is available the information that we require about the error distribution the error in variables distribution in the case of regression is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors e g through repeated measurements in particular we do not need to estimate a function such as a characteristic function which expresses detailed properties of the error distribution this feature of our methods coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages means that the methods are particularly economical in computing time

invariant carnot caratheodory metrics on s 3 so 3 sl 2 and lens spaces in this paper we study the carnot caratheodory metrics on su 2 simeq s 3 so 3 and sl 2 induced by their cartan decomposition and by the killing form besides computing explicitly geodesics and conjugate loci we compute the cut loci globally and we give the expression of the carnot caratheodory distance as the inverse of an elementary function we then prove that the metric given on su 2 projects on the so called lens spaces l p q also for lens spaces we compute the cut loci globally for su 2 the cut locus is a maximal circle without one point in all other cases the cut locus is a stratified set to our knowledge this is the first explicit computation of the whole cut locus in sub riemannian geometry except for the trivial case of the heisenberg group

groups and lie algebras corresponding to the yang baxter equations for a positive integer n we introduce quadratic lie algebras tr n qtr n and finitely discrete groups tr n qtr n naturally associated with the classical and quantum yang baxter equation respectively we prove that the universal enveloping algebras of the lie algebras tr n qtr n are koszul and compute their hilbert series we also compute the cohomology rings for these lie algebras which by koszulity are the quadratic duals of the enveloping algebras finally we construct a basis of u tr n we construct cell complexes which are classifying spaces of the groups tr n and qtr n and show that the boundary maps in them are zero which allows us to compute the integral cohomology of these groups we show that the lie algebras tr n qtr n map onto the associated graded algebras of the malcev lie algebras of the groups tr n qtr n respectively in the case of tr n we use quantization theory of lie bialgebras to show that this map is actually an isomorphism at the same time we show that the groups tr n and qtr n are not formal for n 4

quantization of γ lie bialgebras abstract we introduce the notion of lie bialgebras where is a group these objects give rise to cocommutative co poisson bialgebras for which we construct quantization functors this enlarges the class of co poisson algebras for which a quantization is known our result relies on our earlier work where we showed that twists of lie bialgebras can be quantized we complement this work by studying the behavior of this quantization under compositions of twists

a cohomological construction of quantization functors of lie bialgebras abstract we propose a variant to the etingof kazhdan construction of quantization functors we construct the twistor j associated to an associator using cohomological techniques we then introduce a criterion ensuring that the left hopf algebra of a quasitriangular que algebra is flat we prove that this criterion is satisfied at the universal level this gives a construction of quantization functors equivalent to the etingof kazhdan construction

fundamental solution of a higher step grushin type operator abstract we examine a class of grushin type operators p k where k n 0 defined in 1 1 the operators p k are non elliptic and degenerate on a sub manifold of r n l geometrically they arise via a submersion from a sub laplace operator on a nilpotent lie group of step k 1 we explain the geometric framework and prove some analytic properties such as essential self adjointness the main purpose of the paper is to give an explicit expression of the fundamental solution of p k our methods rely on an appropriate change of coordinates and involve the theory of bessel and modified bessel functions together with weber s second exponential integral

short time asymptotics of heat kernels of hypoelliptic laplacians on unimodular lie groups abstract we consider the problem of computing heat kernel small time asymptotics for hypoelliptic laplacians associated to left invariant sub riemannian structures on unimodular lie groups of type i we use the non commutative fourier transform of the lie group together with perturbation theory for semigroups of operators in deriving these asymptotics we illustrate our approach on the example of the heisenberg group and as an application we compute the short time behaviour of the hypoelliptic heat kernel on the step 3 nilpotent cartan and engel groups for which no closed form expression for the hypoelliptic heat kernel is yet known

a new online calibration method for multidimensional computerized adaptive testing multidimensional method a m method a has been proposed as an efficient and effective online calibration method for multidimensional computerized adaptive testing mcat chen xin paper presented at the 78th meeting of the psychometric society arnhem the netherlands 2013 however a key assumption of m method a is that it treats person parameter estimates as their true values thus this method might yield erroneous item calibration when person parameter estimates contain non ignorable measurement errors to improve the performance of m method a this paper proposes a new mcat online calibration method namely the full functional mle m method a ffmle m method a this new method combines the full functional mle jones jin in psychometrika 59 59 75 1994 stefanski carroll in annals of statistics 13 1335 1351 1985 with the original m method a in an effort to correct for the estimation error of ability vector that might otherwise adversely affect the precision of item calibration two correction schemes are also proposed when implementing the new method a simulation study was conducted to show that the new method generated more accurate item parameter estimation than the original m method a in almost all conditions

anthropomorphic image reconstruction via hypoelliptic diffusion in this paper we study a model of geometry of vision due to petitot citti and sarti one of the main features of this model is that the primary visual cortex v1 lifts an image from mathbb r 2 to the bundle of directions of the plane neurons are grouped into orientation columns each of them corresponding to a point of this bundle in this model a corrupted image is reconstructed by minimizing the energy necessary for the activation of the orientation columns corresponding to regions in which the image is corrupted the minimization process intrinsically defines a hypoelliptic heat equation on the bundle of directions of the plane in the original model directions are considered both with and without orientation giving rise respectively to a problem on the group of rototranslations of the plane se 2 or on the projective tangent bundle of the plane pt mathbb r 2 we provide a mathematical proof of several important facts for this model we first prove that the model is mathematically consis

a modified estimating equation approach to correcting for measurement error in regression summary a modified estimating equation approach is proposed to correct for measurement error in regression problems we allow changing measurement error variances and covariances across units allow the regressors to be fixed allow estimation of the measurement error variances covariances and account for uncertainty arising from this estimation and explicitly model measurement error in the response multiple linear quadratic poisson and logistic regression are considered in detail and it is seen that some previously developed estimators arise as special cases from the proposed approach a small simulation study is presented for logistic regression

covariance analysis in generalized linear measurement error models we summarize some of the recent work on the errors in variables problem in generalized linear models the focus is on covariance analysis and in particular testing for and estimation of treatment effects there is a considerable difference between the randomized and non randomized models when testing for an effect in randomized studies simple techniques exist for testing for a treatment effect in some instances such as linear and multiplicative regression simple methods exist for estimating the treatment effect in other examples such as logistic regression estimating a treatment effect requires careful attention to measurement error in non randomized studies there is no recourse to understanding and modelling measurement error in particular ignoring measurement error can lead to the wrong conclusions for example the true but unobserved data may indicate a positive effect for treatment while the observed data indicate the opposite some of the possible methods are outlined and compared

a design adaptive local polynomial estimator for the errors in variables problem local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature their simplest version the local constant estimator can be easily extended to the errors in variables context by exploiting its similarity with the deconvolution kernel density estimator the generalization of the higher order versions of the estimator however is not straightforward and has remained an open problem for the last 15 years we propose an innovative local polynomial estimator of any order in the errors in variables context derive its design adaptive asymptotic properties and study its finite sample performance on simulated examples we provide not only a solution to a long standing open problem but also provide methodological contributions to error in variable regression including local polynomial estimation of derivative functions

besov and triebel lizorkin spaces on lie groups in this paper we develop a theory of besov and triebel lizorkin spaces on general noncompact connected lie groups endowed with a sub riemannian structure such spaces are defined by means of hypoelliptic sub laplacians with drift and endowed with a measure whose density with respect to a right haar measure is a continuous positive character of the group we prove several equivalent characterizations of their norms we establish comparison results also involving sobolev spaces of recent introduction and investigate their complex interpolation and algebra properties

estimation of the quadratic errors in variables model summary an estimator is presented for the coefficients of the quadratic functional relationship the estimator is shown to be asymptotically normally distributed as the sample size increases in deriving this result it is not assumed that replication occurs a monte carlo study is presented agreeing well with the asymptotic results an example from the earth sciences is analysed

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

sobolev spaces on lie groups embedding theorems and algebra properties abstract let g be a noncompact connected lie group denote with a right haar measure and choose a family of linearly independent left invariant vector fields x on g satisfying hormander s condition let be a positive character of g and consider the measure whose density with respect to is in this paper we introduce sobolev spaces l p adapted to x and 1 p 0 and study embedding theorems and algebra properties of these spaces as an application we prove local well posedness and regularity results of solutions of some nonlinear heat and schrodinger equations on the group

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

intrinsic random walks and sub laplacians in sub riemannian geometry on a sub riemannian manifold we define two type of laplacians the macroscopic laplacian as the divergence of the horizontal gradient once a volume is fixed and the microscopic laplacian as the operator associated with a geodesic random walk we consider a general class of random walks where all sub riemannian geodesics are taken in account this operator depends only on the choice of a complement c to the sub riemannian distribution and is denoted l c we address the problem of equivalence of the two operators this problem is interesting since on equiregular sub riemannian manifolds there is always an intrinsic volume e g popp s one p but not a canonical choice of complement the result depends heavily on the type of structure under investigation on contact structures for every volume there exists a unique complement c such that l c on carnot groups if h is the haar volume then there always exists a complement c such that h l c however this complement is not unique in general for quasi contact structures in general p l c for any choice of c in particular l c is not symmetric w r t popp s measure this is surprising especially in dimension 4 where in a suitable sense p is the unique intrinsic macroscopic laplacian a crucial notion that we introduce here is the n intrinsic volume i e a volume that depends only on the set of parameters of the nilpotent approximation when the nilpotent approximation does not depend on the point a n intrinsic volume is unique up to a scaling by a constant and the corresponding n intrinsic sub laplacian is unique this is what happens for dimension smaller or equal than 4 and in particular in the 4 dimensional quasi contact structure mentioned above

quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres a sharp l p spectral multiplier theorem of mihlin hormander type is proved for a distinguished sub laplacian on quaternionic spheres this is the first such result on compact sub riemannian manifolds where the horizontal space has corank greater than one the proof hinges on the analysis of the quaternionic spherical harmonic decomposition of which we present an elementary derivation

nonparametric methods for solving the berkson errors in variables problem summary it is common in errors in variables problems in regression to assume that the errors are incurred after the experiment in that the observed value of the explanatory variable is an independent perturbation of its true value however if the errors are incurred before the experiment then the true value of the explanatory variable equals a perturbation of its observed value this is the context of the berkson model which is increasingly attracting attention in parametric and semiparametric settings we introduce and discuss nonparametric techniques for analysing data that are generated by the berkson model our approach permits both random and regularly spaced values of the target doses in the absence of data on dosage error it is necessary to propose a distribution for the latter but we show numerically that our method is robust against that assumption the case of dosage error data is also discussed a practical method for smoothing parameter choice is suggested our techniques for errors in variables regression are shown to achieve theoretically optimal convergence rates

the subelliptic heat kernel on the cr sphere we study the heat kernel of the sub laplacian l on the cr sphere mathbb s 2n 1 an explicit and geometrically meaningful formula for the heat kernel is obtained as a by product we recover in a simple way the green function of the conformal sub laplacian l n 2 that was obtained by geller j differ geom 15 417 435 1980 and also get an explicit formula for the sub riemannian distance the key point is to work in a set of coordinates that reflects the symmetries coming from the fibration mathbb s 2n 1 rightarrow mathbb cp n

quantization of coboundary lie bialgebras we show that any coboundary lie bialgebra can be quantized for this we prove that a etingof kazhdan quantization functors are compatible with lie bialgebra twists and b if such a quantization functor corresponds to an even associator then it is also compatible with the operation of taking coopposites we also use the relation between the etingof kazhdan construction of quantization functors and the alternative approach to this problem which was established in a previous work

a comparison of n estimators for the binomial distribution abstract estimating the number n of trials given a sequence of independent success counts obtained by replicating the n trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution both the method of moments and the maximum likelihood estimators of n are considered when p is unknown and small while n is large both estimators become highly unstable stabilized versions of these estimators are proposed and their performance is described in terms of results obtained by simulation

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

curvature dimension inequalities on sub riemannian manifolds obtained from riemannian foliations part ii using the curvature dimension inequality proved in part i we look at consequences of this inequality in terms of the interaction between the sub riemannian geometry and the heat semigroup p t corresponding to the sub laplacian we give bounds for the gradient entropy a poincare inequality and a li yau type inequality these results require that the gradient of p t f remains uniformly bounded whenever the gradient of f is bounded and we give several sufficient conditions for this to hold

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

corrected loss estimation for quantile regression with covariate measurement errors we study estimation in quantile regression when covariates are measured with errors existing methods require stringent assumptions such as spherically symmetric joint distribution of the regression and measurement error variables or linearity of all quantile functions which restrict model flexibility and complicate computation in this paper we develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression the proposed method is simple to implement its validity requires only linearity of the particular quantile function of interest and it requires no parametric assumptions on the regression error distributions finite sample results demonstrate that the proposed estimators are more efficient than the existing methods in various models considered

quantum groups and deformation quantization explicit approaches and implicit aspects deformation quantization which gives a development of quantum mechanics independent of the operator algebra formulation and quantum groups which arose from the inverse scattering method and a study of yang baxter equations share a common idea abstracted earlier in algebraic deformation theory that algebraic objects have infinitesimal deformations which may point in the direction of certain continuous global deformations i e quantizations in deformation quantization the algebraic object is the algebra of observables functions on symplectic phase space whose infinitesimal deformation is the poisson bracket and global deformation a star product in quantum groups it is a hopf algebra generally either of functions on a lie group or often its dual in the topological vector space sense as we briefly explain a completed universal enveloping algebra of a lie algebra with for infinitesimal a matrix satisfying the modified classical yang baxter equation mcybe frequently existence proofs are known but explicit formulas useful for physical applications have been difficult to extract one success here comes from universal deformation formulas udfs expressions built from a lie algebra which deform any algebra on which the lie algebra operates as derivations the most famous of these is the moyal product a special case of a class in which the lie algebra is abelian another comes from recognition that the belavin drinfel d solutions to the mcybe are in fact infinitesimal deformations for which in the case of the special linear groups it is possible to give explicit formulas for the corresponding quantum yang baxter equations this review paper discusses necessarily in brief these and related topics including twisting as a form of udf and finding formulas for preferred deformations of hopf algebras in which the multiplication or comultiplication is rigid and must be preserved in the course of deformation

spectral asymptotics for sub riemannian laplacians i quantum ergodicity and quantum limits in the 3d contact case this is the first paper of a series in which we plan to study spectral asymptotics for sub riemannian laplacians and to extend results that are classical in the riemannian case concerning weyl measures quantum limits quantum ergodicity quasi modes trace formulae even if hypoelliptic operators have been well studied from the point of view of pde s global geometrical and dynamical aspects have not been the subject of much attention as we will see already in the simplest case the statements of the results in the sub riemannian setting are quite different from those in the riemannian one let us consider a sub riemannian sr metric on a closed three dimensional manifold with an oriented contact distribution there exists a privileged choice of the contact form with an associated reeb vector field and a canonical volume form that coincides with the popp measure we establish a quantum ergodicity qe theorem for the eigenfunctions of any associated sr laplacian under the assumption that the reeb flow is ergodic the limit measure is given by the normalized popp measure this is the first time that such a result is established for a hypoelliptic operator whereas the usual shnirelman theorem yields qe for the laplace beltrami operator on a closed riemannian manifold with ergodic geodesic flow to prove our theorem we first establish a microlocal weyl law which allows us to identify the limit measure and to prove the microlocal concentration of the eigenfunctions on the characteristic manifold of the sr laplacian then we derive a birkhoff normal form along this characteristic manifold thus showing that in some sense all 3d contact structures are microlocally equivalent the quantum version of this normal form provides a useful microlocal factorization of the sr laplacian using the normal form the factorization and the ergodicity assumption we finally establish a variance estimate from which qe follows we also obtain a second result which is valid without any ergodicity assumption every quantum limit ql can be interpreted as the sum of two mutually singular measures the first measure is supported on the unit cotangent bundle and is invariant under the sr geodesic flow and the second measure is supported on the characteristic manifold of the sr laplacian and is invariant under the lift of the reeb flow moreover we prove that the first measure is zero for most ql s