analysis of longitudinal binary data from multiphase sampling the efficient use of surrogate or auxiliary information has been investigated within both model based and design based approaches to data analysis particularly in the context of missing data here we consider the use of such data in epidemiological studies of disease incidence in which surrogate measures of disease status are available for all subjects at two time points but definitive diagnoses are available only in stratified subsamples we briefly review methods for the analysis of two phase studies of disease prevalence at a single time point and we discuss the extension of four of these methods to the analysis of incidence studies their performance is compared with special reference to a study of the incidence of senile dementia

inference for imputation estimators we derive an estimator of the asymptotic variance of both single and multiple imputation estimators we assume a parametric imputation model but allow for non and semiparametric analysis models our variance estimator in contrast to the estimator proposed by rubin 1987 is consistent even when the imputation and analysis models are misspecified and incompatible with one another

complex quantum groups and their quantum enveloping algebras we construct complexified versions of the quantum groups associated with the lie algebras of typean 1 bn cn anddn following the ideas of faddeev reshetikhin and takhtajan we obtain the hopf algebras of regular functionals u on these complexified quantum groups in the special examplea1 we derive theq deformed enveloping algebrauq sl 2 in the limitq 1 the undeformeduq sl 2 is recovered

transfer matrix eigenvalues of the anisotropic multiparametric u model a multiparametric extension of the anisotropic u model is discussed which maintains integrability the r matrix solving the yang baxter equation is obtained through a twisting construction applied to the underlying u q sl 2 1 superalgebraic structure which introduces the additional free parameters that arise in the model three forms of bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent

radial fourier multipliers of lp r2 abstract we give sufficient conditions in terms of differentiability and growth properties for a radial function to be an lp r2 fourier multiplier these conditions are in the nature of best possible

sub hopf algebra induced twists of quantum enveloping algebras it is shown that a quasitriangular hopf algebra can be twisted by the universal r matrix of any quasitriangular sub hopf algebra and examples are given of r matrices of quantum groups obtained this way

on the bias of the multiple imputation variance estimator in survey sampling summary multiple imputation is a method of estimating the variances of estimators that are constructed with some imputed data we give an expression for the bias of the multiple imputation variance estimator for data that are collected with a complex sample design the bias may be sizable for certain estimators such as domain means when a large fraction of the values are imputed a bias adjusted variance estimator is suggested

functional calculus for infinitesimal generators of holomorphic semigroups we give a functional calculus formula for infinitesimal generators of holomorphic semigroups of operators on banach spaces which involves the bochner riesz kernels of such generators the rate of smoothness of operating functions is related to the exponent of the growth on vertical lines of the operator norm of the semigroup the strength of the formula is tested on poisson and gauss semigroups inl1 rn andl1 g for a stratified lie groupg we give also a self contained theory of smooth absolutely continuous functions on the half line 0

radial fourier multipliers in high dimensions given a fixed p 2 we prove a simple and effective characterization of all radial multipliers of mathcal f l p left mathbb r d right provided that the dimension d is sufficiently large the method also yields new l q space time regularity results for solutions of the wave equation in high dimensions

parametric fractional imputation for missing data analysis under a parametric model for missing data the em algorithm is a popular tool for flnding the maximum likelihood estimates mle of the parameters of the model imputation when carefully done can be used to facilitate the parameter estimation by applying the complete sample estimators to the imputed dataset the basic idea is to generate the imputed values from the conditional distribution of the missing data given the observed data multiple imputation is a bayesian approach to generate the imputed values from the conditional distribution in this article parametric fractional imputation is proposed as a parametric approach for generating imputed values using fractional weights the e step of the em algorithm can be approximated by the weighted mean of the imputed data likelihood where the fractional weights are computed from the current value of the parameter estimates some computational e ciency can be achieved using the idea of importance sampling in the monte carlo approximation of the conditional expectation the resulting estimator of the specifled parameters will be identical to the mle under missing data if the fractional weights are adjusted using a calibration step the proposed imputation method provides e cient parameter estimates for the model parameters specifled and also provides reasonable estimates for parameters that are not part of the imputation model for example domain means thus the proposed imputation method is a useful tool for general purpose data analysis variance estimation is covered and results from a limited simulation study are presented

large sample theory for parametric multiple imputation procedures we consider the asymptotic behaviour of various parametric multiple imputation procedures which include but are not restricted to the proper imputation procedures proposed by rubin 1978 the asymptotic variance structure of the resulting estimators is provided this result is used to compare the relative efficiencies of different imputation procedures it also provides a basis to understand the behaviour of two monte carlo iterative estimators stochastic em celeux diebolt 1985 wei tanner 1990 and simulated em ruud 1991 we further develop properties of these estimators when they stop at iteration k with imputation size m an application to a mcasurement error problem is used to illustrate the results

subdyadic square functions and applications to weighted harmonic analysis abstract through the study of novel variants of the classical littlewood paley stein g functions we obtain pointwise estimates for broad classes of highly singular fourier multipliers on r d satisfying regularity hypotheses adapted to fine subdyadic scales in particular this allows us to efficiently bound such multipliers by geometrically defined maximal operators via general weighted l 2 inequalities in the spirit of a well known conjecture of stein our framework applies to solution operators for dispersive pde such as the time dependent free schrodinger equation and other highly oscillatory convolution operators that fall well beyond the scope of the calderon zygmund theory

improved bound for the bilinear bochner riesz operator we study l p times l q rightarrow l r bounds for the bilinear bochner riesz operator mathcal b alpha alpha 0 in mathbb r d d ge 2 which is defined by open image in new window we make use of a decomposition which relates the estimates for mathcal b alpha to the square function estimates for the classical bochner riesz operators in consequence we significantly improve the previously known bounds

twisting 2 cocycles for the construction of new non standard quantum groups we introduce a new class of 2 cocycles defined explicitly on the generators of certain multiparameter standard quantum groups these allow us through the process of twisting the familiar standard quantum groups to generate new as well as previously known examples of non standard quantum groups in particular we are able to construct generalisations of both the cremmer gervais deformation of sl 3 and the so called esoteric quantum groups of fronsdal and galindo in an explicit and straightforward manner

twisting cocycles in fundamental representation and triangular bi crossproduct hopf algebras we find the general solution to the twisting equation in the tensor bialgebra t r of an associative unital ring r viewed as that of fundamental representation for a universal enveloping lie algebra and its quantum deformations we suggest a procedure of constructing twisting cocycles belonging to a given quasitriangular sub bialgebra h t r this algorithm generalizes reshetikhin s approach which involves cocycles fulfilling the yang baxter equation within this framework we study a class of quantized inhomogeneous lie algebras related to associative rings in a certain way for which we build twisting cocycles and universal r matrices our approach is a generalization of the methods developed for the case of commutative rings in our recent work including such well known examples as jordanian quantization of the borel subalgebra of sl 2 and the null plane quantized poincare algebra by ballesteros et al we reveal the role of special group 1 cocycles in this process and establish the bi crossproduct stru

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

importance sampling via the estimated sampler monte carlo importance sampling for evaluating numerical integration is discussed we consider a parametric family of sampling distributions and propose the use of the sampling distribution estimated by maximum likelihood the proposed method of importance sampling using the estimated sampling distribution is shown to improve the asymptotic variance of the ordinary method using the true sampling distribution the argument is closely related to the discussion of the paradox in henmi eguchi 2004 we focus on a condition under which the estimated integration value obtained by the proposed method has asymptotic zero variance

some weighted estimates for littlewood paley functions and radial multipliers abstract we prove some weighted estimates for certain littlewood paley operators on the weighted hardy spaces h w p 0 p 1 and on the weighted l p spaces we also prove some weighted estimates for the bochner riesz operators and the spherical means

incomplete data in generalized linear models abstract this article examines incomplete data for the class of generalized linear models in which incompleteness is due to partially missing covariates on some observations under the assumption that the missing data are missing at random it is shown that the e step of the em algorithm for any generalized linear model can be expressed as a weighted complete data log likelihood when the unobserved covariates are assumed to come from a discrete distribution with finite range expressing the e step in this manner allows for a straightforward maximization in the m step thus leading to maximum likelihood estimates mle s for the parameters asymptotic variances of the mle s are also derived and results are illustrated with two examples

improved bounds for stein s square functions supported in part by nrf grant 2009 0072531 korea micinn grant mtm2010 16518 spain erc grant 277778 europe and nsf grant 0652890 usa

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

maximal estimates for the bilinear spherical averages and the bilinear bochner riesz operators abstract we study the maximal estimates for the bilinear spherical average and the bilinear bochner riesz operator first we obtain l p l q l r estimates for the bilinear spherical maximal function on the optimal range thus we settle the problem which was previously considered by geba greenleaf iosevich palsson and sawyer later barrionevo grafakos d he honzik and oliveira and recently heo hong and yang secondly we consider l p l q l r estimates for the maximal bilinear bochner riesz operators and improve the previous known results for the purpose we draw a connection between the maximal estimates and the square function estimates for the classical bochner riesz operators

a unified approach to linearization variance estimation from survey data after imputation for item nonresponse variance estimation after imputation is an important practical problem in survey sampling when deterministic imputation or stochastic imputation is used we show that the variance of the imputed estimator can be consistently estimated by a unifying linearize and reverse approach we provide some applications of the approach to regression imputation fractional categorical imputation multiple imputation and composite imputation results from a simulation study under a factorial structure for the sampling response and imputation mechanisms show that the proposed linearization variance estimator performs well in terms of relative bias assuming a missing at random response mechanism