multiple imputation after 18 years abstract multiple imputation was designed to handle the problem of missing data in public use data bases where the data base constructor and the ultimate user are distinct entities the objective is valid frequency inference for ultimate users who in general have access only to complete data software and possess limited knowledge of specific reasons and models for nonresponse for this situation and objective i believe that multiple imputation by the data base constructor is the method of choice this article first provides a description of the assumed context and objectives and second reviews the multiple imputation framework and its standard results these preliminary discussions are especially important because some recent commentaries on multiple imputation have reflected either misunderstandings of the practical objectives of multiple imputation or misunderstandings of fundamental theoretical results then criticisms of multiple imputation are considered and finally comparisons are made to alt

multiple imputation methods for multivariate one sided tests with missing data summary multivariate one sided hypotheses testing problems arise frequently in practice various tests have been developed in practice there are often missing values in multivariate data in this case standard testing procedures based on complete data may not be applicable or may perform poorly if the missing data are discarded in this article we propose several multiple imputation methods for multivariate one sided testing problem with missing data some theoretical results are presented the proposed methods are evaluated using simulations a real data example is presented to illustrate the methods

large sample significance levels from multiply imputed data using moment based statistics and an f reference distribution abstract we present a procedure for computing significance levels from data sets whose missing values have been multiply imputed data this procedure uses moment based statistics m 3 repeated imputations and an f reference distribution when m we show first that our procedure is essentially the same as the ideal procedure in cases of practical importance and second that its deviations from the ideal are basically a function of the coefficient of variation of the canonical ratios of complete to observed information for small m our procedure s performance is largely governed by this coefficient of variation and the mean of these ratios using simulation techniques with small m we compare our procedure s actual and nominal large sample significance levels and conclude that it is essentially calibrated and thus represents a definite improvement over previously available procedures furthermore we compare the large sample power of the procedure as a function of m and other factors such as the di

convergence rates for inexact newton like methods at singular points and applications newton s method converges linearly rather than quadratically if the initial guess is close to the solution and the frechet derivative is singular at the solution several authors have already tried to improve the rate of convergence for this method in this case the limitations of their approach is twofold first the residuals at each step are assumed to be zero which is not the case in general second the previous works are limited only to the ordinary newton method here we extend and improve on these results by providing convergence rates for inexact newton like methods on a banach space setting moreover our results reduce to the ones already in the literature for special choices of the operators involved we complete our study with some numerical examples appearing in connection with some predator prey problems appearing in population modeling that show how our results improve on the earlier ones

compactness and the fixed point property in l1 abstract in this paper we prove that compactness can be characterized by means of the existence of a fixed point for some classes of mappings defined on convex closed subsets of the space l 1 nominally our result involves nonexpansive mappings uniformly lipschitzian mappings and cascading nonexpansive mappings we also extend the results to some more general classes of banach spaces

geometrical coefficients and the structure of the fixed point set of asymptotically regular mappings in banach spaces abstract it is shown that if e is a separable and uniformly convex banach space with opial s property and c is a nonempty bounded closed convex subset of e then for some asymptotically regular self mappings of c the set of fixed points is not only connected but even a retract of c our results qualitatively complement in the case of a uniformly convex banach space a corresponding result presented in t dominguez m a japon g lopez metric fixed point results concerning measures of noncompactness mappings in w a kirk b sims eds handbook of metric fixed point theory kluwer acad publishers dordrecht 2001 pp 239 268

fixed points of uniformly lipschitzian mappings in spaces with uniformly normal structure dans un espace de banach x on etudie quand reflexivite et structure normale sont suffisantes pour assurer pour de bon 1 la propriete de point fixe pour des auto applications uniformement lipschitziennes

on the structure of fixed point sets of asymptotically regular semigroups abstract we show that the set of fixed points of an asymptotically regular mapping acting on a convex and weakly compact subset of a banach space is in some cases a holder continuous retract of its domain our results qualitatively complement the corresponding fixed point existence theorems and extend a few recent results of gornicki 15 16 17 we also characterize bynum s coefficients and the opial modulus in terms of nets

nonlinear orthomin k methods nonlinear orthomin 1 for solving nonlinear systems of equations as presented and analyzed by a t chronopoulos j comput appl math 40 1992 7389 his method is a nonlinear generalization of orthomin 1 in linear cases in this paper orthomin k for linear systems is generalized to nonlinear orthomin k which can be applied directly to nonlinear operator equations under the same conditions as nonlinear orthomin 1 the nonlinear orthomin k method was proved to converge to a globally unique solution

performing likelihood ratio tests with multiply imputed data sets summary existing procedures for obtaining significance levels from multiply imputed data either i require access to the completed data point estimates and variance covariance matrices which may not be available in practice when the dimensionality of the estimand is high or ii directly combine p values with less satisfactory results taking advantage of the well known relationship between the wald and log likelihood ratio test statistics we propose a complete data log likelihood ratio based procedure it is shown that for any number of multiple imputations the proposed procedure is equivalent in large samples to the existing procedure based on the point estimates and the variance covariance matrices yet it only requires the point estimates and evaluations of the complete data log likelihood ratio statistic as a function of these estimates and the completed data the proposed procedure therefore is especially attractive with highly multiparameter incomplete data problems since it does not involve the computation of any matrices

nonlinear cg like iterative methods abstract a nonlinear conjugate gradient method has been introduced and analyzed by j w daniel this method applies to nonlinear operators with symmetric jacobians orthomin 1 is an iterative method which applies to nonsymmetric and definite linear systems in this article we generalize orthomin 1 to a method which applies directly to nonlinear operator equations each iteration of the new method requires the solution of a scalar nonlinear equation under conditions that the hessian is uniformly bounded away from zero and the jacobian is uniformly positive definite the new method is proved to converge to a globally unique solution error bounds and local convergence results are also obtained numerical experiments on solving nonlinear operator equations arising in the discretization of nonlinear elliptic partial differential equations are presented

on banach space properties that are not invariant under the banach mazur distance 1 abstract we consider which properties of banach spaces are not invariant under the banach mazur distance 1 we will say that a given property p is not invariant under the banach mazur distance 1 if there exist two banach spaces x and y such that x has property p y fails property p and the banach mazur distance d x y 1 the main results of this paper concern the case of separable lindenstrauss spaces first in the setting of preduals of l 1 we give some geometric equivalences for polyhedral properties next we show that even in the restricted framework of preduals of l 1 most of the notions of polyhedral banach spaces and their geometric equivalences fail to be invariant under the banach mazur distance 1 then in the general case of banach spaces we indicate some other geometrical properties that are invariant or not invariant under the banach mazur distance 1

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea