stable weights that balance covariates for estimation with incomplete outcome data weighting methods that adjust for observed covariates such as inverse probability weighting are widely used for causal inference and estimation with incomplete outcome data part of the appeal of such methods is that one set of weights can be used to estimate a range of treatment effects based on different outcomes or a variety of population means for several variables however this appeal can be diminished in practice by the instability of the estimated weights and by the difficulty of adequately adjusting for observed covariates in some settings to address these limitations this article presents a new weighting method that finds the weights of minimum variance that adjust or balance the empirical distribution of the observed covariates up to levels prespecified by the researcher this method allows the researcher to balance very precisely the means of the observed covariates and other features of their marginal and joint distributions such as variances and correlations and also for example the

moving towards best practice when using inverse probability of treatment weighting iptw using the propensity score to estimate causal treatment effects in observational studies the propensity score is defined as a subject s probability of treatment selection conditional on observed baseline covariates weighting subjects by the inverse probability of treatment received creates a synthetic sample in which treatment assignment is independent of measured baseline covariates inverse probability of treatment weighting iptw using the propensity score allows one to obtain unbiased estimates of average treatment effects however these estimates are only valid if there are no residual systematic differences in observed baseline characteristics between treated and control subjects in the sample weighted by the estimated inverse probability of treatment we report on a systematic literature review in which we found that the use of iptw has increased rapidly in recent years but that in the most recent year a majority of studies did not formally examine whether weighting balanced measured covariates between treatment groups we then proceed to describe a suite of quantitative and qualitative methods that allow one to assess whether measured baseline covariates are balanced between treatment groups in the weighted sample the quantitative methods use the weighted standardized difference to compare means prevalences higher order moments and interactions the qualitative methods employ graphical methods to compare the distribution of continuous baseline covariates between treated and control subjects in the weighted sample finally we illustrate the application of these methods in an empirical case study we propose a formal set of balance diagnostics that contribute towards an evolving concept of best practice when using iptw to estimate causal treatment effects using observational data

maximum entropy density estimation with generalized regularization and an application to species distribution modeling we present a unified and complete account of maximum entropy density estimation subject to constraints represented by convex potential functions or alternatively by convex regularization we provide fully general performance guarantees and an algorithm with a complete convergence proof as special cases we easily derive performance guarantees for many known regularization types including l1 l2 l22 and l2 l22 style regularization we propose an algorithm solving a large and general subclass of generalized maximum entropy problems including all discussed in the paper and prove its convergence our approach generalizes and unifies techniques based on information geometry and bregman divergences as well as those based more directly on compactness our work is motivated by a novel application of maximum entropy to species distribution modeling an important problem in conservation biology and ecology in a set of experiments on real world data we demonstrate the utility of maximum entropy in this setting we explore effects of different feature types sample sizes and regularization levels on the performance of maxent and discuss interpretability of the resulting models

abelianisation of orthogonal groups and the fundamental group of modular varieties abstract we study the commutator subgroup of integral orthogonal groups belonging to indefinite quadratic forms we show that the index of this commutator is 2 for many groups that occur in the construction of moduli spaces in algebraic geometry in particular the moduli of k3 surfaces we give applications to modular forms and to computing the fundamental groups of some moduli spaces

parabolic inductions for pro p iwahori hecke algebras abstract we give some properties of parabolic inductions and their adjoint functors for pro p iwahori hecke algebras

globally efficient non parametric inference of average treatment effects by empirical balancing calibration weighting the estimation of average treatment effects based on observational data is extremely important in practice and has been studied by generations of statisticians under different frameworks existing globally efficient estimators require non parametric estimation of a propensity score function an outcome regression function or both but their performance can be poor in practical sample sizes without explicitly estimating either functions we consider a wide class calibration weights constructed to attain an exact three way balance of the moments of observed covariates among the treated the control and the combined group the wide class includes exponential tilting empirical likelihood and generalized regression as important special cases and extends survey calibration estimators to different statistical problems and with important distinctions global semiparametric efficiency for the estimation of average treatment effects is established for this general class of calibration estimators the results show that efficiency can be achieved by solely balancing the covariate distributions without resorting to direct estimation of propensity score or outcome regression function we also propose a consistent estimator for the efficient asymptotic variance which does not involve additional functional estimation of either the propensity score or the outcome regression functions the proposed variance estimator outperforms existing estimators that require a direct approximation of the efficient influence function

covariate association eliminating weights a unified weighting framework for causal effect estimation weighting methods offer an approach to estimating causal treatment effects in observational studies however if weights are estimated by maximum likelihood misspecification of the treatment assignment model can lead to weighted estimators with substantial bias and variance in this paper we propose a unified framework for constructing weights such that a set of measured pretreatment covariates is unassociated with treatment assignment after weighting we derive conditions for weight estimation by eliminating the associations between these covariates and treatment assignment characterized in a chosen treatment assignment model after weighting the moment conditions in covariate balancing weight methods for binary categorical and continuous treatments in cross sectional settings are special cases of the conditions in our framework which extends to longitudinal settings simulation shows that our method gives treatment effect estimates with smaller biases and variances than the maximum likelihood approach under treatment assignment model misspecification we illustrate our method with an application to systemic lupus erythematosus data

moduli spaces of polarized symplectic o grady varieties and borcherds products we study moduli spaces of o grady s ten dimensional irreducible symplectic manifolds these moduli spaces are covers of modular varieties of dimension 21 namely quotients of hermitian symmetric domains by a suitable arithmetic group the interesting and new aspect of this case is that the group in question is strictly bigger than the stable orthogonal group this makes it different from both the k3 and the k3 n case which are of dimension 19 and 20 respectively

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

bounded efficient and doubly robust estimation with inverse weighting consider estimating the mean of an outcome in the presence of missing data or estimating population average treatment effects in causal inference a doubly robust estimator remains consistent if an outcome regression model or a propensity score model is correctly specified we build on a previous nonparametric likelihood approach and propose new doubly robust estimators which have desirable properties in efficiency if the propensity score model is correctly specified and in boundedness even if the inverse probability weights are highly variable we compare the new and existing estimators in a simulation study and find that the robustified likelihood estimators yield overall the smallest mean squared errors

on the universal module of p adic spherical hecke algebras let widetilde g be a split connected reductive group with connected center z over a local non archimedean field f of residue characteristic p let widetilde k be a hyperspecial maximal compact open subgroup in widetilde g let r be a commutative ring let v be a finitely generated r free r widetilde k module for an r algebra b and a character chi frak h v widetilde g widetilde k rightarrow b of the spherical hecke algebra frak h v widetilde g widetilde k rm end r widetilde g rm ind widetilde k widetilde g v we consider the specialization m chi v rm ind widetilde k widetilde g v otimes frak h v widetilde g widetilde k chi b of the universal frak h v widetilde g widetilde k module rm ind widetilde k widetilde g v for large classes of r including cal o f and overline bbb f p v b and chi arguing geometrically on the bruhat tits building we give a sufficient criterion for m chi v to be b free and to admit a widetilde g equivariant resolution by a koszul complex built from finitely many copies of rm ind widetilde k z widetilde g v this criterion is the exactness of certain fairly small and explicit frak n equivariant r module complexes where frak n is the group of cal o f valued points of the unipotent radical of a borel subgroup in widetilde g we verify it if f bbb q p and if v is an irreducible overline bbb f p widetilde k representation with highest weight in the closed bottom p alcove or a lift of it to cal o f we use this to construct p adic integral structures in certain locally algebraic representations of widetilde g

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

toward a curse of dimensionality appropriate coda asymptotic theory for semi parametric models we argue that due to the curse of dimensionality there are major difficulties with any pure or smoothed likelihood based method of inference in designed studies with randomly missing data when missingness depends on a high dimensional vector of variables we study in detail a semi parametric superpopulation version of continuously stratified random sampling we show that all estimators of the population mean that are uniformly consistent or that achieve an algebraic rate of convergence no matter how slow require the use of the selection randomization probabilities we argue that in contrast to likelihood methods which ignore these probabilities inverse selection probability weighted estimators continue to perform well achieving uniform n 1 2 rates of convergence we propose a curse of dimensionality appropriate coda asymptotic theory for inference in non and semi parametric models in an attempt to formalize our arguments we discuss whether our results constitute a fatal blow to the likelihood principle and study the attitude toward these that a committed subjective bayesian would adopt finally we apply our coda theory to analyse the effect of the curse of dimensionality in several interesting semi parametric models including a model for a two armed randomized trial with randomization probabilities depending on a vector of continuous pretreatment covariates x we provide substantive settings under which a subjective bayesian would ignore the randomization probabilities in analysing the trial data we then show that any statistician who ignores the randomization probabilities is unable to construct nominal 95 per cent confidence intervals for the true treatment effect that have both i an expected length which goes to zero with increasing sample size and ii a guaranteed expected actual coverage rate of at least 95 per cent over the ensemble of trials analysed by the statistician during his or her lifetime however we derive a new interval estimator depending on the randomization probabilities that satisfies i and ii

on the kodaira dimension of orthogonal modular varieties we prove that up to scaling there are only finitely many integral lattices l of signature 2 n with n ge 21 or n 17 such that the modular variety defined by the orthogonal group of l is not of general type in particular when n ge 108 every modular variety defined by an arithmetic group for a rational quadratic form of signature 2 n is of general type we also obtain similar finiteness in n ge 9 for the stable orthogonal groups as a byproduct we derive finiteness of lattices admitting reflective modular form of bounded vanishing order which proves a conjecture of gritsenko and nikulin

representations lisses modulo l de gl m d let f be a non archimedean locally compact field of residue characteristic p let d be a finite dimensional central division f algebra and let r be an algebraically closed field of characteristic different from p we classify all smooth irreducible representations of gl m d with coefficients in r in terms of multisegments generalizing works by zelevinski tadic and vigneras we prove that any irreducible r representation of gl m d has a unique supercuspidal support and thus get two classifications one by supercuspidal multisegments classifying representations with a given supercuspidal support and one by aperiodic multisegments classifying representations with a given cuspidal support these constructions are made in a purely local way with a substantial use of type theory

the classification of irreducible admissible mod p representations of a p adic gln let f be a finite extension of p using the mod p satake transform we define what it means for an irreducible admissible smooth representation of an f split p adic reductive group over overline mathbb f p to be supersingular we then give the classification of irreducible admissible smooth gln f representations over overline mathbb f p in terms of supersingular representations as a consequence we deduce that supersingular is the same as supercuspidal these results generalise the work of barthel livne for n 2 for general split reductive groups we obtain similar results under stronger hypotheses

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

the kodaira dimension of the moduli of k3 surfaces the global torelli theorem for projective k3 surfaces was first proved by piatetskii shapiro and shafarevich 35 years ago opening the way to treating moduli problems for k3 surfaces the moduli space of polarised k3 surfaces of degree 2d is a quasi projective variety of dimension 19 for general d very little has been known hitherto about the kodaira dimension of these varieties in this paper we present an almost complete solution to this problem our main result says that this moduli space is of general type for d 61 and for d 46 50 54 57 58 60

smooth duality in natural characteristic abstract we develop a duality theory for admissible smooth representations of p adic lie groups on vector spaces over fields of characteristic p to this end we introduce certain higher smooth duality functors and relate our construction to the auslander duality of completed group rings we study the behavior of smooth duality under tensor products inflation and induction and discuss the dimension theory of smooth mod p representations of a p adic reductive group finally we compute the higher smooth duals of the irreducible smooth representations of gl 2 q p in characteristic p and relate our results to the contragredient operation of colmez

non symplectic involutions of irreducible symplectic manifolds of k3 n type this paper is concerned with non symplectic involutions of irreducible symplectic manifolds of k3 n type we will give a criterion for deformation equivalence and use this to give a lattice theoretic description of all deformation types while moduli spaces of k3 n type manifolds with non symplectic involutions are not necessarily hausdorff we will construct quasi projective moduli spaces for a certain well behaved class of such pairs

on the moduli space of pairs consisting of a cubic threefold and a hyperplane abstract we study the moduli space of pairs x h consisting of a cubic threefold x and a hyperplane h in p 4 the interest in this moduli comes from two sources the study of certain weighted hypersurfaces whose middle cohomology admit hodge structures of k3 type and on the other hand the study of the singularity o 16 the cone over a cubic surface in this paper we give a hodge theoretic construction of the moduli space of cubic pairs by relating x h to certain lattice polarized cubic fourfolds y a period map for the pairs x h is then defined using the periods of the cubic fourfolds y the main result is that the period map induces an isomorphism between a git model for the pairs x h and the baily borel compactification of some locally symmetric domain of type iv

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

calibration estimators in survey sampling abstract this article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information estimation is equivalent to attaching weights to the survey data we focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations we briefly mention an application to the case in which the information consists of known marginal counts in a two or multi way table known as generalized raking the general regression estimator greg was conceived with multivariate auxiliary information in mind ordinarily this estimator is justified by a regression relationship between the study variable y and the auxiliary vector x but we note that the greg can be derived by a different route by focusing instead on the weights the ordinary sampling weights of the kth observation is 1 k where k is the inclusion probabilit

a satake isomorphism for representations modulo p of reductive groups over local fields let f be a local field with finite residue field of characteristic p let g be a connected reductive group over f and b a minimal parabolic subgroup of g with levi decomposition b zu let k be a special parabolic subgroup of g in good position relative to z u fix an absolutely irreducible smooth representation of k on a vector space v over some field c of characteristic p writing h g k v for the intertwining hecke algebra of v in g we define a natural algebra homomorphism from h g k v to h z z k v u k we show it is injective and identify its image we thus generalize work of f herzig who assumed f of characteristic 0 g unramified and k hyperspecial and took for c an algebraic closure of the prime field fp we show that in the general case h g k v need not be commutative that is in contrast with the cases herzig considers and with the more classical situation where v is trivial and the field of coefficients is the field of complex numbers

minimax estimation of a functional on a structured high dimensional model we introduce a new method of estimation of parameters in semi parametric and nonparametric models the method is based on estimating equations that are u statistics in the observations the u statistics are based on higher order influence functions that extend ordinary linear influence functions of the parameter of interest and represent higher derivatives of this parameter for parameters for which the representation cannot be perfect the method leads to a bias variance trade off and results in estimators that converge at a slower than n rate in a number of examples the resulting rate can be shown to be optimal we are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity where the parameter of interest cannot be estimated at n rate but we also consider efficient n estimation using novel nonlinear estimators the general approach is applied in detail to the example of estimating a mean response when the response is not always observed

moduli spaces of twisted k3 surfaces and cubic fourfolds motivated by the relation between twisted k3 surfaces and special cubic fourfolds we construct moduli spaces of polarized twisted k3 surfaces of any fixed degree and order we do this by mimicking the construction of the moduli space of untwisted polarized k3 surfaces as a quotient of a bounded symmetric domain

assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome this paper proposes a simple technique for assessing the range of plausible causal con clusions from observational studies with a binary outcome and an observed categorical covariate the technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response a medical study of coronary artery disease is used to illustrate the technique inevitably the results of clinical studies are subject to dispute in observational studies one basis for dispute is obvious since patients were not assigned to treatments at random patients at greater risk may be over represented in some treatment groups this paper proposes a method for assess ing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response despite their limitations observational studies will continue to be a valuable source of information and therefore it is prudent to develop appropriate methods of analysis for them our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u under several sets of assumptions about u both cornfield et al 1959 and bross 1966 have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment that is whether the treatment effect after adjustment for u could be zero our method has two advantages first cornfield et al 1959 and bross 1966 adjust only for the unmeasured binary covariate u whereas we adjust for measured covariates in addition to the unmeasured covariate u second cornfield et al 1959 and bross 1966 1967 only judge whether the effect of the treatment could be zero having adjusted for u where cornfield et al 1959 employ an implicit yet extreme assumption about u in contrast we provide actual estimates of the treatment effect adjusted for both u and the observed categorical covariates under any assumption about u in principle the ith of the n patients under study has both a binary response r1i that would have resulted if he had received the new treatment and a binary response ro0 that would have resulted if he had received the control treatment in this formulation treatment effects are comparisons of r1i and roi such as r1i roi since each patient receives only one treatment either rli or ro0 is observed but not both and therefore comparisons of rli and roi imply some degree of speculation treatment effects defined as comparisons of the two potential responses r1i and roi of individual patients are implicit in fisher s 1953 randomization test of the sharp null

periods of double epw sextics we study the period map for double epw sextics which are varieties making up a locally versal family of polarized hyperkahler fourfolds double epw sextics are parametrized by lagrangian subspaces of the third wedge product of a 6 dimensional complex vector space we prove that lagrangians in the indeterminacy locus of the period map contain a decomposable 3 vector enjoying very special properties in addition we prove a result about periods of double epw sextics which are either smooth or have isolated singular points with projectivized tangent cone isomorphic to the incidence variety in mathbb p 2 times mathbb p 2 vee

model assisted inference for treatment effects using regularized calibrated estimation with high dimensional data consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models we develop new methods and theory to obtain not only doubly robust point estimators for average treatment effects which remain consistent if either the propensity score model or the outcome regression model is correctly specified but also model assisted confidence intervals which are valid when the propensity score model is correctly specified but the outcome model may be misspecified with a linear outcome model the confidence intervals are doubly robust that is being also valid when the outcome model is correctly specified but the propensity score model may be misspecified our methods involve regularized calibrated estimators with lasso penalties but carefully chosen loss functions for fitting propensity score and outcome regression models we provide high dimensional analysis to establish the desired properties of our methods under comparable sparsity conditions to previous results which give valid confidence intervals when both the propensity score and outcome models are correctly specified we present simulation studies and an empirical application which demonstrate advantages of the proposed methods compared with related methods based on regularized maximum likelihood estimation the methods are implemented in the r package mathtt rcal

bias reduced doubly robust estimation over the past decade doubly robust estimators have been proposed for a variety of target parameters in causal inference and missing data models these are asymptotically unbiased when at least one of two nuisance working models is correctly specified regardless of which while their asymptotic distribution is not affected by the choice of root n consistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified this choice of estimators can have a dramatic impact under misspecification of at least one working model in this article we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models which is designed to improve the performance of the doubly robust estimator of interest relative to the default use of maximum likelihood estimators for the nuisance parameters the proposed approach locally minimizes the squared first order asymptotic bias of the doubly robust estim

on special representations of p adic reductive groups let f be a non archimedean locally compact field let g be a split connected reductive group over f for a parabolic subgroup q g and a ring l we consider the g representation on the l module c g q l

abelian quotients of mapping class groups of highly connected manifolds we compute the abelianisations of the mapping class groups of the manifolds w g 2n g s n times s n for n ge 3 and g ge 5 the answer is a direct sum of two parts the first part arises from the action of the mapping class group on the middle homology and takes values in the abelianisation of the automorphism group of the middle homology the second part arises from bordism classes of mapping tori and takes values in the quotient of the stable homotopy groups of spheres by a certain subgroup which in many cases agrees with the image of the stable j homomorphism we relate its calculation to a purely homotopy theoretic problem

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

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

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

simple design efficient calibration estimators for rejective and high entropy sampling summary for survey calibration consider the situation where the population totals of auxiliary variables are known or where auxiliary variables are measured for all population units for each situation wedevelopdesign efficientcalibrationestimatorsunderrejectiveorhigh entropysampling a general approach is to extend efficient estimators for missing data problems with independent and identically distributed data to the survey setting we show that this approach effectively resolves two long standing issues in existing approaches how to achieve design efficiency regardless of a linear superpopulation model in generalized regression and calibration estimation and how to find a simple approximation in optimal regression estimation moreover the proposed approach sheds light on several issues that seem not to be well studied in the literature examples include use of the weighted kullback leibler distance in calibration estimation and efficient estimation allowing for misspecification of a nonlinear superpopulation model

pro p iwahori hecke ring and supersingular representations the motivation of this paper is the search for a langlands correspondence modulo p we show that the pro p iwahori hecke ring open image in new window of a split reductive p adic group g over a local field f of finite residue field fq with q elements admits an iwahori matsumoto presentation and a bernstein z basis and we determine its centre we prove that the ring open image in new window is finitely generated as a module over its centre these results are proved in 11 only for the iwahori hecke ring let p be the prime number dividing q and let k be an algebraically closed field of characteristic p a character from the centre of open image in new window to k which is as null as possible will be called null the simple open image in new window modules with a null central character are called supersingular when g gl n we show that each simple open image in new window module of dimension n containing a character of the affine subring open image in new window is supersingular using the minimal expressions of haines generalized to open image in new window and that the number of such modules is equal to the number of irreducible k representations of the weil group wf of dimension n when the action of an uniformizer pf in the hecke algebra side and of the determinant of a frobenius frf in the galois side are fixed i e the number nn q of unitary irreducible polynomials in fq x of degree n one knows that the converse is true by explicit computations when n 2 10 and when n 3 rachel ollivier