randomization inference for treatment effect variation summary applied researchers are increasingly interested in whether and how treatment effects vary in randomized evaluations especially variation that is not explained by observed covariates we propose a model free approach for testing for the presence of such unexplained variation to use this randomization based approach we must address the fact that the average treatment effect which is generally the object of interest in randomized experiments actually acts as a nuisance parameter in this setting we explore potential solutions and advocate for a method that guarantees valid tests in finite samples despite this nuisance we also show how this method readily extends to testing for heterogeneity beyond a given model which can be useful for assessing the sufficiency of a given scientific theory we finally apply our method to the national head start impact study which is a large scale randomized evaluation of a federal preschool programme finding that there is indeed significant unexplained treatment effect variation

inference on a new class of sample average treatment effects we derive new variance formulas for inference on a general class of estimands of causal average treatment effects in a randomized control trial we generalize the seminal work of robins and show th

unitarity of the knizhnik zamolodchikov bernard connection and the bethe ansatz for the elliptic hitchin systems we work out finite dimensional integral formulae for the scalar product of genus one states of the groupg chern simons theory with insertions of wilson lines assuming convergence of the integrals we show that unitarity of the elliptic knizhnik zamolodchikov bernard connection with respect to the scalar product of cs states is closely related to the bethe ansatz for the commuting hamiltonians building up the connection and quantizing the quadratic hamiltonians of the elliptic hitchin system

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

conformal blocks on elliptic curves and the knizhnik zamolodchikov bernard equations we give an explicit description of the vector bundle of wzw conformal blocks on elliptic curves with marked points as a subbundle of a vector bundle of weyl group invariant vector valued theta functions on a cartan subalgebra we give a partly conjectural characterization of this subbundle in terms of certain vanishing conditions on affine hyperplanes in some cases explicit calculations are possible and confirm the conjecture the friedan shenker flat connection is calculated and it is shown that horizontal sections are solutions of bernard s generalization of the knizhnik zamolodchikov equation

general forms of finite population central limit theorems with applications to causal inference abstractfrequentists inference often delivers point estimators associated with confidence intervals or sets for parameters of interest constructing the confidence intervals or sets requires understanding the sampling distributions of the point estimators which in many but not all cases are related to asymptotic normal distributions ensured by central limit theorems although previous literature has established various forms of central limit theorems for statistical inference in super population models we still need general and convenient forms of central limit theorems for some randomization based causal analyses of experimental data where the parameters of interests are functions of a finite population and randomness comes solely from the treatment assignment we use central limit theorems for sample surveys and rank statistics to establish general forms of the finite population central limit theorems that are particularly useful for proving asymptotic distributions of randomization tests under th

improving massive experiments with threshold blocking inferences from randomized experiments can be improved by blocking assigning treatment in fixed proportions within groups of similar units however the use of the method is limited by the difficulty in deriving these groups current blocking methods are restricted to special cases or run in exponential time are not sensitive to clustering of data points and are often heuristic providing an unsatisfactory solution in many common instances we present an algorithm that implements a widely applicable class of blocking threshold blocking that solves these problems given a minimum required group size and a distance metric we study the blocking problem of minimizing the maximum distance between any two units within the same group we prove this is a nondeterministic polynomial time hard problem and derive an approximation algorithm that yields a blocking where the maximum distance is guaranteed to be at most four times the optimal value this algorithm runs in o n log n time with o n space complexity this makes it to our knowledge the first blocking method with an ensured level of performance that works in massive experiments whereas many commonly used algorithms form pairs of units our algorithm constructs the groups flexibly for any chosen minimum size this facilitates complex experiments with several treatment arms and clustered data a simulation study demonstrates the efficiency and efficacy of the algorithm tens of millions of units can be blocked using a desktop computer in a few minutes

using regression models to analyze randomized trials asymptotically valid hypothesis tests despite incorrectly specified models regression models are often used to test for cause effect relationships from data collected in randomized trials or experiments this practice has deservedly come under heavy scrutiny because commonly used models such as linear and logistic regression will often not capture the actual relationships between variables and incorrectly specified models potentially lead to incorrect conclusions in this article we focus on hypothesis tests of whether the treatment given in a randomized trial has any effect on the mean of the primary outcome within strata of baseline variables such as age sex and health status our primary concern is ensuring that such hypothesis tests have correct type i error for large samples our main result is that for a surprisingly large class of commonly used regression models standard regression based hypothesis tests but using robust variance estimators are guaranteed to have correct type i error for large samples even when the models are incorrectly specified to the best of our knowledge this robustness of such model based hypothesis tests to incorrectly specified models was previously unknown for poisson regression models and for other commonly used models we consider our results have practical implications for understanding the reliability of commonly used model based tests for analyzing randomized trials

semiparametric exponential families for heavy tailed data we propose a semiparametric method for fitting the tail of a heavy tailed population given a relatively small sample from that population and a larger sample from a related background population we model the tail of the small sample as an exponential tilt of the better observed large sample tail using a robust sufficient statistic motivated by extreme value theory in particular our method induces an estimator of the small population mean and we give theoretical and empirical evidence that this estimator outperforms methods that do not use the background sample we demonstrate substantial efficiency gains over competing methods in simulation and on data from a large controlled experiment conducted by facebook

canonical fuzzy bags and bag fuzzy measures as a basis for madm with mixed non cardinal data abstract this contribution introduces what will be called sine analysis a new approach to multiple attribute decision making madm with mixed noncardinal data this approach is based upon the notion of canonical fuzzy bags and their scalar evaluations by bag fuzzy measures

lasso adjustments of treatment effect estimates in randomized experiments we provide a principled way for investigators to analyze randomized experiments when the number of covariates is large investigators often use linear multivariate regression to analyze randomized experiments instead of simply reporting the difference of means between treatment and control groups their aim is to reduce the variance of the estimated treatment effect by adjusting for covariates if there are a large number of covariates relative to the number of observations regression may perform poorly because of overfitting in such cases the least absolute shrinkage and selection operator lasso may be helpful we study the resulting lasso based treatment effect estimator under the neyman rubin model of randomized experiments we present theoretical conditions that guarantee that the estimator is more efficient than the simple difference of means estimator and we provide a conservative estimator of the asymptotic variance which can yield tighter confidence intervals than the difference of means estimator simulation and data examples show that lasso based adjustment can be advantageous even when the number of covariates is less than the number of observations specifically a variant using lasso for selection and ordinary least squares ols for estimation performs particularly well and it chooses a smoothing parameter based on combined performance of lasso and ols

confidence intervals for uncommon but dramatic responses to treatment a small literature discusses locally most powerful rank tests when only a fraction of treated subjects respond to treatment the ranks used in these tests are very different from conventional ranks being relatively flat for low responses and then rising steeply and the associated tests are much more powerful than conventional rank tests when indeed only a small fraction of treated subjects exhibit dramatic responses because the tests are derived from considerations of local power they do not yield a plausible family of models for effect and therefore they do not yield confidence intervals for the magnitude of effect formed by inverting the tests there is a similarity between these tests and another family of tests originally motivated by different considerations involving peak performance in small subsets exploiting this similarity a method for obtaining confidence statements is proposed in the case of observational studies sensitivity to unobserved bias from nonrandom assignment of treatments is also examined two examples are used as illustrations i a study of smoking during pregnancy and its effects on birth weight in which smokers are matched to six controls and ii a matched pair study of damage to dna among workers at aluminum production plants

repeated randomization and matching in multi arm trials cluster randomized trials with relatively few clusters have been widely used in recent years for evaluation of health care strategies the balance match weighted bmw design introduced in xu and kalbfleisch 2010 biometrics 66 813 823 applies the optimal full matching with constraints technique to a prospective randomized design with the aim of minimizing the mean squared error mse of the treatment effect estimator this is accomplished through consideration of m independent randomizations of the experimental units and then selecting the one which provides the most balance evaluated by matching on the estimated propensity scores often in practice clinical trials may involve more than two treatment arms and multiple treatment options need to be evaluated therefore we consider extensions of the bmw propensity score matching method to allow for studies with three or more arms in this article we propose three approaches to extend the bmw design to clinical trials with more than two arms and evaluate the property of the extended design in simulation studies

the q deformed knizhnik zamolodchikov bernard heat equation we introduce a q deformation of the genus one sl 2 knizhnik zamolodchikov bernard heat equation we show that this equation for the dependence on the moduli of elliptic curves is compatible with the qkzb equations which give the dependence on the marked points

rerandomization and regression adjustment author s li x ding p abstract 2019 royal statistical society randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome generating process appropriately using covariates further yields more precise estimators in randomized experiments r a fisher suggested blocking on discrete covariates in the design stage or conducting analysis of covariance in the analysis stage we can embed blocking in a wider class of experimental design called rerandomization and extend the classical analysis of covariance to more general regression adjustment rerandomization trumps complete randomization in the design stage and regression adjustment trumps the simple difference in means estimator in the analysis stage it is then intuitive to use both rerandomization and regression adjustment under the randomization inference framework we establish a unified theory allowing the designer and analyser to have access to different sets of covariates we find that asymptotically for any given estimator with or without regression adjustment rerandomization never hurts either the sampling precision or the estimated precision and for any given design with or without rerandomization our regression adjusted estimator never hurts the estimated precision therefore combining rerandomization and regression adjustment yields better coverage properties and thus improves statistical inference to quantify these statements theoretically we discuss optimal regression adjusted estimators in terms of the sampling precision and the estimated precision and then measure the additional gains of the designer and the analyser we finally suggest the use of rerandomization in the design and regression adjustment in the analysis followed by the huber white robust standard error

generalized hypergeometric functions on the torus and the adjoint representation ofu q sl 2 we study the homology groups with coefficient in local systems arising in the free field representation of minimal models of conformal field theory on an elliptic curve with punctures we define an action of the quantum enveloping algebrauq sl2 on a space of relative cycles extending results obtained previously for the sphere absolute cycles are identified with singular vectors in the case of one puncture we find that the resulting topological representation is essentially the adjoint representation

modular differential equations for torus one point functions it is shown that in a rational conformal field theory every torus one point function of a given highest weight state satisfies a modular differential equation we derive and solve these differential equations explicitly for some virasoro minimal models in general however the resulting amplitudes do not seem to be expressible in terms of standard transcendental functions

dynamically twisted algebra as current algebra generalizing screening currents of q deformed virasoro algebra in this paper we propose an elliptic algebra which is based on the relations where r and are the dynamical r matrices of type face model with the elliptic moduli shifted by the centre of the algebra from the ding frenkel correspondence we find that its corresponding drinfeld current algebra at level one is the algebra of screening currents for q deformed virasoro algebra we realize the elliptic algebra at level one by miki s construction from the bosonization for the type i and type ii vertex operators we also show that the algebra is related to the algebra by dynamically twisting

a fuzzy bag approach to choosing the best multiattributed potential actions in a multiple judgement and non cardinal data context abstract the present work is concerned with showing how a fuzzy bag construct along with the concept of a positive outstandingness predicate and that of a strict t norm operator can be used to resolve conflicts and aggregation problems in decisions involving multiple judgements and non cardinal data it is also shown how the differential expertness degrees of the judges may be taken into account in the aggregation process the choice device proposed is decisive i e it excludes incomparability

rerandomization to balance tiers of covariates when conducting a randomized experiment if an allocation yields treatment groups that differ meaningfully with respect to relevant covariates groups should be rerandomized the process involves specifying an explicit criterion for whether an allocation is acceptable based on a measure of covariate balance and rerandomizing units until an acceptable allocation is obtained here we illustrate how rerandomization could have improved the design of an already conducted randomized experiment on vocabulary and mathematics training programs then provide a rerandomization procedure for covariates that vary in importance and finally offer other extensions for rerandomization including methods addressing computational efficiency when covariates vary in a priori importance better balance should be required for more important covariates rerandomization based on mahalanobis distance preserves the joint distribution of covariates but balances all covariates equally here we propose rerandomizing based on ma

on dynamical r matrices obtained from dirac reduction and their generalizations to affine lie algebras according to etingof and varchenko the classical dynamical yang baxter equation is a guarantee for the consistency of the poisson bracket on certain poisson lie groupoids here it is noticed that dirac reductions of these poisson manifolds give rise to a mapping from dynamical r matrices on a pair to those on another pair where is a chain of lie algebras for which admits a reductive decomposition as several known dynamical r matrices appear naturally in this setting and its application provides new r matrices too in particular we exhibit a family of r matrices for which the dynamical variable lies in the grade zero subalgebra of an extended affine lie algebra obtained from a twisted loop algebra based on an arbitrary finite dimensional self dual lie algebra

problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak abstract we draw attention to two problems associated with the use of instrumental variables iv the importance of which for empirical work has not been fully appreciated first the use of instruments that explain little of the variation in the endogenous explanatory variables can lead to large inconsistencies in the iv estimates even if only a weak relationship exists between the instruments and the error in the structural equation second in finite samples iv estimates are biased in the same direction as ordinary least squares ols estimates the magnitude of the bias of iv estimates approaches that of ols estimates as the r 2 between the instruments and the endogenous explanatory variable approaches 0 to illustrate these problems we reexamine the results of a recent paper by angrist and krueger who used large samples from the u s census to estimate wage equations in which quarter of birth is used as an instrument for educational attainment we find evidence that despite huge sample sizes th

chern simons states at genus one we present a rigorous analysis of the schrodinger picture quantization for thesu 2 chern simons theory on 3 manifold torusxline with insertions of wilson lines the quantum states defined as gauge covariant holomorphic functionals ofsu 2 connections on the torus are expressed by degree 2k theta functions satisfying additional conditions the conditions are obtained by splitting the space of semistablesu 2 connections into nine submanifolds and by analyzing the behavior of states at four codimension 1 strata we construct the knizhnik zamolodchikov bernard connection allowing to compare the states for different complex structures of the torus and different positions of the wilson lines by letting two wilson lines come together we prove a recursion relation for the dimensions of the spaces of states which together with the unproven absence of states for spins 1 2 level implies the verlinde dimension formula

recursive partitioning for heterogeneous causal effects in this paper we propose methods for estimating heterogeneity in causal effects in experimental and observational studies and for conducting hypothesis tests about the magnitude of differences in treatment effects across subsets of the population we provide a data driven approach to partition the data into subpopulations that differ in the magnitude of their treatment effects the approach enables the construction of valid confidence intervals for treatment effects even with many covariates relative to the sample size and without sparsity assumptions we propose an honest approach to estimation whereby one sample is used to construct the partition and another to estimate treatment effects for each subpopulation our approach builds on regression tree methods modified to optimize for goodness of fit in treatment effects and to account for honest estimation our model selection criterion anticipates that bias will be eliminated by honest estimation and also accounts for the effect of making additional splits on the variance of treatment effect estimates within each subpopulation we address the challenge that the ground truth for a causal effect is not observed for any individual unit so that standard approaches to cross validation must be modified through a simulation study we show that for our preferred method honest estimation results in nominal coverage for 90 confidence intervals whereas coverage ranges between 74 and 84 for nonhonest approaches honest estimation requires estimating the model with a smaller sample size the cost in terms of mean squared error of treatment effects for our preferred method ranges between 7 22

combining propensity score matching with additional adjustments for prognostic covariates abstract propensity score matching refers to a class of multivariate methods used in comparative studies to construct treated and matched control samples that have similar distributions on many covariates this matching is the observational study analog of randomization in ideal experiments but is far less complete as it can only balance the distribution of observed covariates whereas randomization balances the distribution of all covariates both observed and unobserved an important feature of propensity score matching is that it can be easily combined with model based regression adjustments or with matching on a subset of special prognostic covariates or combinations of prognostic covariates that have been identified as being especially predictive of the outcome variables we extend earlier results by developing approximations for the distributions of covariates in matched samples created with linear propensity score methods for the practically important situation where matching uses both the estimat

causal inference from 2k factorial designs by using potential outcomes summary a framework for causal inference from two level factorial designs is proposed which uses potential outcomes to define causal effects the paper explores the effect of non additivity of unit level treatment effects on neyman s repeated sampling approach for estimation of causal effects and on fisher s randomization tests on sharp null hypotheses in these designs the framework allows for statistical inference from a finite population permits definition and estimation of estimands other than average factorial effects and leads to more flexible inference procedures than those based on ordinary least squares estimation from a linear model

decomposing treatment effect variation understanding and characterizing treatment effect variation in randomized experiments has become essential for going beyond the black box of the average treatment effect nonetheless traditional

adjusting treatment effect estimates by post stratification in randomized experiments summary experimenters often use post stratification to adjust estimates post stratification is akin to blocking except that the number of treated units in each stratum is a random variable because stratification occurs after treatment assignment we analyse both post stratification and blocking under the neyman rubin model and compare the efficiency of these designs we derive the variances for a post stratified estimator and a simple difference in means estimator under different randomization schemes post stratification is nearly as efficient as blocking the difference in their variances is of the order of 1 n2 with a constant depending on treatment proportion post stratification is therefore a reasonable alternative to blocking when blocking is not feasible however in finite samples post stratification can increase variance if the number of strata is large and the strata are poorly chosen to examine why the estimators variances are different we extend our results by conditioning on the observed number of treated units in each stratum conditioning also provides more accurate variance estimates because it takes into account how close or far a realized random sample is from a comparable blocked experiment we then show that the practical substance of our results remains under an infinite population sampling model finally we provide an analysis of an actual experiment to illustrate our analytical results

elliptic quantum groups e_ tau eta mathfrak s mathfrak l _2 and quasi hopf algebras we construct an algebra morphism from the elliptic quantum group e tau eta mathfrak s mathfrak l 2 to a certain elliptic version of the quantum loop groups in higher genus studied by v rubtsov and the first author this provides an embedding of e tau eta mathfrak s mathfrak l 2 in an algebra with central extension in particular we construct l operators obeying a dynamical version of the reshetikhin semenov tian shansky relations to do that we construct the factorization of a certain twist of the quantum loop algebra that automatically satisfies the twisted cocycle equation of o babelon d bernard and e billey and therefore provides a solution of the dynamical yang baxter equation

asymptotic theory of rerandomization in treatment control experiments although complete randomization ensures covariate balance on average the chance of observing significant differences between treatment and control covariate distributions increases with many covariates rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion generally resulting in better covariate balance and more precise estimates of causal effects previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes gaussian covariate and outcome distributions or additive causal effects but not for the general sampling distribution of the difference in means estimator for the average causal effect we develop asymptotic theory for rerandomization without these assumptions which reveals a non gaussian asymptotic distribution for this estimator specifically a linear combination of a gaussian random variable and truncated gaussian random variables this distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals we demonstrate that compared with complete randomization rerandomization reduces the asymptotic quantile ranges of the difference in means estimator moreover our work constructs accurate large sample confidence intervals for the average causal effect

a multi attribute method for choosing among potential alternatives with ordinal evaluation abstract some concepts are introduced with a view to dealing with the problem of choosing the best potential alternative s in a multi attribute ordinal data context we assume that we know the possibilistic weights of attributes and ordinal evaluations of each potential alternative on all attributes we define what we refer to as positive negative coalitions of attributes and positiveness negativeness numerical bags associated with each potential alternative we also define what will be called positional advantage operators and we describe how all these concepts are used to lay the foundation for the choice method appearing in this paper

a multiple criteria ranking procedure based on distance between partial preorders abstract in this paper a multiple criteria ranking procedure based on distance between partial preorders is proposed this method consists of two phases in the first phase the decision maker is asked to rank alternatives with a preorder complete or partial for each criterion and provide complete or partial linear information about the relative importance weights of the criteria in the second phase we introduce a distance procedure to aggregate the above individual rankings into a global ranking a partial preorder an algorithm for the aggregation procedure is proposed followed by a numerical illustration

solutions of the quantum dynamical yang baxter equation and dynamical quantum groups the quantum dynamical yang baxter qdyb equation is a useful generalization of the quantum yang baxter qyb equation this generalization was introduced by gervais neveu and felder unlike the qyb equation the qdyb equation is not an algebraic but a difference equation with respect to a matrix function rather than a matrix the qdyb equation and its quasiclassical analogue the classical dynamical yang baxter equation arise in several areas of mathematics and mathematical physics conformal field theory integrable systems representation theory the most interesting solution of the qdyb equation is the elliptic solution discovered by felder in this paper we prove the first classification results for solutions of the qdyb equation these results are parallel to the classification of solutions of the classical dynamical yang baxter equation obtained in our previous paper all solutions we found can be obtained from felder s elliptic solution by a limiting process and gauge transformations fifteen years ago the quantum yang baxter equation gave rise to the theory of quantum groups namely it turned out that the language of quantum groups hopf algebras is the adequate algebraic language to talk about solutions of the quantum yang baxter equation in this paper we propose a similar language originating from felder s ideas which we found to be adequate for the dynamical yang baxter equation this is the language of dynamical quantum groups or hopf algebroids which is the quantum counterpart of the language of dynamical poisson groupoids introduced in our previous paper

model assisted design of experiments in the presence of network correlated outcomes summaryin this paper we consider how to assign treatment in a randomized experiment in which the correlation among the outcomes is informed by a network available pre intervention working within the potential outcome causal framework we develop a class of models that posit such a correlation structure among the outcomes we use these models to develop restricted randomization strategies for allocating treatment optimally by minimizing the mean squared error of the estimated average treatment effect analytical decompositions of the mean squared error due both to the model and to the randomization distribution provide insights into aspects of the optimal designs in particular the analysis suggests new notions of balance based on specific network quantities in addition to classical covariate balance the resulting balanced optimal restricted randomization strategies are still design unbiased when the model used to derive them does not hold we illustrate how the proposed treatment allocation strategies improve on allocations that ignore the network structure

quasi oracle estimation of heterogeneous treatment effects flexible estimation of heterogeneous treatment effects lies at the heart of many statistical challenges such as personalized medicine and optimal resource allocation in this paper we develop a general class of two step algorithms for heterogeneous treatment effect estimation in observational studies we first estimate marginal effects and treatment propensities in order to form an objective function that isolates the causal component of the signal then we optimize this data adaptive objective function our approach has several advantages over existing methods from a practical perspective our method is flexible and easy to use in both steps we can use any loss minimization method e g penalized regression deep neural networks or boosting moreover these methods can be fine tuned by cross validation meanwhile in the case of penalized kernel regression we show that our method has a quasi oracle property even if the pilot estimates for marginal effects and treatment propensities are not particularly accurate we achieve the same error bounds as an oracle who has a priori knowledge of these two nuisance components we implement variants of our approach based on penalized regression kernel ridge regression and boosting in a variety of simulation setups and find promising performance relative to existing baselines

rerandomization to improve covariate balance in experiments randomized experiments are the gold standard for estimating causal effects yet often in practice chance imbalances exist in covariate distributions between treatment groups if covariate data are available before units are exposed to treatments these chance imbalances can be mitigated by first checking covariate balance before the physical experiment takes place provided a precise definition of imbalance has been specified in advance unbalanced randomizations can be discarded followed by a rerandomization and this process can continue until a randomization yielding balance according to the definition is achieved by improving covariate balance rerandomization provides more precise and trustworthy estimates of treatment effects

regression adjustment in completely randomized experiments with a diverging number of covariates extending r a fisher and d a freedman s results on the analysis of covariance lin 2013 proposed an ordinary least squares adjusted estimator of the average treatment effect in completely randomized experiments we further study its statistical properties under the potential outcomes model in the asymptotic regimes allowing for a diverging number of covariates we show that lin 2013 s estimator is consistent when kappa log p rightarrow 0 and asymptotically normal when kappa p rightarrow 0 under mild moment conditions where kappa is the maximum leverage score of the covariate matrix in the favorable case where leverage scores are all close together his estimator is consistent when p o n log n and is asymptotically normal when p o n 1 2 in addition we propose a bias corrected estimator that is consistent when kappa log p rightarrow 0 and is asymptotically normal with the same variance in the fixed p regime when kappa 2 p log p rightarrow 0 in the favorable case the latter condition reduces to p o n 2 3 log n 1 3 similar to lin 2013 our results hold for non random potential outcomes and covariates without any model specification our analysis requires novel analytic tools for sampling without replacement which complement and potentially enrich the theory in other areas such as survey sampling matrix sketching and transductive learning

testing for imbalance of covariates in controlled experiments results of a controlled experiment are often adjusted for covariates found by a preliminary test to differ significantly between the treatment and control groups the resulting test s true significance level is lower than the nominal level greater power can be achieved by always adjusting for a covariate that is highly correlated with the response regardless of its distribution between groups

multivariate matching methods that are monotonic imbalance bounding we introduce a new monotonic imbalance bounding mib class of matching methods for causal inference with a surprisingly large number of attractive statistical properties mib generalizes and extends in several new directions the only existing class equal percent bias reducing epbr which is designed to satisfy weaker properties and only in expectation we also offer strategies to obtain specific members of the mib class and analyze in more detail a member of this class called coarsened exact matching whose properties we analyze from this new perspective we offer a variety of analytical results and numerical simulations that demonstrate how members of the mib class can dramatically improve inferences relative to epbr based matching methods

regression assisted inference for the average treatment effect in paired experiments summaryin paired randomized experiments individuals in a given matched pair may differ on prognostically important covariates despite the best efforts of practitioners we examine the use of regression adjustment to correct for persistent covariate imbalances after randomization and present two regression assisted estimators for the sample average treatment effect in paired experiments using the potential outcomes framework we prove that these estimators are consistent for the sample average treatment effect under mild regularity conditions even if the regression model is improperly specified and describe how asymptotically conservative confidence intervals can be constructed we demonstrate that the variances of the regression assisted estimators are no larger than that of the standard difference in means estimator asymptotically and illustrate the proposed methods by simulation the analysis does not require a superpopulation model a constant treatment effect or the truth of the regression model and hence provides inference for the sample average treatment effect with the potential to increase power without unrealistic assumptions

quantum hitchin systems via beta deformed matrix models we study the quantization of hitchin systems in terms of beta deformations of generalized matrix models related to conformal blocks of liouville theory on punctured riemann surfaces we show that in a suitable limit corresponding to the nekrasov shatashvili one the loop equations of the matrix model reproduce the hamiltonians of the quantum hitchin system on the sphere and the torus with marked points the eigenvalues of these hamiltonians are shown to be the epsilon 1 deformation of the chiral observables of the corresponding mathcal n 2 four dimensional gauge theory moreover we find the exact wave functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions

fock representations and brst cohomology insl 2 current algebra we investigate the structure of the fock modules overa 1 1 introduced by wakimoto we show that irreducible highest weight modules arise as degree zero cohomology groups in a brst like complex of fock modules chiral primary fields are constructed as brst invariant operators acting on fock modules as a result we obtain a free field representation of correlation functions of thesu 2 wzw model on the plane and on the torus we also consider representations of fractional level arising in polyakov s 2d quantum gravity finally we give a geometrical borel weil like interpretation of the wakimoto construction

using standard tools from finite population sampling to improve causal inference for complex experiments abstractthis article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting adopting a neymanian repeated sampling approach that integrates such causal inference with finite population survey sampling an inferential framework is developed for general mechanisms of assigning experimental units to multiple treatments this framework extends classical methods by allowing the possibility of randomization restrictions and unequal replications novel conditions that are milder than strict additivity of treatment effects yet permit unbiased estimation of the finite population sampling variance of any treatment contrast estimator are derived the consequences of departures from such conditions are also studied under the criterion of minimax bias and a new justification for using the neymanian conservative sampling variance estimator in experiments is provided the proposed approach can readily be extended to the case of treatm

estimation and inference of heterogeneous treatment effects using random forests many scientific and engineering challenges ranging from personalized medicine to customized marketing recommendations require an understanding of treatment effect heterogeneity in this article we

on mitigating the analytical limitations of finely stratified experiments although attractive from a theoretical perspective finely stratified experiments such as paired designs suffer from certain analytical limitations that are not present in block randomized experiments with multiple treated and control individuals in each block in short when using a weighted difference in means to estimate the sample average treatment effect the traditional variance estimator in a paired experiment is conservative unless the pairwise average treatment effects are constant across pairs however in more coarsely stratified experiments the corresponding variance estimator is unbiased if treatment effects are constant within blocks even if they vary across blocks using insights from classical least squares theory we present an improved variance estimator that is appropriate in finely stratified experiments the variance estimator remains conservative in expectation but is asymptotically no more conservative than the classical estimator and can be considerably less conservative the magnitude of the improvement depends on the extent to which effect heterogeneity can be explained by observed covariates aided by this estimator a new test for the null hypothesis of a constant treatment effect is proposed these findings extend to some but not all superpopulation models depending on whether the covariates are viewed as fixed across samples

randomization based causal inference from split plot designs author s zhao a ding p mukerjee r dasgupta t abstract institute of mathematical statistics 2018 under the potential outcomes framework we propose a randomization based estimation procedure for causal inference from split plot designs with special emphasis on 22 designs that naturally arise in many social behavioral and biomedical experiments point estimators of factorial effects are obtained and their sampling variances are derived in closed form as linear combinations of the between and within group covariances of the potential outcomes results are compared to those under complete randomization as measures of design efficiency conservative estimators of these sampling variances are proposed connection of the randomization based approach to inference based on the linear mixed effects model is explored results on sampling variances of point estimators and their estimators are extended to general split plot designs the superiority over existing model based alternatives in frequency coverage properties is reported under a variety of simulation settings for both binary and continuous outcomes

testing one hypothesis twice in observational studies in a matched observational study of treatment effects a sensitivity analysis asks about the magnitude of the departure from random assignment that would need to be present to alter the conclusions of an analysis that assumes that matching for measured covariates removes all bias the reported degree of sensitivity to unmeasured biases depends on both the process that generated the data and the chosen methods of analysis so a poor choice of method may lead to an exaggerated report of sensitivity to bias this suggests the possibility of performing more than one analysis with a correction for multiple inference say testing one null hypothesis using two or three different tests in theory and in an example it is shown that in large samples the gains from testing twice will often be large because testing twice has the larger of the two design sensitivities of the component tests and the losses due to correcting for two tests will often be small because two tests of one hypothesis will typically be highly correlated so a correction for multiple testing that takes this into account will be small an illustration uses data from the u s national health and nutrition examination survey concerning lead in the blood of cigarette smokers copyright 2012 oxford university press

twisted wess zumino witten models on elliptic curves investigated is a variant of the wess zumino witten model called a twisted wzw model which is associated to a certain lie group bundle on a family of elliptic curves the lie group bundle is a non trivial bundle with flat connection and related to the classical elliptic r matrix the usual non twisted wzw model is associated to a trivial group bundle with trivial connection on a family of compact riemann surfaces and a family of its principal bundles the twisted wzw model on a fixed elliptic curve at the critical level describes the xyz gaudin model the elliptic knizhnik zamolodchikov equations associated to the classical elliptic r matrix appear as flat connections on the sheaves of conformal blocks in the twisted wzw model

bbtopsis a bag based technique for order preference by similarity to ideal solution abstract this contribution explores the way of accomplishing a topsis ranking of various submitted variants taking into account a our newly developed notions of variant superiority inferiority and noninferiority multiattribute canonical fuzzy bags defined on attributes and b making use of bag metrics to compute the relative closeness of the different variants to an ideal solution in particular we prove the existence and the uniqueness of a bag metric fulfilling a number of interesting properties

classical wakimoto realizations of chiral wznw bloch waves it is well known that the chiral wznw bloch waves satisfy a quadratic classical exchange algebra which implies the affine kac moody algebra for the corresponding currents here we obtain a direct derivation of the exchange algebra by inverting the symplectic form on the space of bloch waves and give a completely algorithmic construction of its generalized free field realizations that extend the classical wakimoto realizations of the current algebra

semiparametric instrumental variable estimation of treatment response models this article introduces a new class of instrumental variable iv estimators for linear and nonlinear treatment response models with covariates the rationale for focusing on nonlinear models is that if the dependent variable is binary or limited or if the effect of the treatment varies with covariates a nonlinear model is appropriate in the spirit of roehrig econometrica 56 1988 433 identification is attained nonparametrically and does not depend on the choice of the parametric specification for the response function of interest one virtue of this approach is that it allows the researcher to construct estimators that can be interpreted as the parameters of a well defined approximation to a treatment response function under functional form misspecification in contrast to some usual iv models heterogeneity of treatment effects is not restricted by the identification conditions the ideas and estimators in this article are illustrated using iv to estimate the effects of 401 k retirement programs on savings

interval estimation for treatment effects using propensity score matching in causal studies without random assignment of treatment causal effects can be estimated using matched treated and control samples where matches are obtained using estimated propensity scores propensity score matching can reduce bias in treatment effect estimators in cases where the matched samples have overlapping covariate distributions despite its application in many applied problems there is no universally employed approach to interval estimation when using propensity score matching in this article we present and evaluate approaches to interval estimation when using propensity score matching

variance identification and efficiency analysis in randomized experiments under the matched pair design in his 1923 landmark article neyman introduced randomization based inference to estimate average treatment effects from experiments under the completely randomized design under this framework neyman considered the statistical estimation of the sample average treatment effect and derived the variance of the standard estimator using the treatment assignment mechanism as the sole basis of inference in this paper i extend neyman s analysis to randomized experiments under the matched pair design where experimental units are paired based on their pre treatment characteristics and the randomization of treatment is subsequently conducted within each matched pair i study the variance identification for the standard estimator of average treatment effects and analyze the relative efficiency of the matched pair design over the completely randomized design i also show how to empirically evaluate the relative efficiency of the two designs using experimental data obtained under the matched pair design my randomization based analysis differs from previous studies in that it avoids modeling and other assumptions as much as possible finally the analytical results are illustrated with numerical and empirical examples

a potential tale of two by two tables from completely randomized experiments causal inference in completely randomized treatment control studies with binary outcomes is discussed from fisherian neymanian and bayesian perspectives using the potential outcomes model a randomization based justification of fisher s exact test is provided arguing that the crucial assumption of constant causal effect is often unrealistic and holds only for extreme cases some new asymptotic and bayesian inferential procedures are proposed the proposed procedures exploit the intrinsic nonadditivity of unit level causal effects can be applied to linear and nonlinear estimands and dominate the existing methods as verified theoretically and also through simulation studies supplementary materials for this article are available online

on algebraic equations satisfied by hypergeometric correlators in wzw models ii the paper contains an explicit description of genus 0 conformal block bundles for wess zumino witten models of conformal field theory we prove that an earlier construction due to the second and the third authors gives a map of these bundles to certain de rham cohomology bundles

geometry and classificatin of solutions of the classical dynamical yang baxter equation the classical yang baxter equation cybe is an algebraic equation central in the theory of integrable systems its nondegenerate solutions were classified by belavin and drinfeld quantization of cybe led to the theory of quantum groups a geometric interpretation of cybe was given by drinfeld and gave rise to the theory of poisson lie groups

optimal matching for observational studies abstract matching is a common method of adjustment in observational studies currently matched samples are constructed using greedy heuristics or stepwise procedures that produce in general suboptimal matchings with respect to a particular criterion a matched sample is suboptimal if it could be improved by changing the controls assigned to specific treated units that is if it could be improved with the data at hand here optimal matched samples are obtained using network flow theory in addition to providing optimal matched pair samples this approach yields optimal constructions for several statistical matching problems that have not been studied previously including the construction of matched samples with multiple controls with a variable number of controls and the construction of balanced matched samples that combine features of pair matching and frequency matching computational efficiency is discussed extensive use is made of ideas from two essentially disjoint literatures namely st

optimal a priori balance in the design of controlled experiments summary we develop a unified theory of designs for controlled experiments that balance baseline covariates a priori before treatment and before randomization using the framework of minimax variance and a new method called kernel allocation we show that any notion of a priori balance must go hand in hand with a notion of structure since with no structure on the dependence of outcomes on baseline covariates complete randomization no special covariate balance is always minimax optimal restricting the structure of dependence either parametrically or non parametrically gives rise to certain covariate imbalance metrics and optimal designs this recovers many popular imbalance metrics and designs previously developed ad hoc including randomized block designs pairwise matched allocation and rerandomization we develop a new design method called kernel allocation based on the optimal design when structure is expressed by using kernels which can be parametric or non parametric relying on modern optimization methods kernel allocation which ensures nearly perfect covariate balance without biasing estimates under model misspecification offers sizable advantages in precision and power as demonstrated in a range of real and synthetic examples we provide strong theoretical guarantees on variance consistency and rates of convergence and develop special algorithms for design and hypothesis testing

realization of the space of conformal blocks in lie algebra modules abstract using integrable irreducible representations of generalized twisted affine lie algebra modules we give a realization of the space of conformal blocks of conformal field theory on a stable algebraic curve many basic properties of the conformal blocks such as finite dimensionality of the space invariance of the conformal blocks under suitable formal neighborhood changes and the property of propagation of vacua are discussed finally a relative local 1 form around a fixed point of the order two automorphism of the curve is given

a randomization based perspective on analysis of variance a test statistic robust to treatment effect heterogeneity summary fisher randomization tests for neyman s null hypothesis of no average treatment effect are considered in a finite population setting associated with completely randomized experiments involving more than two treatments the consequences of using the f statistic to conduct such a test are examined and we argue that under treatment effect heterogeneity use of the f statistic in the fisher randomization test can severely inflate the type i error under neyman s null hypothesis we propose to use an alternative test statistic derive its asymptotic distributions under fisher s and neyman s null hypotheses and demonstrate its advantages through simulations

bosonization and integral representation of solutions of the knizhnik zamolodchikov bernard equations we construct an integral representation of solutions of the knizhnik zamolodchikov bernard equations using the wakimoto modules

randomization tests for weak null hypotheses in randomized experiments the fisher randomization test frt is appropriate for any test statistic under a sharp null hypothesis that can recover all missing potential outcomes however it is often sought after to test a

a unified approach to approximation algorithms for bottleneck problems in this paper a powerful and yet simple technique for devising approximation algorithms for a wide variety of np complete problems in routing location and communication network design is investigated each of the algorithms presented here delivers an approximate solution guaranteed to be within a constant factor of the optimal solution in addition for several of these problems we can show that unless p np there does not exist a polynomial time algorithm that has a better performance guarantee

preference relations on actions and criteria in multicriteria decision making abstract let a be a finite set of feasible actions which are judged following several criteria an outranking relation is defined on a by considering preference of the decision maker as a weak order on each criterion and the relation among criteria as a semi order on the given set of criteria several ways of constructing outranking relations have been proposed one of the most popular introduced by b roy for instance electre s is based on the use of weights related to criteria in our approach the knowledge of weights is replaced by the existence of a semi order a case study is developed it deals with a computer selection problem

elliptic calogero moser systems and isomonodromic deformations we show that various models of the elliptic calogero moser systems are accompanied with an isomonodromic system on a torus the isomonodromic partner is a nonautonomous hamiltonian system defined by the same hamiltonian the role of the time variable is played by the modulus of the base torus a suitably chosen lax pair with an elliptic spectral parameter of the elliptic calogero moser system turns out to give a lax representation of the nonautonomous system as well this lax representation ensures that the nonautonomous system describes isomonodromic deformations of a linear ordinary differential equation on the torus on which the spectral parameter of the lax pair is defined a particularly interesting example is the extended twisted bcl model recently introduced along with some other models by bordner and sasaki who remarked that this system is equivalent to inozemtsev s generalized elliptic calogero moser system we use the root type lax pair developed by bordner et al to formulate the associa

reduced sensitivity to hidden bias at upper quantiles in observational studies with dilated treatment effects summary when a treatment has a dilated effect with larger effects when responses are higher there can be much less sensitivity to bias at upper quantiles than at lower quantiles i e small plausible hidden biases might explain the ostensible effect of the treatment for many subjects and yet only quite large hidden biases could explain the effect on a few subjects having dramatically elevated responses an example concerning kidney function of cadmium workers is discussed in detail in that example the treatment effect is far from additive it is plausibly zero at the lower quartile of responses to control and it is large and fairly insensitive to bias at the upper quartile

hitchin systems at low genera the paper gives a quick account of the simplest cases of the hitchin integrable systems and of the knizhnik zamolodchikov bernard connection at genus 0 1 and 2 in particular we construct the action angle variables of the genus 2 hitchin system with group sl2 by exploiting its relation to the classical neumann integrable systems

the extended qualiflex method for multiple criteria decision analysis based on interval type 2 fuzzy sets and applications to medical decision making abstract qualiflex a generalization of jacquet lagreze s permutation method is a useful outranking method in decision analysis because of its flexibility with respect to cardinal and ordinal information this paper develops an extended qualiflex method for handling multiple criteria decision making problems in the context of interval type 2 fuzzy sets interval type 2 fuzzy sets contain membership values that are crisp intervals which are the most widely used of the higher order fuzzy sets because of their relative simplicity using the linguistic rating system converted into interval type 2 trapezoidal fuzzy numbers the extended qualiflex method investigates all possible permutations of the alternatives with respect to the level of concordance of the complete preference order based on a signed distance based approach this paper proposes the concordance discordance index the weighted concordance discordance index and the comprehensive concordance discordance index as evaluative criteria of the chosen hypothesis for ranking the alternatives the feasibility and applicability of the proposed methods are illustrated by a medical decision making problem concerning acute inflammatory demyelinating disease and a comparative analysis with another outranking approach is conducted to validate the effectiveness of the proposed methodology

large sample randomization inference of causal effects in the presence of interference recently there has been increasing interest in making causal inference when interference is possible in the presence of interference treatment may have several types of effects in this article we consider inference about such effects when the population consists of groups of individuals where interference is possible within groups but not between groups a two stage randomization design is assumed where in the first stage groups are randomized to different treatment allocation strategies and in the second stage individuals are randomized to treatment or control conditional on the strategy assigned to their group in the first stage for this design the asymptotic distributions of estimators of the causal effects are derived when either the number of individuals per group or the number of groups grows large under certain homogeneity assumptions the asymptotic distributions provide justification for wald type confidence intervals cis and tests empirical results demonstrate that the wald cis have g

a short proof of motoo s combinatorial central limit theorem using stein s method a new proof of motoo s combinatorial central limit theorem see motoo 1957 is given using a method of stein 1972 and a combinatorial method of bolthausen 1984 this proof is shorter than motoo s and other wellknown proofs see e g hajek 1961