an exact test for multiple inequality and equality constraints in the linear regression model abstract in this article we consider the linear regression model y x e where e is n 0 2i in this context we derive exact tests of the form h r r versus k rk for the case in which 2 is unknown we extend these results to consider hypothesis tests of the form h r1 r1 and r2 r2 versus k rk for each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming for both tests we derive their exact distribution as a weighted sum of snedecor s f distributions normalized by the numerator degrees of freedom of each f distribution of the sum a methodology for computing critical values as well as probability values for the tests is discussed the relationship between this testing framework and the multivariate one sided hypothesis testing literature is also discussed in this context we show that for any size of the hypothesis test h 0 versus k rk the test statistic and critical value obtained a

likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

bounds on treatment effects from studies with imperfect compliance abstract this article establishes nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect the bounds provided are the tightest possible given the distribution of assignments treatments and responses the formulas show that even with high rates of noncompliance experimental data can yield useful and sometimes accurate information on the average effect of a treatment on the population

irreducible projective representations of the alternating group which remain irreducible in characteristic 2 abstract for any finite group g it is an interesting question to ask which ordinary irreducible representations of g remain irreducible in a given characteristic p we answer this question for p 2 when g is the proper double cover of the alternating group as a key ingredient in the proof we prove a formula for the decomposition numbers in rouquier blocks of double covers of symmetric groups in terms of schur p functions

the 2 blocks of the covering groups of the symmetric groups abstract let n be a double cover of the finite symmetric group s n of degree n i e n has a central involution z such that n z s n an irreducible character of n is called ordinary or spin according to whether it has z in its kernel or not the purpose of this paper is to determine the distribution of the spin characters of n into 2 blocks the methods applied here are essentially different from those applied to previous questions of this type we also discuss some consequences of our main result for the decomposition numbers an analogue of james well known result for the decomposition numbers of the symmetric groups is proved providing also a generalization of a theorem of benson ben theorem 1 2 in section 1 we present the background for our results and give some preliminaries in section 2 we give an explicit formula for the number of spin characters in a 2 block we also prove a result about the weight of a block containing a given non self associate spin character which will be important for the proof of our theorem on the 2 block distribution of spin characters section 3 presents some fundamental combinatorial concepts used in sections 4 and 5 the theorem concerning the spin characters in a given 2 block is proved in section 4 and in section 5 we present our results on the decomposition numbers

the symmetric group branching rules products and plethysms for spin representations it is shown that the symmetric group sn may be usefully embedded in the orthogonal group on and that this embedding leads directly to an n independent reduced notation for both the spin and ordinary representations of sn making use of this embedding together with the properties of q functions or hall littlewood functions branching rules for on spin down sn are developed and the general rule for the decomposition of spin representations under sn spin down sn 1 is obtained simple methods are given for calculating all possible kronecker products involving the spin and ordinary representations of sn and the resolution of kronecker squares into their symmetric and antisymmetric parts the spin representations of sn are systematically classified as to their orthogonal symplectic or complex characters the emphasis throughout is on obtaining results that obviate the need for explicit character tables and presenting results in an n independent manner as much as possible

reducible specht modules abstract james and mathas conjecture a criterion for the specht module s for the symmetric group to be irreducible over a field of prime characteristic we extend a result of lyle to prove this conjecture in one direction our techniques are elementary

asymptotic properties for a class of partially identified models we propose inference procedures for partially identified population features for which the population identification region can be written as a transformation of the aumann expectation of a properly defined set valued random variable svrv an svrv is a mapping that associates a set rather than a real number with each element of the sample space examples of population features in this class include interval identified scalar parameters best linear predictors with interval outcome data and parameters of semiparametric binary models with interval regressor data we extend the analogy principle to svrvs and show that the sample analog estimator of the population identification region is given by a transformation of a minkowski average of svrvs using the results of the mathematics literature on svrvs we show that this estimator converges in probability to the population identification region with respect to the hausdorff distance we then show that the hausdorff distance and the directed hausdorff distance between the population identification region and the estimator when properly normalized by n converge in distribution to functions of a gaussian process whose covariance kernel depends on parameters of the population identification region we provide consistent bootstrap procedures to approximate these limiting distributions using similar arguments as those applied for vector valued random variables we develop a methodology to test assumptions about the true identification region and its subsets we show that these results can be used to construct a confidence collection and a directed confidence collection those are respectively collection of sets that when specified as a null hypothesis for the true value a subset of values of the population identification region cannot be rejected by our tests

inference for parameters defined by moment inequalities using generalized moment selection the topic of this paper is inference in models in which parameters are defined by moment inequalities and or equalities the parameters may or may not be identified this paper introduces a new class of confidence sets and tests based on generalized moment selection gms gms procedures are shown to have correct asymptotic size in a uniform sense and are shown not to be asymptotically conservative the power of gms tests is compared to that of subsampling m out of n bootstrap and plug in asymptotic pa tests the latter three procedures are the only general procedures in the literature that have been shown to have correct asymptotic size in a uniform sense for the moment inequality equality model gms tests are shown to have asymptotic power that dominates that of subsampling m out of n bootstrap and pa tests subsampling and m out of n bootstrap tests are shown to have asymptotic power that dominates that of pa tests

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

wald criteria for jointly testing equality and inequality restrictions on montre comment le test de wald s applique a des ensembles de restrictions d egalite et d inegalite et on presente la distribution pour de grands echantillons du test sous l hypothese nulle

hecke algebras of typeawithq 1 abstract in this paper we study the decomposition matrices of the hecke algebras of type a with q 1 over a field of characteristic 0 we give explicit formulae for the columns of the decomposition matrices indexed by all 2 regular partitions with 1 or 2 parts and an algorithm for calculating the columns of the decomposition matrix indexed by partitions with 3 parts combining these results we find all of the rows of the decomposition matrices which are indexed by partitions with at most four parts all this is accomplished by means of a more general theory which begins by showing that the decomposition numbers in the columns of the decomposition matrices indexed by 2 regular partitions with enormous 2 cores are littlewood richardson coefficients

the local nature of hypothesis tests involving inequality constraints in nonlinear models this paper derives several properties unique to nonlinear model hypothesis testing problems involving linear or nonlinear inequality constraints in the null or alternative hypothesis the paper is organized around a lemma which characterizes the set containing the least favorable parameter value for a nonlinear model inequality constraints hypothesis test we then present two examples which illustrate several implications of this lemma we also discuss the impact of these properties on the empirical implementation and interpretation of these test procedures

confidence sets for partially identified parameters that satisfy a finite number of moment inequalities this paper proposes a computationally simple way to construct confidence sets for a parameter of interest in models comprised of moment inequalities building on results from the literature on multivariate one sided tests i show how to test the hypothesis that any particular parameter value is logically consistent with the maintained moment inequalities the associated test statistic has an asymptotic chi bar square distribution and can be inverted to construct an asymptotic confidence set for the parameter of interest even if that parameter is only partially identified critical values for the test are easily computed and a monte carlo study demonstrates implementation and finite sample performance

nonparametric analysis of randomized experiments with missing covariate and outcome data abstract analysis of randomized experiments with missing covariate and outcome data is problematic because the population parameters of interest are not identified unless one makes untestable assumptions about the distribution of the missing data this article shows how population parameters can be bounded without making untestable distributional assumptions bounds are also derived under the assumption that covariate data are missing completely at random in each case the bounds are sharp they exhaust all of the information available given the data and the maintained assumptions the bounds are illustrated with applications to data obtained from a clinical trial and data relating family structure to the probability that a youth graduates from high school

estimation and confidence regions for parameter sets in econometric models this paper develops a framework for performing estimation and inference in econometric models with partial identification focusing particularly on models characterized by moment inequalities and equalities applications of this framework include the analysis of game theoretic models revealed preference restrictions regressions with missing and corrupted data auction models structural quantile regressions and asset pricing models specifically we provide estimators and confidence regions for the set of minimizers i of an econometric criterion function q in applications the criterion function embodies testable restrictions on economic models a parameter value that describes an economic model satisfies these restrictions if q attains its minimum at this value interest therefore focuses on the set of minimizers called the identified set we use the inversion of the sample analog q n of the population criterion q to construct estimators and confidence regions for the identified set and develop consistency rates of convergence and inference results for these estimators and regions to derive these results we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification

the irreducible representations of the alternating group which remain irreducible in characteristic p let p be an odd prime and an the alternating group of degree n we determine which ordinary irreducible representations of u n remain irreducible in characteristic p verifying the author s conjecture from 2010 given the preparatory work done in 2010 our task is to determine which self conjugate partitions label specht modules for the symmetric group in characteristic p having exactly two composition factors this is accomplished through the use of the robinson brundan kleshchev i restriction functors together with known results on decomposition numbers for the symmetric group and additional results on the mullineux map and homomorphisms between specht modules

inference on regressions with interval data on a regressor or outcome this paper examines inference on regressions when interval data are available on one variable the other variables being measured precisely let a population be characterized by a distribution p y x v v 0 v 1 where y r 1 x r k and the real variables v v 0 v 1 satisfy v 0 v v 1 let a random sample be drawn from p and the realizations of y x v 0 v 1 be observed but not those of v the problem of interest may be to infer e y x v or e v x this analysis maintains interval i monotonicity m and mean independence mi assumptions i p v 0 v v 1 1 m e y x v is monotone in v mi e y x v v 0 v 1 e y x v no restrictions are imposed on the distribution of the unobserved values of v within the observed intervals v 0 v 1 it is found that the immi assumptions alone imply simple nonparametric bounds on e y x v and e v x these assumptions invoked when y is binary and combined with a semiparametric binary regression model yield an identification region for the parameters that may be estimated consistently by a modified maximum score mms method the immi assumptions combined with a parametric model for e y x v or e v x yield an identification region that may be estimated consistently by a modified minimum distance mmd method monte carlo methods are used to characterize the finite sample performance of these estimators empirical case studies are performed using interval wealth data in the health and retirement study and interval income data in the current population survey

el inference for partially identified models large deviations optimality and bootstrap validity this paper addresses the issue of optimal inference for parameters that are partially identied in models with moment inequalities there currently exists a variety of inferential methods for use in this setting however the question of choosing optimally among contending procedures is unresolved in this paper i rst consider a canonical large deviations criterion for optimality and show that inference based on the empirical likelihood ratio statistic is optimal this nding is a direct analog to that in kitamura 2001 for moment equality models second i introduce a new empirical likelihood bootstrap that provides a valid resampling method for moment inequality models and overcomes the implementation challenges that arise as a result of non pivotal limit distributions lastly i analyze the nite sample properties of the proposed framework using monte carlo simulations the

some impossibility theorems in econometrics with applications to structural and dynamic models general characterizations of valid confidence sets and tests in problems which involve locally almost unidentified lau parameters are provided and applied to several econo metric models two types of inference problems are studied i inference about parame ters which are not identifiable on certain subsets of the parameter space and ii inference about parameter transformations with discontinuities when a lau parameter or parametric function has an unbounded range it is shown under general regularity conditions that any valid confidence set with level 1 a for this parameter must be unbounded with probability close to 1 a in the neighborhood of nonidentification subsets and will have a nonzero probability of being unbounded under any distribution compatible with the model no valid confidence set which is almost surely bounded does exist these properties hold even if identifying restrictions are imposed similar results also obtain for parameters with bounded ranges consequently a confidence set which does not satisfy this characterization has zero coverage probability level this will be the case in particular for wald type confidence intervals based on asymptotic standard errors furthermore wald type statistics for testing given values of a lau parameter cannot be pivotal functions i e they have distributions which depend on unknown nuisance param eters and even cannot be usefully bounded over the space of the nuisance parameters these results are applied to several econometric problems inference in simultaneous equations instrumental variables iv regressions linear regressions with autoregressive errors inference about long run multipliers and cointegrating vectors for example it is shown that standard asymptotically justified confidence intervals based on iv estimators such as two stage least squares and the associated standard errors have zero coverage probability and the corresponding t statistics have distributions which cannot be bounded by any finite set of distribution functions a result of interest for interpreting iv regressions with weak instruments furthermore expansion methods e g edgeworth expansions and bootstrap techniques cannot solve these difficulties finally in a number of cases where wald type methods are fundamentally flawed e g iv regressions with poor instruments it is observed that likelihood based methods e g likelihood ratio tests and confidence sets combined with projection techniques can easily yield valid tests and confidence sets

confidence intervals for partially identified parameters recently a growing body of research has studied inference in settings where parameters of interest are partially identified in many cases the parameter is real valued and the identification region is an interval whose lower and upper bounds may be estimated from sample data for this case confidence intervals cis have been proposed that cover the entire identification region with fixed probability here we introduce a conceptually different type of confidence interval rather than cover the entire identification region with fixed probability we propose cis that asymptotically cover the true value of the parameter with this probability however the exact coverage probabilities of the simplest version of our new cis do not converge to their nominal values uniformly across different values for the width of the identification region to avoid the problems associated with this we modify the proposed ci to ensure that its exact coverage probabilities do converge uniformly to their nominal values we motivate this modified ci through exact results for the gaussian case

on holomorphic functions on a compact complex homogeneous supermanifold abstract it is well known that non constant holomorphic functions do not exist on a connected compact complex manifold this statement is false for a supermanifold with a connected compact reduction in this paper we study the question under what conditions non constant holomorphic functions do not exist on a connected compact homogeneous complex supermanifold we describe also the vector bundles determined by split homogeneous complex supermanifolds as an application we compute the algebra of holomorphic functions on the classical flag supermanifolds introduced in manin 1997 11

some reducible specht modules we wish to consider which ordinary irreducible representations of the symmetric group sn remain irreducible modulo a prime p this is the same as asking which partitions of n have the property that the corresponding specht module s is reducible over a field of characteristic p if or its conjugate partition is p regular then the answer is known 6 8 it is also known in the case p 2 7 this paper discusses some of the reducible specht modules in the case that p 3 throughout p will be an odd prime and a partition of some integer n we will prove some cases of a conjecture by james and mathas 9 given below we begin with some definitions

testing parameters in gmm without assuming that they are identified we propose a generalized method of moments gmm lagrange multiplier statistic i e the k statistic that uses the jacobian at the evaluated parameter value instead of the expected jacobian to obtain its limit behavior we use a novel assumption that brings gmm closer to maximum likelihood and which is easily satisfied the usual asymptotic x2 distribution of the k statistic then holds under a wider set of circumstances like weak and many instrument asymptotics and combinations thereof than the standard full rank case for the jacobian the behavior of the k statistic can be spurious around inflexion points and the maximum of the objective function since the moment conditions are then not satisfied combinations of the k statistic with statistics that test the validity of the moment equations overcome the spurious behavior we conduct a power comparison to test for the risk aversion parameter in a stochastic discount factor model and construct its confidence set for observed consumption growth and asset return series

irreducible specht modules for hecke algebras of type a abstract let f be a field n a non negative integer a partition of n and s the corresponding specht module for the iwahori hecke algebra h f q s n james and mathas conjecture a necessary and sufficient condition on for s to be irreducible we prove the sufficiency of this condition in the case where f has infinite characteristic and also in the case where q 1

large sample confidence regions based on subsamples under minimal assumptions in this article the construction of confidence regions by approximating the sampling distribution of some statistic is studied the true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data in the i i d context the method has been studied by wu in regular situations where the statistic is asymptotically normal the goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions essentially all that is required is that the statistic suitably normalized possesses a limit distribution under the true model unlike the bootstrap the convergence to the limit distribution need not be uniform in any sense the method is readily adapted to parameters of stationary time series or more generally homogeneous random fields for example an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field